
_**The Periodic Table**_

# **T HE PERIODIC TABLE**

_Its Story and Its Significance_

ERIC R. SCERRI

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Library of Congress Cataloging-in–Publication Data  
Scerri, Eric R.  
The periodic table : its story and its significance / Eric R. Scerri.  
p. cm.  
Includes bibliographical references  
ISBN-13 978-0-19-530573-9  
ISBN 0-19-530573-6  
1. Periodic law—Tables. 2. Chemical elements. I. Title.  
QD467.S345 2006  
546'.8—dc22 2005037784

1 3 5 7 9 8 6 4 2  
Printed in the United States of America  
on acid–free paper
_I dedicate this book to my mother, Ines,  
and my late father, Edward Scerri,  
for steering me toward the scholarly life_.

_I also dedicate this book to the 100th  
anniversary of the death of Dimitri  
Mendeleev (1834–1907)_.

## **A CKNOWLEDGMENTS**

This book has been in the making for about six years, although perhaps I should say about 20 years since it was that long ago that I undertook my Ph.D. at what was then Chelsea College, University of London, under the excellent supervision of the late Heinz Post. Of course, I could go back even further and mention that my love affair with the periodic table began when I was still in my teens and attending Walpole grammar school in the West London borough of Ealing.

Now that this book is completed, I have the opportunity to thank all those who contributed to it either directly or indirectly as colleagues or mentors at various stages of my own development. At Walpole grammar school, Mrs. Davis was the chemistry teacher who noticed that I was fooling around at the back of the class and ordered me to sit in the front row. At this point, I had no choice but to listen to the lesson and soon discovered that chemistry was rather interesting.

Moving on to Westfield College, which was part of the University of London, I had many wonderful professors, among them John Throssell and Bernard Aylett, a theoretician and an inorganic chemist, respectively. This was followed by a year of theoretical work at Cambridge under the great David Buckingham, who despaired of my asking too many philosophical questions. Then I moved to Southampton University, where I obtained a Master of Philosophy degree in Physical Chemistry with the inimitable Pat Hendra. At this point, I began teaching chemistry in high schools and tutorial colleges. I eventually went back to research and wrote my Ph.D. in history and philosophy and philosophy of science on the question of the reduction of chemistry to quantum mechanics. I cannot overestimate the debt that I owe to Heinz Post, and as all who know him recall, he was perhaps the nearest thing to the archcritic Wolfgang Pauli that ever graced the philosophy of science scene in the United Kingdom. Not that I ever witnessed Pauli, however.

It was Heinz Post who encouraged me to try to develop the philosophy of chemistry, which I have sought to do ever since. I think it was also Heinz who first planted the idea of my going to the United States to teach and carry out research. But before moving on to my story in the United States, let me pause to mention a few other folks in London who have been influential and helpful: Mike Melrose, a theoretical chemist from King's College, London, and John Worrall from the London School of Economics. It has been a great privilege to have subsequently co-authored an article with each of them.

I went to the United States as a postdoctoral fellow at Caltech. Here I must thank my colleagues Diana Kormos-Buchwald, Fiona Cowie, Alan Hayek, and James Woodward in the Humanities Division. I subsequently went for a year to Bradley University in the heart of Illinois, where I was warmly received by Don Glover and Kurt Field, among others, in the chemistry department. Then followed another visiting professorship at Purdue University, where I interacted mainly with George Bodner and historian-chemist-educator Derek Davenport. In the year 2000, I moved to the chemistry department at UCLA, where I am blessed with numerous great colleagues, among others, Miguel Garcia-Garibay, Robin Garrell, Steve Hardinger, Ken Houk, Herb Kaesz, Richard Kaner, Laurence Lavelle, Tom Mason, Craig Merlic and Harold Martinson.

In addition, I am grateful to all the members of the International Philosophy of Chemistry Society, which a small group of us founded in the early 1990s after we realized that there were a sufficient number of people with an interest in this field. My thanks to Michael Akeroyd, Davis Baird, Nalini Bhushan, Paul Boogard, Joseph Earley, Rom Harré, Robin Hendry, David Knight, Mark Leach, Paul Needham, Mary Jo Nye, Jeff Ramsay, Joachim Schummer, Jaap van Brakel, Krishna Vemulapalli, Stephen Weininger, Michael Weisberg, and many others.

Perhaps the largest group to acknowledge consists of the many scholars of the periodic table from diverse fields, who include Peter Atkins, Henry Bent, Bernadette Bensaude, Nathan Brooks, Fernando Dufour, John Emsley, Michael Gordin, Ray Hefferlin, Bill Jensen, Masanori Kaji, Maurice Kibler, Bruce King, Mike Laing, Dennis Rouvray, Oliver Sachs, Mark Winters, and others.

I thank my various co-editors at _Foundations of Chemistry_ , both past and present, including John Bloor, Carmen Giunta, Jeffrey Kovac, and Lee McIntyre. I thank my UCLA colleagues in the Department of Philosophy, including Calvin Normore, Sheldon Smith, and Chris Smeenk and in the Department of History, Ted Porter and Norton Wise.

My thanks to members of various online discussion lists, including Chemed, History of Chemistry, Philchem, Hopos, and CCL (Computational Chemistry Listserver), with whom various points were ironed out, sometimes amidst heated debate.

Last but not least, there are a number of people who helped me specifically with the compilation of this book, especially with collecting photos and images. They include Ted Benfey, Gordon Woods, Ernst Homberg, and Frenando Dufour and Susan Zoske; George Helfand and Andreana Adler from the photographic unit at UCLA who scanned the diagrams; and Marion Peters in the chemistry department library. Special thanks to Daniel Contreras, who was always patient in helping me to unearth those obscure early sources—I am sure he grew quite tired of ordering volumes of _Science News_ for me from the vaults on the other side of campus. Special thanks also go out to Geoffrey Rayner Canham and William Brock for their detailed comments on the entire manuscript and to Jan van Spronsen, the doyen of the periodic table, for his comments on some early chapters of the book. Thanks to Amy Bianco. At OUP I thank my editor Jeremy Lewis, as well as Abby Russell, Michael Seiden, Laura Ikwild, and Lisa Stallings, all of whom made the publishing process a pleasurable experience.

### PHOTO CREDITS

The Edgar Fahs Smith Collection at the University of Pennsylvania for providing photos and permission for use of photos of Cannizzaro, Dalton, Lavoisier, Lewis, and Ramsay, and for permission to use a photo of Lothar Meyer.

The Emilio Segrè collection at the American Institute of Physics for photos and permission for use of photos of Bohr; the Burbidges, Fowler, and Hoyle; Curie; G.N. Lewis; Mendeleev; and Seaborg, and for permission to use photos of Moseley and Pauli.

Gordon Woods for providing the photo and permission for "The Consolidators of the Periodic Law."

Fernando Dufour for providing the photo of his own 3-D periodic system.

### ARTICLE CREDITS

I have drawn from my own previous articles and particularly from four publications:

_British Journal for the Philosophy of Science_ , 42, 309–325, 1991 (published by Oxford University Press, UK).

_Annals of Science_ , 51, 137–150, 1994 (published by Taylor & Francis).

_Studies in History and Philosophy of Science_ , 32, 47–452, 2001 (published by Elsevier).

_Foundations of Chemistry_ , 6, 93–116, 2004 (published by Springer).

All these articles were used by permission from the publishers.

## **C ONTENTS**

Introduction

[CHAPTER 1  
The Periodic System: An Overview](ch01.html#ch01)

[CHAPTER 2  
Quantitative Relationships among the Elements and the Origins of the Periodic Table](ch02.html#ch02)

[CHAPTER 3  
Discoverers of the Periodic System](ch03.html#ch03)

[CHAPTER 4  
Mendeleev](ch04.html#ch04)

[CHAPTER 5  
Prediction and Accommodation: The Acceptance of Mendeleev's Periodic System](ch05.html#ch05)

[CHAPTER 6  
The Nucleus and the Periodic Table: Radioactivity, Atomic Number, and Isotopy](ch06.html#ch06)

[CHAPTER 7  
The Electron and Chemical Periodicity](ch07.html#ch07)

[CHAPTER 8  
Electronic Explanations of the Periodic System Developed by Chemists](ch08.html#ch08)

[CHAPTER 9  
Quantum Mechanics and the Periodic Table](ch09.html#ch09)

[CHAPTER 10  
Astrophysics, Nucleosynthesis, and More Chemistry](ch10.html#ch10)

Notes

Index

## **I NTRODUCTION**

As long as chemistry is studied there will be a periodic table. And even if someday we communicate with another part of the universe, we can be sure that one thing that both cultures will have in common is an ordered system of the elements that will be instantly recognizable by both intelligent life forms.

J. Emsley, _The Elements_

The periodic table of the elements is one of the most powerful icons in science: a single document that captures the essence of chemistry in an elegant pattern. Indeed, nothing quite like it exists in biology or physics, or any other branch of science, for that matter. One sees periodic tables everywhere: in industrial labs, workshops, academic labs, and of course, lecture halls.

### THE PERIODIC SYSTEM OF THE ELEMENTS

It is sometimes said that chemistry has no deep ideas, unlike physics, which can boast quantum mechanics and relativity, and biology, which has produced the theory of evolution. This view is mistaken, however, since there are in fact two big ideas in chemistry. They are chemical periodicity and chemical bonding, and they are deeply interconnected.

The observation that certain elements prefer to combine with specific kinds of elements prompted early chemists to classify the elements in tables of chemical affinity. Later these tables would lead, somewhat indirectly, to the discovery of the periodic system, perhaps the biggest idea in the whole of chemistry. Indeed, periodic tables arose partly through the attempts by Dimitri Mendeleev and numerous others to make sense of the way in which particular elements enter into chemical bonding.

The periodic table of the elements is a wonderful mnemonic and a tool that serves to organize the whole of chemistry. All of the various periodic tables that have been produced are attempts to depict the periodic system. The periodic system is so fundamental and all pervasive in the study of chemistry, as well as in professional research, that it is often taken for granted, as very familiar things in life so frequently are.

In spite of the central, or some might say homely, role of the periodic table, very few authors have felt drawn to write books on its evolution. There is no book that deals adequately with the historical, and especially the conceptual, aspects of the periodic system or its significance in chemistry and science generally. It is with the aim of injecting a more philosophical treatment to understanding the periodic system that the present work has been undertaken. I make no apologies for this approach, which I believe is long overdue and can perhaps be understood in the context of the almost complete neglect of the study of the philosophy of chemistry until its recent resurgence in the mid-1990s.

Only two major books on the periodic system have appeared in the English language, one of these being a translation from the Dutch original. The more contemporary of these books, published in 1969 and authored by J. van Spronsen, is an excellent and detailed exposition of the history of the periodic system. One of the few omissions from van Spronsen's book is a discussion of the way in which modern physics is generally claimed to have explained the periodic system. Van Spronsen at times accepts the usual unspoken, or sometimes explicit, claim that the periodic system has been "reduced" to quantum mechanics, to use a phrase popular in philosophy of science. On my own view, the extent to which quantum mechanics reduces the periodic system is frequently overemphasized. Of course, quantum mechanics provides a better explanation than was available from the classical theories of physics, but in some crucial respects the modern explanation is still lacking, as I hope to explain.

The only other serious treatise on the periodic system, written in English, is a masterly and detailed exposition, published in 1896, by F.P. Venable of the University of North Carolina-Chapel Hill. It goes without saying that, for all its strengths, this book is severely limited, as it covers a period that ended more than 100 years ago, before modern physics began to exercise a major influence on the way the periodic system is understood.

There is also a compilation of more than 700 representations of the periodic system in a book by E. Mazurs, who devoted a lifetime of study to the topic. However, this book is neither a history nor a philosophy of the periodic system but a rather idiosyncratic attempt to develop a system of classification for periodic classifications themselves. It serves as a repository of the huge variety of forms in which the periodic system has been represented and is a testament to how expansive and energetic the quest for the ultimate form of the periodic system has been. This quest appears to be with us to this day, an issue that will be taken up in later chapters. Another virtue of the Mazurs book is that it provides a wealth of references to the primary and secondary literature on the periodic system, although this, too, is now some 25 or so years out of date.

The textbook author Peter Atkins has published a short popular book on the periodic system. There are also a number of books, including those by Puddephatt and Monaghan, as well as by Cooper, Pode, and Sanderson, which use the periodic system as a means of presenting the chemistry of the elements but make little attempt to evaluate critically the foundational basis of the system. The continuing interest in the periodic system is further exemplified by the appearance of three recent books aimed at the nonspecialist by Strathern, Sacks, and Morris. Although the focus of these books is on chemistry generally, they contain sections on the development of the periodic system. Very recently, M. Gordin has published a biography of Mendeleev, which is historically sensitive as well as scientifically accurate, and benefits from the author's first-hand knowledge of the original Russian documents.

### THE ELEMENTS

In this book I examine the concept of an element in some detail, starting from the views expressed by the ancient Greek philosophers and bringing us right up to modern times. Although this topic has seldom been discussed in the context of the evolution of the periodic system, it is difficult to fully understand the classification of the elements without first attempting to understand what an element is and how such a concept has changed over time. There is a sense in which ancient views on the nature of the elements have not been entirely rejected, although they have been changed considerably.

The study of the nature of elements and compounds is at the heart of much of Aristotle's philosophy of substance and matter and even his most general views of "being" and "becoming." This was also true of many of the pre-Socratic philosophers, who were the first to discuss and theorize about the elements. About 20 centuries later, the nature of the elements was a major issue in the revolution of chemistry. Antoine Lavoisier seems to have been one of the first chemists to renounce the metaphysical view of the elements, which he replaced with a form of empiricism, which considered only substances that could actually be isolated as elements. Elements in this latter sense of the term are often called "simple substances."

This essentially philosophical question regarding the nature of elements returned and profoundly shaped the views of Mendeleev, who is arguably the leading discoverer of the periodic system. Indeed, it appears that Mendeleev may have been able to make more progress than some of his contemporaries, who were also developing periodic systems, because of his philosophical ideas about the nature of the elements. Even in the twentieth century, following the discovery of isotopes, fierce debates were waged on the nature and correct definition of the term "element."

Mendeleev held a dual view on the nature of elements, whereby they could be regarded as unobservable basic substances and also as Lavoisier's simple substances at the same time. Mendeleev thus acknowledged one of the central mysteries running throughout the long history of chemistry, which is the question of how, if at all, the elements survive in the compounds they form when they are combined together. For example, how can it be claimed that a poisonous gray metal like sodium is still present when it combines with a green poisonous gas chlorine, given that the compound formed, sodium chloride, or common table salt, is white and not only nonpoisonous but also essential for life? These are the kinds of questions the ancient Greek philosophers wrestled with while trying to understand the nature of matter and change. As I will show, such questions are still with us today, although some aspects of them have been explained by modern physical theory and the theories of chemical bonding.

#### Alchemy

Although in this book I briefly examine the nature of the elements, and of atomism from their earliest origins, not too much time is devoted to issues surrounding alchemy, for various reasons. First, the study of alchemy has been fraught with the obvious difficulties of trying to understand a complex set of practices spanning a number of areas, including what today would be considered religion, psychology, numerology, metallurgy, and so on. In addition, alchemical texts were frequently shrouded in deliberate mystery and obfuscation to protect the practitioners, who were regularly accused of being charlatans. Such mystery also served to restrict alchemical knowledge to a few initiates belonging to particular secret cults.

The question of whether modern chemistry is a direct outgrowth of alchemy, or whether alchemy's fundamental tenets had to be rejected in order for chemistry to get started, has been the source of much debate and continues to be disputed by scholars. All I do here is refer the reader to a few detailed treatments containing more serious discussion of this vast field of study.

One interesting aspect of this issue that has emerged in recent years is a questioning of the notion that the giants of modern science, such as Newton and Boyle, turned their backs on alchemy. Starting about 30 years ago, historians of science, and Betty Jo Dobbs in particular, have argued rather persuasively that Newton was a dedicated alchemist and that he might even have devoted more time to this field than to his work in theoretical physics, for which he is now universally revered. More recently, Lawrence Principe has re-alchemized Boyle in a similar way that Dobbs had re-alchemized Newton. Through painstaking analysis of Boyle's writing, Principe argues that, contrary to the accepted view, Boyle did not reject alchemical ways in his seminal book, _The Sceptical Chymist_. In fact, Principe writes:

We now see that Boyle himself in no way rejected transmutational alchemy but rather pursued it avidly and appropriated several of its theoretical principles.... Boyle was not as "modern" as we thought, nor alchemy as "ancient." What we are witnessing, then, is a rapprochement between what have been previously seen as two separate and irreconcilable halves of the history of chemistry.

#### A Philosophical Approach

As I have already suggested, the study of the periodic system is philosophically important in several ways. Let me be a little more specific. For some time now, philosophers of science have realized that they have placed too much emphasis on the study of scientific theories and not enough on other important aspects of science, such as experimental work and scientific practice in general. This has led many researchers to initiate the study of the philosophy of experimentation. But even within the philosophical investigation of theoretical work, there has been a growing sense that there is much more to scientific theorizing than just appealing to high-level theories.

In many cases, the theory in question is too difficult to apply, and so scientists tend to base their work on models and approximations. The full acceptance of this fact has produced a subdiscipline that studies the nature of scientific models. And yet, as I argue in this book, the periodic table of chemistry is neither a theory nor a model but more akin to an "organizing principle," for want of a better term. This book is partly an attempt to encourage philosophers of science to study the periodic table as an example of yet another scientific entity that does a lot of useful scientific work without being a theory.

Another reason why the periodic table is philosophically important is that it provides an excellent testing ground for the question of whether chemistry is nothing but physics deep down or, as philosophers like to say, whether chemistry reduces to physics. But even asking such a question has become controversial in modern scholarship. The view that physics is the most fundamental of the sciences or, indeed, the very notion of one field being more fundamental than another one is under severe threat from disciplines such a literary criticism, cultural anthropology, and postmodern critiques of science. Such issues have become highly controversial in recent times, producing what is perhaps the major debate in today's academic world, namely, the "science wars." Many scholars, scientists, and intellectuals find themselves pitted against each other over the question of whether science provides a form of objective truth or whether it is no more than a social construction not necessarily governed by the way the world actually is. The traditional view of scientific objectivity is increasingly regarded as a thing of the past, and some scholars are even prepared to embrace a form of relativism, or the view that all forms of knowledge are equally valid.

But many others believe the question of fundamentalism and reduction can still be studied within the context of science. One can still consider the more modest question of whether chemistry reduces to its sister science of physics. This question can be approached in a scientific manner by examining the extent to which chemical models or, indeed, the periodic system, can be explained by the most basic theory of physics, namely, quantum mechanics. It is this question that forms the underlying theme for this entire book, and it is a question that is addressed more and more explicitly in later chapters as the story reaches the impact of modern physical theories on our understanding of the periodic system.

#### The Evolution of the Periodic System

As I try to show in this book, several intermediate and anticipatory steps preceded every important stage in the development of the periodic system. Of all the major developments in the history of science, there may be no better example than that of the periodic system to argue against Thomas Kuhn's thesis that scientific progress occurs through a series of sharp revolutionary stages. Indeed, Kuhn's insistence on the centrality of revolutions in the development of science and his efforts to single out revolutionary contributors has probably unwittingly contributed to the retention of a Whiggish history of science, whereby only the heroes count while blind alleys and failed attempts are written out of the story.

Science is, above all, a collective endeavor involving a large variety of people working sometimes in teams, sometimes in isolation, sometimes aware of the work of their contemporaries, and sometimes not. When trying to examine the development of a system of knowledge such as the periodic system, it may be more important to look at the overall picture complete with wrinkles than to concentrate on who came first or whether a certain development really is an anticipation of a later one. Nevertheless, since priority issues are part of this fascinating story, in this book I try to give an account of some of the most important ones without claiming to provide the final word on any of the long-standing disputes.

Perhaps a further word on a different sense of the term "Whiggism" is appropriate. Since this book is not intended as a work of historical scholarship, there will be many instances in which the story will be driven by what eventually took place in the history of science. I make no apology for this approach since part of the interest is in trying to trace the development of the modern periodic system. For example, when discussing triads of elements, which were based on atomic weights, I will not avoid looking ahead to the use of atomic numbers to see what effects this change might have on the validity or otherwise of triads.

So without further delay, what follows is a brief synopsis of the chapters of the present book. I adopt a historical approach in order to convey the gradual evolution that has taken place around the chemical icon that is the periodic system. However, my primary concern is the evolution of concepts and ideas rather than trying to produce a detailed historical account. At times, I even use strictly ahistorical examples to illustrate particular points.

The book takes the reader on an interdisciplinary tour of the many areas of science that are connected with the periodic system, including physics, mathematics, computational methods, history and philosophy of science, and of course, chemistry. The story begins with the pre-Socratic philosophers in ancient Greece and progresses through the birth of atomism and on to Aristotle's four elements of earth, water, fire, and air. By the Middle Ages, when the full impact of alchemy was reached, a few other elements, such as sulfur and mercury, were added to the list. But this book does not explore the state of chemical knowledge of the elements in the Middle Ages, early medicine, or Arabic chemistry, although these are important preliminaries to modern chemistry. Nor does it visit the theory of phlogiston, which was deposed by the chemical revolution; it merely examines Lavoisier's famous list of 37 fundamental substances.

Instead, the story of the periodic system will take the plunge with the work of William Prout, Johann Döbereiner, Leopold Gmelin, and others who began to explore numerical relationships among the elements in addition to the previously known chemical analogies between them. We encounter the first true periodic system, which was the helical periodic system of Alexandre Emile Béguyer De Chancourtois, as well as the early periodic systems of William Odling, Gustav Hinrichs, Jean Baptiste André Dumas, Max Pettenkofer, John Newlands, and Julius Lothar Meyer, culminating with Mendeleev's tables and his deductions concerning existing as well as completely new elements. In each case, we look into some of the historical background involved as well as specific aspects of the periodic system proposed.

The discovery in the 1890s of the noble gases, a group of elements that did not initially appear to fit into the periodic system, is analyzed, as is the eventual resolution of this problem. The turn of the twentieth century saw the discovery of radioactivity, which led to new ideas about the structure of the atom from J.J. Thomson and Ernest Rutherford. Very soon, isotopes of many of the elements were discovered, and this produced a major challenge to the periodic system. Niels Bohr, Wolfgang Pauli, Erwin Schrödinger, and Werner Heisenberg, who provided the modern explanation of the periodic system in terms of orbiting electrons and quantum numbers, continued the invasion of physics into the understanding of the periodic table.

Whenever scientists are presented with a useful pattern or system of classification, it is only a matter of time before they begin to ask whether there may be some underlying explanation for the pattern. The periodic system is no exception. Attempts to produce explanations of the periodic system have led to major advances in areas of science other than chemistry, especially theoretical physics. The notion that the atom consists of a nucleus with electrons in orbit around it, which is taken for granted in modern science, originated when British physicist J.J. Thomson tried to explain the order of the elements displayed in the periodic table. Similarly, when Bohr, one of the founders of quantum mechanics, applied new ideas about the quantum of energy to the atom, he was specifically trying to obtain a deeper understanding of the periodic system of the elements.

A few years later, Pauli produced his celebrated Exclusion Principle, which is now known to govern the behavior of all matter from materials used to make transistors to the matter in neutron stars. Pauli's original research, carried out in atomic physics, was initially an attempt to explain the form of the periodic system and why the various electron shells of the atom can contain only specific numbers of electrons. In the process, Pauli produced one of the most general principles known to science. His Exclusion Principle tells us, in simple terms, that an electronic orbital can contain only two electrons, which must be spinning in opposite directions. A careful analysis of this, and other general principles of quantum mechanics, has produced a new the discipline of quantum chemistry, which nowadays is exploited in the development of new materials from superconductors to pharmaceutical drugs.

Now a word on the subject of chemical education. Two of the leading discoverers of the periodic system, Lothar Meyer and Mendeleev, were outstanding chemical educators who developed their versions of the periodic system while writing chemistry textbooks. One of the principal roles of the periodic table is as a teaching tool, given that it unifies so much chemical information and establishes unity amidst the diversity of chemical phenomena. In recent years, there has been a growing awareness that chemistry is being taught as though it were a subdiscipline of physics. This tendency has occurred because physics, in the form of quantum mechanics, has been successful in explaining many aspects of chemistry. But this success is frequently overemphasized.

Chemistry students are increasingly fed a diet of orbitals, electronic configurations, and other theoretical concepts instead of being exposed to the more tangible colors, smells, and even explosions of "real chemistry." Some authors advocate making chemical education more "chemical" while at the same time introducing students to the necessary concepts in modern physics. In such an endeavor, the periodic table can serve as an excellent link between macroscopic chemical properties and the underlying quantum mechanical explanations.

But in addition to any pedagogical implications, the relationship between chemistry and physics has become increasingly important in philosophy of science. In particular, the recent growth of the philosophy of chemistry as a distinct subdiscipline has been based to some extent on examining the question of the reduction of chemical laws, chemical models, and representations, such as the periodic system, to fundamental physics.

But even before the advent of philosophy of chemistry, the question of the reduction of scientific theories to successor theories has been an important concern, as has the question of whether any of the special sciences reduce to basic physics. Broadly speaking, as the logical positivist approach to philosophy has been superseded, claims for the reduction of theories and fields of science have been increasingly challenged. The failure to establish the full reduction of theories and the special sciences has been one of the reasons for the demise of logical positivism in philosophy. But this failure of reduction in the manner prescribed by logical positivism has not led to the abandonment of another central tenet of logical positivism, namely, a belief in the unity of the sciences.

In contemporary philosophy of science, the question of reduction is no longer approached in an axiomatic manner. It is rather pursued in a more naturalistic manner by examining the extent to which the periodic system, for example, can be deduced from the first principles of quantum mechanics. While this approach is still rigorous, it is not rigorous in the sense of using formal logic in order to establish the required connection. It is rather by examining the extent to which the facts in the secondary science, if one must use such terms, can be deduced in an _ab initio_ manner, to use a contemporary phrase, from computational chemistry. One needs to examine the way in which the Schrödinger Equation explains the structure of the periodic system, a topic that is specifically addressed in chapter 9. But leading up to these more contemporary developments, there were already claims made by Bohr, and on his behalf, that he had given a reduction of the periodic system using just the old quantum theory. The story of the periodic system is inextricably linked with the increasing influence of modern physics upon chemistry. The question of reduction in many forms thus underlies the developments discussed in this book.

And even further back in the story of the periodic system, one can see the influence of numerical approaches dating back to Prout's hypothesis and Döbereiner's triads, both of which predate the discovery of the periodic system. Hence, it is not just chemistry that enables one to classify the elements but a combination of chemistry with the urge to reduce, in the most general Pythagorean sense of describing facts mathematically. The story of the periodic system is the story of the blending of chemistry, Pythagoreanism, and most recently, quantum physics.

If one takes a realistic view concerning the periodic law, one might claim that there is a definite fact of the matter concerning the point at which approximate repetition occurs among the elements as the atomic number sequence increases. For example, the position of the element helium has led to a certain amount of debate. While most chemists insist that the element is a noble gas, an appeal to the electronic configuration of its atoms suggests that it might be placed among the alkaline earths. A chemist having an antirealist disposition on these issues might consider that the representation of the elements is a matter of convention and that there is no real fact of the matter concerning where helium and other troublesome elements should be placed. These issues are discussed in chapter 10, which also considers the astrophysical origin of the elements as well as some unusual chemical regularities embodied in the periodic table. The question of reduction raises another interesting issue concerning the reduction of chemistry to quantum mechanics. It appears that most chemists are quite willing to accept the reductive claims from physics insofar as it bestows greater theoretical underpinning to chemistry. Nevertheless, in cases such as the positioning of helium, chemists retain the right to classify the element in chemical terms even at the risk of overruling the findings of the reducing science.

Along with the realist view of the periodic system, as referred to above, comes the question of whether to regard the elements as "natural kinds," meaning realistic scientific entities that are differentiated by nature itself rather than by our human attempts at classification. This in turn opens up further dialogue with mainstream philosophy of science, which concerns itself with the question of natural kinds. In philosophy of biology, species have been deemed not to be natural kinds since biological species evolve over time. Many philosophers have sought to locate natural kinds at the chemical level. Elements, in particular, are regarded by many as the quintessential natural kind term. To be gold is to possess atomic number 79 and vice versa. Natural kinds have been regularly invoked in the debates among philosophers of language concerning how linguistic terms such as "gold" or "water" refer to objects in the world. According to the widely held Kripke-Putnam view, we are urged to take a scientific view of natural kind terms. The term "water," for example, is to be taken as denoting just what modern science stipulates water to be, usually taken to be molecules of H2O. This approach raises many issues that continue to exercise contemporary philosophers of science. Water is not simply H2O since it may contain impurities or may be present in ionized form, to cite just two of many objections that have been raised. Even the notion that elements may be natural kinds has been criticized on the basis of the existence of isotopes of many elements. Not all atoms of gold have the same mass, and so it has been claimed that gold is not a unique natural kind.

It appears that one of the best ways to explore the relationship between chemistry and modern physics is to consider the status of the periodic system. Given the renewed interest in the philosophy of chemistry and in the periodic system itself, a reassessment of these basic issues is now required, and this is attempted in the chapters of this book.
_**The Periodic Table**_

## **CHAPTER 1  
THE PERIODIC SYSTEM  
 _An Overview_**

### THE ELEMENTS

In ancient Greek times philosophers recognized just four elements, earth, water, air, and fire, all of which survive in the astrological classification of the 12 signs of the zodiac. At least some of these philosophers believed that these different elements consisted of microscopic components with differing shapes and that this explained the various properties of the elements. These shapes or structures were believed to be in the form of Platonic solids (figure 1.1) made up entirely of the same two-dimensional shape. The Greeks believed that earth consisted of microscopic cubic particles, which explained why it was difficult to move earth. Meanwhile, the liquidity of water was explained by an appeal to the smoother shape possessed by the icosahedron, while fire was said to painful to the touch because it consisted of the sharp particles in the form of tetrahedra. Air was thought to consist of octahedra since that was the only remaining Platonic solid. A little later, a fifth Platonic solid, the dodecahedron, was discovered, and this led to the proposal that their might be a fifth element or "quintessence," which also became known as ether.

Although the notion that elements are made up of Platonic solids is regarded as incorrect from a modern point of view, it is the origin of the very fruitful notion that macroscopic properties of substances are governed by the structures of the microscopic components of which they are comprised. These "elements" survived well into the Middle Ages and beyond, augmented with a few others discovered by the alchemists, the precursors of modern-day chemists. One of the many goals of the alchemists seems to have been the transmutation of elements. Not surprisingly, perhaps, the particular transmutation that most enticed them was the attempt to change the base metal lead into the noble metal gold, whose unusual color, rarity, and chemical inertness have made it one of the most treasured substances since the dawn of civilization.

FIGURE 1.1 The five Platonic solids. O. Benfey, Precursors and Cocursors of the Mendeleev Table: The Pythagorean Spirit in Element Classification, _Bulletin for the History of Chemistry_ , 13–14, 60–66, 1992–1993, figure on p. 60 (by permission).

The earliest understanding of the term "element" among the Greek philosophers was of a "tendency" or "potentiality" that gave rise to the observable properties of the element. This rather subtle distinction between the abstract form of an element and its observable form has been all but forgotten in modern times. It has nonetheless served as a fundamental guiding principle to such noted contributors to the periodic system as Dimitri Mendeleev, its major discoverer.

According to most textbook accounts, chemistry began in earnest only when it turned its back on alchemy and on this seemingly mystical understanding of the nature of elements. The triumph of modern science is generally regarded as resting on direct experimentation and the adoption of an empiricist outlook, which holds that only that which can be observed should count. Not surprisingly, therefore, the more subtle and perhaps more fundamental sense of the concept of elements was rejected. For example, Robert Boyle and Antoine Lavoisier both took the view that an element should be defined by an appeal to empirical observations, thus denying the role of abstract elements. They recommended that an element should be defined as a material substance that has yet to be broken down into any more fundamental components by chemical means. In 1789, Lavoisier published a list of 33 simple substances or elements according to this empiricist criterion (figure 1.2). Gone were the ancient elements of earth, water, air, and fire, which had by now been shown to consist of simpler substances.

FIGURE 1.2 List of 33 simple substances compiled by Lavoisier. _Traité Elémentaire de Chimie_ , Cuchet, Paris, 1789, p. 192

Many of these substances would qualify as elements by modern standards, while others, such as _lumiére_ (light) and _calorèque_ (heat), are certainly no longer regarded as elements. Rapid advances in techniques of separation and characterization of chemical substances over the forthcoming years would help chemists expand and refine this list. The important technique of spectroscopy, which measures the emission and absorption spectra of various kinds of radiation, would eventually yield a very accurate means by which each element could be identified through its unique "fingerprint." In modern times, we recognize 91 naturally occurring elements, and it has even been possible to extend the range of the elements beyond those that occur naturally.

### THE DISCOVERY OF THE ELEMENTS

The story of the discovery of the elements is a fascinating one and has been the subject of at least one classic account. A time line for the discoveries is given in table 1.1. This story is not systematically addressed in the present book, although references to predictions and discovery of elements are made throughout.

There have been a number of major episodes in the history of chemistry when half a dozen or so elements were discovered almost at once, or within a period of a few years. Of course, some elements, such as iron, copper, gold, and other metals, have been known since antiquity. In fact, historians and archeologists refer to certain epochs in human history as the Iron Age or the Copper Age. The alchemists added several more elements to the list, including sulfur, mercury, and phosphorus. In relatively modern times, the discovery of electricity enabled chemists to isolate many of the more reactive elements that, unlike copper and iron, could not be obtained by heating their ores with carbon. The English chemist Humphry Davy seized upon the use of electricity or, more specifically, electrolysis to isolate as many as 10 elements, including calcium, barium, magnesium, sodium, and chlorine.

Following the discovery of radioactivity and nuclear fission, and the development of techniques in radiochemistry, it became possible to fill the remaining few gaps in the periodic table. The last gap to be filled was that corresponding to element 43, which became known as technetium from the Greek _techne_ , meaning artificial or manufactured. It was "manufactured" in the course of some radiochemical reactions that would not have been feasible before the advent of nuclear physics. Until recently, it was believed that this element did not occur naturally, but a reexamination of old evidence has now suggested that it does in fact occur naturally and that early reports of its discovery made in the 1925 may have been unjustly discredited.

The most recent spate of elemental discoveries is also based on technological developments, involving the production and harnessing of beams of pure atoms or pure elementary particles such as neutrons. These particles can be fired at each other with great precision to achieve nuclear fusion reactions and to thereby create new elements with extremely high atomic numbers. The initiator of this field was the American chemist Glenn Seaborg, who first synthesized plutonium in 1943 and went on to head research teams that were responsible for the synthesis of many more trans-uranium elements.

### NAMES AND SYMBOLS OF THE MODERN ELEMENTS

Part of the appeal of the periodic table derives from the individual nature of the elements and from their names. The chemist and concentration camp survivor Primo Levi began each chapter of his much-acclaimed book _The Periodic Table_ with a vivid description of an element such as gold, lead, or oxygen. The book itself is about his relations and acquaintances, but each anecdote is motivated by Levi's love of a particular element. More recently, the well-known neurologist and author Oliver Sacks has written a book called _Uncle Tungsten_ , in which he tells of his boyhood fascination with chemistry and in particular the periodic table.

TABLE 1.1  
Discovery Time Line for the Elements and Approximate Dates of Contributions from Major Chemists and Physicists Connected with the Periodic System

During the many centuries over which the elements have been discovered, many different themes have been used to select their names. Just reading a list of the names of elements can conjure up episodes from Greek mythology. Promethium, element 61, takes its name from Prometheus, the god who stole fire from heaven and gave it to human beings only to be punished for this act by Zeus. The connection of this tale to element 61 seems to be the extreme effort that was needed to isolate it, just as the task performed by Prometheus was difficult and dangerous. Promethium is one of the very few elements that do not occur naturally on the earth. It was obtained as a decay product from the fission of another element, uranium.

Planets and other celestial bodies have been used to name some elements. For example, palladium, which was discovered in 1803, is named after Pallas, or the second asteroid that was itself discovered just one year earlier in 1802. Helium is named after _helios_ , the Greek name for the sun. It was first observed in the spectrum of the sun in 1868, and it was not until 1895 that it was first identified in terrestrial samples.

Many elements derive their names from colors. Cesium is named after the Latin color _caesium_ , which means gray-blue, because it has prominent gray-blue lines in its spectrum. The yellow-green gas chlorine comes from the Greek word _khloros_ , which denotes the color yellow-green. The salts of the element rhodium often have a pink color, and this explains why the name of the element was chosen from _rhodon_ , the Greek for rose. In cases of more recently synthesized elements, their names come from those of the discoverer or a person that the discoverers wish to honor. This is why we have bohrium, curium, einsteinium, fermium, gadolinium, lawrencium, meitnerium, mendeleevium, nobelium, roentgenium, ruther-fordium, and seaborgium.

A large number of elements—15, to be precise—have come from the place where their discoverer lived, or wished to honor: americium, berkelium, californium, darmstadtium, europium, francium, germanium, hassium, polonium, gallium, hafnium, lutetium, rhenium, ruthenium, and scandium. Yet other element names are derived from geographical locations connected with minerals in which they were found. This category includes the remarkable case of four elements named after the Swedish village of Ytterby, which lies close to Stockholm. Erbium, terbium, ytterbium, and yttrium were all found in ores located around this village, while a fifth element, holmium, was named after the Latin for Stockholm.

The naming of the later trans-uranium elements is a separate story in itself, complete with nationalistic controversies and, in some cases, acrimonious disputes over who first synthesized the element and should therefore be accorded the honor of selecting a name for it. In an attempt to resolve such disputes, the International Union of Pure and Applied Chemistry (IUPAC) decreed that the elements should be named impartially and systematically with the Latin numerals for the atomic number of the element in each case. Element 105, for example, would be known as un-nil-pentium, while element 106 would be un-nil-hexium. But more recently, after much deliberation over the true discoverers of some of these later superheavy elements, IUPAC has returned the naming rights to the discoverers or synthesizers who were judged to have established priority in each case. Instead of their impersonal Latin names, elements 105 and 106 are now called bohrium and seaborgium, respectively.

Seaborgium is a particularly interesting case, since for many years the committee did not approve of the choice of the American chemist Glenn Seaborg's name even though he had been responsible for the synthesis of about 10 new elements, including number 106. Their official reason seems to have been an old rule that required that no element could be named after a person still living. Following much campaigning by chemists in the United States and other parts of the world, Seaborg was finally granted his element while he was still alive.

Another curious case concerns the German chemist Otto Hahn, whose name was unofficially given to the element hahnium only to be removed later and changed to the name dubnium after the place where several trans-uranium elements were synthesized. Meanwhile, an element has been named after Hahn's onetime colleague Lise Meitner. To many observers, this is a just move since Hahn had been awarded the Nobel Prize for the discovery of nuclear fission while Meitner, who had participated in many of the crucial steps in the work, was denied the prize. To others, it represents an excess of political correctness.

The symbols that are used to depict each element in the periodic table also have a rich and interesting story. In alchemical times, the symbols for the elements often coincided with those of the planets from which they were named or with which they were associated (figure 1.3). The element mercury, for example, shared the same symbol as that of Mercury, the innermost planetary body. Copper was associated with the planet Venus, and both the element and the planet shared the same symbol.

When Dalton published his atomic theory in 1805, he retained several of the alchemical symbols for the elements. These were rather cumbersome, however, and did not lend themselves easily to reproduction in articles and books. The modern use of simple letter symbols was introduced by the Swedish chemist Jacob Berzelius a little later in 1813.

In the modern periodic table, a small minority of elements are represented by a single letter of the alphabet. These include hydrogen, carbon, oxygen, nitrogen, sulfur, and fluorine, which appear as H, C, O, N, S, and F Most elements are depicted by two letters, the first of which is a capital letter and the second a lowercase letter. This gives rise to such element symbols as Li, Be, Ne, Ca, and Sc, for lithium, beryllium, neon, calcium, and scandium, respectively. Some of these two-letter symbols are by no means intuitively obvious, such as Cu, Na, Fe, Pb, Hg, Ag, and Au, which are derived from the Latin names for the elements copper, sodium, iron, lead, mercury, silver, and gold. Tungsten is represented by a W after the German name for the element, which is _wolfram_. For a brief period of time, some heavy elements were depicted by three letters, as mentioned above, but many have now been given particular names, such as seaborgium for element 106. But the very recently discovered elements, such as 112, 114, and 116, whose official discoverers are still under discussion, continue to be depicted by three letters, namely, Uub, Uuq, and Uuh.

FIGURE 1.3 Names and symbols of the ancient metals compared to names of celestial bodies and days of the week.V. Rignes, _Journal of Chemical Education_ , 66, 731–738, 1989, p. 731 (by permission).

### THE MODERN PERIODIC TABLE

The manner in which the elements are arranged in rows and columns in the modern periodic table, also called the medium-long form (figure 1.4), reveals many relationships among them. Some of these relationships are very well known, while others still await discovery. To take just one example, in the 1990s scientists discovered that the property of high temperature superconductivity, the flow of current with zero resistance, could be observed at relatively high temperatures of about 100 Kelvin. This discovery was partly serendipitous. When the elements lanthanum, copper, oxygen, and barium were combined together in a particular manner, the resulting compound happened to display high-temperature superconductivity. There followed a flurry of worldwide activity in an effort to raise the temperature at which the effect could be maintained. The ultimate goal was to achieve room temperature superconductivity, which would allow technological breakthroughs such as levitating trains gliding effortlessly along superconducting rails. One of the main guiding principles used in this quest was the periodic table of the elements. The table allowed researchers to replace some of the elements in the compound with others that are known to behave in a similar manner and then examine the effect on superconducting behavior. This is how the element yttrium was incorporated into a new set of superconducting compounds, to produce the compound YBa2Cu3O7 with a superconducting temperature of 93K. This knowledge, and undoubtedly much more, lies dormant within the periodic system waiting to be discovered and put to good use.

The conventional periodic table consists of rows and columns. Trends can be observed among the elements going across and down the table. Each horizontal row represents a single period of the table. On crossing a period, one passes from metals such as potassium and calcium on the left, through transition metals such as iron, cobalt, and nickel, then through some semimetallic elements such as germanium, and on to some nonmetals such as arsenic, selenium, and bromine on the right side of the table. In general, there is a smooth gradation in chemical and physical properties as a period is crossed, but exceptions to this general rule abound and make the study of chemistry a fascinating and unpredictably complex field.

Metals themselves can vary from soft dull solids such as sodium or potassium to hard shiny substances such as chromium, platinum, and gold. Nonmetals, on the other hand, tend to be solids or gases, such as carbon and oxygen, respectively. In terms of their appearance, it is sometimes difficult to distinguish between solid metals and solid nonmetals. To the layperson, a hard and shiny metal may seem to be more metallic than a soft metal such as sodium. But in a chemical sense, elements that have the greater ability to lose electrons (lower ionization energies) are regarded as being the more metallic. Sodium is therefore regarded by chemists as being more metallic than such elements as iron or copper. The periodic trend from metals to nonmetals is repeated with each period, such that when the rows are stacked they form columns, or groups, of similar elements. Elements within a single group tend to share many important physical and chemical properties, although there are many exceptions.

The manner in which the groups in the modern periodic table are labeled is complicated and controversial. The groups, or columns, of main-group elements, which are also referred to as representative elements, lie on the extreme left and right of the modern periodic table. In the United States, these groups are generally labeled with Roman numerals from I to VIII, with the letter A sometimes added to differentiate them from transition metals or groups IB to VIIIB, which lie in the central portion of the table. However, in Europe the convention is different in that all groups are sequentially labeled from left to right as IA to VIIIA until one reaches the group headed by copper, where the labeling becomes IB up to the noble gases, which are said to be in group VIIIB (figure 1.5). Both of these systems use the same Roman numeral for each column, which, in the case of main-group elements, also denotes the number of outer-shell electrons.

FIGURE 1.4 The modern or medium-long form table.

FIGURE 1.5 Diagram of conventional periodic table format with alternative numbering systems for groups: the more recent IUPAC system (top line), U.S. system (second line), and European system (third line). Note that three columns are labeled VIII in the U.S./European systems but that each column has a distinct number in the IUPAC system.

Given the confusion that these conventions have caused, there has been much attention directed at obtaining a unified system. Recently, IUPAC recommended that groups should be sequentially numbered with Arabic numerals from left to right, as groups 1 to 18, without the use of the letters A or B. The unfortunate result of this proposal is that the direct correlation between the number of outer-shell electrons in the atoms of main-group elements and the group labels in the old U.S. and European systems is lost. For example, the atom of oxygen has six outer-shell electrons and is said to be in group VI (followed by an A or B) in the older systems, whereas in the IUPAC system it is considered to be in group 16-. As a result, although many textbooks display the IUPAC recommendation on periodic tables, they generally fail to adhere to it when discussing the properties of the elements.

This book mainly uses Roman numerals for the representative, or main-group elements, and refers to transition metal groups by the name of their first element. For example, group IVA in the U.S. system (carbon, silicon, germanium, tin, and lead) is referred to as simply group IV. Meanwhile, group IVB in the U.S. system (chromium, molybdenum, tungsten) is referred to as the chromium group. Nevertheless, in chapter 10 the IUPAC system of numbering groups is used to avoid any possible confusion.

And so with this proviso, on the extreme left of the table, group I contains such elements as the metals sodium, potassium, and rubidium. These are unusually soft and reactive substances, quite unlike what are normally considered metals, such as iron, chromium, gold, and silver. The metals of group I are so reactive that merely placing a small piece of one of them into pure water gives rise to a vigorous reaction that produces hydrogen gas and leaves behind a colorless alkaline solution. The elements in group II include magnesium, calcium, and barium and tend to be less reactive than those of group I in most respects.

Moving to the right, one encounters a central rectangular block of elements collectively known as the transition metals, which includes such examples as iron, copper, and zinc. In early periodic tables, known as short-form tables (figure 1.6), these elements were placed among the groups of what are now called the main-group elements. Several valuable features of the chemistry of these elements are lost in the modern table because of the manner in which they have been separated from the main body of the table, although the advantages of this later organization outweigh these losses. To the right of the transition metals lies another block of representative elements starting with group III and ending with group VIII, the noble gases on the extreme right of the table.

Sometimes the properties a group shares are not immediately obvious. This is the case with group IV, which consists of carbon, silicon, germanium, tin, and lead. Here one notices a great diversity on progressing down the group. Carbon, at the head of the group, is a nonmetal solid that occurs in three completely different structural forms (diamond, graphite, and fullerenes) and forms the basis of all living systems. The next element below, silicon, is a semimetal that, interestingly, may form the basis of artificial life, or at least "artificial intelligence", since it lies at the heart of all computers. The next element down, germanium, is a more recently discovered semimetal that was predicted by Mendeleev and later found to have many of the properties he foresaw. On moving down to tin and lead, one arrives at two metals known since antiquity. In spite of this wide variation among them, in terms of metal–nonmetal behavior, the elements of group IV nevertheless are similar in an important chemical sense in that they all display a maximum combining power, or valence, of 4.

FIGURE 1.6 Short-form table: the original Mendeleev table published in 1869. D.I. Mendeleev, Sootnoshenie svoistv s atomnym vesom elementov, _Zhurnal Russkeo Fiziko-Khimicheskoe Obshchestv_ , 1, 60–77, 1869, table on p. 70.

The apparent diversity of the elements in group VII is even more pronounced. The elements fluorine and chlorine, which head the group, are both poisonous gases. The next member, bromine, is one of the only two known elements that exist as a liquid at room temperature, the other one being the metal mercury. Moving further down the group, one then encounters iodine, a violet-black solid element. If a novice chemist were asked to group these elements according to their appearances, it is inconceivable that he or she would consider classifying together fluorine, chlorine, bromine, and iodine. This is one instance where the subtle distinction between the observable and the abstract sense of the concept of an element can be helpful. The similarity between them lies primarily in the nature of the abstract elements and not the elements as substances that can be isolated and observed.

On moving all the way to the right, a remarkable group of elements, the noble gases, is encountered, all of which were first isolated just before, or at, the turn of the twentieth century. Their main property, rather paradoxically, at least when they were first isolated, was that they lacked chemical properties. These elements, such as helium, neon, argon, and krypton, were not even included in early periodic tables, since they were unknown and completely unanticipated. When they were discovered, their existence posed a formidable challenge to the periodic system, but one that was eventually successfully accommodated by the extension of the table to include a new group, labeled group VIII, or group 18 in the IUPAC system.

Another block of elements, found at the foot of the modern table, consists of the rare earths that are commonly depicted as being literally disconnected. But this is just an apparent feature of this generally used display of the periodic system. Just as the transition metals are generally inserted as a block into the main body of the table, it is quite possible to do the same with the rare earths. Indeed, many such long-form displays have been published. While the long-form tables (figure 1.7) give the rare earths a more natural place among the rest of the elements, they are rather cumbersome and do not readily lend themselves to conveniently shaped wall charts of the periodic system. Although there are a number of different forms of the periodic table, what underlies the entire edifice, no matter the form of its representation, is the periodic law.

### THE PERIODIC LAW

The periodic law states that after certain regular but varying intervals the chemical elements show an approximate repetition in their properties. For example, fluorine, chlorine, and bromine, which all fall into group VII, share the property of forming white crystalline salts of general formula NaX with the metal sodium. This periodic repetition of properties is the essential fact that underlies all aspects of the periodic system.

This talk of the periodic law raises some interesting philosophical issues. First of all, periodicity among the elements is neither constant nor exact. In the generally used medium-long form of the periodic table, the first row has two elements, the second and third each contains eight, the fourth and fifth contain 18, and so on. This implies a varying periodicity consisting of 3, 9, 9, 19, and so on, quite unlike the kind of periodicity one finds in the days of the week or notes in a musical scale. In these latter cases, the period length is constant, such as eight for the days of the week as well as the number of notes on a Western musical scale.

FIGURE 1.7 Long-form periodic table.

Among the elements, however, not only does the period length vary, but also the periodicity is not exact. The elements within any column of the periodic table are not exact recurrences of each other. In this respect, their periodicity is not unlike the musical scale, in which one returns to a note denoted by the same letter, which sounds like the original note but is definitely not identical to it, being an octave higher.

The varying length of the periods of elements and the approximate nature of the repetition have caused some chemists to abandon the term "law" in connection with chemical periodicity. Chemical periodicity may not seem as lawlike as the laws of physics, but whether this fact is of great importance is a matter of debate. It can be argued that chemical periodicity offers an example of a typically chemical law, approximate and complex, but still fundamentally displaying lawlike behavior.

Perhaps this is a good place to discuss some other points of terminology. How is a periodic table different from a periodic system? The term "periodic system" is the more general of the two. The periodic system is the more abstract notion that holds that there is a fundamental relationship among the elements. Once it becomes a matter of displaying the periodic system, one can choose a three-dimensional arrangement, a circular shape, or any number of different two-dimensional tables. Of course, the term "table" strictly implies a two-dimensional dimensional representation. So although the term "periodic table" is by far the best known of the three terms law, system, and table, it is actually the most restricted.

### REACTING ELEMENTS AND ORDERING THE ELEMENTS

Much of what is known about the elements has been learned from the way they react with other elements and from their bonding properties. The metals on the left-hand side of the conventional periodic table are the complementary opposites of the nonmetals, which tend to lie toward the right-hand side. This is so because, in modern terms, metals form positive ions by the loss of electrons, while nonmetals gain electrons to form negative ions. Such oppositely charged ions combine together to form neutrally charged salts such as sodium chloride or calcium bromide. There are further complementary aspects of metals and nonmet-als. Metal oxides or hydroxides dissolve in water to form bases while nonmetal oxides or hydroxides dissolve in water to form acids. An acid and a base react together in a "neutralization" reaction to form a salt and water. Bases and acids, just like metals and nonmetals from which they are formed, are also opposite but complementary.

Acids and bases have a connection with the origins of the periodic system since they featured prominently in the concept of equivalent weights, which was first used to order the elements. The equivalent weight of any particular metal, for example, was originally obtained from the amount of metal that reacts with a certain amount of a chosen standard acid. The term "equivalent weight" was subsequently generalized to denote the amount of an element that reacts with a standard amount of oxygen. Historically, the ordering of the elements across periods was determined by equivalent weight, then later by atomic weight, and eventually by atomic number.

Chemists first began to make quantitative comparisons among the amounts of acids and bases that reacted together. This procedure was then extended to reactions between acids and metals. This allowed chemists to order the metals on a numerical scale according to their equivalent weight, which, as mentioned, is just the amount of the metal that combines with a fixed amount of acid. The concept of equivalent weights is, at least in principle, an empirical one since it seems not to rest on the theoretical assumption that the elements are ultimately composed of atoms.

Atomic weights, as distinct from equivalent weights, were first obtained in the early 1800s by John Dalton, who indirectly inferred them from measurements on the masses of the relevant elements combined together. But there were complications in this apparently simple method that forced Dalton to make assumptions about the chemical formulas of the compounds in question. The key to this question is the valence, or combining power, of an element. For example, a univalent atom combines with hydrogen atoms in a ratio of 1:1; divalent atoms, such as oxygen, combine in a ratio of 2:1; and so on.

Equivalent weight, as mentioned above, is sometimes regarded as a purely empirical concept since it does not seem to depend upon whether one believes in the existence of atoms. Following the introduction of atomic weights, many chemists who felt uneasy about the notion of atoms attempted to revert to the older concept of equivalent weights. They believed that equivalent weights would be purely empirical and therefore more reliable. But as many authors have argued, most recently Alan Rocke, such hopes were an illusion since equivalent weights also rested on the assumption of particular formulas for compounds, and formulas are theoretical notions.

For many years, there was a great deal of confusion created by the alternative use of equivalent weight and atomic weight. Dalton himself assumed that water consisted of one atom of hydrogen combined with one atom of oxygen, which would make its atomic weight and equivalent weight the same, but his guess at the valence of oxygen turned out to be incorrect. Many authors used the terms "equivalent weight" and "atomic weight" interchangeably, thus further adding to the confusion. The true relationship between equivalent weight, atomic weight, and valency was clearly established only in 1860 at the first major scientific conference, which was held in Karlsruhe, Germany. This clarification and the general adoption of consistent atomic weights cleared the path for the independent discovery of the periodic system by as many as six individuals in various countries, who each proposed forms of the periodic table that were successful to varying degrees. Each placed the elements generally in order of increasing atomic weight.

The third, and most modern, of the ordering concepts mentioned above is atomic number. Once atomic number was understood, it displaced atomic weight as the ordering principle for the elements. No longer dependent on combining weights in any way, atomic number can be given a simple microscopic interpretation in terms of the structure of the atoms of any element. The atomic number of an element is given by the number of protons, or units of positive charge, in the nucleus of any of its atoms. Thus, each element on the periodic table has one more proton than the element preceding it. Since the number of neutrons in the nucleus also tends to increase as one moves through the periodic table, this makes atomic number and atomic weights roughly correspondent, but it is the atomic number that identifies any element. This is to say that atoms of any particular element always have the same number of protons, although they can differ in the number of neutrons they contain.

### DIFFERENT REPRESENTATIONS OF THE PERIODIC SYSTEM

The modern periodic system succeeds remarkably well in ordering the elements by atomic number in such a way that they fall into natural groups, but this system can be represented in more than one way. Thus, there are many forms of the periodic table, some designed for different uses. Whereas a chemist might favor a form that highlights the reactivity of the elements, an electrical engineer might wish to focus on similarities and patterns in electrical conductivities.

The way in which the periodic system is displayed is a fascinating issue, and one that especially appeals to the popular imagination. Since the time of the early periodic tables of John Newlands, Julius Lothar Meyer, and Dimitri Mendeleev, there have been many attempts to obtain the "ultimate" periodic table. Indeed, it has been estimated that within 100 years of the introduction of Mendeleev's famous table of 1869, approximately 700 different versions of the periodic table were published. These include all kinds of alternatives, including three-dimensional tables, helices, concentric circles, spirals, zigzags, step tables, and mirror image tables. Even today, articles are regularly published in the _Journal of ChemicalEducation_, for example, purporting to show new and improved versions of the periodic system.

What is fundamental to all these attempts is the periodic _law_ itself, which exists in only one form. None of the multitude of displays changes this aspect of the periodic system. Many chemists stress that it does not matter how this law is physically represented, provided that certain basic requirements are met. Nevertheless, from a philosophical point of view, it may still be relevant to consider the most fundamental representation of the elements, or the ultimate form of the periodic system, especially as this relates to the question of whether the periodic law should be regarded in a realistic manner or as a matter of convention. The usual response that representation is only a matter of convention would seem to clash with the realist notion that there may be a fact of the matter concerning the points at which the repetitions in properties occur.

### RECENT CHANGES IN THE PERIODIC TABLE

In 1945, Glenn Seaborg (figure 1.8) suggested that the elements beginning with actinium, number 89, should be considered a rare earth series, whereas it had previously been supposed that the new series of rare earths would begin after element 92, or uranium (figure 1.9). Seaborg's new periodic table revealed an analogy between europium (63) and gadolinium (64) and the as yet undiscovered elements 95 and 96, respectively. On the basis of these analogies, Seaborg succeeded in synthesizing and identifying the two new elements, which were subsequently named americium and curium. A number of further trans-uranium elements have subsequently been synthesized.

The standard form of the periodic table has also undergone some minor changes regarding the elements that mark the beginning of the third and fourth rows of the transition elements. Whereas older periodic tables show these elements to be lanthanum (57) and actinium (89), more recent experimental evidence and analysis have put lutetium (71) and lawrencium (103) in their former places. It is also interesting to note that some even older periodic tables based on macroscopic properties had anticipated these changes.

These are examples of ambiguities in what may be termed secondary classification, which is not as unequivocal as primary classification, or the sequential ordering of the elements. In classical chemical terms, secondary classification corresponds to the chemical similarities between the various elements in a group. Meanwhile, in modern terms, secondary classification is explained by recourse to the concept of electronic configurations. Regardless of whether one takes a classical qualitative chemical approach or a more physical approach based on electronic configurations, secondary classification of this type is more tenuous than primary classification and cannot be established as categorically. The way in which secondary classification, as defined here, is established is a modern example of the tension between using chemical properties or physical properties for classification. The precise placement of an element within groups of the periodic table can vary depending on whether one puts more emphasis on electronic configuration (a physical property) or its chemical properties. In fact, many recent debates on the placement of helium in the periodic system revolve around the relative importance that should be assigned to these two approaches.

FIGURE 1.8 Glen Seaborg. Photo from Emilio Segré Collection, by permission.

In recent years, the number of elements has increased well beyond 100 as the result of the synthesis of artificial elements. At the time of writing, conclusive evidence has been reported for element 111. Such elements are typically very unstable, and only a few atoms are produced at any time. However, ingenious chemical techniques have been devised that permit the chemical properties of these so-called superheavy elements to be examined and allow one to check whether extrapolations of chemical properties are maintained for such highly massive atoms. On a more philosophical note, the production of these elements allows us to examine whether the periodic law is an exceptionless law, of the same kind as Newton's law of gravitation, or whether deviations to the expected recurrences in chemical properties might take place once a sufficiently high atomic number is reached. No surprises have been found so far, but the question of whether some of these superheavy elements have the expected chemical properties is far from being fully resolved. One important complication that arises in this region of the periodic table is the increasing significance of relativistic effects due to very rapidly moving electrons. These effects cause the adoption of unexpected electronic configurations in some atoms and may result in equally unexpected chemical properties.

FIGURE 1.9 Pre-Seaborg (a) and post-Seaborg (b) periodic tables. RE denotes rare earth elements from 57–71 inclusive; LA, lanthanides (Z = 57–71); AC, actinides beginning with _Z =_ 89, where _Z_ is atomic number.

### UNDERSTANDING THE PERIODIC SYSTEM

Developments in physics have had a profound influence on the manner in which the periodic system is now understood. The two important theories in modern physics are Einstein's theory of relativity and quantum mechanics.

The first of these has had a limited impact on our understanding of the periodic system but is becoming increasingly important in accurate calculations carried out on atoms and molecules. The need to take account of relativity arises whenever objects move at speeds close to that of light. Inner electrons, especially those in the heavier atoms in the periodic system, can readily attain such relativistic velocities. It would be impossible to carry out an accurate calculation, especially on a heavy atom, without applying the necessary relativistic corrections. In addition, many seemingly mundane properties of elements such as the characteristic color of gold or the liquidity of mercury can best be explained as relativistic effects due to fast-moving inner-shell electrons.

But it is the second theory of modern physics that has exerted by far the more important influence in attempts to understand the periodic system theoretically. Quantum theory was actually born in the year 1900, some 14 years before the discovery of atomic number. It was first applied to atoms by Niels Bohr, who pursued the notion that the similarities between the elements in any group of the periodic table could be explained by there having equal numbers of outer-shell electrons. The very notion of a particular number of electrons in an electron shell is an essentially quantumlike concept. Electrons are assumed to possess only certain quanta, or packets, of energy, and depending on how many such quanta they possess, they lie in one or another shell around the nucleus of the atom.

Soon after Bohr had introduced the concept of the quantum to the understanding of the atom, many others developed his theory until the old quantum theory gave rise to quantum mechanics. Under the new description, electrons are regarded as much as waves as they are as particles. Even stranger is the notion that electrons no longer follow definite trajectories or orbits around the nucleus. Instead, the description changes to talk of smeared-out electron clouds, which occupy so-called orbitals. The most recent explanation of the periodic system is given in terms of how many such orbitals are populated by electrons. The explanation depends on the electron arrangement or "configuration" of an atom, which is spelled out in terms of the occupation of its orbitals.

The interesting question raised here is the relationship between chemistry and modern atomic physics and, in particular, quantum mechanics. The popular view reinforced in most textbooks is that chemistry is nothing but physics "deep down" and that all chemical phenomena, and especially the periodic system, can be developed on the basis of quantum mechanics. There are some problems with this view, however, which are considered in this book.

For example, chapter 9 it is suggested that the quantum mechanical explanation for the periodic system is still far from perfect. This is important because chemistry books, especially textbooks aimed at teaching, tend to give the impression that our current explanation of the periodic system is essentially complete. This is just not the case, or so it will be argued.

### MOLECULAR TABLES

Another recent departure has been the invention of periodic tables designed to summarize the properties of compounds rather than elements. In 1980, Ray Hef-ferlin produced a periodic system for all the conceivable diatomic molecules that can be formed between the first 118 elements. In order to represent this vast number of entries, Hefferlin used four three-dimensional blocks of varying sizes. His representation reveals that interatomic distances, spectroscopic frequencies, and molecular ionization energies are periodic properties. It also provided successful predictions regarding the properties of diatomic molecules.

Jerry Dias, a chemist at the University of Missouri-Kansas City, has devised a periodic classification of a class of organic molecules called benzenoid aromatic hydrocarbons, of which naphthalene, C10H8, is the simplest example (figure 1.10). By analogy with Johann Döbereiner's triads of elements, described in chapter 2, these molecules can be sorted into groups of three in which the central molecule has a total number of carbon and hydrogen atoms that is the mean of the flanking entries, both downward and across the table. This periodic scheme has been applied to making a systematic study of the properties of benzenoid aromatic hydrocarbons, which has led to the predictions of the stability and reactivity of many of their isomers.

However, it is the periodic table of elements that has had the widest and most enduring influence. The periodic table ranks as one of the most fruitful and unifying ideas in the whole of modern science, comparable perhaps with Darwin's theory of evolution by natural selection. Unlike such theories as Newtonian mechanics, the periodic table has not been falsified by developments in modern physics but has evolved while remaining essentially unchanged. After evolving for nearly 150 years through the work of numerous individuals, the periodic table remains at the heart of the study of chemistry. This is mainly because it is of immense practical benefit for making predictions about all manner of chemical and physical properties of the elements and possibilities for bond formation. Instead of having to learn the properties of the more than 100 elements, the modern chemist, or the student of chemistry, can make effective predictions from knowing the properties of typical members of each of the eight main groups and those of the transition metals and rare earth elements.

FIGURE 1.10 Dias's periodic classification of benzenoid aromatic hydrocarbons. J. Dias, Setting Benzenoids to Order, _Chemistry in Britain_ , 30, 384–386, 1994, p. 384 (by permission).

Having laid some thematic foundations and defined some key terms, in chapter 1 I begin the story of the development of the modern periodic system, starting with its birth in the eighteenth and nineteenth centuries.

## **CHAPTER 2  
QUANTITATIVE RELATIONSHIPS AMONG THE ELEMENTS AND THE ORIGINS OF THE PERIODIC TABLE**

Elements within a vertical group on the periodic table share certain chemical similarities, but the modern periodic system is not derived purely from descriptive characteristics. If chemical similarities were the sole basis for their classification, there would be many cases where the order and placement of the elements would be ambiguous. The development of the modern periodic system began when it was recognized that there are precise numerical relationships among the elements. Its subsequent evolution has also involved contributions from physics, as described in subsequent chapters. But whereas the latter contributions drew on fundamental physical theories, the ones that are examined in this chapter do not share this aspect. Instead, they involved looking for patterns among the numerical properties, such as equivalent weight or atomic weight, associated with each element.

Throughout its history, the development of the periodic table has involved a delicate interplay between two contrasting approaches: discerning quantitative physical data, on one hand, and observing qualitative similarities among the elements as a form of natural history, on the other. Both approaches are essential, and the balance that has been struck between them has been of crucial importance at various stages in our story.

### QUANTITATIVE ANALYSIS

Whereas attention to qualitative aspects has always been an essential part of chemistry, the use of quantitative data has been a relatively new addition. The time when chemists began to pay attention to quantitative aspects of chemical reactions and chemical substances has been the source of much debate among historians. The traditional view has been that this step was taken by Antoine Lavoisier (figure 2.1), who is regarded as the founder of modern chemistry. The more recent historical opinion is that Lavoisier made few original contributions and that much of his fame lay in his abilities as an organizer and presenter of chemical knowledge.

FIGURE 2.1 Antoine Lavoisier. Photo from Edgar Fahs Smith Collection by permission.

Nevertheless, Lavoisier was able to dispel some of the vagueness and confusion that dogged the field of chemistry as he found it. The confusion included the chaotic way in which substances were named as well as the uncertain knowledge of weight changes accompanying chemical reactions. Prior to Lavoisier and his contemporaries, it was believed that when substances burned they would release a substance called phlogiston. Although some substances do appear to lose weight when they are burned, many others show a gain in weight. Lavoisier used his considerable personal wealth to commission the making of the finest balances of his day, some of which could measure changes as accurately as one part in 600,000. As a result of his weighing experiments, Lavoisier succeeded in showing that substances that burned did not in fact give off phlogiston and that the notion of phlogiston was redundant.  He also showed that what is essential for burning is the element oxygen, a substance that had previously been discovered by Swedish chemist Carl Scheele and had been subjected to several earlier studies by the Englishman Joseph Priestley.

Moreover, by accurately weighing reacting substances, Lavoisier was able to announce the law of conservation of matter, which states:

_In every chemical operation, an equal quantity of matter exists before and after the operation_.

Lavoisier's emphasis on the quantification of chemistry also paved the way for the laws of chemical combination, which soon prompted John Dalton to develop his atomic theory.

Returning to the revisionary accounts of Lavoisier, it has been argued that a more significant development from the dismissal of phlogiston was the question of composition. What Lavoisier achieved was a reversal of the compositional order that had been held by earlier chemists starting with Georg Stahl. In Lavoisier's chemistry, sulfur and phosphorus were simpler than their acids, thus displaying the opposite order than in the old chemistry. Contrary to the view of the old chemistry, metals were simpler than their calxes (oxides) according to Lavoisier. Likewise, hydrogen and oxygen were regarded as simpler than water in Lavoisier's compositional order, once again quite opposite the view held in the old chemistry.  Some historians even regard Lavoisier's work as a culmination of the tradition begun a good deal earlier by the likes of Stahl on the question of chemical composition, rather than the start of a new tradition in chemistry.

But perhaps Lavoisier's greatest contribution, particularly for our story, was one already mentioned briefly in chapter 1: Lavoisier was highly critical of the classical abstract element scheme of the Greeks and subsequent chemists. By adopting an empiricist approach, he attempted to eradicate any talk of abstract elements or principles in favor of elements as simple substances, which could be isolated and which could not be further decomposed. This anti-metaphysical departure may have been just what was needed in chemistry at the time,  although Lavoisier did not succeed in completely dispensing with the need for elements as principles, as many authors have pointed out.

### EQUIVALENT WEIGHTS

One of the next major developments, following along quantitative lines, was due to Jeremias Benjamin Richter, who between 1792 and 1794 published a set of quantities that later became known as equivalent weights (table 2.1). He first measured amounts of acids that combined with certain amounts of bases. He then extended this procedure to measuring the amount of some metals that combine with a certain fixed amount of acid, and thus obtained an indirect measure of the relative amounts in which elements can combine together. This perhaps marked the first time that the properties of the elements could be compared to each other on a simple numerical scale. This irresistible urge to find numerical patterns in nature would prove to be a powerful force in the development of the periodic table.

TABLE 2.1 Richter's table of equivalent weights, as modiK ed by E. Fischer in 1802

### A SHORT DIGRESSION ON GREEK ATOMISM

The ancient Greek philosophers introduced atomism partly as a response to what they considered as the awkward notion of infinity.  Zeno had introduced a famous paradox whose effect depended on the existence of infinity. According to the paradox, if a person needs to cover a certain distance between points A and B, he or she may do so by a series of steps. In the first step, the person covers half the distance. The second step involves covering half of the remaining distance, and so on. Clearly, this process will continue ad infinitum since each time a step is taken it takes the person closer to the destination but never allows arrival. This paradox and many others like it depend on taking an infinite number of steps between points A and B.

If infinity is deemed to be unreal or unphysical, however, the problem appears to evaporate. One does indeed reach a destination because one cannot take an infinite number of steps. If distances are not infinitely subdivisible, there is no longer any paradox. But the Greek philosophers did not stop at denying infinite subdivisibility of distances. They applied the same denial to matter. They reasoned that a chunk of matter could likewise not be infinitely subdivided, that there would come a point in the subdivision when one had reached the smallest possible chunk of matter or _atomos_ , meaning indivisible matter. Atoms of distance and atoms of matter were thus born of a philosophical desire to banish infinities from distances and from matter. But atomism of this kind remained a purely philosophical idea, and the Greek philosophers showed little inclination to perform experiments to support their notion.

### DALTON'S ATOMIC THEORY

In 1801, Dalton (figure 2.2), a Manchester school teacher, published an article on meteorology, which was one of his main scientific interests. This work was to be the beginning of his reintroduction of atomic theory into science. Atomism had been proposed in ancient Greece, but it had subsequently been abandoned for about 2,000 years, although the mention of atoms or small "particles" had not been entirely forgotten in scientific circles.  For example, Isaac Newton referred frequently to atoms, although not by name, including in the following passage, which Dalton knew well:

It seems probable to me, that God in the beginning form'd matter in solid, massy, hard, impenetrable, moveable particles of such sizes and figures, and with such other properties, and in such proportion to space, as most conduced to the end for which he form'd them; and that these primitive particles being solids, are incomparably harder than any porous bodies compounded of them, even so very hard, as never to wear or break in pieces; no ordinary power being able to divide what God himself made one in the first creation.

FIGURE 2.2 John Dalton. Photo from Edgar Fahs Smith Collection by permission.

But in spite of Newton's notions on the quantification of chemistry, expressed in other passages, little more had been achieved in the field apart from the work of Lavoisier and others using the balance to try to understand chemical reactions, and Richter's little known work on equivalent weights. Lavoisier had taken a firmly empiricist  approach of ignoring the possible existence of unobservable atoms and by focusing on elements as the final stages of chemical analysis of substances. Dalton rejected this position and embraced a realistic conception in which atoms actually exist and have particular sizes and weights.

His ideas on atomism can be summarized under three main points. First, Dalton assumed that all matter was composed of atoms that were indestructible and nonchangeable, thus denying the possibility of the transmutation of elements. Dalton thus belonged to the new chemical tradition that consciously distanced itself from the alchemical doctrine of transmutation. Dalton was not the only one to do so, but he provides an interesting contrast to Robert Boyle, for example, who 150 years earlier also did important quantitative work in chemistry while at the same time being steeped in alchemy, as recent scholarly work has shown.

Second, and contrary to many of his contemporaries, who believed strongly in the unity of all matter, Dalton believed that there were as many different kinds of atoms as there were elements.  Finally, Dalton suggested that the weights of atoms would serve as a kind of bridge between the realm of microscopic unobservable atoms and the world of observable properties. But atomic weight is not necessarily the same as an equivalent weight, an issue raised in chapter 1 that will be revisited here.

The precise origin of Dalton's ideas has been traced by historians to his research into the nature of the air, which had been found to consist of a mixture of gases. At the time, it was not understood why the various component gases of air did not separate out according to their different densities. In broad terms, Dalton reasoned that if gases consist of tiny particles, or atoms, they would be more likely to form a mixture than if they consisted of continuous fluids. This argument is plausible if one accepts that continuous fluids cannot intermingle to the extent that tiny isolated particles can. It is also clear that part of Dalton's motivation for supporting an atomic theory lay in Newton's view that like particles should repel each other. According to this view, the different gases in the air intermingled rather than forming separate strata, because particles of each gas would move away from each other to fill the available space, ignoring the particles of the other gases in the space.

It is interesting to examine briefly how Dalton arrived at the values of atomic weights of the elements shown in table 2.2. For example, he referred to Lavoisier's data on the composition of water, namely, 85% oxygen and 15% hydrogen. Assuming a formula of HO, Dalton calculated the weight of an oxygen atom to be 85/15 = approximately 5.5, by taking the weight of a hydrogen atom as unity. Similarly, Dalton obtained a value for the nitrogen atom by drawing on William Austin's data showing that ammonia consists of 80% nitrogen and 20% hydrogen. Again, Dalton assumed the formula of this compound to be of the binary form NH.

TABLE 2.2 Part of an early table of atomic and molecular weights published by Dalton

Dalton also suggested that the gases in the air diffused into one another because the particles were of different sizes, but he soon realized that it was the different weights of these particles, and not their sizes, which was the key feature in determining how gases would combine. In a paper published in 1803, he estimated the relative atomic weights of a number of different elements. The publication associated with this work represents the first ever list of atomic weights. Eventually, systems of classification would begin to be developed in which atomic weight would replace equivalent weight as the chief criterion by which elements were arranged, but this process was to take a period of about 60 years. Table 2.2 shows an early set of atomic and molecular weights, in modern terms, published by Dalton in 1805.

Another important consequence of Dalton's hypothesis that matter consists of atoms was that it provided an explanation of the long recognized law of constant proportion. As Richter had pointed out, when any two elements combine together, for example, hydrogen and oxygen, they always do so in a constant ratio of their masses. This fact can be understood if one assumes that a certain precise number of atoms of one element combine with a particular number of atoms of the other element. According to this view, macroscopic observations summarized in the law of constant proportion represent a scaled up version of millions of such atomic combinations. If, on the other hand, matter did not consist of atoms but could be infinitely subdivided, it is not clear why oxygen and hydrogen, or any other elements, should always react together in the same particular ratio of masses.

Meanwhile, others had made observations concerning the combination of masses of any two elements in more than one compound. It had been realized that if A reacts with B to form more than one compound, the various amounts of B that react with a fixed amount of A bear a simple whole number ratio to each other. Dalton carried out further experiments on this relationship, and as a result of his work, this, too, became regarded as a law of chemical combination (the law of multiple proportions), and one that his atomic hypothesis could readily explain. On the atomic hypothesis, the law of multiple proportions results from the fact that, for example, one oxygen atom can combine with one atom of carbon to form a compound, and in addition, two atoms of oxygen can combine with one atom of carbon to form a different compound. The ratio of amounts of oxygen combining with a fixed amount of carbon is therefore the simple ratio of 2 to 1. These two compounds are carbon monoxide and carbon dioxide, respectively.

At first, Dalton's concept of atomic weight did not improve the prospects of classifying the elements, since there were problems involved in calculating this quantity. While the equivalent weights introduced by Richter  at least appeared to have a clear experimental basis, Dalton's atomic weights, and those published by several of his contemporaries, seemed to be more theoretical, although this difference later turned out to be an illusion. The determination of atomic weights depended on assuming a particular formula for a compound since formulas could not yet be verified experimentally. The case of water provides a good example. One gram of hydrogen always reacts with approximately 8 grams of oxygen,  and thus the equivalent weight of oxygen is given as 8 relative to that of hydrogen. What Dalton did was assume that hydrogen and oxygen occur as individual atoms and that they combine at the atomic level, thereby accounting for the macroscopic facts about the combination of specific volumes of hydrogen and oxygen. The problem is that unless the formula of water is known, this assumption can tell us nothing about the relative weights of the atoms of hydrogen and oxygen since it is not known how many hydrogen atoms are combining with each oxygen atom. At this point, Dalton was forced to make a guess as to whether one atom of each element had combined together or whether it was two of hydrogen and one of oxygen, or perhaps vice versa, or any other ratio of atoms. Dalton based such choices on what he called the rule of simplicity, meaning that in the absence of additional information, he would assume the simplest possible ratio of 1:1.  Accordingly he assumed the formula of water to be HO and determined the atomic weight of oxygen to be eight, just like its equivalent weight.

The question of finding the correct formulas for compounds was only conclusively resolved a good deal later when the concept of valency, the combining power of a particular element, was clarified by the chemists Edward Frankland and Auguste Kekulé working separately. Hydrogen, for example, has a valence of 1, while the value for oxygen is 2. It follows that two atoms of hydrogen combine with one of oxygen. With this new knowledge, the relationship between atomic weight and equivalent weight could be stated simply:

atomic weight = valence × equivalent weight

Since oxygen has a valence of 2 and its equivalent weight is 8, as many early chemists had determined, its correct atomic weight is therefore twice that number, or 16. The correct formula for water is H2O and not HO, as Dalton had assumed.

### LAW OF DEFINITE PROPORTIONS BY VOLUMES

Soon after Dalton began to publish articles on his atomic theory, experiments were performed by Alexander von Humbolt and Joseph Louis Gay-Lussac leading to what was termed a law of definite proportions by volumes.  These scientists experimented on forming water vapor by passing electric sparks through a mixture of oxygen and hydrogen. They found that whatever volume of oxygen reacted, it was necessary to use almost exactly twice the volume of hydrogen to within ± 0.19%. They also noted that the volume of water vapor formed was almost identical to the volume of hydrogen initially used. Thus:

2 volumes of hydrogen + 1 volume of oxygen → 2 volumes of water vapor

They were able to extend this finding of whole number ratios to several other reactions involving gases. For example:

3 volumes of hydrogen + 1 volume of nitrogen → 2 volumes of ammonia

2 volumes of carbon monoxide + 1 volume of oxygen → 2 volumes of carbon dioxide

Gay-Lussac summarized these results in a new law announced in 1809, which stated:

### _The volumes of gases entering into chemical reaction and the gaseous products are in a ratio of small integers_.

Recall that Dalton's main idea was that matter was composed of indivisible elementary atoms of fixed characteristic weight. Their combination in simple numbers gave rise to compound atoms and accounted for chemical laws such as the law of constant composition and the law of multiple proportions. However, when it came to Gay-Lussac's law, Dalton's original idea was unable to explain the observations summarized in equations such as those above. Consider the first equation again:

2 volumes of hydrogen + 1 volume of oxygen → 2 volumes of water

Using the benefit of hindsight, the cause of the problem can easily be appreciated. Since one volume of oxygen was combining with two volumes of hydrogen, this implied that particles of oxygen must have been dividing.

But this idea contradicts the very heart of Dalton's notion that the smallest particles of any element are supposed to be indivisible. Dalton's own reaction to Gay-Lussac's law was to question the data and to repeat the experiments. This led to his claiming that the ratios were not in fact as simple as reported by von Humbolt and Gay-Lussac. Nevertheless, the simple ratio continued to be reproduced by others and has passed the test of time. Dalton could have accepted the existence of molecules of elements composed of two or more atoms of an element while still holding that such a body represented the simplest chemical unit that retains the properties of the element in question, but he failed to do so.

Meanwhile, Gay-Lussac suggested the very plausible notion that the appearance of small integers relating volumes in the reactions implied that equal volumes of gases contained equal numbers of particles, EVEN. The step of reconciling Dalton's ideas on the existence of atoms with Gay-Lussac's law was taken by the Italian scientist Amadeo Avogadro in 1811. The crucial new ingredient introduced by Avogadro was that, contrary to what had previously been believed, the ultimate particles of a gas were not necessarily composed of single atoms but could equally well be assemblies of two or more atoms. Such assemblies or molecules could thus form the ultimate particles of any gaseous element.

Avogadro's idea was to provide the solution to Gay-Lussac's law while still maintaining the existence of Dalton's ultimate particles, although such particles could now be diatomic molecules, which were capable of subdivision. Unfortunately, Avogadro's resolution was understood by very few chemists at the time and had to wait a further 50 years before it became firmly established at the hands of fellow Italian chemist Stanislao Cannizzaro. It was Cannizzaro who helped to bring order to the prevailing confusion regarding atomic weights, as described in chapter 3.

### PROUT'S HYPOTHESIS

A rather remarkable fact began to emerge after values of equivalent weights and atomic weights had been published by various people. Apart from some exceptions, many of the equivalent weights and atomic weights appeared to be approximate whole number multiples of the weight of hydrogen. To some chemists, this stubborn fact pointed against Dalton's idea of distinct elements and represented support for the essential unity of all the elements. More specifically, it suggested that all the elements, or their atoms, might be multiples of atoms of hydrogen. This would mean that there was really only one kind of matter, which could occur in different states of combination.

The first person to articulate this view clearly was the Scottish physician William Prout. Since the equivalent weights and atomic weights of the elements were nowhere near being exact multiples of each other, Prout rounded them off to the nearest whole number and gave hydrogen a value of 1. Such was the seductive lure of the Pythagorean tradition for seeking simple ratios, and it was this conviction that allowed Prout to ignore the apparent discrepancies as seen in the nonintegral values of the weights of some elements.

Prout's first articles on this subject appeared anonymously in Thomas Thomson's _Annals of Philosophy_ along with a rather modest disclaimer:

The author of the following essay submits it to the public with the greatest diffidence; for though he has taken the utmost pains to arrive at the truth, he has not such confidence in his abilities as an experimentalist as to induce him to dictate to others far superior to himself in chemical acquirements and fame.

In his second paper on this hypothesis, Prout adds,

If the views we have ventured to advance be correct, we may almost consider the _protyle_ of the ancients to be realized in hydrogen; an opinion by-the-bye, not altogether new.

The term "protyle" refers to an underlying primary matter, which was believed by some Greek philosophers to be the basis of all matter. The word itself is derived from _proto-hyle_ , or "first stuff." Whereas for Dalton there were numerous distinct kinds of basic substances or elements, those with a more unitary view of matter, such as Prout, could not accept such a notion. Prout's mention of the fact that his idea was not entirely new in the above quotation has given rise to much speculation by subsequent commentators. It seems to be agreed that he may well have obtained at least part of his idea from the writings of the English chemist Humphry Davy, who believed that many elements literally contained hydrogen. In 1808, Davy had written,

The existence of hydrogen in sulphur is fully proved, and we have no right to consider a substance, which can be produced from it in such large quantities, merely as an accidental ingredient.

Experiments inspired by Prout's hypothesis provided an increasingly accurate set of atomic weights, which could then be used to try to order the elements in the periodic system. Many of the pioneers of the periodic system, including Wolfgang Döbereiner, Leopold Gmelin, Max Pettenkofer, Jean Baptiste André Dumas, and Alexandre De Chancourtois, were very interested in Prout's hypothesis, and it figured prominently in their ideas regarding the classification of the elements.

Though Prout's hypothesis fared well initially, at least in England, where it was supported by Thomas Thomson, who had first published the work, it would fall in and out of favor for years to come. In 1825, Jons Jacob Berzelius, who would become one of the most influential chemists of his era, compiled a set of improved atomic weights that refuted Prout's hypothesis. For example, the values in table 2.3 are the atomic weights of some selected elements according to Dalton and Berzelius, respectively.

Berzelius objected to the practice of rounding off atomic weights to obtain whole numbers, which was common among supporters of the hypothesis, and had the following rather harsh words to say about Thomson, who as mentioned above was a supporter of Prout:

This investigator belongs to that very small class from which science can derive no advantage whatever . . . and the greatest consideration which contemporaries can show to the author is to treat this work as if it had never happened.

In 1827, the German chemist Gmelin, undaunted by such warnings, proceeded to round off even Berzelius's values, such as the ones shown in table 2.3, and to thereby reassert support for Prout's hypothesis:

It is surprising that in the case of many substances the combining [equivalent] weight is an integral multiple of that of hydrogen, and it may be a law of nature that the combining weights of all other substances can be evenly divided by that of the smallest of them all.

As other chemists continued to improve the accuracy of the atomic weights for existing elements and determined values for new elements, much of their data seemed to point away from the hypothesis. At the same time, however, new coincidences emerged where the more accurate atomic weights of some key elements were found to be very close to exact ratios. This in part inspired Dumas, another influential French chemist, to revive Prout's hypothesis once again in 1857. These ratios included those for carbon, oxygen, and nitrogen thus:

Throughout this period, however, there was one unavoidable obstacle to the ready acceptance of Prout's hypothesis, which no amount of rounding or remea-suring would redress. This was the fact that the atomic weight of chlorine stubbornly refused to change from its measured value of about 35.5, thus providing an apparently clear contradiction to the hypothesis.

Then, in 1844 the French chemist Charles Marignac made the ingenious suggestion of considering the basic unit of measurement as half the mass of the hydrogen atom, thus making chlorine almost exactly 71 times the weight of this unit. In 1858, Dumas took a further step and suggested a quarter of the weight of hydrogen as the basic unit, which made even more elements fall into line with the revised form of Prout's hypothesis. Of course there is no limit to how small one might make the basic unit, but the smaller it became, the more the strength of Prout's original hypothesis appeared to be weakened.

The person who did the most to refute Prout's hypothesis was the Belgian Jean Servais Stas, who began his researches into atomic weight determination in 1841 by writing, "I will say it loudly. When I undertook my researches I had an almost absolute faith in the correctness of Prout's hypothesis."

Almost 25 years later, however, after measuring the atomic weights of numerous elements with as yet unheard of precision, Stas drastically changed his opinion and declared, "One must consider Prout's hypothesis as pure illusion." Whereas he had originally thought that an increased precision in atomic weight determination would reveal integral multiples of the value for hydrogen, it served only to show the opposite. Far too many elements showed weights that were clearly not whole number multiples of the weight of hydrogen.

Despite the apparent problems with Prout's hypothesis, it remained true that many elements, far more than chance seemed to allow, had atomic weight values that are almost integral. As R.J. Strutt (later Lord Rayleigh) wrote in 1901, long after Prout's hypothesis seemed to have fallen by the wayside,

The atomic weights tend to approximate to whole numbers far more closely than can reasonably be accounted for by any accidental coincidence. . . . [T]he chance of any such coincidence being the explanation is not more than one in one thousand.

The explanation for why some elements did not show integral atomic weights had to await the discovery of isotopes. Eventually, it would be understood that the elements whose values on a hydrogen scale are close to being whole numbers are those that exist only in one form or whose other forms, or isotopes, occur only in very small amounts. By contrast, many elements showed values that differed markedly from whole numbers, such as chlorine (35.46), copper (63.57), zinc (65.38), and mercury (200.6). Their atomic weights were not exact or even close to exact multiples of hydrogen's because they occur as mixtures of several isotopes that are present in comparable amounts.

So Prout's hypothesis turned out to be incorrect in that the elements are not composites of hydrogen according to their atomic weights, and yet there is a sense in which his idea can be said to have now been vindicated by modern physics. In terms of numbers of protons, the nuclei of all the elements are indeed composites of the nucleus of the hydrogen atom, which contains just a single proton. But, even at the time it was first proposed, Prout's hypothesis proved to be very fruitful, because it encouraged the determination of accurate atomic weights by numerous chemists who were trying to either confirm or refute it. From the point of view of Karl Popper's philosophy of science, this all makes perfect sense. A useful scientific idea need not necessarily be correct, but it is essential that it should be refutable in the light of experimental evidence.

### DöBEREINER DISCOVERS TRIADS

Just as the examination of atomic weight data led to Prout's hypothesis, so it was to produce another fruitful philosophical principle, that of triads. This development originated with the German chemist Döbereiner, who was active in the city of Jena in the early 1800s. Döbereiner became interested in the emerging study of stoichiometry, the study of proportions in chemical reactions, and became an early adherent of the newly developed theory of chemical atomism. He was the first to notice the existence of various groups of three elements, subsequently called triads, which showed chemical similarities and which displayed an important numerical relationship, namely, that the equivalent weight, or atomic weight, of the middle element is the approximate mean of the values of the two flanking elements in the triad.

In 1817, Döbereiner found that if certain elements were combined with oxygen in binary compounds, a numerical relationship could be discerned among the equivalent weights of these compounds. Thus, when oxides of calcium, strontium, and barium were considered, the equivalent weight of strontium oxide was approximately the mean of those of calcium oxide and barium oxide. The three elements in question, strontium, calcium, and barium, were said to form a triad:

SrO = (CaO + BaO)/2 = 107 = (59 + 155)/2

Though Döbereiner was working with weights that had been deduced with the relatively crude experimental methods of the time, his values compare rather well with current values for the triad:

104.75 = (56 + 153.5)/2

Döbereiner's observation had little impact on the chemical world at first but later became very influential. He is now regarded as one of the earliest pioneers of the development of the periodic system. What is not often reported in modern accounts is that Döbereiner considered the possibility that the middle element of his triad might actually be a mixture of the other two elements in question and that his observations might support the notion of transmutation among the three elements.

Very little happened regarding triads until 12 years later, in 1829, when Döbereiner added three new triads. The first involved the element bromine, which had been isolated in the previous year. He compared bromine to chlorine and iodine, using the atomic weights obtained earlier by Berzelius:

Br = (Cl + I)/2 = (35.470 + 126.470)/2 = 80.470

The mean value for this triad is reasonably close to Berzelius's value for bromine of 78.383. Döbereiner also obtained a triad involving some alkali metals, sodium, lithium, and potassium, which were known to share many chemical properties:

Na = (Li + K)/2 = (15.25 + 78.39)/2 = 46.82

In addition, he produced a fourth triad:

Se = (S + Te)/2 = (39.239 + 129.243)/2 = 80.741

Once again, the mean of the flanking elements, sulfur and tellurium, compares well with Berzelius's value of 79.5 for selenium.

Döbereiner also required that, in order to be meaningful, his triads should reveal chemical relationships among the elements as well as numerical relationships. On the other hand, he refused to group fluorine, a halogen, together with chlorine, bromine, and iodine, as he might have done on chemical grounds, because he failed to find a triadic relationship among the atomic weights of fluorine and those of these other halogens. He was also reluctant to take the occurrence of triads among dissimilar elements, such as nitrogen, carbon, and oxygen, as being in any sense significant even though they did display the triadic numerical relationship.

Suffice it to say that Döbereiner's research established the notion of triads as a powerful concept, which several other chemists were soon to take up with much effect. Indeed, Döbereiner's triads, which would appear on the periodic table grouped in vertical columns, represented the first step in fitting the elements into a system that would account for their chemical properties and would reveal their physical relationships.

Before the correct relationship between atomic and equivalent weights had been discovered, some chemists regularly referred to atomic weights as equivalents and vice versa. To make matters worse, even when the same terminology was used by any given two chemists, there was still disagreement as to actual values, since various standards were used by different workers. In addition, the methods for obtaining atomic weights were applicable only to gases. Initially, it was not possible to estimate the atomic weights of liquids and solids, and this made it difficult to recognize periodic relationships, since on crossing a period one typically moves from solids to gases.

It is therefore not surprising that groups of similar elements in the periodic table were discovered long before periods involving dissimilar elements or, in other words, that vertical relationships were discovered before horizontal ones, in modern terms. Of course, there is a more immediate reason why groups were discovered long before periods: elements within groups share chemical properties, thus rendering their grouping intuitively obvious. Although this is quite true, what is being addressed here is the separate issue of the recognition of numerical relationships among elements in groups. The existence of the periodic table depends not only on chemical properties but also almost as much on numerical aspects and on physical principles, although the latter in particular raises certain philosophical questions concerning the reduction of chemistry.

### GMELIN'S REMARKABLE SYSTEM

In 1843, a full 26 years before the publication of Dimitri Mendeleev's famous system of 1869, a much neglected and underrated periodic system was published (figure 2.3). This was the work of Gmelin, the author of the rather voluminous _Handbuch der Chemie_ and one of the most influential chemical writers of this time.

Although Döbereiner is rightly regarded as the originator of the notion of triads, Gmelin also did much useful work in this area, and it was he who coined the term "triad." Like Döbereiner, Gmelin considered both chemical and numerical relationships when looking for triads, and he was able to extend his predecessor's work using improved atomic weights that had been unavailable to Döbereiner. For example, whereas Döbereiner had grouped magnesium together with the alkaline earths based on their chemical similarities, he was unable to find a triad relationship involving it and other alkaline earth elements. Gmelin, on the other hand, was able to discern the following relationship among magnesium, barium, and calcium, using his own newly obtained values for atomic weights, which he published in the same book in 1827:

(Mg + Ba)/4 = Ca

(12 + 68.6)/4 = 20.15 (Ca = 20.5)

FIGURE 2.3 System of 1843. L. Gmelin, _Handbuch der anorganischen chemie_ 4th ed., Heidelberg, 1843, vol. 1, p. 52.

But let us now turn to the more remarkable aspects of Gmelin's system of 1843. From the existence of four unconnected triads discovered by Döbereiner, Gmelin was able to make a huge leap forward in obtaining a system based on triads consisting of as many as 55 elements. In addition, his system as a whole was essentially ordered according to increasing atomic weight. With this work, Gmelin succeeded in capturing the correct grouping of most of the then known main-group elements. Gmelin arranged his triads horizontally in the V-shaped schematic shown in figure 2.3.

Suppose we take the right arm of Gmelin's V-shape and make it point downward, and then consider the arrangement obtained (figure 2.4). It is important to appreciate that this change does not alter Gmelin's table in any fundamental way but merely re-presents its contents. If atomic weights are introduced explicitly into the table, something that Gmelin did not do, a general increase in this quantity in both wings of main-group elements is seen.

On removing all the elements in the central portion of figure 2.4, the entire table can be rotated by 90°, and all the columns can be stacked together, as shown in figure 2.5. What Gmelin's table achieves, granted this artistic license, is an essentially correct grouping of many of the representative, or main-group, elements. Though he failed to arrange the transition metals and inner transition metals correctly, this can hardly be taken as a reason for thinking any less of his system, since problems with transition metals were common even in later, more mature periodic systems.

The fact that Gmelin could have produced such an arrangement of the main-group elements so early in the evolution of the periodic system, as shown in figure 2.5, is rather remarkable. In the case of groups I, II, IV, V, VI, and VII, _all_ the elements included are shown in the correct order of increasing atomic weight going left to right. Boron and bismuth, which would have been placed incorrectly in group IV on moving from figure 2.4 to 2.5, have been omitted from figure 2.5. The only main-group misplacements appear to be nitrogen and oxygen, but Gmelin clearly recognizes that oxygen belongs with sulfur, selenium, and tellurium when he points out the following relationship, which also includes antimony:

FIGURE 2.4 Flattened version of Gmelin's system.

O = 8, S = 16, Se = 40, Te = 64, Sb = 129 = 1:2:5:8:16

Perhaps Gmelin's table cannot be properly called a periodic system, since it does not depict the well-known tendency of the elements to recur, that is, to show periodicity after certain regular intervals. Moreover, Gmelin's system does not _explicitly_ arrange the elements in increasing order of atomic weight. But there may have been an implicit use of atomic weight ordering in Gmelin's system, since his placing of many of the triads side by side produces the correct order as found in subsequent more mature periodic systems. It is also known that Gmelin was very interested in values of atomic weights, since in 1827 he produced an early list of atomic weights for as many as 45 elements.

About 25 years before Mendeleev, Gmelin used his own rudimentary system of the elements to give an overall structure and direction to his chemical textbook. He was thus possibly the first chemistry textbook author to do so. Although Mendeleev is usually credited with basing a textbook around the periodic system of the elements, he used an inductive approach, not presenting his system until the final chapter of the first volume of his textbook, even in later editions. Gmelin, on the other hand, gives the system immediately on the very first page, at the start of volume 2 of his series, and the remainder of this volume is a detailed 500 or so page survey of the chemistry of 12 nonmetallic elements.

FIGURE 2.5 Gmelin's table rotated, after removing the remaining 34 elements.

Moreover, the order that Gmelin elects to follow in his presentation is dictated by the system itself. He begins with oxygen and hydrogen, two of the three elements at the head of his table. His following chapters discuss the chemistry of carbon and boron, which Gmelin has placed together in the same group. He then discusses the chemistry of phosphorus, the only nonmetal in group V of the modern table apart from nitrogen. This is followed by chapters on sulfur and selenium, which are the nonmetals in what became group VI. After that comes a survey of the chemistry of all four of the then-known nonmetals in group VII of the modern periodic table.

Finally, the volume closes with the chemistry of nitrogen, the remaining one of the three elements that Gmelin placed at the head of his system of elements. Apart from the misplacement of boron along with carbon, in what would correspond to the modern group IV, Gmelin has given a systematic survey of most of the important nonmetals in the order of groups IV, V, VI, and VII, from the perspective of the mature periodic system, which emerged only with the work of Mendeleev in 1869. This, I submit, suggests remarkable foresight and intuition on the part of Gmelin, as does the way in which he uses his system to ground the presentation of the chemistry of these elements. Yet Gmelin's contribution to the classification of the elements has not been sufficiently appreciated by historians of chemistry, or even historians of the periodic system. Johannes van Spronsen, the author of the only scholarly book on the history of the periodic system, mentions Gmelin's remarkable table of 1843, but does so somewhat dismissively:

In 1843 Gmelin also tried to find a relationship existing between all elements. This however, meant demoting the atomic weight. . . . The elements oxygen, nitrogen and hydrogen, for which he apparently could find no homologues, form the basis for his classification.

But van Spronsen appears not to notice that Gmelin did in fact correctly classify at least one of these elements, oxygen, correctly with sulfur, selenium, and tellurium. Perhaps Gmelin's system should no longer be regarded as something of a footnote to Döbereiner's discovery of the existence of triads but as an important discovery of almost equal stature.

### A QUALITATIVE INTERMISSION

In order to appreciate the advances that were made by considering quantitative properties of the elements, it is necessary to also consider what was known in qualitative terms at the time that the periodic system was beginning to ferment. One obvious way to do this is to consult some chemistry textbooks of the period, since they serve as the repository of the chemical knowledge known at the time. For the sake of brevity, I describe the set of textbooks written by Gmelin, whose successive editions would eventually give rise to a very influential set of books on inorganic chemistry. It is not possible to divorce quantitative aspects altogether, given that, as noted above, Gmelin recognized triads based on atomic weights and even appears to have ordered the elements to some implicit extent on their atomic weights. Nevertheless, the influential series of books by Gmelin was primarily a summary of all the qualitative knowledge on the elements available at the time.

In volume 2 of his series, Gmelin gives a classification system for the elements that had been identified at the time (figure 2.2). As he puts it, these are 61 "undecomposable ponderable bodies," of which 12 are nonmetallic and 49 are metallic.

These elements are arranged in groups horizontally according to their chemical and physical properties, with the more electronegative elements on the left and the more electropositive ones on the right side. Gmelin does not specify more precisely what determines the order of the elements from left to right. One can only suppose that it might be degrees of electronegativity. For example, the halogens are arranged in a row starting with fluorine, which is the most electronegative of them, followed, in decreasing order of electronegativity, by chlorine, bromine, and iodine.

The halogens represent a family of elements whose group similarities became apparent almost as soon as they were isolated and, in the case of fluorine, even before its isolation. Considering these elements in historical order, chlorine was first discovered by Scheele in 1774, although he believed that it contained oxygen. It was first isolated in 1810 by Davy, who was the first to recognize that it was an element. That same year saw the first isolation of iodine by Bernard Courtois, followed by bromine in 1826 by Antoine Balard. Fluorine had not yet been isolated at the time that Gmelin was writing, although it had been recognized as an element. It was finally isolated in 1886, sometime after Gmelin devised his system. However, it had been studied in compound form by many chemists, including Davy, Gay-Lussac, and Lavoisier, all of whom experimented on one of its most common compounds, hydrofluoric acid.

Writing in 1843, Gmelin devoted a total of 123 pages to these four elements alone. Starting with the least electronegative of them, he discusses the reactions of iodine with water and oxygen and the existence of various oxides of iodine, such as IO5 and 107. This is followed by discussion of the reactions of iodine with a number of other elements, namely, hydrogen, boron, phosphorus, sulfur, selenium, and the other halogens. He proceeds to discuss the chemistry of bromine and chlorine, which give analogous reactions with all the same elements as iodine and which form analogous acids with a few minor exceptions.

In the case of fluorine, the same pattern of reactivity is described with a few more exceptions. These more noticeable differences might be explained by the fact that the element had not yet been isolated, so it was not as easy to examine its reactions with all the elements as had been possible in the case of iodine, bromine, and chlorine. Overall, the well-established similarity among chlorine, bromine, and iodine would explain why it was one of the first set of elements grouped together as a chemically significant triad by Döbereiner. The differences with fluorine might explain why the latter element was frequently omitted from triads or extended triads, called tetrads.

Another nonmetallic group of elements given by Gmelin in his classification consists of sulfur, selenium, and tellurium. As in the case of the halogens, Gmelin does not specifically discuss the analogies among these elements, but the reader is left in no doubt by a study of the detailed chemistry of the elements in Gmelin's text. Sulfur and selenium are discussed, one after the other, over a total of 94 pages, only 20 of which are devoted to selenium. As in the case of the halogens, the chemical similarities, at least for sulfur and selenium, are abundantly obvious. They include reaction with oxygen, acid formation, and reaction with hydrogen, phosphorus, sulfur, bromine, chlorine, and a number of metals. Although the element tellurium is clearly grouped with sulfur and selenium, Gmelin does not discuss its chemistry along with these latter two elements. This would seem to indicate some ambiguity in the classification of the element tellurium. In fact, the chemistry of tellurium is delayed until volume 4, when it finally makes an appearance following descriptions of the reactions of the group consisting of phosphorus, antimony, and bismuth. It would appear that Gmelin is ambivalent about the classification of tellurium. Whereas in the system shown in figure 2.2 it is included among the elements of what would become group VI in the modern periodic table, in discussing the detailed chemistry of the element Gmelin appears to contradict his earlier choice. The chemical and physical properties of tellurium are discussed in the context of the elements of the modern group V, along with phosphorus, arsenic, and antimony.

The element nitrogen, which heads the modern group V, is separated from all these elements, however, and is discussed at a very early stage in volume 2. Recall that nitrogen, along with hydrogen and oxygen, is shown at the head of the system with no particular group membership.

Turning to Gmelin's grouping of metals, we encounter a group containing lithium, sodium, and potassium. As well as being one of the triads discovered by Döbereiner, the chemical grouping of the elements is virtually inescapable. The elements are all soft, have a low density, and react with water to form alkaline solutions. The analogies among them are remarkable given that all of them react, without fail, with oxygen, boron, carbon, phosphorus, sulfur, selenium, and the halogens, although to varying degrees.

Similarly, Gmelin summarizes the chemical similarities among another group of metals consisting of magnesium, calcium, strontium, and barium, the last three of which had been recognized as the very first triad of elements by Döbereiner. These elements are physically harder and less reactive than those of Gmelin's group consisting of lithium, sodium, and potassium. In modern terms, the major difference between these two groups of elements is that lithium, sodium, and potassium show a valence of 1 while magnesium, calcium, strontium, and barium show a valence of 2. Gmelin appears not to have recognized this feature however, since thet formulas he gives for all their oxides, for example, consist of one atom of the metal combined to one atom of oxygen. It would seem that the qualitative differences alone between the members of the two groups sufficed to convince Gmelin and others that the elements concerned belonged in two different groups.

### PETTENKOFER'S DIFFERENCE RELATIONSHIPS

In 1850, Pettenkofer, at the University of Munich, another supporter of Prout's hypothesis, published an article dealing with numerical relationships among the equivalent weights of the elements. But unlike his predecessors, he did not focus on triads, believing that the findings by Döbereiner and others were due to mere chance. As an example, Pettenkofer pointed out that while the atomic weight of the middle member of the chlorine, bromine, iodine triad was indeed the mean of the flanking elements, this was not the case in the chemically analogous triad of fluorine, chlorine, and bromine.

Nevertheless, Pettenkofer, too, created what essentially amounted to triads, and even larger groups of elements, although by a quite different approach. In the course of an examination of the data on the known elements, Pettenkofer realized that some series of chemically similar elements tended to show constant differences among their equivalent weights. He noted, for example, that the weights of lithium, sodium, and potassium differed by gaps of 16 units (table 2.4). As some authors remark, Pettenkofer thus failed to notice that this was tantamount to Döbereiner's recognition that the middle element has an equivalent weight that is the mean of the two flanking elements.

TABLE 2.4 Pettenkofer's atomic weight gaps

In some other series of elements, Pettenkofer pointed out that the differences in equivalent weights were a multiple of a certain number, such as 8 in the case of the alkaline earths and the oxygen group (table 2.5).

In taking these steps, Pettenkofer was already going beyond triads to considering larger series of elements. In the case of carbon, boron, and silicon, which were often grouped together in early classifications of the elements, as well as in the case of the halogens, the differences were factors of 5. In addition, there was another series, containing nitrogen, phosphorus, arsenic, and antimony, in which the differences involved factors of both 5 and 8, as shown in table 2.6.

On the basis of this theory of constant differences, and multiples of constant differences, Pettenkofer proposed the idea of calculating the equivalent weights for elements whose values would be difficult to measure otherwise. It is perhaps significant that Mendeleev some time later mentioned the name of Pettenkofer in his own articles as one of the few who had influenced his work on the periodic system. As is well known, Mendeleev made much use of predictions based on interpolations among atomic weights, and also used interpolations to correct the atomic weights of already known elements. Given the work of such chemists as Pettenkofer, it is clear that the idea of making such predictions did not originate with Mendeleev.

TABLE 2.5  
Pettenkofer's differences in atomic weights for alkaline earths and oxygen group

TABLE 2.6  
Pettenkofer's atomic weight differences for the "nitrogen series"

### DUMAS'S CONTRIBUTIONS AND HIS REVIVAL OF TRANSMUTATION

The year 1851 was a rather busy one for the famous French chemist Dumas, who published two important papers and delivered an influential public lecture in Ipswich, England, on the classification of the elements. Throughout this work, Dumas drew attention to four triads—(S, Se, Te), (Cl, Br, I), (Li, Na, K), and (Ca, Sr, Ba)—but without mentioning Döbereiner as their original discoverer. Whereas the German chemist had suggested that the middle member of each triad might be a mixture of the two extreme elements, Dumas thought that the middle member was a compound of its flanking partners and offered this idea as support for Prout's hypothesis.

Dumas went as far as to suggest that transmutation might be possible among the elements in each triad and that research should be carried out to discover the mechanism of these possible transformations. He also took the fact that elements such as cobalt and nickel are often found associated together in nature as further evidence of the possibility of elemental transmutation. Interestingly, the English scientist Michael Faraday praised Dumas's public lecture and agreed that some form of transmutation was suggested by these findings. Faraday said:

Thus we have here one of the many scientific developments of late origin, which tend to lead us back into speculations analogous with those of the alchemists . . . and now we find, after our attention has been led in that direction, that the triad of chlorine, bromine and iodine not only offers well-marked progression of certain chemical manifestations, but that the same progression is accordant with the numerical exponents of their combining weights. We seem here to have a dawning of a new light, indicative of the mutual convertibility of certain groups of elements, although under conditions which as yet are hidden from scrutiny.

I draw attention to this passage because it reveals that at least some leading chemists appeared to continue to believe in this central alchemical doctrine long after alchemy is supposed to have been abandoned.

### KREMERS GOES HORIZONTAL

Peter Kremers, working in Koln, Germany, was one of the earliest chemists to begin to consider what would eventually form horizontal series of elements in the mature periodic systems of the future. He did this by examining the numerical relationships among the atomic weights of elements with little in common. For example, he noted the regularity among a short series of elements that included oxygen, sulfur, titanium, phosphorus, and selenium shown in table 2.7. Kremers also discovered some new triads, such as

From a modern standpoint, these triads may not seem to be chemically significant. There are two reasons for this. The modern medium-long form of the periodic table fails to display secondary kinships among some elements. Sulfur and titanium both show a valence of 4, for example, though they do not appear in the same group in the medium-long form of the periodic table. But it is not so far fetched to consider them as being chemically analogous. Given the fact that both titanium and phosphorus commonly display valences of 3, this grouping, too, is not as incorrect as a modern reader may think. The second reason why one should not be too surprised by some of the less plausible triad groupings made by Kremers is that the notion of a triad had begun to take on a life of its own as distinct from chemical analogies. The aim had become one of finding triad relationships among the weights of the elements irrespective of whether or not this had a chemical significance. Mendeleev later described such activity among his colleagues as an obsession with triads, which he believed to have delayed the discovery of the mature periodic system.

TABLE 2.7  
Kremers's atomic weight differences for the oxygen series

But to return to Kremers, perhaps his most incisive contribution lay in the suggestion of a bidirectional scheme of what he termed "conjugated triads." Here, certain elements would serve as members of two distinct triads lying perpendicularly to each other,

Thus, in a more profound way than any of his predecessors, Kremers was comparing chemically dissimilar elements, a practice that would reach full maturity only with the tables of Julius Lothar Meyer and Mendeleev.

In 1856, Kremers mistakenly claimed that the divergences from exact values in the relationships among triads were caused by changes in temperature and that each triad would show an exact numerical relationship at a particular temperature. In the course of this research, he produced the table shown in table 2.8. One suspects that most people studying this table would have been seduced into thinking that the divergences were indeed very small, and might well be spurious, thus further strengthening the notion of triads.

TABLE 2.8  
Kremers's diY erences between calculated and observed atomic weight triads

### SUPERTRIADS

The most ambitious scheme of all involving triads was created by the 20-year-old Ernst Lenssen while he was working at an agricultural institute in Wiesbaden. In 1857, Lenssen published an article in which virtually all of the 58 known elements were arranged into a total of 20 triads, with the exception of niobium, which he could not fit into any triad (table 2.9). Ten of his triads consisted of nonmetals and acid-forming metals, and the remaining 10 of just metals.

Lenssen also suggested further relationships involving groups of triads. Using the 20 triads in table 2.9, he was able to identify a total of seven enneads, or supertriads, in which the mean equivalent weight of each middle triad lies approximately midway between the mean weights of the other triads in a group of three triads (table 2.10). However, as the table shows, he was forced to combine his triads in a somewhat arbitrary order to achieve this goal. In addition, one supertriad involves just one element, hydrogen, rather than a triad of elements.

TABLE 2.9  
The 20 triads of Lenssen

TABLE 2.10  
Lenssen's supertriads

Lenssen was another early pioneer who was prepared to make predictions on the basis of his system. For example, he predicted the atomic weights of erbium and terbium, neither of which had yet been isolated. This is mentioned just to emphasize again that Mendeleev did not "invent" the idea of making predictions using classification systems for the elements, as seems to be popularly believed. The fact remains, however, that Lenssen's predictions were found to be incorrect.

Many philosophical issues regarding the prediction of new elements and properties of elements are examined at various points in this book. One of these issues concerns the importance that is attributed to predictions while a theory is in the process of being accepted. This is a theme that has been actively debated by recent historians and philosophers of science, and it has some implications for the story of the periodic table, the development of which is usually presented as relying heavily on the prediction of new elements.

But at the close of this chapter, it should be appreciated how far chemistry had advanced from the introduction of numerical aspects by Lavoisier and others at the time of the chemical revolution to the growing realization that such numerical aspects of chemistry were also essential to the classification of the elements. Indeed, it appears that real progress was achieved only when the debate over Prout's hypothesis and the hunt for triads served to focus attention on the role of numerical values, whereas the previous attempts to sort the elements according to chemical similarities had failed to produce any coherent scheme. And all of this occurred before it was discovered that simply ordering the elements according to increasing values of atomic weight would reveal a periodicity in their properties.

The story of the early development of the periodic table demonstrates very effectively how scientific ideas can progress in spite of what later appear to be mistakes. For example, many of the triads that were identified have turned out to be incorrect in that they made no chemical sense, and yet the general project of examining triad relationships was still rather fruitful. Local mistakes do not seem to matter too much. One might consider the case of Dalton, for example. Three of his main ideas—the importance of repulsions between like particles; the existence of a caloric, or heat envelope, around atoms; and the formula of OH he assumed for water—have all turned out to be incorrect. Nevertheless, Dalton's general project has been tremendously influential. His atomic theory represents one of the pillars of modern science, providing a theoretical understanding of the observed laws of chemical combination, among other chemical facts. It is as if scientific evolution somehow transcends any logical stepwise progression yet still displays a form of organic growth within which any "mistakes" are subsumed. This overall evolution seems to have a life of its own, which overrides mistakes on the part of individual scientists, or even collective errors, in the light of subsequent knowledge.

### POSTSCRIPT ON TRIADS

As I have shown, the recognition of triads represented the first important step toward the eventual construction of the modern periodic system. The limitations of the concept of triads had more to do with the data that were being used by the early pioneers than with the concept itself. It is interesting to consider how triads fare in the modern periodic system.

It is now realized that atomic weight is not the fundamental property determining the placement of each element in the periodic table. The elements can indeed for the most part be ordered by increasing weight, but the atomic weight of any particular element depends upon the contingencies of terrestrial abundances of all the isotopes of that particular element. When they measured the atomic weight of an element, nineteenth-century chemists were unwittingly measuring the average weight of a mixture of isotopes (except for those elements that occur as a single isotope in nature.

As was discovered well after the turn of the twentieth century, when the structure of the atom was discerned, the order of the elements is determined unambiguously by the property of atomic number, which corresponds to the number of protons in the nucleus of the atoms of any particular element. It emerges that in certain parts of the modern periodic table the triad relationship turns out to be exact if atomic numbers are used instead of atomic weights (table 2.11). For example, a number of the triads discovered by Döbereiner behave in this manner.

I postpone the full explanation for why perfect triads occur in parts of the periodic system until chapter 6, where I give an account of the discovery of isotopes and atomic number. From the perspective of the modern periodic table, about 50% of all possible vertical triads, using atomic numbers, are in fact exact.

### ATOMIC WEIGHT DETERMINATION

In this final section I take up the question of the determination of atomic weights that was begun by Dalton at the beginning of the nineteenth century. As noted above, Dalton adopted the rule of maximum simplicity regarding formulas, but unfortunately, this rule is broken in the vast majority of compounds such as water, ammonia, and all the oxides of nitrogen apart from NO. Moreover, whereas Dalton began by using comparative densities of gases to estimate atomic weights along with the notion of equal volumes equal numbers of particles (EVEN), he later turned against this hypothesis.

The next major contributor to the project of determining atomic weights was Berzelius, who published tables of atomic weights in 1814 and 1818, which he greatly extended and revised in 1826. Among the many problems encountered by chemists working to determine atomic weights was the question of selection of a standard. Whereas Dalton had quite reasonably chosen H = 1, not all elements combine with hydrogen. To determine the atomic weight of an element that does not react directly with hydrogen required using an intermediate element, thus increasing the sources of errors.

Since oxygen forms compounds with most elements, it was adopted as the standard but was confusingly given different values by different chemists. Berzelius was one of the few who tried to go beyond equivalent weights in order to determine atomic weights. As mentioned above, the determination of atomic weights depended on recognizing the correct formula for a compound. Using Gay-Lussac's law of definite proportions by volumes, Berzelius arrived at the correct formulas for water, ammonia, hydrogen chloride, and hydrogen sulfide: H2O, NH3, HCl, and H2S. But Gay-Lussac's law was limited to combining gases, although Berzelius devised a method for compounds such as PbSO4 and also ventured to estimate the atomic weights of a number of metals by similar approaches. In his earliest tables of 1814 and 1818, Berzelius regarded metals as dioxides, giving them formulas such as AgO2 and FeO2. In 1826, he changed to regarding them as monoxides, thus making the values of alkali metals twice what they should have been but obtaining correct values for the alkaline earths.

Two major developments then followed that permitted better atomic weight determinations. They were the law of Pierre-Louis Dulong and Alexis-Thérèse Petit and the law of isomorphism.

Dulong and Petit discovered that the specific heat of any solid element multiplied by its atomic weight is approximately equal to a constant (table 2.12). In fact, they adjusted the atomic weights of many elements with uncertain weights so that their behavior would fit their new law. There was little justification for taking such an action except that it seemed to preserve the putative law. Although they had originally hoped to use the law in order to determine unknown atomic weights, its approximate nature meant that this was not possible. Nevertheless, the law of Dulong and Petit proved to have another important use. It could be used to check possible atomic weights and to settle cases in which there was some doubt as to whether the supposed value needed to be halved, doubled, or kept intact. For example, from Dulong and Petit's law, it quickly became clear that Berzelius's values for the alkali metals were in error by a factor of 2 and that his formulas needed adjustment to M2O instead of MO.

TABLE 2.12  
Table from Dulong and Petit's article of 1819

In 1819, Eilhard Mitscherlich began to publish articles in Berlin on what would become a law named after him. He found that certain elements could substitute for each other to produce analogous or, as he termed them, isomorphic structures having the same crystalline form apart from some minor variations in the angles between crystal planes. He suggested that the crystal form was determined uniquely by the number of atoms in the chemical compound in question. One could therefore deduce the atomic weight of one element in a compound from the known atomic weight of another element that could act as a substitute for the first element. Recall that the problem had been to assign a particular number of atoms of any particular element to a compound, such as the classic case of Dalton's HO as opposed to Berzelius's H2O. Here was a new way of settling such questions in the case of solid crystalline compounds. For example, by considering the two isomorphous compounds of potassium sulfate (K2SO4) and potassium selenate (K2SeO4), and from the known atomic weight of sulfur, which was 32, Mitscherlich was able to deduce the correct atomic weight of selenium to be approximately 79.

Another chemist to make important contributions to the determination of atomic weights was Dumas, as mentioned above in connection with his work on triads. In 1826, he devised a new method that permitted atomic weights to be determined for any liquid or solid substance that could be vaporized. The density of the vapor produced could be compared with that of hydrogen, and on the basis of the EVEN hypothesis, the atomic weight of the vaporized element could be determined. Dumas was thus one of the few chemists making use of the hypothesis of Avogadro and André Ampère. But later, Dumas found a number of clearly anomalous atomic weights for elements, including sulfur, phosphorus, and arsenic. Faced with these problems, Dumas turned against the EVEN hypothesis, believing it to be defective in the case of elements in the gaseous state. In 1836, Dumas became even more pessimistic and now directed his criticisms against the use of atoms in chemistry. He wrote,

What remains of the ambitious excursion we allowed ourselves into the domain of atoms? Nothing, at least nothing necessary. What remains is the conviction that chemistry lost its way, as usual when, abandoning experiment, it tried to find its way through the mists without a guide. . . . If I were master I would erase the word "atom" from the science, persuaded that it goes beyond experiment; and in chemistry we should never go beyond experiment.

### CONCLUSION

It is rather surprising that both Prout's hypothesis and the notion of triads are essentially correct and appeared problematic only because the early researchers were working with the wrong data. Prout was essentially correct when he asserted that the elements could be ordered in such a way that they represented whole multiples of hydrogen. It is now known that each element contains one more proton than the last as one moves across the periodic table, and this is what determines atomic number. Thus, in a sense all the elements are indeed composites of hydrogen atom, since the number of protons in any element is an exact multiple of the single proton found in the nucleus of the hydrogen atom. The problem had been that chemists had focused on trying to make atomic weights exact multiples of each other, not realizing that atomic weights included contributions from neutrons. But the numbers of neutrons vary among each isotope, thus upsetting the simple ratios expected from Prout's hypothesis. Eventually, the switch from atomic weight to atomic number would remove the inexactness that caused chemists to abandon Prout's hypothesis as a useful tool in the classification of elements.

Similarly, the notion of triads was essentially correct but did not always work perfectly because early chemists were using the wrong data. Indeed, from the perspective of the modern table and using atomic numbers, about 50% of all possible triads are exact.

FIGURE 2.6 Stanislao Cannizzaro. Photo from Edgar Fahs Smith Collection by permission.

Finally, it should be borne in mind that much of this work was carried out using equivalent weights or incorrect atomic weights. It became possible to develop successful periodic systems, which would accommodate all the elements into coherent systems, only when a set of consistent atomic weight could be obtained.

Atomic weights as distinct from equivalent weights were determined starting with Dalton's researches. However, these weights depended on knowing how many atoms of a particular element were present in a compound, something that was not well understood and over which Dalton made many errors because of his assumption of maximum simplicity. Atomic weight measurements were originally restricted to gaseous elements such as oxygen or nitrogen. Soon new methods were developed by Dulong and Petit as well as Mitscherlich and Dumas, which could be applied to elements in other states of aggregation.

Nevertheless, much confusion still remained. For example, very few chemists accepted the EVEN hypothesis as first announced by Avogadro and Ampère. Dumas, one of the few who did, lost his nerve when he ran across elements that yielded what seemed to be highly anomalous atomic weights. The problems would be resolved only when Cannizzaro (figure 2.6) insisted on the correctness of Avogadro's hypothesis and elaborated a method that finally gave a set of correct and consistent atomic weights. It is to Cannizzaro's work that we turn our attention in the next chapter.

## **CHAPTER 3  
DISCOVERERS OF THE PERIODIC SYSTEM**

The periodic system was not discovered by Dimitri Mendeleev alone, as is commonly thought, or even just by Mendeleev and Julius Lothar Meyer. It was discovered by as many as five or six individuals at about the same time, in the decade of the 1860s, following the rationalization of atomic weights at the Karlsruhe conference.

It became apparent by the middle of the nineteenth century that something needed to be done to resolve the widespread confusion over equivalent and atomic weights. Amedeo Avogadro had already proposed a solution to Joseph Louis Gay-Lussac's law that preserved John Dalton's indivisible elemental particles. Recall that Gay-Lussac had observed that volumes of gases entering into chemical combination and their gaseous products are in a ratio of small integers. Dalton had refused to accept this because it implied that atoms appeared to divide in some instances, such as the combination of hydrogen and oxygen to create steam. Avogadro had suggested that such "atoms" must be diatomic; that is, in their most elemental form they must be double. Thus, the oxygen atom was not dividing; rather, it was an oxygen molecule, which consisted of two oxygen atoms, that was coming apart.

Unfortunately, the terms in which Avogadro expressed his views were rather obscure and failed to make much impression on the chemists of the day. Two exceptions were the French physicist and chemist André Ampère and the Alsatian chemist Charles Gerhardt, both of whom adopted the view that elemental gases were composed of diatomic molecules.

One of the consequences of the general refusal to recognize the existence of diatomic molecules as the ultimate "atoms" of gaseous elements was that, as mentioned in chapter 2, the confusion between equivalent weights and atomic weights continued to reign. Although the relative weights of oxygen to hydrogen in water are approximately 8 to 1, the relative weight of the oxygen atom to the hydrogen atom takes on values of 8 or 16 depending on what one considers the correct formula for water to be. Dalton opted for a formula of HO for water, which meant that he was forced to assume an atomic weight of 8 for oxygen. Dalton allowed his insistence on the indivisibility of atoms to obscure the possibility that in some substances the smallest atom, in the chemical sense, consisted of two atoms combined together. Since this unit is still the smallest possible unit of the element in question, Dalton need not have been concerned.

But although Avogadro had proposed the solution as early as 1811, its acceptance would have to wait until 1860, by which time great confusion had developed among different chemists regarding the atomic weights of many elements and, consequently, the formulas of many compounds. The rapid growth of organic chemistry during this period and the proliferation of varying formulas for the same compounds added to the need to find a solution. When the chemist August Kekulé prepared a textbook of chemistry in the early 1860s, he listed as many as 19 different formulas for acetic acid, all of which had been used in the literature.

It was against this background that the Karlsruhe conference was convened. Its aims were to clarify the notions of "atom" and "molecule" and the related issues of equivalent weight and atomic weight. It fell to Stanislao Cannizzaro to resuscitate the work of his countryman Avogadro and to make it more palatable to the chemists who attended the conference. No new science was required, just a careful analysis of the problems at hand and a desire to bring order to the chaos surrounding the conflicting use of different atomic weights and the consequent different formulas. Once the notion that elemental gases consisted of diatomic molecules was accepted, the whole substructure of chemistry was corrected. At last, chemists interested in classifying the elements had a firm foundation on which they could build with confidence.

Cannizzaro accepted Avogadro's hypothesis, namely, that equal volumes of all gases, at the same temperature and pressure, contain the same number of particles. As a result, he argued that the relative density of a gas would provide a measure of its relative mass. This much was not new and had been assumed by others. What Cannizzaro did was to pursue Avogadro's hypothesis in a comprehensive manner in such a way as to finally usher in the acceptance of the hypothesis and to break the deadlock over the measurement of atomic weights. He began with the elementary assumption that if the molecular mass of hydrogen were M and if that of an element is found to be N times that of hydrogen, and then the molecular mass of the unknown element would be NM. But the aim is to obtain the atomic mass (a) of any element A; Cannizzaro recognized that one could analyze a large number of compounds of the element. If it turned out, as it always did, that all the intramolecular masses of A were whole number multiples of 1 and the same mass, then that mass had the right to be called the atomic weight of A.

TABLE 3.1

For example, in the case of carbon, Cannizzaro published a table, on which table 3.1 is based, and proceeded to lend his full support to the idea of regarding atoms realistically:

Compare, I say... the various quantities of the same element contained in the molecule of the free substance and in those of all its different compounds, and you will not be able to escape the following law: The different quantities of the same element contained in different molecules are all whole multiples of one and the same quantity, which always being entire, has the right to be called an atom....

### ANOTHER BRIEF INTERLUDE ON QUALITATIVE CHEMISTRY

Let us consider another textbook, written in 1867 by the French chemist Alfred Naquet, to see how much was known about the chemistry of the elements at the time when the mature periodic system was being discovered. Table 3.2, of families of the elements, has been constructed on the basis of the groups, or families, listed by Naquet.

Several improvements can be seen when this table is compared with the grouping by Leopold Gmelin given in chapter 2. Naquet's 2° _famille_ (family) shows that oxygen has now been correctly included among elements such as sulfur and selenium. In addition, Naquet correctly includes nitrogen among the group containing phosphorus, arsenic, and antimony and also adds bismuth. Whereas Gmelin had grouped only carbon and silicon together in his own system, Naquet includes tin, in addition to two transition metals. The final improvement is seen in Naquet's 1° family of metals, in which he has included the newly discovered rubidium and cesium. Different textbook authors of this period listed similar families of elements, and this kind of information would have been available to all discoverers of the periodic system, at least in principle. It is in relation to such qualitatively based systems that one must consider the discovery of the quantitatively based periodic systems that follow.

TABLE 3.2

### THE RAPID APPEARANCE OF SEVERAL PERIODIC SYSTEMS

What permitted the rapid progress toward the development of the periodic system in several different countries during the 1860s was the publication, between 1858 and 1860, of a set of consistent atomic weights by Cannizzaro, based on the above method, which he compiled in preparation for the Karlsruhe conference. Once Cannizzaro had clearly established the distinction between molecular and atomic weights, the relative weights of the known elements could be compared in a reliable manner, although a number of these values were still incorrect and would be corrected only by the discoverers of the periodic system.

Despite the pivotal role played by the rationalization of atomic weights in preparing the way for the successful sorting of the elements, it is debatable whether the fairly rapid and independent discovery of the mature periodic system over the following decade represented a scientific revolution in the Kuhnian sense. Indeed, as remarked in the introduction, the history of the periodic system appears to be the supreme counterexample to Thomas Kuhn's thesis, whereby scientific developments proceed in a sudden, revolutionary fashion. The more one examines the development of the periodic system, the more one sees continuity rather than sudden breaks in understanding. Looking at the events leading up to the introduction of Mendeleev's periodic system in 1869, the concept of periodicity can be seen as evolving in distinct stages through the work of other chemists. Thus, rather than six actual discoveries of the system, it may be more correct to see it as an evolution through several systems, discovered within a period of less than 10 years. The final one of these was by Mendeleev, who also worked harder than anyone else to establish the validity of the fully mature system. There are good reasons for singling out Mendeleev (and Lothar Meyer) in this story, and further grounds for making Mendeleev the one leading discoverer of the periodic system. But as I argue in this chapter, the _idea_ of periodicity, which is central to the periodic system, did not originate with Mendeleev.

Other factors hastened the sudden explosion of periodic systems published in the 1860s. One of these was the discovery of new elements as a result of the development of the novel technique of spectroscopy. Having more elements to work with meant that there would be fewer gaps among them, making periodicity easier to discern. And spectroscopy itself, which permitted the characterization of each element by its unique spectral fingerprint, would in turn allow a much greater understanding of the chemical nature of the elements.

Another important change that occurred around this time and helped to make the discovery of the periodic system possible was the increased questioning of William Prout's hypothesis (that all elements are composites of hydrogen), which had figured rather prominently in the previous wave of discoveries leading up to the periodic system. In fact, such was the decline in support for Prout's hypothesis in the 1860s that chemists who still harbored such thoughts felt compelled to conceal their names. This was the case with one "Studiosus" who published an article in 1864, in response to John Newlands's periodic system, claiming that the atomic weights of the elements were multiples of 8. Meanwhile another pro-Proutian author, who called himself "Inquirer," attempted to mediate the controversy that ensued between Newlands and Studiosus.

With the decline of the Prout's hypothesis, chemists became less concerned with finding neat, integral relationships among the elements. At the same time, other kinds of numerical regularities that had held the fascination of noted chemists, such as Jean-Baptiste Dumas and Max Pettenkofer, also began to subside. While the craze for searching for numerical regularities started to fade away, the work of chemists began to show a different aim and method. Instead of trying to find isolated triads or unconnected groups, researchers were now free to focus on seeking an integrated system that would include all the known elements in a meaningful way.

In examining the work of the six discoverers of the periodic system, it is important to consider their published articles in some detail. In trying to portray an overall picture of the evolution of the periodic system, I do not concentrate exclusively on the final published tables given by these authors. In the case of Newlands and John Odling, as well as some of the others, I examine several subsidiary tables, sometimes dealing with specific comparisons between the elements. This approach reveals important aspects in the evolution of their ideas that are missed by concentrating only on the finished work of any of the discoverers.

### ALEXANDRE EMILE BEGUYER DE CHANCOURTOIS

There are valid reasons for declaring that the periodic system was essentially discovered in 1862 by De Chancourtois, a French geologist. De Chancourtois appears to have taken not just an important step in the story of the periodic system but, in many ways, the single most important step. It was he who first recognized that the properties of the elements are a periodic function of their atomic weights, a full seven years before Mendeleev arrived at the same conclusion.

Although he hit upon this crucial notion underlying the entire edifice of the periodic system, De Chancourtois is not generally accorded very much credit, partly because his publication did not appear in a chemistry journal, and because he did not develop his insight any further over subsequent years. Indeed, it was only about 30 years after his paper appeared that De Chancourtois's claim to priority came to light through the efforts of Philip Hartog in England and Paul Emile Le Coq De Boisbaudran and Albert Auguste De Lapparent in France.

De Chancourtois became professor of subterranean topography at the Ecole de Mines in Paris in 1848 and then in 1856 assumed a professorship in geology at the same institution. He attempted to systematize many different areas, including knowledge of minerals, geology, and geography, and even produced a form of universal alphabet. De Chancourtois presented his system of the chemical elements to the Acadèmie des Sciences and also published it in its journal, the _Comptes Rendus._ He proposed a three-dimensional representation of the periodicity of properties as a function of atomic weight (figure 3.1). De Chancourtois used equivalent weights for the elements, although he divided many values by 2, as a result of which most of his values agreed approximately with the new atomic weights of Cannizzaro. De Chancourtois also consistently rounded off the weights to produce whole number values. Although he did not commit himself specifically to the Proutian idea of atoms being composites of hydrogen, De Chancourtois did express his support for what he called "Prout's law," whereby the values for all elements should be whole number multiples of the value for the element hydrogen.

In 1862, De Chancourtois arranged the elements according to what he termed increasing "numbers" along a spiral. These numbers were written along a vertical line that served to generate a vertical cylinder. The circular base of the cylinder was divided into 16 equal parts. The helix was traced at an angle of 45° to its vertical axis, and its screw thread was similarly divided, at each of its turns, into 16 portions. Thus, the seventeenth point along the thread was directly above the first, the eighteenth above the second, and so on. As a result of this representation, elements whose characteristic numbers differed by 16 units were aligned in vertical columns. Sodium, for example, with a weight of 23, appeared one complete turn above lithium, whose value was taken as 7. The next column contained the elements magnesium, calcium, iron, strontium, uranium, and barium. One may begin to see the modern alkaline earth group emerging, the only difference being that several transition elements have also been included along the same vertical alignment. But this feature is not surprising since De Chancourtois's table is a short-form table that does not separate main-group elements from transition metals.

The first full turn of the spiral ended with the element oxygen, and the second full turn was completed at sulfur. Periodic relationships, or chemical groupings, could be seen in De Chancourtois's system, although only approximately, by moving vertically downward along the surface of the cylinder. The eighth such turn, and coincidentally the halfway point down the cylinder, occurred at tellurium. This rather arbitrary feature provided De Chancourtois with the name of _vis tellurique_ , or telluric screw, for his system. This name may also have been chosen by De Chancourtois from _tellos_ , Greek for earth, given that as a geologist, he was primarily interested in classifying the elements of the earth.

De Chancourtois's system did not create much impression on chemists for a number of reasons. The original published article failed to include a diagram, mainly because of the complexity faced by the publisher in trying to reproduce it, with the result that its visual force was lost. Another problem was that the system did not convey chemical similarities convincingly, as a result of the style of representation (the spiral) adopted by its author. While some of the intended chemical groupings, such as the alkali metals, the alkaline earths, and the halogens, did indeed fall into vertical columns, many others did not, thus making it a less successful system than it might have been. Yet another drawback to the system was the inclusion of radicals such as NH4+ and CH3, as well as such compounds as cyanogen, some oxides and acids, and even some alloys.

FIGURE 3.1 Telluric Screw of 1862. A.E. Béguyer De Chancourtois, Vis Tellurique: Classement naturel des corps simples ou radicaux, obtenu au moyen d'un système de classification hélicoïdale et numérique, _Comptes Rendus de L'Académie_ , 54, 757-761, 840-843, 967-971, 1862. Redrawn in J. van Spronsen, _The Periodic System of the Chemical Elements, the First One Hundred Years_ , Elsevier, Amsterdam, 1969, p. 99. Reproduced by permission of Elsevier.

Frustrated that the journal _Comptes Rendus_ failed to include a diagram, De Chancourtois had his system republished in 1863. But, because it was published privately, this further article received even less notice from other scientists than did the original one. Still, it cannot be denied that De Chancourtois was the first to show that the properties of the elements are a periodic function of their atomic weights, or as he said himself, _"Les proprietées des corps sont les proprietées des nombres_. [The properties of bodies are the properties of numbers]."

Of course, De Chancourtois intended the term "numbers" to mean the values of atomic weights, and even the improved atomic weights did not always yield clean intervals among the elements or line them up in what would appear to be the right order. However, following the eventual discovery of atomic numbers, De Chancourtois turned out to be even more correct than he might have himself imagined, as the properties of the elements are indeed a periodic function of their atomic numbers. De Chancourtois was also inadvertently prophetic in that he used whole number atomic weights, thus in effect creating an ordinal series of elements. To regard this as an anticipation of atomic number is not altogether implausible, although unlike Newlands (described below), De Chancourtois did not have a complete sequence of whole numbers in his system.

De Chancourtois's system was later criticized by Mendeleev, who in his Faraday lecture rather unfairly stated that De Chancourtois himself had not regarded his work as being a "natural system" of the elements. This lecture, given in London in 1889, seems to have provoked the English chemist Hartog, who had studied extensively in France, into making a belated priority claim on behalf of De Chancourtois. A couple of years later, De Chancourtois's cause was taken up by the French chemists Paul Emile Le Coq De Boisbaudran and Albert Auguste De Laparrent, who attempted to make their fellow Frenchmen more aware of the neglected work on the telluric screw.

It is also interesting to note another remark De Chancourtois made in his article:

Will not my series, for instance, essentially chromatic as they are, be a guide in researches on the spectrum? Will not the relations of the different rays of the spectrum prove to be derived directly from the law of numerical characteristics, or vice versa?

The periodic table did indeed turn out to be a very powerful guide to the study of atomic spectra, and vice versa, as shown when the influence of quantum theory is considered in later chapters. In many instances, the periodic system reveals periodicity in physical as well as chemical properties. The way in which spectral lines are split by a magnetic field, for example, be it into doublets, triplets, or quartets, is something that shows periodicity, just as do chemical properties such as reactivities toward particular elements.

One final comment should perhaps be made about De Chancourtois. His lack of chemical knowledge may have been a hindrance in some cases, and conversely, his emphasis on geological factors may have misled him in the development of the periodic system. For example, he stated that the isomorphism between feldspars and pyroxenes had been the starting point of his system. The element aluminum appears to function analogously to the alkali metals, a fact that does not necessarily indicate that aluminum should be grouped together with the alkali metals such as sodium and potassium. But this is precisely what De Chancourtois did in his system. In fact, he even changed the atomic weight, or characteristic weight, as he termed it, in the case of aluminum to make it fall neatly into line with the alkali metals. Had he known more chemistry, he might not have taken this unjustified step.

### JOHN NEWLANDS

Newlands was born in 1837 in Southwark, a suburb of London, which by a coincidence was also the birthplace of Odling, another pioneer of the periodic system. After studying at the Royal College of Chemistry in London, Newlands became the assistant to the chief chemist of the Royal Agricultural Society of Great Britain. In 1860, he served briefly as an army volunteer with Giuseppe Garibaldi, who was fighting the revolutionary war in Italy. The reason for Newlands's sortie seems to have been connected to the fact that his mother was of Italian descent. It also meant that Newlands was not able to attend the Karlsruhe conference of the same year, although since he was not a major chemist at the time he would probably not have been invited. After returning to London, Newlands began working as a sugar chemist, while also supplementing his income by teaching chemistry privately, but he was never to hold an academic position.

Newlands's first attempt at classification concerned a system for organic compounds that he published in 1862 along with proposals for a new system of nomenclature. In the following year, he published the first of what would be many classification systems for the elements. Although the year was 1863, New-lands developed his first system without the benefit of the atomic weight values that had been issued following the Karlsruhe conference of 1860, as he was unaware of them. Nevertheless, he did use the atomic weight values favored by Gerhardt, who had begun to revise atomic weights even before the Karlsruhe conference. Thus, Newlands was able to produce a table consisting of 11 groups of elements with analogous properties whose weights differed by a factor of 8 or some multiple of 8. Because it was unfashionably Proutian, Newlands published his first article on classification of the elements anonymously, although he revealed his identity soon afterward in response to criticisms by the equally anonymous "Studiosus" (figure 3.2).

FIGURE 3.2 Newlands's groups of elements. J.A.R. Newlands, On Relations among the Equivalents, _Chemical News_ , 7, 70—72, 1863, table on p. 71

Newlands's grouping of elements in 1863 is surprisingly suggestive, especially bearing in mind that it utilizes pre-Karlsruhe atomic weights. Ever since Prout, investigators had struggled with the fact that arithmetic intervals in atomic weights among the elements are not as exact or as regular as it seems they should be. The fact that atomic weights depend upon the vagaries of isotopic mixtures for any particular element was not, of course, suspected at the time. In addition to the isotope issue, the atomic weights of many elements had not been correctly determined. Nevertheless, one cannot fail to be struck by the good fortune that New-lands and the other pioneers of the periodic system experienced in that the ordering of the elements according to atomic weight, despite their irregular intervals, corresponds almost exactly to that based on atomic number. It is almost as though nature's mixtures of isotopes had conspired together to announce the ordering that would later be discovered in terms of atomic numbers.

In his 1863 article, Newlands described a relationship among atomic weights of the alkali metals and used it to predict the existence of a new element of weight 163, as well as a new element that would be placed between iridium and rhodium. Unfortunately for Newlands, neither of these elements ever materialized. However, as has recently been pointed out, Mendeleev also made similar predictions that failed to materialize among elements with high atomic weights. These failures can be attributed to the existence of the lanthanide elements, which occur between the second and third transition series of elements in modern terms. The lanthanides would be a problem for all the discoverers of the periodic system, as only 6 of the 14 lanthanides had been discovered prior to the 1860s, when these early periodic systems were being developed.

In 1864, Newlands published his second article on the classification of the elements (table 3.3, figure 3.3). This time he drew on the more correct, post-Karlsruhe atomic weights, a version of which had been published in England by Alexander Williamson. Newlands now found a difference of 16, or very close to this value, instead of 8, between the weights of six sets of first and second members among groups of similar elements. Again, this finding seems unexpectedly accurate given that he was working with atomic weights and not atomic numbers. A very similar table comparing differences in atomic weights between first and second members of groups of analogous elements was discovered independently and published in the very same year by Odling (described below). Indeed, Odling outdid Newlands in recognizing 10 such relationships, to Newlands's six. This fact has not been given any exposure in histories of the periodic system, which sometimes fail to even mention Odling as one of the discoverers.

Less than a month after his second system appeared in 1864, Newlands published a third system that same year (figure 3.4), but in this table he included fewer elements (24, plus a space for a new element) and made no mention of atomic weights. The article is nevertheless of considerable merit since Newlands assigned an ordinal number to each of the elements, thus in a sense anticipating the modern notion of atomic number. Abandoning the arithmetic progressions in atomic weights that had bedeviled earlier investigators, Newlands simply lined the elements up in order of increasing atomic weight without concern for the values of those weights. Nevertheless, any anticipation of the modern concept of atomic number is marred by the several cases where the sequence of elements does not strictly follow Newlands's ordinal numbers. The modern ordering based on atomic number does not show any such exceptions.

TABLE 3.3  
Newlands's first table of 1864

FIGURE 3.3 System of 1864. J.A.R. Newlands, Relations between Equivalents, _Chemical News_ , 10, 59—60, 1864, p. 59.

FIGURE 3.4 Newlands's later system of 1864. J.A.R. Newlands, On Relations among Equivalents, _Chemical News_ , 10, 94-95, 1864, p.94.

The most important thing Newland did in his third publication on the classification of the elements was to present a periodic _system;_ that is, he revealed a pattern of repetition in the properties of the elements after certain regular intervals. This, of course, is the essence of the periodic law, and Newlands deserves credit for having recognized this fact so early, along with De Chancourtois. Another innovation of Newlands's later system of 1864, which is almost universally attributed to Mendeleev, although it was also carried out by Odling, was the way in which Newlands reversed the positions of the elements iodine and tellurium in order to give precedence to chemical properties over the apparent atomic weight ordering. Newlands thus holds the distinction of having been the first of these three discoverers to make a so-called pair reversal. It is somewhat surprising, however, especially given his emphasis on chemical properties, that Newlands failed to display analogies between several other obviously related elements, such as lithium and sodium.

#### The Law of Octaves

In 1865, Newlands developed yet another system, which was a vast improvement on that of the previous year in that he now included 65 elements, in increasing order of atomic weight, while once again using ordinal numbers rather than actual values of atomic weight. This system was built upon his famous "law of octaves," whereby the elements showed a repetition in their chemical properties after intervals of eight elements. Newlands went so far as to draw an analogy between a period of elements and a musical octave, in which the tones display a repetition involving an interval of eight notes (counting from one note of C, e.g., to the next note C inclusive). In the words of Newlands himself:

If the elements are arranged in the order of their equivalents with a few slight transpositions, as in the accompanying table, it will be observed that elements belonging to the same group usually appear on the same horizontal line. It will also be seen that the numbers of analogous elements differ either by 7 or by some multiple of seven; in other words, members of the same group stand to each other in the same relation as the extremities of one or more octaves in music.... The eighth element starting from a given one is a kind of repetition of the first. This particular relationship I propose to term the _Law of Octaves._

This statement marks a rather important step in the evolution of the periodic system since it represents the first clear announcement of a new law of nature relating to the repetition of the properties of the elements after certain intervals in their sequence. As mentioned before, the periodic _law_ , though not a fashionable term nowadays, is perhaps the most important aspect of the periodic table. The periodic table in all its many forms is, after all, just an attempt to represent this law graphically.

There remains the question raised earlier as to whether De Chancourtois might have been the first to recognize the existence of the periodic law. As Wendell Taylor has suggested, Newlands was far more explicit about the existence of a periodic law than was De Chancourtois, who merely mentioned it as a possibility. There is little doubt that Odling also failed to recognize the existence of a fundamental law, though he did recognize the existence of a periodic system. Odling specifically claimed that, after a detailed examination of the numerical differences between the atomic weights of analogous elements, he had decided that these relations were "too numerous to depend upon some hitherto unrecognized law."

Returning to Newlands's system of 1865, even though it is a genuine _periodic_ system, compared with his earlier lists or groups of elements, Newlands did not see the need to separate the elements into subgroups as Mendeleev later did by offsetting certain elements within main groups. In modern terms, he did not see the need to separate out the transition metals, as is now carried out in the modern medium-long form of the periodic table. (See chapter 1 for diagrams of the short and medium-long forms of the periodic table.) The law of octaves applies perfectly to the first two periods, excluding the noble gases, which had not yet been discovered. Beyond that, Newlands's periodicities were bound to run into difficulties since the inclusion of the transition metals makes the later periods much longer than 8. Only his fellow London chemist, Odling, anticipated this problem, as described below.

Newlands first announced his law of octaves in a paper delivered to the London Chemical Society in 1866, but to his great misfortune, his insight was badly received. This event is perhaps Newlands's best-known legacy to the history of the periodic system and is repeated _ad nauseam_ in textbooks and popular accounts. What Newlands presented to the society was an improved version of his 1865 system, in which more elements were arranged strictly according to his ordinal numbers. In his earlier published table of 1865, this had not been the case, especially for the elements with ordinal numbers beyond 50. The new table presented to the society (table 3.4) also shows some chemical improvements in that the element lead is now placed in the same group as carbon, silicon, and tin, whereas it had not appeared in the table of 1865.

As the popular story goes, Newlands included the mention of a law of octaves in his presentation and proceeded to draw an analogy with the musical scale. Whether he seriously intended to suggest a connection between chemistry and music is not clear. In any case, his fanciful analogy was probably not the reason why the chemists in attendance were quick to dismiss Newlands's scheme. Their hostility is perhaps better attributed to the British tendency, of the time, to be suspicious of theoretical ideas in general. The best-known response to Newlands is the much-quoted one of George Carey Foster, who suggested that Newlands might well have obtained a superior classification scheme if he had merely ordered the elements alphabetically according to the first letter of each of their names.

Some modern commentators have tried to exonerate Newlands by saying that he was unlucky to have been working at the time before the noble gases had been discovered. They suggest that if he had known of this additional group, he would have realized that chemical repetition follows a "nonet law," not an octet rule. In that case, he might not have been tempted to make analogies with the musical scale and thus might not have fallen prey to the assembled scientists at the London Chemical Society. These attempts to exonerate Newlands are in fact rather unnecessary, since he specifically anticipated the possibility of the repeat period being greater than 8, as discussed below.

Another aspect of the Newlands mythology concerns the fact that the chemists gathered at the London Chemical Society meeting decided not to permit publication of Newlands's article in the society's proceedings. Although this is quite true, it should not be taken to imply that Newlands was prevented from publishing his ideas on the classification of the elements. In fact, he had already published several articles in the highly respected journal _Chemical News_ and would succeed in publishing the contents of his presentation to the London Chemical Society a few months later in this same journal. The reason why Newlands's ill-fated talk had been denied publication by the London Chemical Society only emerged seven years after the event, when Odling, who had chaired the meeting, wrote that the society had made it a rule not to publish papers of a purely theoretical nature, since it was likely to lead to controversy. One cannot rule out the possibility that there may have been a certain amount of rivalry between Odling and Newlands regarding the construction of periodic systems and that this may have influenced Odling's view. Nevertheless, this seems rather tenuous since Newlands was something of an outsider among academic chemists, and it is unlikely that Odling would have regarded him as a threat. Odling was a more rounded chemist whose main interests lay in the wider question of the relationship between atomic weight and equivalent weight and the related question of the difference between atoms and molecules. Unlike in the case of Newlands, the classification of the elements was only a sideline for Odling.

TABLE 3.4  
Newlands's table illustrating the law of octaves as presented to the Chemical Society in 1866

In an article published in 1866, Newlands tried to answer the criticisms that had been leveled at him in the course of his fateful presentation to the London Chemical Society. The accompanying table published by Newlands represents the first time that he arranged chemical groups arranged in vertical columns, and once again, the ordering of the elements follows a numerical order with the exception of three reversals (Ce and La with Zr, U with Sn, and Te with I). Newlands responded to a criticism that he had not left any gaps and that this would be a problem when future elements were discovered:

The fact that such a simple relation [the law of octaves] exists now, affords a strong presumptive proof that it will always continue to exist, even should hundreds of new elements be discovered. For, although the difference in the number of analogous elements might, in that case, be altered from 7, to a multiple of 7, of 8, 9, 10, 20, or any conceivable figure, the existence of a simple relation among the elements would be none the less evident.

Newlands is, of course, correct. In fact he was vindicated by the subsequent discovery of the noble gases, which, instead of disrupting the repeating pattern, simply increased the repeat distance between successive periods to eight rather than seven. In a later system, of 1878, Newlands would carry out just such an expansion by establishing periods with 10 elements, although the net result of this was to create far too many empty spaces that were not subsequently filled by new elements (figure 3.5).

Following the publication of Mendeleev's periodic system in 1869, Newlands began to publish a series of letters in which he attempted to establish his priority in arriving at the first successful periodic system. Meanwhile, much to his chagrin, the Davy medal was awarded jointly to Mendeleev and Lothar Meyer in 1882 for their discovery of the periodic system. Newlands renewed his efforts, publishing a further summary of his own achievements in 1882 and again in 1884 in book form. His tenacity was at least partly rewarded when the Davy medal was finally awarded to him in 1887. As late as 1890, Newlands published a rejoinder to a critique that had been expressed by Mendeleev in his Faraday lecture of two years before. It is also worth noting that, despite this critique, Mendeleev regarded the work of Newlands more highly than that of Lothar Meyer.

During the period 1863—1890, Newlands published a total of 16 articles, in which he tried many different schemes on the classification of the elements. These met with varying degrees of success both in scientific terms and in terms of recognition. There can be no doubt, however, that Newlands ranks among the true pioneers of the modern periodic system, in particular for being the first to recognize explicitly the existence of the periodic law, which in many ways is the real crux of the matter.

### WILLIAM ODLING

Unlike many of the discoverers of the periodic system, who were otherwise marginal figures in the history of chemistry, Odling was a distinguished chemist and scientist who held some very important positions in the course of his career. Most notably, he succeeded Michael Faraday as director of the Royal Institution in London. Odling also had the advantage of having attended the Karlsruhe conference, where he had given a lecture on the need to adopt a unified system of atomic weights. Unlike Newlands, whose first attempts at a periodic system were carried out in ignorance of Cannizzaro's recommended values of atomic weights, Odling was able to avail himself of these values from the beginning of his attempts at producing a table of the elements. In fact, after Karlsruhe, Odling rapidly became the leading champion of the views of Cannizzaro and Avogadro in England. Odling above all others would therefore have recognized the significance of the new atomic weight values.

Odling's main article on the periodic system appeared in 1864, while he was a reader in chemistry at St. Bartholomew's Hospital in London. Whereas Newlands's system of the same year had only included 24 of the 60 known elements, Odling succeeded in including 57 of them (figure 3.6). Furthermore, Odling's paper preceded Newlands's announcement of periodicity to the London Chemical Society, which was made shortly afterward in 1865. Nevertheless, it appears that the two chemists worked quite independently of each other.

Odling begins his article by stating, "Upon arranging the atomic weights or proportional numbers of the sixty or so recognized elements in order of their several magnitudes, we observe a marked continuity in the resulting arithmetical series," and goes on to point out a few exceptions to this regularity. Then he makes an observation that amounts to an independent discovery of the periodic system:

With what ease this purely arithmetical seriation may be made to accord with a horizontal arrangement of the elements according to their usually received groupings, is shown in the following table, in the first three columns of which the numerical sequence is perfect, while in the other two the irregularities are but few and trivial.

That Odling had recognized the periodicity in chemical properties is clearly seen in the horizontal groupings that he organizes in this table.

FIGURE 3.6 Table of 1864. W. Odling, On the Proportional Numbers of the Elements, _Quarterly Journal of Science_ , 1, 642-648, 1864, p. 643.

Odling notes that there are a considerable number of pairs of chemically analogous elements, indeed, half of all the known elements, whose difference in atomic weights lies between the values of 84.5 and 97. Some of these pairs are shown in table 3.5. He then notices that about half of these cases include the first and third members of previously known triads. He suggests that a middle member might be found for the other half, stating that, "the discovery of intermediate elements in the case of some or all of the other pairs is not altogether improbable." This is clearly an example of a prediction made on the basis of a periodic system, although admittedly a rather tentative one that was not further developed with specific examples.

TABLE 3.5  
Odling's first table of differences

A table is then given of as many as 17 pairs of elements whose members differ by atomic weights of 40—48. This is followed by yet a third set of pairs of elements, 10 instances in all, of "more or less analogous elements" that differ in atomic weight by 16 units, or something close to this amount. It is worth noting perhaps, that in 7 out of these 10 instances, the element with the lower atomic weight of the pair is the first member of the group of similar chemical elements to which they both belong.

It would appear that, in identifying these gaps, Odling was making a rather remarkable observation that seemed to go beyond the earlier triadic relationships, since the 16-unit gap appears with approximate consistency in so many of Odling's three sets of element pairs. One might claim that just this observation constitutes the recognition of periodicity. What Odling appears to have realized, particularly in the case of the last set of elements, is that, in as many as 10 important cases, there is an approximate repetition in the properties of any of these elements following a difference in atomic weight of 16, or very close to this value. Bearing in mind that he used atomic weights, which are approximately double the values of atomic number, this is also very close to being the recognition of the law of octaves. In other words, Odling appears to have realized that the repetition occurs after a difference in atomic number of eight units, which corresponds to an atomic weight difference of 16.

TABLE 3.6  
Odling's third table of differences

Odling makes the further claim that the chemical similarities between elements separated by differences of about 48 in atomic weight, such as cadmium and zinc, are greater than those between pairs of elements, such as zinc and magnesium, that are separated by other intervals, such as 41 in this case. Thus, it would appear that he recognized the need to separate certain elements (those that would eventually become known as the transition metals) from the main body of the table. In this way, periodicity could be retained in the properties of the majority of the elements, as is done in the modern medium-long form of the table. If the transition metals are separated out of the short-form table, the primary periodic relationship between main-group elements is emphasized and the fact that period lengths vary is accommodated in a natural manner.

It so happens that Odling was correct in this case. From the perspective of the modern periodic table, cadmium and zinc are both transition metals that show a primary kinship, whereas zinc and magnesium belong to the transition metals and main-group elements, respectively, and show only secondary kinships. Odling may have anticipated the modern trend to separate zinc and magnesium into different groups and, indeed, different blocks of the periodic table.

Any claim that Odling is making a significant anticipation here is vitiated, however, by the fact that in the same paragraph he goes on to give what he considers to be other examples of this behavior, all of which are incorrect. He claims that there is a greater chemical similarity among cesium, rubidium, and potassium, as well as among barium, strontium, and calcium, both of which sets show common differences of about 48 between closest members, than between potassium and sodium, where the difference is only 18. This is simply not the case.

If we are to judge these suggestions from the perspective of the modern table, we see that Odling is correct in drawing the first distinction, given that magnesium does not belong with the transition elements zinc and cadmium. However, in the second example, it has turned out that no comparable difference exists between potassium and sodium, both of which are now classified as main-group elements of group I. In any case, separating the transition metals from the main body of the table would not affect any of these groupings, as they are all composed of main-group elements.

What is confusing the issue, as far as the numerical relationships are concerned, is precisely the fact that successive periods in the mature periodic table do not all have the same length. Odling does not appear to have realized that different periods have different lengths, even though he has deliberately separated some elements out from the main body of the table. The suggestion that Odling anticipated the existence of transition metal groups in the periodic table to preserve periodicity is thus somewhat debatable.

### GUSTAVUS HINRICHS

The case of Hinrichs is rather unusual among the discoverers of the periodic system. This is because his scientific interests were so far ranging, and the evidence he brought to bear on producing a classification of the elements was so diverse as to lead some commentators to regard him as a mere crank. Although he held a number of academic appointments, first at Iowa State University and later at the University of Missouri—St. Louis, Hinrichs seemed to go out of his way to cultivate eccentricity. In addition, he seldom gave references to other authors in his numerous publications, thus making a balanced assessment of his contributions rather more difficult.

Hinrichs was born in 1836 in Holstein, which was then a part of Denmark but later became a German province. Hinrichs published his first book at the age of 20, while attending the University of Copenhagen. He immigrated to United States in 1861 to escape political persecution and, after a year of teaching high school, was appointed head of Modern Languages at the University of Iowa. A mere one year later, he became Professor of Natural Philosophy, Chemistry, and Modern Languages. He is also credited with founding the first meteorological station in the United States in 1875, acting as its director for 14 years.

Hinrichs was a prolific author who published some 3,000 articles in Danish, French, and German, as well as in English, in addition to about 25 books of varying lengths in English and German. These books include the highly eccentric _Atomechanik_ of 1867, in German, in which Hinrichs gives his definitive views on the classification of the elements. It is interesting to note that the majority of Hinrichs's articles were published in languages other than English. He seems to have disliked American journals, complaining that their insistence on correcting his work caused unacceptable delays in publication. Karl Zapffe, the author of a detailed analysis of Hinrichs's work, has suggested that Hinrichs's disaffection with American journals may have been part of his distaste for all things American. This may have included his American colleagues and may have led to his eventual dismissal from the University of Iowa in 1885.

As Zapffe writes:

It is not necessary to read far into Hinrichs' numerous publications to recognize the marks of an egocentric zeal which defaced many of his contributions with an untrustworthy eccentricity. Only at this late date does it become possible to separate those inspirations which were real—and which swept him off his feet—from background material which was captured in the course of his own learning. Whatever the source, Hinrichs usually dressed it with multilingual ostentation, and to such a point of disguise that he even came to regard Greek philosophy as his own.

The jury is still out on Hinrichs. While Jan van Spronsen includes him in his list of six genuine discoverers of the periodic system, William Jensen, a chemist and chemical educator at the University of Cincinnati, is among those who regard Hinrichs as a scientific maverick and a crank. This also seems to be the conclusion of Cassebaum and George Kauffman, who include just six lines on Hinrichs in an article on the codiscoverers of the periodic system and who devote considerable space to a footnote pointing out his unconventional scientific attitudes. But careful consideration of Hinrichs's work shows that there was much useful science, if one is prepared to take time to examine the various strands of his research.

Hinrichs took a rather Pythagorean approach to science in that he was captivated by numerical relationships, even those involving very diverse phenomena. Whereas Pythagoreanism had already figured in the early research on triads and Prout's hypothesis, Hinrichs's own brand of Pythagoreanism was far more extreme. By an ingenious argument (examined shortly below), he was led to postulate the notion that atomic spectra can provide information on the dimensions of atoms, an idea that is essentially correct from the modern perspective. Since Hinrichs's idea has not been clearly described in previous accounts of the evolution of the periodic system, or at least the few accounts that even mention his work, I attempt to describe it here.

Hinrichs's wide range of interests extended to astronomy. Like many authors before him, as far back as Plato, Hinrichs noticed some numerical regularities regarding the sizes of the planetary orbits. In an article published in 1864, Hinrichs showed a table (table 3.7) that he proceeded to interpret. Hinrichs expressed the differences in these distances by the formula 2x × _n_ , in which _n_ is the difference in the distances of Venus and Mercury from the sun, or 20 units. Depending on the value of _x_ , the formula therefore gives the following distances:

20 x 20 = 20

21 x 20 = 40

22 x 20 = 80

23 x 20 = 160

24 x 20 = 320

etc.

A few years previously, in 1859, the Germans Gustav Robert Kirchhoff and Robert Bunsen had discovered that each element could be made to emit light, which could then be dispersed with a glass prism and analyzed quantitatively. What they also discovered was that every single element gave a unique spectrum consisting of a set of specific spectral lines, which they set about measuring and publishing in elaborate tables. Some authors suggested that these spectral lines might provide information about the various elements that had produced them, but these suggestions met with strenuous criticism from one of their discoverers, Bunsen. Indeed, Bunsen remained quite opposed to the idea of studying spectra in order to study atoms or to classify them in some way.

TABLE 3.7  
Hinrichs's 1864 table of planetary distances

Hinrichs, however, had no hesitation in connecting spectra with the atoms of the elements. In particular, he became interested in the fact that, with any particular element, the frequencies of its spectral lines always seemed to be whole number multiples of the smallest difference. For example, in the case of calcium, a ratio of 1:2:4 had been observed among its spectral frequencies. Hinrichs's interpretation of this fact was bold and elegant: If the sizes of planetary orbits produce a regular series of whole numbers, and if the ratios among spectral line differences also produce whole number ratios, the cause of the latter might lie in the size ratios among the atomic dimensions of the various elements (table 3.8). This is Pythagoreanism with a vengeance, but it proved to be fruitful in that it led Hinrichs to a successful, and highly novel, means of classifying the elements into a periodic system.

By closely studying the work of Kirchoff and Bunsen, Hinrichs found that some of the spectral line frequencies, those referred to as "dark lines," could be related to the chemistry of the elements through their atomic weights, as well as to their postulated atomic dimensions. The difference between the spectral line frequencies seemed to be inversely proportional to the atomic weights of the elements in question. Hinrichs quoted the values of calcium, where the frequency difference is 4.8 units, and barium, which is chemically similar but has a higher atomic weight and shows a frequency difference of 4.4 units.

TABLE 3.8  
Schematic form of Hinrichs's argument

Hinrichs then proposed the following formula to connect the atomic weight of any element with its atomic dimensions:

_A_ = _a_ x _b_ x _c_

_A_ is the atomic weight and a, b, and _c_ are the respective lengths of the sides of a prism denoting the shape of the atom. The base of the prism, which is taken as the dimension _a_ , would be of the same size for all the elements belonging to a particular chemical group. If a particular group contained square prisms, their formula would reduce to

_A_ = _a 2_ x _b_

In other cases, where the base of the prism took on a triangular shape, the formula would be expressed as

_A_ = ( _a_ x _b_ x _c_ ) + _k_

where _k_ is a constant. Given how improbable this whole approach might seem, it is quite remarkable how useful it turned out to be when Hinrichs applied it to rationalizing the atomic weights of the elements. For example, it served quite successfully as a basis for deciding which elements should be grouped together in his periodic system. Table 3.9 shows some of his groups and demonstrates how in each case one of the formulas given above is able to accommodate, rather accurately, the atomic weight of each element in the proposed groups. Of course, this was not the only reason Hinrichs grouped elements together. Many of the groupings suggested themselves primarily on the basis of chemical similarities, with which Hinrichs would have been well acquainted through his knowledge of chemistry.

In the course of this work, Hinrichs expressed his support for the notion of primary matter, which had been the basis of Prout's hypothesis of half a century earlier. Hinrichs was convinced that the atomic weights of the elements were whole numbers. Because the value of chlorine was 35.5 according to Cannizzaro's atomic weights, Hinrichs concluded that the primary atom had a weight of half the value of hydrogen and so took H/2 to be the basic unit for expressing all the other weights. The weight of chlorine therefore assumed a value of 71, and the Cannizzaro atomic weights of all the other elements were similarly doubled. These are the values that are seen in the culmination of Hinrichs's work on the classification of the elements, his spiral periodic system, as shown in figure 3.7.

TABLE 3.9  
Hinrichs's table of atomic weights and atomic dimensions for several groups of elements

The 11 "spokes" radiating from the center of this wheel-like system consist of three predominantly nonmetal groups and eight groups containing metals. From a modern perspective, the nonmetal groups appear to be incorrectly ordered, in that the sequence is groups VI, V, and then VII when proceeding from left to right at the top of the spiral. The group containing carbon and silicon is classed with the metallic groups by Hinrichs, presumably because it also includes the metals titanium, palladium, and platinum. In the modern table, these three metals are indeed classified together, but not in the same group as carbon and silicon, which belong with germanium, tin, and lead in group IV.

FIGURE 3.7 Hinrichs's spiral periodic system of 1867. G.D. Hinrichs, _Programm der Atomechanik oder die Chemie eine Mechanik de Pantome_ , Augustus Hageboek, Iowa City, IA, 1867. As simplified by J. van Spronsen, _The Periodic System of the Chemical Elements, the First One Hundred Years_ , Elsevier, Amsterdam, 1969 (by permission from Elsevier).

Overall, however, Hinrichs's periodic system is rather successful in grouping together many important elements. One of its main advantages is the clarity of its groupings, compared, say, with the more elaborate but less successful periodic systems of Newlands in 1864 and 1865. For example, Hinrichs groups together oxygen, sulfur, selenium, and tellurium. Newlands also groups these elements together but includes osmium (Os) with them. Hinrichs groups together nitrogen, phosphorus, arsenic, antimony, and bismuth. So does Newlands, but he incorrectly includes manganese, as well as didymium and molybdenum in one space. Hinrichs groups together lithium, sodium, potassium, and rubidium. Newlands also groups these elements together but also incorrectly includes copper, silver, gold, and tellurium.

Although it is not arranged as a long-form table, Hinrichs's classification seems to capture many of the primary periodicity relationships seen in the modern periodic table, and unlike many of Newlands's tables, it is not cluttered by attempts to show secondary kinship relationships. Hinrichs, for example, groups together copper, silver, and gold. In the case of Newlands, these elements are grouped separately, with the exception of one table in 1865, which classifies the three elements together and also intersperses them with such other elements as potassium, rubidium, and cesium.

It is clear from his books that Hinrichs possessed a deep knowledge of chemistry, as well as a proficiency in mineralogy. Yet his approach to the classification of the elements was only partly chemical. He was perhaps the most interdisciplinary of all the discoverers of the periodic system. Indeed, the fact that Hinrichs arrived at his system from such a different direction as the others might be taken to lend the periodic system itself independent support, just as Lothar Meyer's studies of physical periodicity (described below) also do.

In an article published in _The Pharmacists_ in 1869, Hinrichs discusses previous unsuccessful attempts to classify the elements, but in doing so fails to mention any of his codiscoverers, such as De Chancourtois, Newlands, Odling, Lothar Meyer, and Mendeleev. Hinrichs characteristically appears to have completely ignored all other attempts to base the classification of the elements directly on atomic weights, though one can assume that he was aware of them given his knowledge of foreign languages. This is not to say that his classification is unconnected with atomic weights, only that the connection is rather indirect in view of the astronomical argument that seems to be the basis of the approach.

Finally, it should be stressed that Hinrichs appeared to be ahead of his time in assigning great importance to the analysis of the spectra of the elements and in trying to relate these facts to the periodic classification. However, his spectral studies are by no means universally accepted. Some contemporary historians, including Klaus Hentschel, have criticized Hinrichs's work, claiming that he was somewhat selective in what data he admitted into his calculations.

More than that of any other scientist discussed in this book, the work of Hinrichs is so idiosyncratic and labyrinthine that a more complete study will be required before anyone can venture to pronounce on its real value.

### JULIUS LOTHAR MEYER

Lothar Meyer (figure 3.8) was born in 1830 in Varel (Oldenburg), Germany. He was the fourth of seven children of a physician father and a mother whose own father was also a local physician. Julius and one of his brothers, Oskar, began their studies with the intention of continuing this family medical tradition, but it was not long before both of them had turned to other fields. Oskar became a physicist, while Julius became one of the most influential chemists of his time.

FIGURE 3.8 Julius Lothar Meyer. Photo from author's collection, permission from Edgar Fahs Smith Collection.

Lothar Meyer is best remembered for his independent discovery of the periodic system, although more credit is invariably accorded to Mendeleev. The two chemists eventually became engaged in a rather bitter priority dispute, which Mendeleev apparently won, although how much of that was due to Mendeleev's more forceful personality is difficult to ascertain fully. Certainly Mendeleev had a more complete system and went on to make predictions on the basis of his system. He was also to champion the cause of the periodic law to a far greater extent than was Lothar Meyer. But if one asks the question of who arrived at the mature periodic system first, a strong case can be made for saying that in many crucial details the system of Lothar Meyer was not only first but also more correct.

Lothar Meyer attended the Karlsruhe conference in 1860 and learned firsthand of Cannizzaro's groundbreaking work on the atomic weights of the elements. He then edited a version of Cannizzaro's article that appeared in Germany in Wilhelm Ostwald's series under the title _Klassiker der Wissenschaften_. Lothar Meyer later described the effect that Cannizzaro's article had on him by saying, "[T]he scales fell from my eyes and my doubts disappeared and were replaced by a feeling of quiet certainty." In 1864, Lothar Meyer published the first edition of a chemistry textbook, _Die Modernen Theorie der Chemie_ , which was deeply influenced by the work of Cannizzaro. The book appeared in five editions and was translated into English, French, and Russian, eventually becoming one of the most authoritative treatments on the theoretical principles of chemistry before the advent of physical chemistry in the late 1800s.

By the time Lothar Meyer had written the manuscript for his book in 1862, he had produced a table of 28 elements arranged in order of increasing atomic weight. An adjacent table containing a further 22 elements also appeared in the book, although these were not arranged according to atomic weight order. All this took place only two years after the Karlsruhe conference. It should perhaps be noted in passing that it took Mendeleev something like nine years from the time of his attending the same conference before he, too, produced a table of elements arranged in order of increasing atomic weights.

Lothar Meyer was also deeply influenced by the work of Johann Döbereiner and Pettenkofer, both of whom, as described in chapter 2, had published articles on the existence of triads of elements, where the weight of the middle member was the approximate mean of that of the flanking elements. Going further, Pettenkofer had pointed to an analogy between the regular increase in the weights of successive members of any homologous series in organic chemistry and the almost regular increase in the atomic weights of similar elements within any triad, something that had also been noticed by Dumas.

Most organic compounds can be classified according to the homologous series to which they belong. Such series are created in an iterative fashion with the repeated addition of a chemical unit, such as CH3 in the case of the alkanes. This regularity suggested to Pettenkofer and Dumas that the molecules of such series must be composed of regular units.

If the analogy between these organic compounds were also applied to inorganic atoms, it would suggest that atoms are likewise composed of parts. In other words, just as the regularity in the increasing molecular weights in a homologous series suggests that its members contain some sort of building block universal to that series, so the regularity seen in the intervals between atomic weights of members of a triad would suggest that the atoms of those members are somehow modular. Lothar Meyer did indeed regard such evidence as pointing to the composite nature of inorganic atoms, something that Mendeleev never accepted throughout his life.

Lothar Meyer published his table of 28 elements for the first time in 1864 (figure 3.9). His arrangement of elements in order of increasing atomic weights and the clear establishment of horizontal relationships among these elements are other instances in which Lothar Meyer anticipated Mendeleev by several years. As described in chapter 4, where we encounter the details of Mendeleev's work, this recognition of the need to order the elements in terms of increasing atomic weight, and especially the recognition of horizontal relationships, has wrongly been regarded as a first by Mendeleev. Yet here in 1864, Lothar Meyer is publishing both ideas simultaneously, without, in most cases, receiving due recognition for these advances from contemporary, or later, commentators.

FIGURE 3.9 Table of 1864. J. Lothar Meyer, _Die modernen thoerien und ihre Bedeutung fur die chemische Statisik_ , Breslau (Wroclaw), 1864, p. 135.

Lothar Meyer's 1864 table also showed clearly for the first time a regular variation in valency of the elements, from 4 to 1 on moving from left to right across the table, followed by a repetition of valence 1 and a further increase to elements with valence 2. This table suggests that Lothar Meyer struggled to arrange elements in terms of atomic weight as well as chemical properties. He seems to have decided to let chemical properties outweigh strict atomic weight ordering in some cases. An example of this is in his grouping of tellurium with elements such as oxygen and sulfur, while iodine is grouped with the halogens, in spite of their ordering according to atomic weight. Lothar Meyer also separated the elements into two tables in a manner corresponding to the separation of our modern main-group elements from the modern transition elements. As mentioned above in the case of Odling, such a separation has become a feature of the modern medium-long—form and long-form tables.

Another very noteworthy feature of Lothar Meyer's table of 1862 (published in 1864) is the presence of many gaps to denote unknown elements. Once again, it appears that the leaving of gaps did not originate with Mendeleev, who was to wait a further five years before even venturing to publish a periodic system and eventually making the detailed predictions for which he subsequently became so well known. Lothar Meyer's table contains interpolations between neighboring elements. In the space below the element silicon, for example, he indicates that there should be an element whose atomic weight would be greater than silicon's by a difference of 44.55. This implies an atomic weight of 73.1 for this unknown element, which when discovered was found to have an atomic weight of 72.3. This prediction of the element germanium, which was first isolated in 1886, is usually attributed to Mendeleev even though it was clearly anticipated by Lothar Meyer in this early table of 1864.

The criticism has been made that Lothar Meyer did not explicitly refer to atomic weight in his 1864 table. This objection seems a little excessive, however, since with regard to the 28-element table, the arrangement is clearly based on increasing atomic weight, such that Lothar Meyer may not have felt the need to comment on this rather obvious feature. Of course, the same cannot be said for the smaller table consisting of 22 elements. But the fact that these elements have been separated from the other 28 may indicate that Lothar Meyer realized that in these cases the concept of increasing atomic weight did not apply strictly to the classification he chose to adopt. Nevertheless, atomic weight increases vertically down each column, and there are only six inconsistencies in the increase in atomic weight going across the table. Given that Lothar Meyer had classified a total of 50 elements while showing only six mistaken reversals in atomic weights, all of which occur among the problematic transition metals (in the modern usage of the term), this cannot be considered a significant failing on his part. The only serious misplacements he made in terms of atomic weight increase concern just two elements, molybdenum and vanadium. All of his other reversals are quite within the possible bounds of error in measured atomic weights.

FIGURE 3.10 Plot of atomic volume versus atomic weight. J. Lothar Meyer, Die Natur der Chemischen Elemente als Function ihrer Atomgewichte, _Annalen der Chemie, Supplementband_ , 7, 354–364, 1870. Redrawn by T. Bayley, _Philosophical Magazine_ , 13, 26-37, 1882, p. 26.

But perhaps Lothar Meyer's greatest strength lay in his additional knowledge of physical properties and his use of them in constructing representations of the periodic system. He paid close attention to atomic volumes, densities, and fusibilities of the elements, for example. His published diagram showing the periodicity among atomic volumes of the elements (i.e., atomic weight divided by specific gravity), in particular, is generally considered to have contributed favorably to the general acceptance of the periodic system (figure 3.10). Indeed, one can see the periodicity among the elements almost at a glance from this diagram. Mendeleev, too, was aware of the importance of atomic volume. In fact, he made predictions on atomic volumes beginning in his first article of 1869. But he did not emphasize the periodicity in this physical property of atoms, nor did he display such suggestive diagrams of its trend.

### THE REMELÉ-SEUBERT EPISODE: THE UNPUBLISHED TABLE OF 1868

In the course of the controversy between Mendeleev and Lothar Meyer, which followed the publication of their respective periodic systems, it seems fair to say that Mendeleev was the victor at least as far as the scientific public was concerned. However, there is a rather intriguing episode that did not come to light until much later, and that might have made a significant difference in this controversy had it become known earlier. In 1868, when Lothar Meyer was preparing the second edition of his book, he produced a vastly expanded periodic system that included a further 24 elements and nine new vertical families of elements (figure 3.11). This system preceded Mendeleev's famous table of 1869 that subsequently claimed all the glory. Moreover, Lothar Meyer's system was more accurate than Mendeleev's. For example, Lothar Meyer correctly placed mercury with cadmium, and lead with tin. In both of these cases, Mendeleev's table failed to make this connection.

It appears that for some reason Lothar Meyer's 1868 table was not published. A full 25 years later, Adolf Remelé, a German chemist who succeeded Lothar Meyer as professor of chemistry in Eberswalde, showed the table to Lothar Meyer, who in the meantime seemed to have forgotten all about its existence. In 1895, after Lothar Meyer's death, Carl Seubert, one of his colleagues, finally published the forgotten table. Unfortunately, this attempt to restore some semblance of priority to Lothar Meyer, after this almost comical time delay, fell largely on deaf ears.

FIGURE 3.11 Unpublished system of 1868. J. Lothar Meyer.

### CONCLUSION

As I hope to have shown in this chapter, the periodic system developed through a process of gradual evolution rather than revolution, especially after Cannizzaro had published an accurate set of atomic weights. The discovery was made, essentially independently, by six diverse scientists who differed greatly in their fields of expertise and in their approaches. De Chancourtois, a French geologist, was unlucky to produce a rather complicated three-dimensional representation that suffered further at the hands of his publisher. But the fact remains that he made the first discovery of periodicity. In addition, many chemical mistakes led to the almost complete oblivion of his system. An English sugar chemist, Newlands, was the first to recognize the lawlike status of chemical periodicity but was somewhat ignored because, among other things, he compared periodicity to musical octaves. A more established English chemist, Odling, also designed successful periodic systems, but somewhat surprisingly denied the lawfulness of chemical periodicity. Hinrichs, a polymath working in the United States, developed a spiral periodic system using an extravagant form of Pythagoreanism in which he compared the dimensions of the solar system to the dimensions within the atom. Then came the fully mature periodic systems of Lothar Meyer and Mendeleev, two established chemistry professors in Germany and Russia, respectively, both of whom were engaged in writing chemistry textbooks. Lothar Meyer appears to have placed greater emphasis on physical properties of the atoms but hesitated to make predictions. Mendeleev, meanwhile, was the consummate chemist, familiar with the detailed chemical behavior of all the known elements and, as described in chapter 4, also ventured to make bold predictions concerning yet undiscovered elements.

## **CHAPTER 4  
MENDELEEV**

Dimitri Ivanovich Mendeleev (figure 4.1) is the undisputed champion of the periodic system in at least two senses. First of all, he is by far the leading discoverer of the system. Although he was not the first to develop a periodic system, his version is the one that created the biggest impact on the scientific community at the time it was introduced and thereafter. His name is invariably and justifiably connected with the periodic system, to the same extent perhaps as Darwin's name is synonymous with the theory of evolution and Einstein's with the theory of relativity.

Although it may be possible to quibble about certain priority aspects of his contributions, there is no denying that Mendeleev was also the champion of the periodic system in the literal sense of propagating the system, defending its validity, and devoting time to its elaboration. As discussed in chapter 3, there were others who produced significant work on the system, but many of them, such as Alexandre-Emile De Chancourtois, William Odling, and Gustav Hinrichs, moved on to other scientific endeavors. After publishing their initial ideas, these contributors devoted their attention to other fields and never seriously returned to the periodic system to examine its full consequences to the extent that Mendeleev did.

This is not to suggest that Mendeleev himself worked only on the periodic system. He is also known for many other scientific contributions, as well as for working in several applied fields, such as the Russian oil industry and as the director of the Russian institute for weights and measures. But the periodic system remained as Mendeleev's pride and joy throughout his adult life. Even toward the end of his life he published an intriguing essay in which he returned to the periodic system and, among other speculations, attempted to place the physicist's ether within the periodic system as a chemical element.

Much has been written on Mendeleev, and it would be impossible to do justice to his contributions in the space of a few pages. Here I concentrate, as in other parts of this book, on the fundamental scientific and philosophical ideas that underpinned the evolution of the system. An important part of this investigation consists of trying to understand Mendeleev's conception of the nature of chemical elements. This issue forms the basis of what is perhaps the most philosophical aspect of the periodic system, and one that has been almost completely neglected by books and articles on Mendeleev and the periodic system generally.

FIGURE 4.1 Dimitri Ivanovich Mendeleev. Photo and permission from Emilio Segrég Collection.

### EARLY LIFE AND SCIENTIFIC WORK

Mendeleev was born in 1834 in the Siberian city of Tobolsk. He was the last child in a family of 14 children. His father died when he was very young, and his mother, who was devoted to encouraging his scientific studies, died when Dimitri was about 15 years old. Before her death, she went to great lengths and sacrifices to enroll her son at the Main Pedagogical Institute of St. Petersburg, where he took classes in chemistry, biology, and physics, as well as pedagogy. The last of these in particular was to have a profound influence on his scientific work, since it was in the course of writing a textbook for the teaching of inorganic chemistry that Mendeleev was to develop his periodic system.

Mendeleev's early scientific work involved a detailed examination of the chemical properties as well as the specific volumes of many substances. In 1856 he spent some time working at Robert Bunsen's laboratory in Heidelberg, where he studied the behavior of gases and their deviations from the laws of perfect gases. By 1860, he had become sufficiently prominent a chemist to be Karlsruhe conference, where he met the likes of Jean-Baptiste Dumas, Charles-Adolphe Wurtz, and Stanislao Cannizzaro. The following year he published a textbook of organic chemistry, which enjoyed considerable success in his native Russia and for which he was awarded the prestigious Demidov Prize.

It was not until 1865 that Mendeleev defended his doctoral thesis, which was based on his study of the interaction between alcohol and water. At about this time, having already written a book aimed at systematizing organic chemistry, he began to consider the possibility of producing a book that would likewise attempt to systematize inorganic chemistry. These efforts eventually resulted in his discovery of the periodic system, which is now virtually synonymous with his name.

Although it is clear that Mendeleev's periodic system was conceived while he was writing his textbook _The Principles of Chemistry_ , it is essential also to consider his shorter publications announcing the discovery of the periodic system, as well as earlier written evidence, in order to place this discovery in the wider context of his work. Many myths and legends have developed around the genesis of Mendeleev's periodic system, one of the most common being that he conceived of the idea in the course of a dream, or that it occurred to him while playing a game of patience with cards marked with the symbols of the elements. In fact, the idea took many years to mature and may have begun to do so around the time of the Karlsruhe conference, as long as 10 years before the publication of his famous table of 1869.

At the end of 1868, Mendeleev had completed the first volume of his textbook on inorganic chemistry, in which he made a systematic examination of different kinds of elements and compounds and dealt with the most common elements, such as hydrogen, oxygen, and nitrogen. He initially grouped the elements according to the valences they displayed when combining with hydrogen. This offered at least some means of organization, but at this stage there was no sign of any overarching organizing principle or any system of classification. Mendeleev ended volume 1 with a survey of the halogens and began volume 2 with a survey of the alkali metals. He was then faced with the question of which elements to treat next. As legend has it, he solved the problem in the course of a single day, in which he declined to fulfill an obligation to inspect a nearby cheese factory, instead working furiously on his new element scheme.

The question of an organizing principle had to be faced, and unlike the precursors of the periodic system, with which he was familiar, Mendeleev did not embrace either the concept of triads or the existence of a primary substance. Mendeleev knew the work of the Belgian chemist Jean-Servais Stas, for example, who had begun as an advocate of William Prout's hypothesis but, as noted in chapter 2, had become its strongest critic following a series of accurate atomic weight determinations he had himself undertaken. Mendeleev specifically refers to Staas in volume 1 of his book and expresses his distaste for Prout's hypothesis. Mendeleev's objection to a literal conception of triads is clear when he insists, also in volume 1, that rubidium, cesium, and thallium all belong to the alkali metals, along with the members of the original triad group, which are lithium, sodium, and potassium. Mendeleev is thus extending a group of elements previously thought to consist of just three elements to a group containing twice that number. In addition, he states that fluorine belongs to the halogens, thus extending the triad of chlorine, bromine, and iodine into a fourth member, a feat some others had resisted simply because it seemed to contradict the strict notion of a triad. Mendeleev thus explicitly freed himself from these pervasive general notions in order that his views might be judged on their own merit and so that the full originality of his work might be better appreciated.

On the other hand, although Mendeleev had grasped the importance of atomic weight early on, he had not fully embraced this means of characterizing the elements when he set out to write his textbook. The historian Donald Rawson, who has conducted a search of Mendeleev's views on atomic weights, finds that as early as 1855–1856, while an undergraduate at the Pedagogical Institute in St. Petersburg, Mendeleev was still using the atomic weights of Jacob Berzelius. In his master's thesis, written shortly thereafter, Mendeleev had converted to the atomic weights of Charles Gerhardt, who had halved many of the values given by Berzelius. These values in turn also contained errors, including those for oxygen and carbon, which had been halved, thus resulting in the formula of water being considered H202 and that of benzene C12H6. Both of these are quite incorrect when compared with the modern formulas of H2O and C6H6. Fortunately, Mendeleev readily abandoned Gerhardt's values when he attended the conference at Karlsruhe.

Nevertheless, it took some further time before Mendeleev had fully converted to the atomic weights of Cannizzaro. In lecture notes written between the years 1864 and 1865, for example, Mendeleev listed 53 elements but still continued to use the more outdated equivalent weights for 13 of them. By 1868, when he began writing the second volume of his textbook, he was listing 22 elements, all of them given their new atomic weights according to Cannizzaro. Whether this is a coincidence or not, it implies that by the time Mendeleev had begun consciously to work on the classification of the elements, he had fully assimilated the use of the modern atomic weights, an approach that would prove to be so essential for his discovery.

It has been claimed that it was simply in seeking a quantitative justification for ordering the elements that Mendeleev arrived at the idea of using increasing atomic weights. Although Mendeleev himself has written at some length on the genesis of his ideas, it is difficult to arrive at a clear and accurate picture of his motivations or even the course of the development of his thinking. For example, he steadfastly maintained in all subsequent writings that he did not see any of the systems developed by the five other discoverers of the periodic system, namely, De Chancourtois, Odling, Newlands, Hinrichs, and Lothar Meyer. This seems a little odd, given that he repeatedly acknowledged his debts to some earlier pioneers of the system, including Peter Kremers, Josiah Cooke, Max Pettenkofer, Jean-Baptiste Dumas, and Ernst Lenssen. Nor can it be supposed that this omission might have been due to isolation, since Russian chemistry, in particular, was rather advanced at this time, and Mendeleev had traveled in Europe and was well aware of the published literature in several languages.

Also puzzling is the suggestion made by Mendeleev himself, as well as some later commentators, that it was the realization of the need to order the elements by atomic weight that was _the_ bold and original step in the development of his system. Even if one grants that Mendeleev knew nothing of the work of the five other discoverers, surely the early precursors, whom Mendeleev so openly acknowledges, were already utilizing the concept of atomic weight in order to place the elements into some sort of order. One might rationalize this situation by recognizing that there is an important sense in which Mendeleev was indeed the first to recognize the _full_ significance of the concept of atomic weight. This question is addressed after considering Mendeleev's actual discovery and the periodic tables he produced.

### THE CRUCIAL DISCOVERY

We now consider the crucial steps that led Mendeleev to begin comparing elements horizontally (in the sense of the modern periodic table) in terms of atomic weights. There is a letter in the Mendeleev archives, dated February 17, 1869, which is also the date of the famous first table he produced. This letter, from one Alexei Ivanovich Khodnev, secretary of the Free Economic Society in St. Petersburg, to Mendeleev concerns arrangements regarding the visit to a cheese factory where Mendeleev was due to conduct an inspection. On the back of the letter, Mendeleev has made a comparison of the atomic weights of the following elements:

This is where Mendeleev is possibly trying to decide which elements to discuss after the alkali metals in his book. It could either be zinc and cadmium or the alkaline earth elements, or perhaps even both together as shown in the fragment periodic table above. In fact, this fragment may represent the first time that a horizontal comparison of the atomic weights of elements had been consciously carried out.

Another early fragment periodic system that Mendeleev produced involves a comparison of three groups of elements:

On the same day, Mendeleev appears to have realized the need also to compare all the other groups of elements horizontally, thus allowing him to arrive at his first manuscript table, as shown in figure 4.2.

And so, in the space of a single day, February 17, 1869, Mendeleev not only began to make horizontal comparisons but also produced the first version of a full periodic table that included most of the known elements. There should be no doubt, therefore, that a sudden decisive step _did_ indeed occur, even though the background ideas may have been developing over a period of about 10 years.

We turn now to Mendeleev's announcement of his discovery. Having arrived at a consistent periodic system, Mendeleev had 200 copies of his table printed and sent them to chemists in Russia and the rest of Europe. Nicolai Alexandrovich Menshutkin communicated the initial discovery to the Russian Chemical Society on March 6. Later in the same month, it appeared in print (in Russian) in the first volume of the journal of the newly formed Russian Chemical Society. The full article contained several periodic tables, and a shorter abstract was published in German a few weeks later.

This first published periodic system of Mendeleev's (figure 4.3) contains divisions into main and subgroups. The first column of elements, for example, all show valences of 1 but are divided into the alkali metals, such as lithium, sodium, and potassium, and the noble metals, including copper, silver, and gold. Significantly, there are several vacant spaces in the table, and Mendeleev proceeds even in this first publication to make several predictions, specifically anticipating "many yet unknown elements e.g. elements analogous to aluminium and silicon with atomic weights 65-75."

Mendeleev's most famous predictions would be for the elements scandium, gallium, and germanium, all of which were anticipated in the periodic tables published in this 1869 paper. He made highly accurate entries for the expected atomic weights of two of these unknown elements in the form of "? = 68" and "? = 70" in the rows containing aluminum and silicon, respectively. (The atomic weights of these new elements turned out to be gallium = 69.2 and germanium = 72, respectively.) Moreover, his "attempt at a system" of 1869 contains an entry "? = 45", which turned out to correspond to scandium with an atomic weight of 44.6, although it has been the subject of some debate whether Mendeleev's early prediction of this element can be strictly identified with scandium.

Not only did Mendeleev predict the atomic weights of his famous three new elements as early as 1869, but he also made predictions of some of their other properties. In a talk to a Moscow Congress in that same year, he suggested that two elements missing from the system would show resemblances to aluminum and silicon and would have atomic volumes of 10 or 15 and specific gravities of about 6. In the following year, 1870, Mendeleev listed the expected atomic volumes of the elements that would become known as scandium, gallium, and germanium as 15, 11.5, and 13, respectively.

FIGURE 4.2 Mendeleev's first periodic system, in draft form: photocopy of original manuscript (left), and clarified version (right). D.I. Mendeleev, _Periodicheskii Zakon: Klassiki Nauki_ , B.M. Kedrov (ed.), Izdatel'stvo Akademii nauk Soyuz sovietskikh sotsial'sticheskikh respublik, Moscow, 1958. Reproduced from J. van Spronsen, _The Periodic System of the Chemical Elements, the First One Hundred Years_ , Elsevier, Amsterdam, 1969 (by permission from Elsevier).

FIGURE 4.3 Mendeleev's published periodic system, of 1869. D.I. Mendeleev, Sootnoshenie svoistv s atomnym vesom elementov, _Zhurnal Russkeo Fiziko-Khimicheskoe Obshchestv_ , 1, 60-77, 1869, p. 70.

Another evident feature of this system is the reversal of the elements tellurium and iodine, although, as mentioned in chapter 3, this step had already been taken by Odling and Lothar Meyer, regardless of whether or not Mendeleev might have been aware of this fact. In putting tellurium before iodine, Mendeleev was departing from his general approach of ordering the elements by atomic weight. As mentioned in chapter 3, tellurium has a higher atomic weight than iodine, and yet in terms of its valence, tellurium should occur before iodine in the ordering of the elements. But apart from this particular case, Mendeleev did not maintain the use of valence as a criterion for classification as had Lothar Meyer, for example, because many elements show variable valence and because of his philosophical preference for concentrating on elements as basic substances rather than elements with manifest chemical properties, as discussed below. Some aspects of this attitude is revealed in his writing:

Not being susceptible to exact measurements, the above mentioned chemical properties can hardly serve to generalize chemical knowledge: They alone cannot serve as a basis for chemical considerations. However, the properties should not be altogether neglected as they explain a great number of chemical phenomena.

Mendeleev consequently put more faith in his newly discovered criterion for ordering the elements according to atomic weight.

Some idea of the sophistication of Mendeleev's first article, as well as the German abstract, can be seen from the list of eight points with which he ends these publications:

1. The elements if arranged according to their atomic weights, exhibit an evident _periodicity_ of properties.

2. Elements which are similar as regards their chemical properties have atomic weights which are either of nearly the same value (e.g. platinum, iridium, osmium), or which increase regularly (e.g. potassium, rubidium, caesium).

3. The arrangement of the elements, or of groups of elements, in the order of their atomic weights corresponds to their so-called _valences_ as well as, to some extent, to their distinctive chemical properties—as is apparent among other series—in that of lithium, beryllium, boron, carbon, nitrogen, oxygen and fluorine.

4. The elements which are most widely diffused have _small_ atomic weights.

5. The _magnitude_ of the atomic weight determines the character of the element, just as the magnitude of the molecule determines the character of a compound body.

6. We must expect the discovery of many yet _unknown_ elements, for example, elements analogous to aluminium and silicon, whose atomic weight should be between 65 and 71.

7. The atomic weight of an element may sometimes be amended by a knowledge of those of contiguous elements. Thus, the atomic weight of tellurium must lie between 123 and 126, and cannot be 128.

8. Certain characteristic properties of the elements can be foretold from their atomic weights. (All italics original.)

The manner and clarity with which Mendeleev makes these points are rather striking in that he makes quite explicit what many of the codiscoverers only hinted at. It also shows us clearly the depth of Mendeleev's chemical knowledge, a theme that will be further explored in chapter 5, where the manner in which he placed particular elements into his system is considered.

In the same year of 1869, Mendeleev also published a lesser known system in which the separation into main and subgroups does not feature in any way whatsoever (table 4.1). For example, the elements lithium, sodium, potassium, copper, rubidium, silver, cesium, and thallium are all just grouped together as the first horizontal row of the table. This publication, his second major one on the periodic system, appeared as a report of a meeting of the Russian chemists and is dated August 23, 1869.

In his third article, published in 1870, Mendeleev was already considering the possibility that his system had been completed, at least in principle. Among the features displayed in this article are the relocation of uranium from the boron group to the chromium group and a corresponding change in its atomic weight from 116 to 240. In addition, the atomic weight of indium is changed from 75 to 113, which allows Mendeleev to locate the element in the boron group rather than merely leaving it ungrouped at the very top of his table as he did in 1869. Other changes included cerium being given a new atomic weight and its being moved. Thallium is also given a new atomic weight. With the exception of that for uranium, all of these changes are essentially correct from a modern perspective.

TABLE 4.1  
Mendeleev's Spiral Table of 1869

Redrawn from D.I. Mendeleev, _Zhurnal Russkeo Fiziko-Khimicheskoe Obshchestvo_ , 1, 60-77, 1869. The table is located in a footnote, which begins on p. 69 and ends on p.70.

FIGURE 4.4 Mendeleev's table of 1871. English version of a table that appeared in Die periodische Gesetzmässigkeit der chemischen Elemente, Annalen der Chemie und Pharmacie, 8 (Supplementband), 133–229, 1871.

TABLE 4.2  
Mendeleev's Long-Form Periodic Table of 1879

In 1871 Mendeleev published an extensive 96-page article in German containing tables in which he grouped elements vertically (figure 4.4) as well as horizontally. It was in this article that Mendeleev spelled out his detailed predictions that, when later confirmed, were to make him famous.

In all, Mendeleev published approximately 30 periodic tables and designed a further 30 tables which remained in manuscript form. These included horizontal tables, vertical tables, helical tables, and even long-form tables. The latter are popularly thought to have originated following the introduction of quantum mechanics into chemistry and yet an example of such a table, by Mendeleev from 1879, is shown in table 4.2.

### THE NATURE OF THE ELEMENTS

This brief summary of the progression of Mendeleev's tables brings us to what I believe is the core philosophical idea at the heart of the periodic system. It is an idea so philosophically rich that it has hardly begun to be explored by modern scholars. It may perhaps be the key to many previously unanswered questions regarding the periodic system, such as why it was Mendeleev, above all others, who was prepared to venture forth to make bold predictions while others tended to be "intimidated" by the prevailing empirical data on the elements.

In the course of developing his system, Mendeleev acknowledged the question of how the elements manage to survive intact in any compound in which they might find themselves. One may consider the common example of sodium chloride, and the fact that the gray and poisonous metal sodium, and the green poisonous gas chlorine, apparently are nowhere to be found after their chemical combination to form the white crystalline compound sodium chloride.

In order to answer this question, Mendeleev appealed to a long-standing notion in chemical philosophy dating back to Aristotle. For Aristotle, the elements themselves were to be regarded as abstract even though they gave rise to all the physical variety that is observed. The four elements (fire, earth, water, air) were considered as property bearers, responsible for the tangible features of substances although they were themselves unobservable. The elements were immaterial qualities impressed on an otherwise undifferentiated primordial matter and were present in all substances. Thus, the proportion of the four elements present within a specific substance governed its properties.

This view was challenged, by, among others, Antoine Lavoisier during the course of the chemical revolution in the eighteenth century, giving rise to a "new chemistry," which drew upon the Aristotelian tradition while making important modifications. The new chemistry introduced the concepts of _simple substance_ and _material ingredient_ of substances. A simple substance was one that could not be decomposed by any known means. The inclusion of the word "known" here is very important, since the scheme proposed that simple substances were to be regarded as such only provisionally, since they might lose this status following future refinements in analytical techniques. A major departure from Aristotle's scheme was that not all substances had to contain every one of these simple substances. There was no longer thought to be one undifferentiated primordial matter but instead a number of elementary constituents, or simple substances, now possessed of observable properties.

As a result of Lavoisier's work, it became a relatively simple experimental question to determine which substances were simple and which were not, and as mentioned in chapter 1, Lavoisier and his contemporaries created a list of the 37 simple substances known at the time. One consequence of Lavoisier's scheme, however, was that abstract elements did not necessarily correspond to particular known simple substances. Since it was possible that what was regarded as a simple substance at a particular stage in history might turn out to be decomposable, one would need to have perfect confidence in one's analytical techniques to be certain of the correspondence between a simple substance and an abstract element. To his credit, Lavoisier only provisionally identified abstract elements with those simple substances that had been isolated. Such caution began to fade toward the end of the nineteenth century, however, to the extent that simple substances began to be regarded as the only form of an element, and the abstract counterpart to each simple substance was largely forgotten.

And yet the abstract/metaphysical aspect of elements was not completely neglected, continuing to serve an explanatory function in nineteenth-century chemistry, though not necessarily as a microscopic explanation. A chemist could be skeptical of atomistic explanations, as Mendeleev and many others were in the nineteenth century, and yet could readily accept a metaphysical explanation for chemical phenomena. In fact, one of the benefits of regarding the elements as having a metaphysical status is that it provides a way out of the apparent paradox, which Mendeleev was attempting to address, concerning the nature of elements when combined together in compounds. Again, with sodium chloride, one can ask in what sense the elements sodium and chlorine continue to exist in common salt. Clearly, the elements themselves, in the modern sense of the word, do not appear to survive or else they would be detectable, and one would have a mixture of sodium and chlorine that could show the properties of both these elements. The response available from the nineteenth-century element scheme is that simple substances do _not_ survive in the compound, only abstract elements do.

According to the nineteenth-century scheme, these abstract elements were believed to be permanent and responsible for the observable properties of simple bodies and compounds. However, in a major departure from the Aristotelian view, the abstract elements were also regarded as being "material ingredients" of simple bodies and compounds. This concept of material ingredient thus served to link the metaphysical world of abstract elements and the observable, material realm of simple substances. For example, the stoichiometric relationships observed in chemical changes were explained in terms of amounts of abstract elements present in the reacting substances through the agency of the material ingredient.

There are thus three important concepts regarding elements carried over into the nineteenth century. The abstract element is a property bearer and owes its heritage to the Aristotelian element scheme. In addition to being a property bearer, the abstract element is an indestructible material ingredient of substances, behaving according to Lavoisier's law of the conservation of matter. The third concept is that an abstract element is unobservable, whereas simple substances such as sodium, chlorine, and oxygen can be observed. It should be noted that in contemporary chemistry only the last notion seems to be retained, in that the term "element" is limited to what a nineteenth-century chemist would have called a simple substance.

The culmination of the nineteenth-century element scheme was reached with the discovery of the periodic system and the work of Mendeleev, who begins his book by paying tribute to Lavoisier. More than any other discoverer, Mendeleev was concerned with the philosophical status of the elements. It is an important and rather overlooked aspect of Mendeleev's approach to the periodic system that he distinguished carefully between what he terms "simple substance" and "element." Unlike the periodic law itself, which seemed to have achieved full maturity only when Mendeleev had reached the end of the first volume, the discussion of simple substance and abstract element occurs right at the beginning of the first volume and is revisited on several occasions in the course of the book:

It is useful in this sense to make a clear distinction between the conception of an element as a _separate_ homogeneous substance, and as a _material_ but invisible _part_ of a compound. Mercury oxide does not contain two simple bodies, a gas and a metal, but two elements, mercury and oxygen, which, when free, are a gas and a metal. Neither mercury as a metal nor oxygen as a gas is contained in mercury oxide; it only contains the substance of the elements, just as steam only contains the substance of ice, but not ice itself, or as corn contains the substance of the seed but not the seed itself.

For Mendeleev, the element was an entity, which was essentially unobservable but formed the inner essence of simple bodies. Whereas a particular "element" was to be regarded as unchanging, its corresponding simple body aspect could take many forms, such as charcoal, diamond, and graphite, in the case of carbon. In this respect, Mendeleev may be thought of as upholding the ancient philosophical tradition regarding the nature of elements as bearers of properties. Mendeleev's genius now lay in recognizing that just as it was the "element" that survived intact in the course of compound formation, so atomic weight was the only quantity that survived in terms of measurable attributes. He therefore took the step of associating these two features together. An element (basic substance) was to be characterized by its atomic weight. In a sense, an abstract element had acquired a single measurable attribute that would remain unchanged in all its chemical combinations. Here is a profound justification for using atomic weight as the basis for the classification of the elements, quite unlike anything produced by other discoverers or precursors of the periodic system. How else is one to make sense of Mendeleev's otherwise rather naive-sounding claim that he had realized the need to order the elements according to atomic weight given that others had done so before him? The point is that he was providing a detailed account of why this was the correct approach to take.

Mendeleev's periodic system was presented at the end of the first of the two volumes of his textbook on inorganic chemistry. His book was first published in Russian but then eventually translated into English, French, and German. The first English edition, a translation of the fifth Russian edition, appeared in 1891, that is, about 20 years after the first Russian edition. Of course, most serious chemists in Europe first heard about Mendeleev's work through published articles rather than his book. Although Mendeleev never fully revised his textbook for its successive editions, the gradual evolution of his thoughts on atomic weight and the ordering of the elements can be traced through the voluminous footnotes that were added to it at various stages.

The Japanese historian Masanori Kaji has conducted a detailed survey of all eight successive editions of Mendeleev's book in the original Russian. By studying the first Russian edition, which was never translated, Kaji argues that Mendeleev began his textbook by using the concept of valency as a means of ordering the elements. This is clearly revealed in the fact that Mendeleev considers the following elements in order: hydrogen, oxygen, nitrogen, and carbon, whose valences are 1, 2, 3, and 4, respectively.

Then Mendeleev turns to the halogens, beginning again with the valence of 1. These are followed by a consideration of the alkali metals, also of valence 1, and then the divalent alkaline earths. As mentioned above, it was while making the transition between the alkali metals and the alkaline earths that Mendeleev appears to have made the crucial discovery that allowed him to produce the periodic system. Essentially, he realized that the key to classifying the elements was not valency but atomic weight. Now, of course, many previous chemists had been aware of this fact either implicitly or explicitly in proposing tables based on triads or differences between atomic weights of the elements. Nevertheless, Mendeleev added an important ingredient in realizing the possibility of comparing chemically dissimilar elements or, as one might say with hindsight, comparing elements placed horizontally in the present form of the periodic table. As Mendeleev states:

The purpose of my paper would be entirely attained if I succeed in turning the attention of investigators to the very relationships in the size of the atomic weights of nonsimilar elements, which have, as far as I know, been almost entirely neglected until now.

Kaji claims that at least three noted authorities on the periodic system have been mistaken in proposing that Mendeleev deliberately refrained from revising successive editions of his textbook in order to show his readers how his ideas evolved over time. Some of these authors have even proposed that we should ignore what Mendeleev himself says about the genesis of his periodic system and that we should trace the development of his ideas in the textbook itself, in all its permutations. But this suggestion is rather unconvincing since Mendeleev may have simply been too busy to undertake a thorough revision of the textbook, especially given his many and widely scattered interests. Perhaps we should also be less inclined to dismiss Mendeleev's own accounts of how he arrived at the periodic system. Clearly, this topic has not yet been sufficiently researched by Mendeleev scholars.

What still remains unexplained is why Mendeleev did not completely revise the first part of the book to comply with the way the elements were arranged in his newly discovered periodic system. In the third edition, the second of the two volumes was rearranged so that the discussion of the elements would follow the sequence in which they appear in the periodic system. There has been some debate as to whether this should be considered a major reorganization, but clearly the third edition bears some signs of the discovery of the periodic system. Indeed, it would also have been rather surprising if later editions of Mendeleev's book had borne absolutely no benefits from his discovery of the periodic system.

The fifth edition of _The Principles of Chemistry_ , which appeared in 1889, is of particular importance to Western scholars since it was the first one to be translated into English, French, and German. It contains some changes from the previous editions, but still, these are not substantial enough to constitute a major revision. Three further editions, the sixth, seventh, and eight, were published, and a few changes were made to these editions. For example, in the seventh edition of 1903 the recently discovered element argon was incorporated into the periodic system but discussed in the course of the chapter on nitrogen and the air, presumably because argon was first isolated in small amounts from samples of nitrogen. Mendeleev also mentions the newly isolated element radium, while denying any possibility of transmutation of elements and while attempting to explain the phenomenon of radioactivity by appealing to the ether. Moreover, Mendeleev, who had struggled with the placement of the rare earth elements for an extended period of time, finally relinquished all attempts to do so to the Czech chemist Bohuslav Brauner, who contributed the chapter on the rare earths in the last edition of Mendeleev's book. In this, the eighth and final edition to be published during Mendeleev's lifetime, all footnotes are finally separated from the main text and placed in the second half of the book.

### MAKING PREDICTIONS

Lothar Meyer and others preceded Mendeleev in predicting the existence of unknown elements, but it is beyond dispute is that Mendeleev made far more extensive predictions than any of the codiscoverers of the periodic system. Not only did he successfully predict new elements, but he also corrected the atomic weights of a number of known elements, as well as correctly reversing the positions of the elements tellurium and iodine. Why was it Mendeleev who was able to make such striking predictions and not Lothar Meyer or others? Is it simply that the others lacked the courage to do so, as many historians of science state? I want to suggest that Mendeleev's advantage lay in his philosophical approach to chemistry, for it allowed him to arrive at insights his less philosophically minded contemporaries could not have entertained.

Mendeleev realized that abstract elements were to be regarded as more fundamental than simple substances. The explanation of why "elements" persist in their compounds was to be found in abstract elements and not simple substances, and as a consequence, if the periodic system were to be of fundamental importance, it would primarily have to classify the abstract elements. The predictions Mendeleev made were thus conceived of with the abstract elements in mind. If the available observational data on simple substances pointed in a certain direction, these features could be partly overlooked in the belief that the properties of the more fundamental abstract elements might be different from what had been observed up to that point in the form of a particular "simple substance." Of course, any prediction must eventually be realized by the isolation of a corresponding simple substance, precisely because "elements," in the more subtle sense of the term, are beyond observation. This requirement presented no problem to Mendeleev, however, for he believed that elements possess one significant and measurable attribute, namely, their atomic weight. In other words, his predictions of abstract elements could be identified empirically through their material ingredient in the form of their atomic weights. As noted above, Mendeleev believed that atomic weight was the one property that does not change when an element combines to form compounds, whereas all the other properties of simple substances seem to be radically altered upon chemical combination.

Because he was attempting to classify abstract elements, not simple substances, Mendeleev was not misled by nonessential chemical properties. For example, the elements in the halogen group (fluorine, chlorine, bromine, and iodine) appear to be rather different from each other when one focuses on them as isolable simple substances, since they consist of two gases, a liquid, and a solid, respectively. The similarities among the members of the group are more noticeable when considering the compounds each one forms with sodium, for example, all of which are crystalline white powders. The point is that in these compounds, fluorine, chlorine, bromine, and iodine, are present not as simple substances but in a latent, or essential, form as basic substances.

Thus, his view of the elements allowed Mendeleev to maintain the validity of the periodic law even in instances where observational evidence seemed to point against it. Such boldness may have resulted from a deeply held beliefs that the periodic law applied to the abstract elements as basic substances and that this law was as fundamental and equal in status to Newton's laws of mechanics. Had he been more of a positivist, Mendeleev might easily have lost sight of the importance of the periodic law and might have harbored doubts about some of his predictions.

On one of the few occasions that Mendeleev allowed himself to express his philosophical views, he wrote of the relationship between "matter, force, and spirit." He claimed that contemporary philosophical problems stemmed from a tendency to search for one unifying principle, while he favored three basic components of nature: matter (substance), force (energy), and spirit (soul). Everything was composed of these three components, and no one category could be reduced to any of the others. According to Michael Gordin, Mendeleev's use of "spirit" amounts to the modern notion of essentialism, or that which is irreducibly peculiar to the object in question. Gordin also adds that Mendeleev's position is clearly metaphysical, thus removing him from the "companionship of positivists" and thus consistent with the position adopted by the present author.

### MENDELEEV AS REDUCTIONIST?

Whereas Mendeleev was clearly ahead of his competitors when it came to the prediction of elements, he does not seem to have fared so well with regard to his views on the reduction of chemistry. Textbooks often wax lyrical about the manner in which it is now believed the periodic system is dependent upon the electronic structure of atoms, whereas Mendeleev was concerned almost exclusively with chemical properties. Sometimes the fact that Mendeleev could construct the periodic system merely from considering chemical properties is marveled at in a rather patronizing fashion. Textbook accounts typically express surprise that he was able to deduce the periodic system from such apparently crude data. But as I have argued here, Mendeleev did not primarily classify the elements according to chemical properties.

More specifically, Mendeleev's denial of the reduction of chemistry has generally been held to be mistaken, especially in view of the subsequent discoveries of radioactivity and the structure of the atom. That historians of chemistry have reached such a conclusion is not at all surprising, especially given some of Mendeleev's own pronouncements on the subject. In his Faraday lecture, delivered at the Royal Institution in London, he said:

[T]he periodic law... has been evolved independently of any conception as to the nature of the elements; it does not in the least originate in the idea of a unique matter; it has no historical connection with that relic of the torments of classical thought.

Here Mendeleev is expressing his opposition to one kind of reductionism, namely, the reduction of all matter to one form of matter, as in Prout's hypothesis.

In other instances, Mendeleev appears to express views on an altogether different form of reductionism. This is the view that elements, or atoms of the elements, in modern terms, can be broken down:

By many methods founded both on experiment and theory, has it been tried to prove the compound nature of the elements. All labour in this direction has as yet been in vain, and the assurance that elementary matter is not so homogeneous (single) as the mind would desire in its first transport of rapid generalization is strengthened from year to year.

Not only did Mendeleev deny that all elements could be reduced to one form of matter, namely, hydrogen, as in Prout's view, but he also denied that the various elements would be found to be composed of more universal building blocks. But modern physics has revealed that the atoms of the elements do indeed have a "compound" nature, since they are composed of protons, neutrons, and electrons. Moreover, the nucleus of the atom, which in simple terms contains just protons and neutrons, has been found to give rise to a staggering 300 or so subnuclear particles. Needless to say, Mendeleev could not have known of these developments.

In emphasizing atomic weight as the key criterion for ordering the elements, Mendeleev also relegates chemical properties to a certain extent. Depending on how much importance one is prepared to place on this feature, Mendeleev might be viewed as a direct precursor to the modern reductionist tendency in chemistry. This is the tendency that reached greater heights in the 1920s and 1930s via the implementation of quantum mechanics, which continues to this day. Mendeleev's emphasis on atomic weight, above all else, might thus be regarded as a classic example of reductionism that places him in the vanguard of the twentieth-century approach to science rather than at the tail end of the classical chemical tradition, where some authors believe that he belongs.

There are many kinds of reductionism. Mendeleev may not have believed in the unity of all matter, but he was an influential proponent of the reduction of chemistry to physics in another sense, that is, in attaching great importance to physical data concerning the elements and especially their atomic weights. Indeed, it was the essence of his achievement that he elevated the ordering of the elements by atomic weight to the status of a law, protecting his emerging periodic system from the uncertainties of the chemical knowledge of his time. At the same time, Mendeleev's understanding of the individual chemical natures of the elements, and their compounds, was profound. This understanding gave him an intuitive sense of how the elements should be grouped. In fact, it can be argued that, although his views on the compound nature of elements and their atoms would turn out to be incorrect, Mendeleev would not have needed to change his position on the basis of current knowledge. As Fritz Paneth suggests,

Yet I believe that something very essential in his [Mendeleev's] fundamental philosophical tenets would have remained untouched by the progress in physics and could be successfully defended even today; and it is just these "philosophical principles of our science" which he regarded as the main substance of his textbook.

This resolution can be appreciated by realizing that Mendeleev adopted an intermediate position between realism and reduction to physics. Even though physics has revealed that atoms of the elements can be decomposed, it is still the case that chemists can continue to ignore this deeper structure for many chemical purposes. This is the essence of Mendeleev's intermediate position, whereby it is more useful to regard the elements as having distinct identities and yet as also being decomposable into the same fundamental particles such as protons and electrons, in modern terms. It is the view that every science can decide for itself the level at which it should operate and that the deepest foundations are by no means always the best for every purpose.

As the French philosopher Gaston Bachelard, who began his career as a physical chemist, has written,

La pensée du chimiste nous parait osciller entre le pluralisme d'une part et la reduction du pluralisme d'autre part. (The chemist's thinking seems to oscillate between pluralism on one hand, and the reduction of pluralism on the other hand.)

Mendeleev, the creator of the periodic system of the elements, drew the philosophical distinction between basic substances (abstract elements) and simple substances. He cannot, therefore, be regarded as a naive realist. However, having arrived at the periodic classification by giving emphasis to abstract elements, he resisted the prevalent reductionist tendency of supposing the existence of a primary matter. He considered the elements as distinct individuals and adopted an intermediate position between realism and reduction. This may be Mendeleev's true legacy. Perhaps it can provide the foundation of a genuine "philosophy of chemistry," which is as relevant today as ever, though it has been largely neglected.

## **CHAPTER 5  
PREDICTION AND ACCOMMODATION**

### _The Acceptance of Mendeleev's  
Periodic System_

Although periodic systems were produced independently by six codiscoverers in the space of a decade, Dimitri Mendeleev's system is the one that has had the greatest impact by far. Not only was Mendeleev's system more complete than the others, but he also worked much harder and longer for its acceptance. He also went much further than the other codiscoverers in publicly demonstrating the validity of his system by using it to predict the existence of a number of hitherto unknown elements.

According to the popular story, it was Mendeleev's many successful predictions that were directly responsible for the widespread acceptance of the periodic system, while his competitors either failed to make predictions or did so in a rather feeble manner. Several of his predictions were indeed widely celebrated, especially those of the elements germanium, gallium, and scandium, and it has been argued by many historians that it was such spectacular feats that assured the acceptance of Mendeleev's periodic system by the scientific community.

The notion that scientific theories are accepted primarily if they make successful predictions seems to be rather well ingrained into scientific culture, and the history of the periodic table has been one of the episodes through which this notion has been propagated. However, philosophers, and some scientists, have long debated the extent to which predictions influence the acceptance of scientific theories, and it is by no means a foregone conclusion that successful predictions are more telling than other factors.

In looking closely at the bulk of Mendeleev's predictions in this chapter, it becomes clear that, at best, only half of them proved to be correct. This raises a number of questions. First of all, why is it that history has been so kind to Mendeleev as a maker of predictions? As historian of chemistry William Brock has pointed out, "Not all of Mendeleev's predictions had such a happy outcome; like astrologers' failures, they are commonly forgotten." To put the question another way, why is it that Mendeleev's successful predictions served to bolster the validity of his system while his unsuccessful ones failed to undermine it?

If we accept that it was his predictions that carried the most weight in the acceptance of Mendeleev's periodic system, then we are at a loss to answer this question. But perhaps, as some have argued, it is by no means established that prediction is the single most important factor in demonstrating the validity of a new scientific idea. In fact, rather than proving the value of prediction, the development and acceptance of the periodic table may provide us with a powerful illustration of the importance of accommodation, that is, the ability of a new scientific theory to explain already known facts.

From the time he first published his mature periodic system, in 1869, Mendeleev began to predict the existence of specific unknown elements and also to correct the values of atomic weights of already known elements. Both of these forms of prediction were essential to the refinement of his system and are examined in the course of this chapter. Although the prediction of new elements and the correction of atomic weights of existing elements both represent forms of predictions, they are of a somewhat different character, an aspect that will be explored. The historian Stephen Brush has coined the apt phrase "contrapredictions" to describe the correction of already known elements., He, too, believes that they represent a different category from the prediction of previously unknown elements.

The questions examined in this chapter are (1) whether the prediction of new elements by itself was such a decisive factor in the acceptance of Mendeleev's system, as the popular accounts would have it, and (2) whether successful predictions in general (new elements and contrapredictions) had significantly more impact than did successful accommodations (the fitting of elements into the periodic system).

Mendeleev's extraordinary proficiency as a chemist, combined with his unwavering belief in atomic weight as the supreme ordering principle among the elements, guided him in developing his system. His genius lay in his ability to sift intuitively through the mass of correct and incorrect knowledge of the elements that had accumulated, to produce a system, an _idea_ , that was both elegant and durable enough to withstand the chemical and physical discoveries that would follow its introduction.

#### MENDELEEV'S APPROACH

Mendeleev can be distinguished from his competitors by a devotion to, and love for, the individuality of the elements that went hand in hand with an intimate knowledge of their chemical characteristics. Whereas Julius Lothar Meyer, for example, seemed more concerned with physical properties in his own quest to arrive at a periodic classification, Mendeleev's approach can be described as a "natural history" of the elements. The depth of knowledge of the elements that Mendeleev possessed was something most of today's chemists could not match.

Contrary to many myths and legends, which would have us believe that Mendeleev arrived at the periodic system by juggling with playing cards and by tinkering with values of atomic weights, this was only a small part of the story. The real work consisted in being very familiar with the chemical and physical properties of the building blocks from which the periodic system was to be fashioned. Mendeleev was expert in such matters and knew what kinds of salts all the elements were capable of forming and which reagents could be used to obtained precipitates from their salts. These and countless other details were synthesized and carefully weighed as evidence when he was deciding where to place any particular element.

It is important to understand Mendeleev's modus operandi regarding the placement of elements in the periodic system if we are to appreciate the motivation for many of his corrections of atomic weights and his predictions of unknown elements. Mendeleev considered a number of criteria in addition to atomic weight ordering, such as family resemblance among elements and the concept of the single occupancy of elements in any space in the periodic table. However, all these criteria could be, and often were, overridden as individual cases presented themselves to him.

Family resemblance among the elements was very important to Mendeleev. He looked for chemical similarities as revealed by reactions with other elements, the nature of salts, precipitation reactions, and the acid-base chemistry of the elements. In contrast to the approach of Lothar Meyer, Mendeleev believed chemical properties should take precedence over physical criteria, with the important exception of atomic weight, of course. Lothar Meyer had established his own periodic system by concentrating predominantly on physical resemblance in properties, such as atomic volumes, densities, and fusibilities. For Mendeleev, it was so important that chemically similar elements be grouped together that he was willing to violate the concept of single occupancy, according to which each place in the periodic table may contain only a single element. This was the case in what he labeled group VIII of his table, where sets of three elements, for example, iron, cobalt, and nickel, occupied what should have been several single spaces.

The strictest criterion Mendeleev employed was that of the ordering of elements according to increasing atomic weight. As noted in chapter 4, he had stronger philosophical reasons than the other discoverers of the periodic system for insisting on the fundamental role of atomic weight, so much so that he was willing to try to bend nature to fit his grand philosophical scheme. He would occasionally seem to violate even this principle, however, in cases where the chemical character of an element seemed to demand it. An example is his placement of tellurium before iodine, as the atomic weight of tellurium has the higher value of the two elements. But while making this reversal, Mendeleev did not just disregard the issue of atomic weight, but rather insisted that the atomic weight of at least one of these elements had to have been determined incorrectly, and that future experiments would eventually reveal an atomic weight ordering in conformity with his placement of tellurium before iodine. Thus, Mendeleev's main guiding principle was that any apparent misplacement of an element in his original system, or those of others, was primarily the result of an incorrect atomic weight having been assigned to that element.

In some cases, Mendeleev would correct the atomic weights of a misplaced element, but there were also cases where he considered it sufficient to move an element in order to reflect more faithfully certain family resemblances, without changing the atomic weight in question. This is what he did with mercury, which he came to regard as an analogue of zinc and cadmium rather than of copper and silver, as he had done in his earliest tables.

There are many elements over which Mendeleev deliberated for considerable periods of time and published several accounts. These include indium, erbium, and lanthanum, all of which involved subtle arguments having to do with atomic weight corrections, some of which are examined below.

#### CORRECTING ATOMIC WEIGHTS

Correcting the atomic weight of an element sometimes involved changing the multiple employed for obtaining its atomic weight from its equivalent weight. The repositioning of elements by this method of atomic weight change would prove to be particularly successful for Mendeleev. In adopting an alternative multiple of the equivalent weight, what Mendeleev was doing was adopting an alternative valence for certain elements, in view of the relationship

atomic weight = valence × equivalent weight

In some cases, the valence of an element could be determined only indirectly through group resemblance. This approach was used by Mendeleev in the cases of beryllium, uranium, indium, and thorium, among others. Any suggested changes in group resemblance had to be carefully considered in order to determine whether the resulting change in valence, and hence atomic weight, was really warranted. For example, in the case of uranium, the element did not form any compounds with hydrogen, thus removing any possibility of arriving at its valence in the most direct manner. With other elements uranium shows valences of 2, 3, 4, 5, 6, and even 8, variable valence being a common characteristic of transition metals. Mendeleev had to rely on uranium's other forms of chemical behavior to determine its group and to give it a primary valence of 4.

In other cases, Mendeleev called for a small adjustment in the equivalent weight, which in turn led to corresponding small changes in the value of the atomic weight on multiplication by the appropriate valence. Examples of this kind included titanium, tellurium, iodine, platinum, gold, cobalt, nickel, and potassium. The case of titanium is rather interesting because the element already had a secure place in the periodic table according to atomic weight ordering as well as in terms of family resemblances with other elements. Nevertheless, Mendeleev chose to alter its atomic weight from 50 to 48 in order to create greater regularity among differences between the values of consecutive elements ordered by atomic weight. Whether such regularity can be regarded as another criterion of Mendeleev's is open to question, given that he appears to have used it only in this single case. But the fact remains that Mendeleev was correct since the modern value for titanium is indeed closer to 48 than it is to 50. Mendeleev's uncanny sense for correcting atomic weights, which often seemed to defy logical reconstruction, served him well in this and other cases.

#### BERYLLIUM

The placement of the metal beryllium provided one of the most severe tests for Mendeleev's system. Its case proved to be historically significant because it involved a controversy that lasted a considerable period of time, ending with the complete vindication of Mendeleev's position. The question was whether the element should be assigned a valence of 2 or 3, which would affect its atomic weight and thus would in turn govern the position it took in the periodic table.

Stanislao Cannizzaro's method for determining atomic weights was not easy to apply to the metallic elements, as it required volatile compounds. Instead, other methods continued to be used for metals. One important way of obtaining atomic weights was through the 1819 law of Pierre-Louis Dulong and Alexis-Thérèse Petit. As discussed in chapter 2, these authors had found an approximate relationship between the specific heat and atomic weight of a solid element to be

atomic weight X specific heat = a constant = 5.96

The measured specific heat of 0.4079 for beryllium indicated an atomic weight of 14.6, which would place the element in the same group as the trivalent aluminum.

In addition to atomic weight, there were other reasons to place beryllium with aluminum. Clues to beryllium's valence could be obtained by combining it with oxygen to create an oxide. Metal oxides or hydroxides dissolve in water to form bases, while nonmetal oxides or hydroxides dissolve in water to form acids. Moreover, the chemical characteristics of the oxides generally provide an approximate indication of the valence of the metal concerned according to certain rules. These are summarized below for any metal in general, denoted as M:

Beryllium oxide is weakly basic, with a metallic structure unlike that of magnesium, and beryllium chloride is volatile just like aluminum chloride. Taking these facts together, the association of beryllium with aluminum appears to be compelling.

In spite of all this evidence, Mendeleev supported the view that beryllium is divalent using arguments that were purely chemical, as well as arguments based on the periodic system. He pointed out that beryllium sulfate presents a greater similarity to magnesium sulfate than to aluminum sulfate and that, whereas the elements analogous to aluminum form alums, beryllium fails to do so. He also argued that if the atomic weight of beryllium were about 14, it would not find a place in the periodic system. Mendeleev noted that such an atomic weight would place beryllium near nitrogen, toward the right side of the table, where it should show distinctly acidic properties and have higher oxides of the type Be2O5 and BeO3, which is not the case. Instead, Mendeleev argued that the atomic weight of beryllium might be approximately 9, which would place it between lithium (7) and boron (11) in the periodic table, and thus put it in group II.

In 1885, the issue was finally settled conclusively in favor of Mendeleev by measurements of the specific heat of beryllium at elevated temperatures. The specific heat of any element increases with temperature, and as a result, the constant value that appears in Dulong and Petit's law is achieved only if the measurements are carried out at high temperatures. This became appreciated soon after the discovery of Dulong and Petit's law and allowed more accurate measurements of atomic weight to be made. Further experiments with beryllium pointed to an atomic weight of 9.0, in reasonable agreement with Dulong and Petit's law, and supported the divalence of the element as Mendeleev had argued.

#### URANIUM

One of Mendeleev's boldest atomic weight changes was in the case of uranium, where the atomic weight was changed by a whole multiple. The element uranium was first isolated in 1841 by Eugéne Peligot in France. In his famous first table of 1869, Mendeleev placed the element, with its assumed weight of 116, between cadmium at 112 and tin at 118, thus making it a chemical analogue of boron and aluminum in group III of the table.

Mendeleev avoided using Cannizzaro's atomic weight of 120 for uranium, for such a value would not have allowed him to place it in the periodic table. If uranium had an atomic weight of 120, it would need to be placed between tin (118) and antimony (122). These two elements show valences of 4 and 3, respectively, and so the inclusion of uranium between them would have violated the gradual decrease in valence on moving across the elements in group IV through group VII. In addition, the placement of both tin and antimony appeared quite secure and in little doubt. Tin was in the same group as silicon and lead, both of which show valences of 4, and antimony was in the same group as phosphorus, arsenic, and bismuth, all of which show valences of 3.

In an early manuscript table, Mendeleev designated uranium as "U 120" and listed it outside the table at the foot of the page. Later he crossed this out and replaced it with "U 116?" placed in the main body of the table between cadmium and tin. This place should have been filled by the element indium, but Mendeleev also initially misplaced this element because he wrongly assumed that its atomic weight was 75.6.

In the spring of 1869, Mendeleev personally undertook the experimental study of the atomic volume of uranium with the object of resolving the uranium problem. He decided that the element did not in fact fit between cadmium and tin, and considered that Cannizzaro's value of 120 might indeed be correct. Now he was back where he had started, with no place for uranium in the table, so he suggested again that perhaps there had been an error in the determination of its atomic weight. This time he proposed that the value should be doubled because the high density of uranium (18.4) was typical of heavy-atomic-weight elements such as platinum (197), osmium (199), and iridium (198). He then set his assistant Bohuslav Brauner the task of measuring the specific heat of uranium, but since the results were somewhat inconclusive, Mendeleev announced the atomic weight modification without the support of experimental evidence.

In conceptual terms, the doubling of Cannizzaro's value was not as great a leap as it might appear. Since atomic weight is a product of valence and equivalent weight, all that was required in doubling uranium's atomic weight was for its valence to be regarded as double of what it was previously thought to be namely, six instead of three. Mendeleev argued that uranium, which forms UO3, is analogous to chromium, which forms CrO3. He therefore began grouping uranium with chromium.

In late 1870, Mendeleev actually placed "U = 240" for the first time in the periodic table. Experimental support for the corrected atomic weight of uranium came later, in 1874, from Henry Roscoe in England. It took its place as a higher chemical analogue of chromium, molybdenum, and tungsten, where it remained throughout the rest of Mendeleev's life and indeed until the middle of the twentieth century. Eventually American chemist Glenn Seaborg's discovery of the actinide series prompted a major readjustment of the periodic table, which included the repositioning of uranium.

#### TELLURIUM AND IODINE

The case of tellurium and iodine is one of only four pair reversals in the periodic system and the best known among them. Many historical accounts make a point of recounting how astute Mendeleev was to reverse the positions of these elements, thus putting chemical properties over and above the ordering according to atomic weight. In doing so, these accounts err in several respects. First of all, Mendeleev was by no means the first chemist to make this particular reversal. As mentioned in chapter 3, William Odling, John Newlands, and Lothar Meyer all published tables in which the positions of tellurium and iodine had been reversed, well before the appearance of Mendeleev's articles. Second, Mendeleev was not, in fact, placing a greater emphasis on chemical properties than on atomic weight ordering in this case. Mendeleev held to his criterion of ordering according to increasing atomic weight and repeatedly stated that this principle would tolerate no exceptions. Mendeleev's thinking regarding tellurium and iodine was rather that the atomic weights for one or both of these elements had been incorrectly determined and that future work would reveal that even on the basis of atomic weight ordering tellurium should be placed before iodine. On this point, as in many instances that tend to go unreported, Mendeleev was wrong.

But let us look into the historical sequence of events regarding tellurium and iodine, since it is only by examining the circumstances closely that the reader can obtain a clear notion of the nature of the work in which Mendeleev and other pioneers of the periodic system were engaged. At the time when Mendeleev proposed his first periodic systems, the atomic weights for tellurium and iodine were thought to be 128 and 127, respectively. Mendeleev's belief that atomic weight was the fundamental ordering principle meant that he had no choice but to question the accuracy of these two values. This was because it was clear that, in terms of chemical similarities, tellurium should be grouped with the elements in group VI and iodine with those in group VII or, in other words, that this pair of elements should be "reversed." Mendeleev continued to question the reliability of these atomic weights until the end of his life. This was one problem he was not able to solve.

Initially, he doubted the atomic weight of tellurium while believing that that of iodine was essentially correct. Mendeleev began to list tellurium as having an atomic weight of 125 in some of his subsequent periodic tables. At one time, he asserted that the commonly reported value of 128 was the result of measurements having been made on a mixture of tellurium and a new element he called eka-tel-lurium. Prompted by these pronouncements, Bohuslav Brauner began a series of experiments in the early 1880s aimed at the redetermination of the atomic weight of tellurium. By 1883, he was able to report that the value for tellurium should be 125. Mendeleev was duly sent a telegram of congratulations by other participants present at the meeting at which Brauner had made this announcement. In response, Mendeleev went as far as to list Brauner as one of the four "consolidators" of the periodic law in 1886. In 1889, Brauner obtained new results that seemed to further strengthen the earlier finding that the atomic weight of tellurium is 125.

But in 1895, everything changed as Brauner himself began reporting a new value for tellurium that was greater than that of iodine, thus returning matters to their initial starting point. Mendeleev's response was now to begin to question the accuracy of the accepted atomic weight value for iodine instead of tellurium. This time he requested a redetermination for the atomic weight of iodine and hoped that its value would turn out to be higher. In some of his later periodic tables, Mendeleev listed tellurium and iodine as both having atomic weights of 127. Clearly, the real story is far more complicated than is usually reported, and in the final analysis, it does not appear to further Mendeleev's reputation very much, since the atomic weight of tellurium simply _is_ higher than that of iodine. The problem would not be resolved until 1913 and 1914 by Henry Moseley, who showed that the elements should be ordered according to atomic number rather than atomic weight. While tellurium has the higher atomic weight than iodine, it has a lower atomic number, and this is why it should be placed before iodine in agreement with its chemical behavior.

#### MENDELEEV'S PREDICTIONS

As is well known, Mendeleev successfully predicted the existence of several unknown elements. He arrived at his conclusions mainly through interpolation among atomic weights as well as among other chemical and physical properties. In a few cases he also used extrapolations, but only while warning of the less secure basis of this form of activity, since there is no guarantee that the trend shown among the measured data points will extend into regions where no measurements have been made.

In the case of interpolations, Mendeleev was attempting to fill in prescribed gaps in the table among elements that had already been placed and in many cases were well characterized. In his earliest periodic tables, of 1869, these unknown elements were represented by dashes or a predicted atomic weight value accompanied by a question mark, for it was clear to Mendeleev that there must be elements that would fill these gaps. As described below in some detail, Mendeleev was able to predict many of the characteristics of these unknown elements very successfully. By contrast, extrapolating the existence of unknown elements was a much more tenuous process, and there was no assurance that this was warranted. Mendeleev would later make use of such extrapolations and, not surprisingly, was rather unsuccessful in these cases.

Mendeleev first focused on two gaps in the periodic table, one below aluminum and one below silicon, and proposed to fill them with new elements. Such gaps were more or less demanded by the vertical grouping of the known elements that surrounded them. The known elements could not be moved round at will because they had to fit together according to chemical similarities. Gaps in the horizontal sequence of increasing atomic weights might also suggest the presence of a missing element, though not as reliably since the increase in atomic weights is not perfectly uniform even among a complete sequence of known elements.

The first hint of these famous predictions was published along with his original table of 1869, when Mendeleev declared, "We must expect the discovery of yet unknown elements, e.g. elements analogous to Al and Si, with atomic weights 65-75". In a talk to the Moscow Congress of the Russian Scientists and Physicians a couple of months later, Mendeleev stated that "those two elements which are still missing from the system and which show a resemblance to Al and Si, and have atomic weights of about 70, will have atomic volumes of 10 or 15, i.e. will have specific gravities of about 6," but he thought the lighter of these two might be indium, a known element.

In the autumn of 1870, Mendeleev had also begun to look for an element analogous to boron, and he listed the atomic volumes of these three elements to be Subsequent manuscripts listed the atomic weights for these three elements as 44, 68, and 74, respectively, and a little later as 44, 68, and 72.

In early 1871, Mendeleev published a list of detailed predictions on each element for the first time. It was also in this paper that he now referred to them provisionally as eka-boron (scandium), eka-aluminum (gallium), and eka-silicon (germanium). These were his most celebrated cases, and he was able to predict their chemical and physical properties to an astonishing degree. It would take 15 years from the time of these detailed predictions for all three of these new elements to be isolated and characterized, but in the end Mendeleev would be almost completely vindicated.

Mendeleev could interpolate many of the properties of his predicted elements by considering the properties of the elements on each side of the missing element and hypothesizing that the properties of the middle element would be intermediate between its two neighbors. Sometimes he took the average of all four flanking elements, one on each side and those above and below the predicted element. This interpolation in two directions was the method he used to calculate the atomic weights of the elements occupying gaps in his table, at least in principle.

In the various editions of his textbook, and in the publications dealing specifically with his predictions, Mendeleev repeatedly illustrates his method using the known element selenium as an example. The atomic weight of selenium was known at the time and so could be used to test the reliability of his method. Given the position of selenium and the atomic weights of its four flanking elements: the flanking atomic weights can be averaged to yield approximately the correct value for the atomic weight of selenium:

(32 + 75 + 80 + 127.5)/4 = 79

However, Mendeleev did not always operate according to this clear procedure, even in the case of some of his most famous predictions. For example, if his method is applied to predicting the atomic weights, atomic volumes, densities, and other properties of gallium, germanium, and scandium, it produces values that differ significantly from those Mendeleev actually published. Employing Mendeleev's stated method of taking an average of the atomic weights of four flanking elements around gallium, using the atomic weights available at the time, gives a prediction of 70.9. In fact Mendeleev modified this value to "about 69" by means of a more complicated averaging method that he explained only briefly in a single German publication. The accepted value of the atomic weight of gallium at the time of its discovery was 69.35.

Table 5.1 contains Mendeleev's predicted properties of eka-aluminum, subsequently named gallium, as well as the observed properties of the element.

#### THE DISCOVERY OF GALLIUM

Eka-aluminum, or gallium as it was subsequently called, was discovered by French chemist Emile Lecoq De Boisbaudran in 1875. De Boisbaudran had been studying the spectra of the elements for a period of 15 years prior to making the discovery. He was aware of the fact that elements in the same family, or group, show the same general spectral features. De Boisbaudran did _not_ discover gallium as a result of testing Mendeleev's prediction, however. Instead, he operated quite independently by empirical means, in ignorance of Mendeleev's prediction, and proceeded to characterize the new element spectroscopically. After working with 52 kg of zinc blende for a period of about 18 months, De Boisbaudran was able to observe a few spectral lines that had never been observed before, although he was unable to isolate the element. But following a further three months of work, using an additional several hundred kilograms of the same ore, De Boisbaudran isolated about a gram of the new element and reported his findings in the _Comptes Rendus de L'Académie des Sciences_.

On reading a Russian translation of this paper, Mendeleev sent a note to the journal claiming that this was the element he had predicted and provisionally named eka-aluminum. De Boisbaudran at first reacted suspiciously to this claim, apparently believing that Mendeleev was asserting priority over the discovery of the element. He initially maintained that his own element had significantly different properties from those of the element predicted by Mendeleev, although he later changed his mind on this score. De Boisbaudran did, however, continue to insist that his discovery of gallium involved empirical techniques quite separate from anything related to Mendeleev's work and that prior knowledge of it would, if anything, have hindered his discovery of the new element. He named the new element gallium after the Latin for France. As it turned out, the remaining two of Mendeleev's three famous predictions would also result in new elements named from other European countries, namely eka-boron, which became scandium, and eka-silicon, which was named germanium.

In a note to the French journal, Mendeleev repeated some of his earlier predictions and made several new ones. Interestingly, one of these newer predictions was rather dubious, and it is surprising that Mendeleev should have claimed it as a prediction. He claimed to predict that eka-aluminum oxide would be precipitated from aqueous solutions of eka-aluminum salts by barium carbonate. In fact, Mendeleev already knew that this was the case for the simple reason that it had already been reported by De Boisbaudran and, worse yet, Mendeleev himself had acknowledged this observation of the precipitation by BaCO3 in a published note!

On a quite separate issue, Mendeleev had predicted in 1871 that eka-aluminum, or gallium, would "in all respects" have properties intermediate between those of the elements above and below it, namely, aluminum and indium. However, the melting point of gallium (30°C) is nowhere close to being intermediate between those of aluminum (660°C) and indium (155°C). In 1879, Mendeleev gave what appears to be an ad hoc rationalization of the anomalously low melting point for gallium. He first emphasized that gallium does indeed have an anomalously low melting point and that it can even melt in the hand. He then claimed that this was not unexpected since it could be rationalized by looking at trends within groups of elements on either side of the group containing gallium.

At this point, Mendeleev gives this fragment table: and claims that for the group containing magnesium, zinc, and cadmium, the element with the lowest atomic weight, magnesium, has the highest melting point. On the other hand, Mendeleev states that in the case of the group at the right-hand side of this fragment table, it is the element with the highest atomic weight, namely, iodine (J), that has the highest melting point.

Mendeleev then makes an almost comical claim that elements falling in a group between these two groups should show intermediate behavior in that it should be the middle element of the group that shows the lowest melting point. This is supposed to explain why gallium, which lies in the middle column flanked by aluminum and indium, would be "expected" to show the lowest melting point of the three. In his words:

In a transitory group such as Al, Ga, In, _we must_ expect an intermediate phenomenon; the heaviest (In) and the lightest (Al), should be less fusible than the middle one, which is as it is in reality.

Not only had such ad hoc arguments ever before been given by Mendeleev as a means of predicting trends in properties, but it also runs contrary to the spirit of his method of simple interpolation, which he used so successfully in many other instances. The ad hoc nature of the argument is compounded by the fact that it is by no means clear that the lesser fusibility of indium and aluminum truly represents "an intermediate phenomenon" with respect to the other groups mentioned. Nor is it clear why this somewhat contrived trend should begin at this particular place in the periodic table. In spite of his use of the word "must," there is nothing in the least bit compelling about Mendeleev's argument. Although nobody would consider denying Mendeleev his triumphs because of such indiscretions, there would probably be little harm caused if historical accounts were to mention some of Mendeleev's failings instead of merely concentrating on his spectacular successes.

#### SCANDIUM

Scandium was discovered in 1879 by the Swedish chemist Lars Frederick Nilson, in a mineral ore called euxenite. It was identified as Mendeleev's predicted eka-boron by a Swedish chemist Per Cleve. The discoverer, Nilson, promptly named the new element scandium after Scandinavia, where the ore had first been discovered.

Although it was not discovered spectroscopically, contrary to Mendeleev's prediction, the properties of the new element were very close to what Mendeleev had listed for eka-boron (table 5.2).

#### GERMANIUM

Another of Mendeleev's most successful predictions, eka-silicon, was discovered by Clemens Winkler in 1886 and named germanium. Winkler and other comfirmers of the periodic law, as Mendeleev called them, are shown in figure 5.1. The manner in which germanium was connected with Mendeleev's prediction of eka-silicon is rather interesting because it shows the complications that were involved in such cases compared with the sanitized historical accounts that one often encounters.

Germanium was not immediately identified with Mendeleev's eka-silicon. Winkler initially believed that he had discovered another of Mendeleev's predictions, eka-stibium, an element that was supposed to be placed between stibium (antimony) and bismuth. Mendeleev responded to this claim by publishing a paper in which he gave a revised account of the properties expected of ekastibium in order to argue that Winkler had not in fact found this element. Mendeleev believed that the new element was to be identified with yet another of his predictions, eka-cadmium, which he believed would lie between cadmium and mercury. Theodor Hieronymus Richter, from Breslau, Germany, then wrote to Winkler to suggest that the new element might in fact be Mendeleev's eka-silicon. At about the same time, Lothar Meyer agreed with Richter and further pointed out that this element coincided with his own predictions for a new element. So it was that Winkler went back to work on isolating larger quantities of the element and, on further characterization, was able to announce that it was indeed Mendeleev's predicted eka-silicon. Table 5.3 summarizes the main predictions as well as the findings on this element.

FIGURE 5.1 The comfirmers of the periodic law. Clockwise from left: Nilson, De Boisbaudran, Winkler, and Brauner. Photo and permission provided by Gordon Woods.

Although Mendeleev had foreseen a number of properties, as table 5.3 shows, he had been wrong in thinking that the element would be difficult to liquify and difficult to volatilize, whereas Lothar Meyer's predictions on these points had been correct. Clearly, Mendeleev was spectacularly successful in these predictions, but perhaps not quite to the extent that is implied by the more selective tables of comparison that regularly appear in chemistry textbooks and even histories of chemistry.

#### MENDELEEV'S LESS SUCCESSFUL  
PREDICTIONS

In his later years, Mendeleev devoted considerable attention to elements occurring before hydrogen in the periodic table. He gave a number of reasons for taking such a possibility seriously: First of all, the discovery of a whole new series of elements, the noble gases, in the closing years of the nineteenth century led him to think that this series could be extended upward to earlier analogues of the first two noble gases, helium and neon. Second, the apparent success of the ether theory in optical physics suggested to him that ether should be identified as a new element, which he chose to call newtonium. Third, ether would have to lack the ability for chemical combination since it was believed to permeate all substances. In addition, the notion of a completely unreactive element had become highly plausible after the discovery of the unreactive noble gases.

Mendeleev predicted the existence of two elements lighter than hydrogen, calling them elements x and y, based on numerical relations between atomic weight ratios in a periodic table, which he devised in 1904 (table 5.4).

In order to predict the atomic weight of the ether (newtonium), or element x, Mendeleev considered the atomic weight ratios of the known noble gas elements:

Xe:Kr = 1.56, Kr:Ar = 2.15, Ar:He = 9.5

From these figures, he extrapolated the ratio He: Newt = 23.6, thus giving a maximum possible atomic mass of 0.17 for newtonium.

To estimate the atomic weight for the element that he designated as y, Mendeleev considered the ratios of atomic weights for the first two members of adjacent groups in the periodic table. He noted that the value for this ratio decreased smoothly from left to right:

Extrapolating from the atomic weight of newtonium and the additional ratio of Li: H = 6.97, Mendeleev estimated that the ratio of He:y should be at least 10, from which he deduced a value of at least 0.4 for element y. Thus, it would seem that Mendeleev, who had earlier avoided any involvement with numerical relationships concerning triads, had now also succumbed to a very similar form of numerology. Indeed, he asserted this claim in the strongest possible terms:

At the present time, when there remains not the slightest doubt that group I, which contains hydrogen, is preceded by a zero group containing elements of lesser atomic weights than the elements of group I, it seems to me _impossible_ to deny the existence of elements lighter than hydrogen.

But Mendeleev's elements x and y would never be found.

The discovery of the noble gases at the turn of the twentieth century also suggested to Mendeleev the possible presence of six new elements between hydrogen and lithium, as he indicated in his periodic table of 1904. In one of these cases, Mendeleev was more specific; namely, he predicted a possible analogue of the halogen fluorine. He claimed that the new element would serve to restore symmetry to the table by making the number of halogens five, to coincide with the five known alkali metals. Once again, we are forced to conclude that Mendeleev was mistaken about these predictions, since none of the six elements was subsequently discovered.

Mendeleev made a number of other unsuccessful predictions. In two unpublished tables dated 1869, he made two entries indicating elements he thought would be discovered:? = 8 and ? = 22. As with some of his other predictions of atomic weights of new elements, Mendeleev gave no indication of how he arrived as these predicted values, which were later removed and never appeared again in published form. Mendeleev also predicted the occurrence of elements with atomic weights of 2, 20, and 36, which, again, were never found.

In addition, he predicted lighter analogues of calcium and explicitly ruled out beryllium and magnesium as occupying these places. This proved to be another mistake in that both of beryllium and magnesium are indeed the missing analogues of calcium, which Mendeleev had misplaced elsewhere in his original tables.

One cannot help speculating as to the cause of these unfortunate cases. It appears that Mendeleev was relying exclusively on atomic weight calculations and disregarding the many subtle chemical clues that had guided him so well in his successful cases. As Jan van Spronsen has aptly commented, Mendeleev's approach in these unsuccessful cases "stands as a warning to the investigators when applying the deductive scientific method exclusively."

Unlike in physics, chemical reasoning does not generally proceed unambiguously from general principles. Chemistry is a more inductive science in which large amounts of observational data must be carefully weighed before reaching any conclusion, as Mendeleev had previously done when correcting atomic weights and predicting new properties by interpolation among known elements. The cases under consideration here seem to represent the speculations of an elderly and established scientist with nothing to lose. Here Mendeleev is not being guided by the chemical intuition that had served him so well in the past but is venturing into the less familiar field of attempting to produce new elements by deduction.

It is puzzling that Mendeleev's unsuccessful predictions do not seem to have counted against the acceptance of the periodic system. There seem to have been as many as 10 failed predictions of elements by Mendeleev. In fact, if one considers all of Mendeleev's predictions, it appears that he was successful in only half of them. This fact has not been given much consideration, as it is much more common for scholars to be impressed by his dramatic successes.

Table 5.5 lists all of Mendeleev's firm predictions. It contains only the elements to which he gave provisional names. Thus, it does not include elements such as astatine and actinium, which he predicted successfully but did not name. Neither does it include predictions that were represented just by dashes in Mendeleev's periodic systems. Among some other failures, not included in the table, is an inert gas element between barium and tantalum, which would have been called ekaxenon, although Mendeleev did not refer to it as such.

A success rate of half is clearly not outstanding by any stretch of the imagination. The fact that Mendeleev made as many failed predictions as successful ones seems to belie the notion that what counted most in the acceptance of the periodic system were Mendeleev's successful predictions.

#### THE ACCEPTANCE OF MENDELEEV'S  
PERIODIC SYSTEM

As mentioned in chapter 4, Mendeleev's mature periodic system first appeared in print in 1869 in the Russian chemical literature, and a German abstract of the article appeared in the same year. This was followed by a number of German translations of his articles in 1871. The first English announcement of an article by Mendeleev appeared in 1871 in the journal _Chemical News_. French translations began appearing in 1875. Although his textbook _The Principles of Chemistry_ did not appear in German until 1890, in English until 1891, or French until 1895, most European chemists would have heard of the new system much sooner through Mendeleev's various journal articles.

Many historians have argued that despite its prompt publication in the major European languages, Mendeleev's system did not attract much attention until the discovery of gallium by De Boisbaudran in 1875. Some point to this delay to suggest that it was Mendeleev's successful predictions that paved the way for the acceptance of his periodic system. While there is no doubt that his predictions of gallium, germanium, and scandium, especially, received much attention, the question is whether these predictions and others greatly outweighed the system's many successful accommodations in bringing about its acceptance. In fact, a careful examination of the events following the system's first appearance in 1869 reveals that they may not have done so.

Mendeleev was awarded the prestigious Davy Medal in 1882, after gallium and scandium had been discovered. The philosophers Patrick Maher and Peter Lipton have recently pointed to this award as proof that it was not until Mendeleev's predicted elements had begun to be discovered that his system received the recognition it deserved. They take this to indicate that prediction weighed much more heavily than accommodation in the acceptance of the periodic system. In fact, Lipton goes so far as to say, "Sixty accommodations [the placement of the known elements] paled next to two predictions."

Maher and Lipton both imply that there was a time lag between Mendeleev's accommodation of the known elements, in his constructing the periodic system, and his prediction of the three unknown elements. The existence of such a time lag is important to their argument. If it had not occurred, and the accommodations and predictions had been made in the same paper, it would be very difficult to ascertain whether the acceptance of Mendeleev's scheme rested primarily on its ability to accommodate or to predict.

In fact, Lipton, in paraphrasing Maher, claims quite specifically that when Mendeleev accommodated the 60 known elements (it should be 62), "the scientific community was only modestly impressed," thus clearly indicating a supposed time lag between the initial accommodation and later predictions. Maher implies such a time lag between accommodation and prediction by dating the predictions to 1871. Both of these authors are committing a historical fallacy relevant to the central issue, however, for although he did not give them names until 1871, Mendeleev left gaps for eka-boron, eka-aluminum, and eka-silicon, with their predicted atomic weights, when he first announced his periodic system in his famous paper of 1869. And in 1869 and 1870, he predicted their atomic volumes and specific gravities. Thus, the time lag that Maher and Lipton imply did not in fact take place.

The only justification Maher and Lipton might have for concentrating on the 1871 article is that it contained Mendeleev's first set of detailed predictions. Another factor may be that it was not until this paper that Mendeleev gave his predicted elements provisional names. But it is hard to imagine that Maher and Lipton would claim the 1871 predictions as more definitive than those of 1869 from the mere fact that Mendeleev was only then prepared to give the elements names, and provisional ones, at that. The whole question of prediction is fraught with problems. For example, should we consider predictions made in unpublished manuscripts or a talk given to a learned society? Similarly, one might well ask just how detailed the prediction itself should be to count as a true prediction.

In any case, Maher and Lipton were not the first to suggest there was such a time lag between Mendeleev's original announcement of the periodic system and his predictions of unknown elements. Other historians, too, have conveyed the impression that Mendeleev's predictions were decisive in the acceptance of the periodic table, but they regularly fail to cite reactions by chemists at the time that might support this view. This is, of course, the crucial issue, namely, whether the scientific community values predictions above explanations of already known facts, and not what later historians might report. It would seem that these historians are merely reconstructing the course of events while incorporating the popular myth regarding predictions, and that Maher and Lipton have recently revived this view in the philosophical literature. Of course, the fact that Mendeleev's accommodations and predictions were published simultaneously does not rule out the Maher-Lipton position that scientists attach more importance to predictions. But to maintain their claim, these authors would need to cite historical evidence to the effect that scientists did indeed prefer the predictive aspects of the periodic system.

#### DAVY MEDAL CITATION

Since two eminent philosophers of science have cited the award of the Royal Society's Davy Medal to Mendeleev as evidence for the superiority of predictions in the acceptance of the periodic system, it is necessary to consider the citation of this award in full.

The Davy Medal has been awarded to Dimitri Ivanovich Mendeleeff and Lothar Meyer.

The attention of the chemists had for many years been directed to the relations between the atomic weights of the elements and their respective physical and chemical properties; and a considerable number of remarkable facts had been established by previous workers in this field of inquiry.

The labors of Mendeleeff and Lothar Meyer have generalized and extended our knowledge of those relations, and have laid the foundation of a general system of classification of the elements. They arrange the elements in the empirical order of their atomic weights, beginning with the lightest and proceeding step by step to the heaviest known elementary atom. After hydrogen the first fifteen terms of this series are the following, viz.:

No one who is acquainted with the most fundamental properties of these elements can fail to recognize the marvelous regularity with which the differ ences of property, distinguishing each of the first seven terms in the series from the next term, are reproduced in the next seven terms.

Such periodic re-appearance of analogous properties in the series of elements has been graphically illustrated in a very striking manner with respect to their physical properties, such as the melting points and atomic volumes. In the curve which represents the relations of atomic volumes and atomic weights analogous elements occupy very similar positions, and the same thing holds good in a striking manner with respect to the curve representing the relations of melting-points and atomic weights.

Like every great step in our knowledge of the order of nature, this periodic series not only enables us to see clearly much that we could not see before; it also raises new difficulties, and points to many problems which need investigation. It is certainly a most important extension to the science of chemistry.

The first thing to emerge from an examination of this citation is that the medal is being jointly awarded to Mendeleev and Lothar Meyer. This feature has been conveniently omitted by Maher and Lipton, both of whom favor prediction over accommodation. The very fact that the award is to both of these pioneers of the periodic system already argues strongly against the predictivist thesis since, according to the popular account, Mendeleev is given priority precisely because he made predictions, which were subsequently confirmed, whereas Lothar Meyer failed to make any significant predictions.

Second, the entire citation concerns the accommodation of chemical and physical phenomena of the elements and not the prediction of new elements, as Maher and Lipton's statements would seem to require. The only part of the citation that could remotely be linked with the prediction of gallium and scandium by Mendeleev is the phrase in the final paragraph that alludes to "seeing clearly much that we could not see before." However, this comment is too vague to allow such an interpretation, and even if it is a veiled reference to the prediction of the two new elements, it is clearly not stating that the medal is being awarded primarily as a result of them. So perhaps Maher and Lipton are mistaken in citing the award of the Davy Medal as an indication of the Royal Society's high regard for predictions, since the entire Davy award citation makes no mention whatsoever of the prediction of new elements.

#### CONTEMPORARY REACTIONS TO THE  
PERIODIC TABLE

Let us now examine the wider question of how scientists at large in this period of history reacted to the introduction of Mendeleev's periodic system, and whether they regarded predictions connected with the periodic table more favorably than the accommodation of already known elements.

The second successful prediction by Mendeleev concerned the element scandium, and this case offers a good opportunity for obtaining reactions of other scientists, since the identification of the newly discovered element was carried out by a third party, that is, neither the discover of the element nor Mendeleev. This third party was the French chemist Clève, who wrote,

The great interest of scandium is that its existence had been predicted. Mendeleef in his memoir on the law of periodicity, had foreseen the existence of a metal which he named ekaboron, and whose characters agree fairly well with those of scandium.

Clève is clearly attaching some importance to this prediction, although there is no indication that he regards the overall case for Mendeleev's periodic system to be strengthened by this finding.

In 1879, shortly after the above translation of Clève's article was published in the British journal _Chemical News_ , the same journal undertook the serialization of Mendeleev's 1871 paper on the periodic law. The following interesting editorial appears along with a specially written introductory article by Mendeleev:

Considerable attention having been drawn to M. Mendeleef's memoir 'On the Periodic Law of the Chemical Elements', in consequence of the newly discovered elements gallium and scandium being apparently identical with two predicted elements ekaluminum and ekaboron, it has been thought desirable to reproduce the entire article in CHEMICAL NEWS....

There followed a weekly serialization of Mendeleev's memoir in 17 parts. This may be among the strongest evidence that suggests that Mendeleev's predictions were indeed taken seriously at the time. Nevertheless, the above editorial gives no indication whether the successful predictions did anything to enhance the status of the periodic system.

In 1881, a year after the serialization of Mendeleev's memoir appeared, the famous priority dispute between Mendeleev and Lothar Meyer broke out in the pages of the same journal, _Chemical News_. After giving precise details as to the publication of his early papers in a note to the journal, Mendeleev adds the following more general remark concerning what he believes to be the essence of the priority question:

That person is rightly regarded as the creator of a particular scientific idea who perceives not merely its philosophical, but its real aspect, and who understands so to illustrate the matter so that everyone can become convinced of its truth. Then alone the idea, like matter, becomes indestructible.

Interestingly, Mendeleev does not specifically mention any of his predictions in arguing for his priority over Lothar Meyer. His note is followed by one from Lothar Meyer, in which he, in turn, defends his own claim to priority with regard to the discovery of the periodic system. This note is followed by a third item by the well-known organic chemist Charles-Adolphe Wurtz, who is not impressed with the periodic system at all, let alone with Mendeleev's predictions. Wurtz grants that Mendeleev's proposition is a "powerful generalization and must in future be taken into account whenever we regard the facts of chemistry from a lofty and comprehensive point of view." Nevertheless he points out that the system contains many imperfections, such as the way it reflects the [then] available knowledge of the rare earths. He discusses the problem with tellurium and iodine, whose atomic weight ordering is inconsistent with their chemical properties. Wurtz alludes to similar problems with cobalt and nickel, whose properties should coincide in view of their almost identical atomic weights. Wurtz also points out the large chemical differences between such elements as vanadium and bromine, whose atomic weights are very closely related, which might therefore be expected to be chemically similar. He adds that the alleged gradations in properties do not in fact progress smoothly or regularly as Mendeleev would have us believe.

Wurtz then turns specifically to consider Mendeleev's predictions.

In Mendelejeff's table we are chiefly struck with the gaps between two elements, the atomic weights of which show a greater difference that two or three units, thus marking an interruption in the progression of the atomic weights. Between zinc (64.9) and arsenic (74.9) there are two, one of which has been lately filled up by the discovery of gallium. But the considerations by which Lecoq de Boisbaudran was led in the search for gallium have nothing in common with the conception of Mendelejeff. Though gallium has filled up a gap between zinc and arsenic, and though other intervals may be filled up in future, it does not follow that the atomic weights of such new elements will be those assigned to them by this principle of classification. The atomic weight of gallium is sensibly different from that predicted by Mendelejeff. It is also possible that the future may have in reserve for us the discovery of a new element whose atomic weight will closely coincide with that of a known element, as do the atomic weights of nickel and cobalt. Such a discovery would not fill any foreseen gap. If cobalt were unknown it would not be discovered in consequence of Mendelejeff's classification.

The inclusion of this rather severe criticism might be viewed as an attempt by the editor of _Chemical News_ to temper his initial enthusiasm for Mendeleev's system, which had led to the 17-part serialization. Why he would otherwise choose to follow the priority dispute with this note is difficult to understand.

The fact that the successful predictions made by Mendeleev by no means gained universal acceptance for his periodic system can also be seen from further criticisms voiced by the likes of the chemist Marcellin Berthelot. In 1885, even after two of Mendeleev's predictions had been highly successful, Bertholet launched a highly critical attack on the periodic systems that had been introduced by Mendeleev and others. Not only was he unimpressed with Mendeleev's predictions, but Berthelot even refused to be seduced by the ability of the periodic system to accommodate what was already known about the elements. Bertholet began by pointing out that the relations between atomic weights, atomic volumes, and physical and chemical properties had been known before the elements were placed into a periodic system. He claimed that, since these relations resulted from atomic weight relations, it was a coincidence that they reemerged when considered in the context of the periodic table. To Bertholet, this was not, therefore, proof of the existence of periodic series. He then turned to predictions and admitted that the periodic system should prove interesting in this respect. Bertholet also accepted that certain elements appeared to be missing but stressed that this was evident just from the gaps in the sequence of atomic weights. He claimed that, in their haste to fill such gaps, the authors of the periodic systems had made some mistakes, such as in the insertion of molybdenum between scandium and tellurium.

Similarly, Bertholet mocks the common grouping of hydrogen and lithium at one end of a group and copper, silver, and gold at the other end of the same group, as carried out by Mendeleev, as being "fanciful." He further accuses the authors of the periodic systems of making it too elastic in admitting elements that differ by no more than two units throughout the table. He suggests that _any_ future discoveries could be accommodated if this was the case. Bertholet claims that there is no systematic means of predicting new elements from the periodic system or any means of synthetically forming the elements, thus referring to the hypothetical transmutation of the elements. Finally, Bertholet warns about the dangers of falling back into what he calls a mystical enthusiasm similar to that of the alchemists.

Up to this point, Bertholet's critique seemed to have been very reasonable, but in this final remark he gave Mendeleev an easy way of responding. Mendeleev took issue in particular with Bertholet's reference to a "mystic enthusiasm" and responded by accusing Bertholet of confusing the idea of the law of periodicity with the ideas of William Prout, as well as with those of the alchemists and of Democritus on primary matter. It was in response to these criticisms by Bertholet that Mendeleev also made a much quoted remark, already cited in chapter 4, in which he emphasized that the periodic system owed nothing to the idea of a "unique matter" and had no connection with the "relic of the torments of classical thought...."

A look at the historical record thus reveals that the acceptance of Mendeleev's system was not a simple matter, and certainly was not assured by either his accommodations or his successful predictions. Many of Mendeleev's contemporaries were impressed with the accommodations his system achieved; others, like Bertholet, seemed to not be impressed by either the predictions or the accommodations. Thus, the question remains regarding the manner in which Mendeleev's periodic system did indeed take hold fairly quickly in the decades following its introduction and how it came to occupy the central position in chemistry it still holds today.

#### THE POWER OF AN IDEA

Although his chemical knowledge was extensive, Mendeleev was primarily considered to be a systematizer. He produced an _idea_ , the periodic system, within which chemical phenomena could be systematized. He used this idea to sort through the mass of chemical data available in his time, and though he was not always correct, he demonstrated an uncanny ability to separate valid facts from irrelevant ones. It was because he could see patterns among the properties of the elements that he was able to predict not only the existence of new elements but also their chemical and physical characteristics. The historian of chemistry Brock has quoted Bonifatii Kedrov, the Russian historian of chemistry, as saying, "[T]he scientific world was astounded to note that Mendeleev, the theorist, had seen the properties of a new element more clearly than the chemist who had discovered it." Meanwhile, the science historian Brush has posed an interesting question in asking whether theorists should be considered less trustworthy than observers. The reason one tends to give more credit to predictions than to accommodations is presumably because we suspect that a theorist might have designed his theory to fit the facts. But is it not equally possible, Brush asks, for observers to be influenced by a theory in their report of experimental facts? If so, then perhaps we should give greater consideration to observations obtained before a theory is announced than to observations produced in response to a theory.

Although Mendeleev was not above occasionally resorting to ad hoc arguments, as witnessed in his discussion of the melting point of gallium, there was nothing ad hoc about his atomic weight corrections, as unlikely as many of them may have appeared to be at the time. It is important to emphasize that there turned out to be independent empirical evidence for the new values assigned to these atomic weights. It was not that chemists simply came to accept the new values because they made elements fit Mendeleev's table better. The corrected value of the atomic weight of beryllium, for example, was confirmed independently of any consideration of its place in any table by Lars-Frederick Nilson and O. Pettersen's discovery of one of its gaseous compounds, beryllium chloride. This discovery meant that an evaluation of beryllium's atomic weight could be made using already accepted background knowledge.

In ordering the elements, Mendeleev was accommodating all that was known about them up to his time, their atomic weights, their physical properties, and their chemical character, in addition to being able to make dramatic predictions. Mendeleev did not have to correctly predict every element that would be discovered, and experimentalists were not restricted to looking only for elements that the system implied. The successful incorporation of the rare earths and the noble gases would ultimately do much to prove the validity of the periodic system. What is more, the system would be further strengthened by more general developments to come, such as the discovery of isotopes, atomic number, and later, quantum theory.

#### THE INERT GASES

The case of the inert, or noble, gases represents an interesting counterexample to the predictivist thesis in the sense that almost nobody, including Mendeleev, had predicted or even suspected the existence of an entire family of new elements. Once they had begun to be discovered, it was immediately understood that the existence of the inert gases might pose a major threat to the periodic system. Indeed, a failure to incorporate them might have led to an abandonment of the periodic system, regardless of the earlier predictive successes achieved. As it turned out, the correct placement of the noble gases did not cause any harm to the periodic system, but did much to enhance it.

The first of the noble gases to be discovered, argon, was particularly difficult to place in the periodic system. Not only had it not been predicted from the periodic system, but there was the further difficulty that physical measurements suggested the gas was monoatomic, and this was regarded with some suspicion since the only other monoatomic gas then known was vaporized mercury.

The atomicity of argon was crucial to determining its atomic weight, which in turn was essential for its accommodation into the periodic system. As Mendeleev had repeatedly stressed, atomic weight was considered to be the one essential criterion on which the periodic law was founded. Further complications regarding the atomic weight of argon arose due to doubts over the purity of the gas. There was considerable debate as to whether it consisted of a mixture of gases, and whether what was being measured was actually an average atomic weight determined by the relative proportion of several components. While the interdependent issues of atomicity and the possibility of a mixture were still being discussed, a deeper and unsuspected complicating factor was operating to confuse the issue. The elements argon and the subsequent element potassium represent one of the very few examples of "pair reversals" in the periodic table.

Argon was discovered in 1894 by Lord Rayleigh and William Ramsay (figure 5.2), who were studying nitrogen. Convinced by spectroscopic evidence that they had a new element on their hands, they set out to determine its properties. Because the gas was completely inert, they were forced to rely on physical measurements to determine its atomic weight. The determination of argon's specific heat was carried out through the measurement of the specific heat capacities of the gas at constant pressure and at constant volume, _C p_ and _C v_, respectively.

From these measurements, Rayleigh and Ramsay could determine the ratio of translational energy to kinetic energy, which would in turn reveal the atomicity of the gas. In general, the total kinetic energy of a molecule is made up of three contributions: translational, rotational, and vibrational energy. In the case of a monoatomic system, there is only translational motion, and so kinetic energy is equal to translational energy. Rudolf Clausius had shown in 1857 that if _K_ is the translational energy of the molecules of a gas and _H_ is the total kinetic energy, then

FIGURE 5.2 William Ramsay. Photo and permission from Edgar Fahs Smith Collection.

_K/H_ = 3(C _p_ \- C _v_ )/2C _v_

If C _p_ /C _v_ is found to be 1.66, substitution into the equation shows that _K_ = H, or in other words, all the kinetic energy of the molecules occurs in translational form. This means that the molecules are exhibiting no rotational or vibrational energy, which in turn implies the presence of an isolated atom, or monoatomicity. The experimental result obtained by Rayleigh and Ramsay was that _C/C v_ was very nearly 1.66, from which they therefore inferred that argon is monoatomic. The account just given benefits from the knowledge of hindsight, since it is now well established that argon is indeed monoatomic. It took considerably more effort to arrive at this conclusion at the time when the mysterious gas was first discovered.

The public announcement of the argon problem took place on January 31, 1895, at a specially convened meeting of the Royal Society of London, and it was met with considerable debate by the leading chemists and physicists of the day. The meeting began with an exposition of the findings on the new substance given by Ramsay, including the specific heat ratio of nearly 1.66. Ramsay and Rayleigh interpreted this result to mean that the new constituent was either an element or a mixture of elements and was probably monoatomic. They admitted that the results were also consistent with diatomic or polyatomic molecules whose atoms acquire no relative motion, not even that of rotation. They added that the latter possibility seemed improbable, however, in that it would have required such a complex group of atoms to be spherical.

Rayleigh and Ramsay failed to take up a decisive position on the question of the purity of the new substance. They acknowledged that the spectral evidence provided by William Crookes, in a paper read the same evening, suggested a mixture. But they also pointed to the measurements on critical data, which indicated a sharp boiling point and melting point, as well as an observed constant pressure during boiling, all of which pointed to a single pure substance.

Their overall conclusion was that "the balance of evidence seemed to point to simplicity," meaning to a single element, but that this fact together with the probable monoatomicity suggested an atomic weight of 39.9. From this they were forced to conclude that such an element would find no place in the periodic table. On the other hand, Ramsay and Rayleigh proceeded to speculate that a 93.3% to 6.7% mixture of two unknown elements with atomic weights 37 and 82, one lying between chlorine and potassium and the other between bromine and rubidium, would also account for the observed density.

Henry Armstrong, the then president of the Chemical Society, politely congratulated Ramsay and Rayleigh on their researches but went on to make some criticisms. He suggested that the account of the probable nature of the new element was "of a wildly speculative character" and drew attention to the doubts expressed by Ramsay and Rayleigh over the interpretation of the specific heat data. He then proceeded to draw an analogy between nitrogen and argon. He pointed out that while nitrogen, as it occurs in the atmosphere in molecular form, is highly inert, so its constituent atoms are highly reactive. Similarly, he argued that argon, which is evidently even more inert than nitrogen, might consist of even more reactive constituent atoms. Their extreme reactivity would produce very strong interatomic bonding, thus producing a diatomic molecule so locked together that it would display translational motion without any form of relative motion between the constituent atoms.

Further support for Armstrong's view came from the Irish physicist George Fitzgerald, better known for his contributions to the theory of relativity, whose opinion had been communicated earlier in a letter to Rayleigh. Like Armstrong, Fitzgerald was willing to contemplate a diatomic molecule in which the two atoms are so firmly bound together as to produce very little internal motion and added that this view would be in keeping with the chemical inertness of the new gas.

Lord Rayleigh, however, had difficulty imagining such a diatomic molecule, and expressed his reservations by saying,

That argument is no doubt perfectly sound, but the difficulty remains how you can imagine two molecules joined together, which one figures roughly in the mind, and I suppose not wholly inaccurately, as somewhat like two spheres put together and touching one another—how it would be possible such an excentrically-shaped atom as that to move about without acquiring a considerable energy of rotation.

William Arthur Rücker, the president of the Physical Society, pointed out that such a diatomic molecule would actually have to be spherical to produce the observed ratio of specific heats of 1.66. He acknowledged that this would represent something of a problem, but he also admitted less concern about the problem of fitting the element into the periodic table, as he did not think Mendeleev's system to be so well established that overturning it would shake the foundations of chemistry.

Finally, the chair of the meeting, Lord Kelvin, added his own comment on the issue of the specific heat ratio of 1.66, also expressing reservations about the possibility of a diatomic molecule. "I do not admit that a spherical atom could fulfill that condition," he said. "A spherical atom would not be absolutely smooth." Kelvin also disputed the notion of a rigidly connected diatomic molecule since he felt that at least some relative vibrational motion would have been detected from such a mechanical system.

About two months later, a report of Mendeleev's views on the accommodation of argon appeared in _Nature_. Here, Mendeleev stated that the supposition that argon is a mixture "lies beyond all probabilities." He also considered it probable that the gas was an element due to its inert nature. He then moved on to a systematic consideration of atomic weights for the element, suggesting the following set of possible molecules:

A1, A2, A3,... An

Taking each of the possible atomicities in turn, he first discussed monoatomicity. Mendeleev was reluctant to accept the evidence for monoatomicity obtained from specific heat measurements on the grounds that there might be a chemical contribution to the kinetic energy of the molecule. He pointed to the difference between the values for _C p/Cv_ of 1.3 in the case of chlorine and 1.4 in the case of nitrogen, thus emphasizing the variation among diatomics and implying that even a value of 1.6, as observed in argon, might still belong to a diatomic molecule.

As might be expected, Mendeleev was most concerned with the problem of fitting the new element into his periodic system, but he dismissed monoatomicity on the grounds that there was no room in the periodic table for such an element. He reasoned that monoatomicity implied an atomic weight for argon falling between chlorine and potassium and that this would imply "an eighth group in the third series," something that he found inadmissible. This is a surprising error on the part of the master chemist, since there is in fact no fundamental reason why an eighth group should not be introduced. In fact, this is precisely how the problem was solved in due course.

Mendeleev raised similar objections against the notion of a diatomic argon molecule. Continuing with his original list of possible atomicities, he then settled on triatomicity, concluding that argon was nothing but a triatomic form of nitrogen and not a new element after all:

If we suppose further that the molecule of argon contains three atoms, its atomic weight would be about 14, and in such case we might consider argon as condensed nitrogen N3. There is much to be said in favour of this last hypothesis....

Among the reasons for favoring this molecule, Mendeleev argued that it would account for the "concurrent existence of nitrogen and argon in nature" and similarly that the inertness of argon might be related to the fact that it is derived from nitrogen. Molecules with higher atomicities, namely, 4 and 5, were ruled out because they would require atomic weights of 10 and 8, respectively, and could not thus be accommodated into the periodic system. As for hexatomicity, Mendeleev considered this plausible and indeed thought it to be the second most likely atomicity after triatomic N3.

Meanwhile, the debate had spread to the larger scientific community. John Hall Gladstone, one of the pioneers of the relationship between refractive index and molecular structure, gave five reasons for why an element with an atomic weight of 20 would fail to fit into the periodic system. He then gave a further five reasons why he considered an element of atomic weight 40 would be well accommodated into the periodic table. One cannot help concluding that Gladstone was wrong on a total of 10 counts!

Within two years, terrestrial helium had been discovered, and the problem became one of accommodating two elements, namely, argon and helium. A further three years were to pass before the discovery of krypton, neon, and xenon. A whole new family of elements had been discovered without having been predicted, and the accommodation of these new elements into the periodic table was proving to be far from trivial. Indeed, it presented a severe threat to the survival of Mendeleev's system.

Mendeleev visited London in late 1895 and discussed the argon problem with Ramsay. He reported back to the Russian Physico-Chemical Society on his return to Moscow, "The subject has progressed little. There is little for its solution and the matter seems particularly obscure." Two years later, he wrote that since no compounds could be formed from argon and helium, their atomic weights should be regarded as doubtful. For Mendeleev, the study of compounds played an essential role in the incorporation of elements into the periodic system. He was reluctant to accept argon and helium as new elements, as he would not entertain the possibility that an element could be completely inert.

Finally, in the spring of 1900, at a meeting in Berlin, Ramsay suggested to Mendeleev that argon and its analogues should be placed in a new group between the halogens and the alkali metals. They would thus appear at the right-hand edge of the table and would serve to extend the length of each period by one element. In spite of all his previous views on the inert gases, Mendeleev received this suggestion favorably and wrote of his response in 1902: "This was extremely important for him [Ramsay] as an affirmation of the position of the newly discovered elements, and for me as a glorious confirmation of the general applicability of the periodic law." Mendeleev also adds that this step represented the "magnificent survival" of the periodic system in what had been a "critical test." Indeed, the periodic system had come through this test with "flying colors." Could it be that the eventual successful incorporation of the noble gases into the periodic table counted as much in favor of the periodic system's acceptance as Mendeleev's celebrated predictions? My own belief is that it did, as did the eventual successful incorporation of the rare earth elements.

#### CONCLUSION

The claim is sometimes made that successful prediction gives more credit to a theory than does the accommodation of known facts. But it is difficult to find clear-cut evidence for this claim in the technical writings of scientists. A successful prediction may yield much favorable publicity for a theory and thereby force other scientists to give it serious consideration. But subsequent evaluations of the theory in the scientific literature usually do not give greater weight to the prediction of novel facts than to the persuasive deductions of known facts.

This may be what happened with Mendeleev's periodic system. It was announced in 1869 to mixed reviews but seems to have received more favorable attention after the discovery of gallium in 1875. Rather than confirming that prediction of new elements was the overwhelming factor in the eventual acceptance of the system, the discovery of gallium, scandium, and germanium may have served simply to bring the system to the attention of the scientific community. From there, it appears that its many strengths began to be appreciated. In addition to the prediction of new elements, Mendeleev successfully predicted the correct atomic weights of many already existing elements, and these successes would have contributed to the acceptance of his periodic system.

But the placement of difficult elements such as beryllium, the accommodation of the newly discovered noble gases, and the ongoing struggle to position the rare earths all contributed to an atmosphere of productive debate that surrounded the periodic system. These factors may well have contributed just as much as the predictions to the eventual acceptance of the system, contrary to the popular myth that assigns the greatest credit to Mendeleev almost exclusively on the basis of his successful predictions. By 1890, Mendeleev's system was a permanent fixture on the landscape of chemistry. Almost all the lacunae of the magnificent edifice had been explored, revealing its profound elegance and propelling the research agenda for chemistry, and even physics, into the next century.

## **CHAPTER 6  
THE NUCLEUS AND THE PERIODIC TABLE**

### _Radioactivity, Atomic Number, and Isotopy_

Theories of the atom were reintroduced into science by John Dalton and were taken up and debated by chemists in the nineteenth century. As noted in preceding chapters, atomic weights and equivalent weights were determined and began to influence attempts to classify the elements. Many physicists were at first reluctant to accept the notion of atoms, with the tragic exception of Ludwig Boltzmann, who came under such harsh criticism for his support of atomism that he eventually took his own life. But around the turn of the twentieth century, the tide began to turn, and physicists not only adopted the atom but transformed the whole of science by performing numerous experiments aimed at probing its structure. Their work had a profound influence on chemistry and, more specifically for our interests here, the explanation and presentation of the periodic table.

Beginning with J.J. Thomson's discovery of the electron in 1897, developments came quickly. In 1911, Ernest Rutherford proposed the nuclear structure of the atom, and by 1920 he had named the proton and the neutron. All of this work was made possible by the discovery of X-rays in 1895, which allowed physicists to probe the atom, and by the discovery of radioactivity in 1896. The phenomenon of radioactivity destroyed the ancient concept of the immutability of the atom once and for all and demonstrated that one element could be transformed into another, thus in a sense achieving the goal that the alchemists had sought in vain.

The discovery of radioactivity led to the eventual realization that the atom, which took its name from the idea that it was indivisible, could in fact be subdivided into more basic particles: the proton, neutron, and electron. Rutherford was the first to try to "split the atom," something he achieved by using one of the newly discovered products of radioactive decay, the alpha particle.

In addition to its well-known medical applications, the earlier discovery of X-rays was to provide a powerful tool that could be used to study the inner structure of matter. By using these rays, Henry Moseley later discovered that a better ordering principle for the periodic system is atomic number rather than atomic weight. He did this by subjecting samples of many different elements to bombardment with X-radiation.

The dual discoveries of radioactivity and X-rays made possible the further discovery and identification of several new elements, such as radium and polonium, which needed to be accommodated, and thus provided further tests of the robustness of the periodic system and its ability to adapt to changes. Indeed, while it is the electron that is mainly responsible for the chemical properties of the elements, discoveries connected with the nucleus of the atom nevertheless have had a profound influence on the evolution of the periodic system. The exploration of the nucleus, along with further work on the nature of X-rays and radioactivity, led to the discovery of atomic number and isotopy, two developments that would together resolve many of the lingering uncertainties surrounding Dimitri Mendeleev's periodic system.

The discovery of isotopy initially presented certain dangers for the periodic system. The large number of new isotopes that were discovered suggested that there were many more "atoms," in the sense of smallest possible particles, of any particular element than had previously been recognized. Some chemists even suggested that the periodic table would have to be abandoned in favor of a classification system that included a separate place for every single isotope. Luckily, this idea was resisted since, as it turned out, isotopes of the same element showed identical chemical properties.

The discovery of atomic number provided one of the most clear-cut modifications the periodic system had undergone since its foundation had been laid by the likes of Johann Dobereiner some 100 years previously. When the concept of atomic number was combined with the new understanding of isotopy, it became possible to appreciate why William Prout's hypothesis (that all elements are composites of hydrogen) had been so tantalizing to the early pioneers of the periodic system. Indeed, Prout's hypothesis could now be said to be valid in the somewhat modified form that all atoms in the periodic table were multiples of a single unit of atomic number or, as it was subsequently named, the proton. It also became possible to explain why triads had been so enticing and so instrumental in the early evolution of the periodic system.

The four main discoveries of X-rays, radioactivity, atomic number, and isotopy are examined in this chapter by following a roughly historical order, although it must be appreciated that there was much overlap among these four themes.

### X-RAYS AND BECQUEREL RAYS

By the beginning of 1895 Röntgen had written forty-eight papers now practically forgotten. With his forty-ninth he struck gold.

Emilio Segré, _From X-rays to Quarks_

This is how the Italian-born physicist Segré has described the career of Wilhelm Conrad Röntgen before his momentous discovery of X-rays.

On November 8, 1895, Röntgen, a German physics professor, was working in his darkened laboratory in Würzburg. His experiments focused on passing an electrical current into highly evacuated glass tubes known as Crookes tubes. To Röntgen's surprise, he noted that when one of his tubes was charged, an object across the room began to glow. This proved to be a barium platinocyanide-coated screen too far away to be reacting to the cathode rays coming from the tube. Over the next few days, Röntgen experimented in various ways with what he began to suspect might be a new form of emanation. Quite by accident, while holding materials between the tube and screen to test the new rays, he saw the bones of his hand clearly displayed on the screen in an outline of flesh. This was the first time anyone had ever seen a medical X-ray image. Röntgen plunged into seven weeks of intense and secretive experimentation in order to determine the nature of the mysterious rays. He worked in isolation, telling a friend that he had discovered something interesting but that he did not know whether his observations were correct.

On December 28, 1895 Röntgen gave his preliminary report to the president of the Würzburg Physical-Medical Society, accompanied by experimental radiographs, including an image of his wife's hand, which survives to this day. A few days later, he sent printed reports to physicist friends across Europe, and by January the world had been gripped by "X-ray mania." Röntgen was acclaimed as the discoverer of a medical miracle, and although he accepted the first Nobel Prize in physics in 1901, he decided not to seek patents or proprietary claims on X-rays.

One of the many scientists to whom Röntgen sent his X-ray images was Henri Poincaré. Poincarté in turn showed one of these radiographs to his colleagues at the Academy of Sciences in Paris, on January 20, 1896. Henri Becquerel, a professor at the Museé d'Histoire Naturelle and member of the academy, took note of a remark by Poincare on the possible link between X-rays and luminescence. On returning to his laboratory, he designed an experiment to test the hypothesis that X-ray emission and luminescence are related. In order to see if a phosphorescent body emitted X-rays, he chose a hydrated salt of uranium that he had prepared some years before. On February 20, Becquerel placed a transparent crystal of the salt on a photographic plate wrapped between two thick sheets of black paper, and the experimental setup was exposed to sunlight for several hours. After development, the silhouette of the crystal appeared in black on the photograph, and Becquerel concluded that the phosphorescent substance emitted a penetrating radiation able to pass through black paper.

Unable to repeat such experiments in the following days because of a lack of sunshine, Becquerel put away his salt crystal, placing it by chance on an undeveloped photographic plate in a drawer. Later he developed the plate in order to determine the amount by which the phosphorescence had decreased. To his great surprise, he found that the phosphorescence had not decreased at all but was more intense than it had been on the first day. Noticing a shadow on the plate made by a piece of metal he had placed between it and the salt, Becquerel realized that the salt's activity had continued in the darkness. Clearly, sunlight had been unnecessary for the emission of the penetrating rays. Could it be that just one year after the discovery of X-rays, another new form of emanation was beginning to reveal itself?

Becquerel also found that the activity of his uranium salt did not diminish with time, even after several months. He also tried to use a nonphosphorescent uranium salt and found that the new effect persisted. He soon concluded that the emanation was due to the element uranium itself. Even after about a year had passed, from when he first began his experiments, the intensity of the new rays had shown no signs of decreasing. But Becquerel was soon to move onto other scientific interests, and it was left to others to explore the rays in greater detail.

### RADIOACTIVITY

The Polish born chemist-physicist Marie Curie (figure 6.1), nee Sklodowska, was the first to take up the study of Becquerel rays. For her doctoral project, Marie Curie began to explore whether elements other than uranium might also produce Becquerel rays. She found that thorium, which occurs two places before uranium in the periodic table, also shows this form of behavior and coined the term "radioactivity" to describe this new property of matter.

While experimenting with pitchblende, an ore of uranium, she found that this material exhibited a more intense level of radioactivity than did pure uranium, which itself showed greater radioactivity than did uranium salts. She made the obvious deduction that a new element might be present in pitchblende and, working in 1898 with Pierre Curie, quickly succeeded in extracting a substance with 400 times the activity of uranium, which she named polonium after her native country. This element would find its place at the foot of group VI of the periodic table, below selenium and tellurium and eight places before uranium.

Continuing to work with the pitchblende they had used to extract polonium, the Curies found that it showed traces of yet another substance, which after much separation and purification, displayed an even more pronounced level of radioactivity, amounting to about 900 times that of uranium. This element, also discovered in 1898, was named radium.

Meanwhile, other physicists were also exploring Becquerel's rays. After studying in Cambridge under Thomson, the New Zealand–born physicist Rutherford moved to McGill University in Montreal. There he undertook a line of inquiry connected with Becquerel's rays by investigating the nature of the radiation itself.

FIGURE 6.1 Marie Curie. Photo and permission from Emilio Segreé Collection.

In 1899, he showed that radioactivity, as displayed by uranium, for example, produced a species of rays that could easily be absorbed by a thin metallic surface. He called them alpha rays. He also discovered a more penetrating species of rays, which he termed beta rays. Rutherford's identification of alpha rays, which, as he eventually realized, consisted of atoms of helium stripped of its two electrons, was to provide a powerful tool for probing the structure of the atom.

Between the years 1900 and 1903, Rutherford began to study the chemistry of radioactive substances. Working with a young colleague, the chemist Frederick Soddy, who will feature prominently later in this chapter, he made an epochal discovery, remarkable especially for its impact on understanding of the nature of the chemical elements. Rutherford and Soddy were compelled to announce that, in the course of radioactive reactions, certain elements were transformed into completely new elements. While fully aware of the possible criticism that such a notion might bring, they went as far as to describe this new phenomenon as chemical transmutation, thus evoking the age-old dream of the alchemists.

Some authors believe that the interpretation of the properties of the elements passed from chemistry to physics as a result of the discovery of radioactivity. They speak of "the redefinition of Mendeleev's chemical element, which would lead to its appropriation by physics." I believe this view to be overly reductionistic, as presumably did Fritz Paneth, who formulated his "intermediate position" in order to uphold the integrity of the chemical view of the elements and of the periodic system.

### THE DISCOVERY OF THE NUCLEUS

In 1911, following some experiments by his students Hans Geiger and Ernest Marsden, Rutherford revived the notion of a planetary atom in which electrons were believed to circulate around a central nucleus. As discussed in chapter 7, Jean Perrin and, in a somewhat different version, Hantaro Nagaoka were the first to propose such atomic models. But the nuclear atom had since been eclipsed by the work of Thomson, which had suggested that the electrons were embedded in the main body of the atom.

Upon firing a stream of positively charged alpha particles at a thin foil made of gold, Geiger and Marsden observed that some of the particles were scattered at very large angles and some even appeared to rebound straight back toward the incoming direction. Such a set of findings was inexplicable in terms of Thomson's model, in which the positive charge of the atom was diffused throughout the atom. This model predicted that almost all of the alpha particles would pass through the foil. Rutherford was forced to conclude that the atoms in the foil must contain concentrations of positive charge intense enough to deflect some of the alpha particles. He thus discovered that the positive charge is localized in a very small volume at the center of the atom, while the negative charge is diffused throughout the entire volume.

On the basis of his analysis of the alpha-scattering experiments of Geiger and Marsden, Rutherford further concluded that the charge on an atom is approximately half of its atomic weight. Rutherford and his colleagues observed that the degree of scattering is proportional to the square of the atomic weight of any particular atom. This effect was checked in a number of different target elements ranging from aluminum to lead. This, in turn, led to the conclusion that the scattering was proportional to the square of the nuclear charge, given that it is charge, rather than weight, that causes scattering of charged alpha particles. From further analysis of the scattering data, they arrived at the following approximate relationship between charge ( _Z_ ) and atomic weight _(A):_

Another British physicist, Charles Barkla, had arrived at precisely the same conclusion, also in 1911, by analyzing the scattering of X-rays from various substances. Barkla found that heavier elements produced a greater scattering in amounts proportional to their atomic weights and concluded that "the number of scattering electrons per atom is about half the atomic weight in the case of the light atoms." Since in the case of neutral atoms the number of positive charges is equal to the number of electrons, the conclusions of Rutherford and Barkla are identical.

### ATOMIC NUMBER

Rutherford's and Barkla's work on atomic charge contributed to the discovery of atomic number, but it was not the main evidence that brought it to the foreground. The discovery of atomic number provides the opportunity for a little digression on how the history of science is frequently rewritten and sanitized by subsequent commentators. The real discoverer was the amateur scientist Anton van den Broek (figure 6.2), whose contributions tend to be neglected. It is often thought that van den Broek merely summarized the work of physicists Rutherford and Barkla, but the true story is altogether different. It was van den Broek's close study of Mendeleev's periodic table, and his prolonged attempts to improve upon it, that led to his discovery of an ordinal number associated with each element. It also led to the identification of this number with the nuclear charge as well as the number of electrons in any atom.

Van den Broek trained in law and econometrics but published a number of influential articles in the leading scientific journals of his day. His first paper appeared in 1907 under the title "The a particle and the Periodic System of the Elements." It took as its point of departure a paper of the previous year in which Rutherford had suggested various explanations for the nature of the a particle. One of these suggestions, and the one favored by van den Broek, was that this particle consisted of half of a helium atom with a charge of +1. Van den Broek gave the name of alphon to this particle and proposed that it might take the place of the hydrogen atom in Prout's theory that all elements are composites of one basic particle.

FIGURE 6.2 Anton van den Broek. Photo and permission from Jan van Spronsen.

According to van den Broek's scheme, each particular number of aggregated alphons would thus correspond to a particular chemical element. Since the weight of the helium atom was known to be four units, the alphon would have a weight of 2, and all even numbers of composite alphons would correspond to the weights of the known elements. An atom of uranium, for example, with an atomic weight of 240, would be composed of 120 alphons, and so on. Since atomic weights are not exact multiples of each other, van den Broek realized that this suggestion would not be precise, but in the Pythagorean spirit of previous Proutian speculations, he was not unduly concerned by this aspect.

Of course, such a system required many more elements than were known to exist at the time if there were to be a total of 120, ending with uranium, which was the heaviest known element. Van den Broek made up for part of this deficit by incorporating many of the new radio-elements that had recently been discovered. These species would turn out to be isotopes rather than genuine new elements, but to enter into such matters now would be to get ahead of the story. At the time, the work on radioactivity that was emerging gave van den Broek confidence that the gaps in his table would be filled. In addition, the question of how to accommodate the rare earth elements into the periodic system had still not been settled, and it seemed plausible that several new rare earth elements awaited discovery.

In his paper of 1907, van den Broek included a periodic table constructed according to his scheme, showing a total of 41 gaps representing undiscovered elements that would have to be filled between hydrogen and uranium (figure 6.3). Each even number in the table corresponds to a chemical element, and the difference in atomic weight between any two adjacent elements is two units.

In 1911, van den Broek published a second paper, in which he claimed that Mendeleev had not sufficiently satisfied the requirements of chemical periodicity of the elements. He also noted that Mendeleev had intended to devise a three-dimensional periodic system, which would have remedied the situation, and it was this task that van den Broek was proposing to take up now. Despite this assertion, the table that van den Broek published in this paper was in fact two dimensional, although he implied that it could be constructed in three dimensions (figure 6.4). The third dimension would consist of short series of three elements, each of which is shown diagonally on the two-dimensional table. In any case, none of the conclusions that van den Broek drew from this new table depended on its supposed three-dimensional nature.

In the 1911 article, the notion of the alphon had disappeared, but van den Broek retained the idea of successive elements differing by two units of weight, whereas in Mendeleev's table successive elements typically showed alternating mean differences of approximately two and four units.

FIGURE 6.3 Van den Broek table of 1907. From The a Particle and the Periodic System of the Elements, _Annalen der Physik_ , 23, 199–203, 1907, p. 201. This version is from T. Hirosige, The Van den Broek Hypothesis, _Japanese Studies in the History of Science_ , 10, 143-162, 1971, p. 148 (by permission from the publisher).

That same year, van den Broek also published a very brief, 20-line letter to _Nature_ magazine. This letter may represent the first anticipation of the concept of atomic number, given that John Newlands's much earlier suggestion of an ordinal number for each of the elements (see chapter 3) was rather more tenuous. Van den Broek began by drawing attention to the fact that two lines of experimental research, namely, Rutherford's and Barkla's, supported the view that the charge on an atom is approximately half its atomic weight, or to repeat an equation that appeared just above, _Z≈A/2_. This evidence had provided support for his speculation of 1907 that atomic weight increases by approximately two units between each two consecutive elements. He then referred to his new periodic table and his prediction that 120 elements exist altogether, ending with the words,

If this cubic periodic system should prove to be correct, then the number of possible elements is equal to the number of possible permanent charges of each sign per atom, or to each possible permanent charge (of both signs) per atom belongs a possible element.

Van den Broek was suggesting that since the nuclear charge on an atom was half its atomic weight, and the atomic weights of successive elements increased in stepwise fashion by two, then the nuclear charge defined the position of an element in the periodic table. In other words, each successive element in the periodic table would have a nuclear charge greater by one than the previous element. In proposing this, van den Broek was going beyond Rutherford and Barkla, neither of whom had been primarily concerned with elements in the periodic table. Whereas Rutherford and Barkla realized that _Z ≈ A/2_ , van den Broek also realized that _Z ≈ A/2=_ atomic number. As the well-known physicist and author Abraham Pais has commented, "Thus based on an incorrect periodic table and on an incorrect relation (Z _≈_ A/2), did the primacy of Z as an ordering number of the periodic table enter physics for the first time."

FIGURE 6.4 Van den Broek table of 1911. From Das Mendelejeffsche "kubische" periodische System der Elemente und die Einordnuung der Radioelemente in dieses System, _Physikalishe Zeitschrift_ , 12, 490-497, 1911, p. 491. This version is from T. Hirosige, The Van den Broek Hypothesis, _Japanese Studies in the History of Science_ , 10, 143-162, 1971, p. 149 (by permission from the publisher).

But van den Broek's claim to fame does not lie just with this crude premonition of atomic number. By 1913, he abandoned his cubiform table and replaced it with an elaborate two-dimensional version (figure 6.5) and the clearly stated rule that "the serial number of every element in the sequence ordered by increasing atomic weight equals half the atomic weight and therefore the intra-atomic charge." Although this step takes matters a little further by mentioning serial numbers for each of the elements, it is still somewhat incorrect in being tied rather firmly to atomic weight, albeit atomic weight divided in half. Nevertheless, van den Broek's article was cited by no less a person than Niels Bohr in his trilogy paper of 1913, in which he introduced quantum theory to the atom.

Van den Broek's most significant contribution came in another short communication to _Nature_ magazine, published in 1913, in which he explicitly connected the serial number with the charge on each atom and disconnected it from atomic weight: "The hypothesis [about the serial number of the elements being equal to Z] holds good for Mendeleev's table but the nuclear charge is not equal to half the atomic weight." Van den Broek was able to take this important liberating step on the basis of more scattering experiments by Geiger and Marsden, which he analyzed in detail and discussed in his short note. This contribution was praised by Soddy in the next issue of _Nature_ and one week later also by Rutherford, who nevertheless privately resented the intrusion of amateurs. It was at this point that Rutherford actually coined the expression "atomic number":

TABLE 3

FIGURE 6.5 Van den Broek's table of 1913. From Die Radioelemente das Periodische System und die Konstitution der Atome, _Physikalische Zeitschrift_ , 14, 32-41, 1913, table on p. 37. This version is from T. Hirosige, The Van den Broek Hypothesis, Japanese _Studies in the History of Science_ , 10, 143-162, 1971, p. 152 (by permission from the publisher).

The original suggestion made by van den Broek that the charge on the nucleus is equal to the atomic number [i.e., the serial number in the periodic table] and not to half the atomic weight seems to me very promising.

### HENRY MOSELEY

So it was the amateur scientist van den Broek who confounded all the professional experts and first perceived the importance of atomic number as the ordering criterion for the elements. But as is often the case with scientific discoveries, it is the person who completes the task who is given the most credit, as seen in the case of Mendeleev and the discovery of periodicity.

Such is the case of Moseley (figure 6.6), who died in the First World War at the tender age of 26, before anyone outside the then very small circle of atomic physicists had heard of him. His subsequent fame lies in two brief articles that firmly established that atomic number, rather than atomic weight, was indeed a superior ordering principle for the elements. In addition, he was able to lay the groundwork by which others could settle conclusively that there were a total of 92 naturally occurring elements and could specify precisely where the remaining gaps were situated in the periodic table.

Moseley went to work as a research student with Rutherford, who was at this time in Manchester. There, he was given a project connected with radioactivity. In 1911, Moseley published an article with a fellow graduate student, the Polish born chemist Kasimir Fajans, concerning the measurement of half-lives of some radioactive products obtained from the element actinium.

A year later Max von Laue in Zürich was investigating the nature of X-rays. Believing that they were extremely short electromagnetic rays and therefore should exhibit interference effects, von Laue was attempting to diffract X-rays by bouncing them off planes of atoms in crystalline substances such as sodium chloride. By this time, it was known that X-rays came in two varieties. The first was a type originally observed by Röntgen, which were produced when electrons were stopped by some means, such as the glass walls of an evacuated Crookes tube. Second, Charles Barkla had discovered another kind of X-ray phenomenon brought about when electrons struck targets made of metals. Each different metal would produce X-ray lines showing a characteristic frequency. It was these X-rays, the ones coming off a metal target, and in particular the so-called Kα rays, that Moseley would exploit in his own research.

FIGURE 6.6 Henry Moseley. Photo from author's collection used by permission from Emilio Segré Collection.

Moseley made it clear in his articles that he was essentially setting out to test van den Broek's speculation regarding the characterization of each element according to its atomic number. In addition, it is known that he had several meetings with the young Bohr while he, too, was a visitor in Rutherford's Manchester laboratory around 1912-1913. Bohr and Moseley discussed the question of the ordering of nickel and cobalt, an example of pair reversal. Bohr is known to have favored placing cobalt before nickel, to which Moseley is said to have responded "we shall see." Moseley devised an ingenious apparatus in which many different metal plates could be rotated so that each one would become the target for a beam of electrons, and the emitted Kα X-rays would be measured. He first experimented on 14 elements, nine of which, titanium to zinc, formed a continuous series in the periodic table. Moseley discovered that a plot of the frequency of the lines of the K series of spectral lines of each element was directly proportional to the square of an integer representing the position of each successive element in the periodic table. He found that the frequency, _n_ , of the K _a_ X-rays obtained from each sample target varied according to an expression of the form where _Q_ is a number that increases by a constant amount on moving through the elements.

Moseley had discovered a fundamental quantity that increased by regular intervals as he moved through his sequence of elements in the order in which they appeared in the periodic table. He quickly recognized this quantity as the positive charge on the nucleus, or van den Broek's atomic number. As he stated:

We have here a proof that there is in the atom a fundamental quantity, which increases by regular steps as we pass from one element to the next. This quantity can only be the charge on the central positive nucleus, of the existence of which we already have definite proof.

Moseley acknowledged the previous work of Barkla, van den Broek, and Bohr, all of whom had anticipated his own findings. He also showed that _Q = N_ – 1, where _N_ represents the number of unit charges in the nucleus and therefore the atomic number.

Moseley's second famous paper appeared in print in April 1914. He now reported measurements on a further 30 elements. By examining the K series from aluminum to silver, and the L series of spectral lines from zinc to gold, he found a general expression of the form,

where _b_ = 1 for the K series and

Similarly, for the L series _b_ = 7.4 and

As soon as Moseley had established the importance of atomic number experimentally, he began to apply this work in settling various questions regarding new elements that had been claimed by various chemists. A total of approximately 70 proposed new elements competed to fill the 16 gaps in Mendeleev's periodic table. Moseley succeeded in showing that many of these were spurious and was able to resolve some priority disputes regarding the discovery of certain elements.

For example, a Japanese chemist, Masataka Ogawa, claimed to have isolated an element that he called nipponium and that he believed to be Mendeleev's eka-manganese. Moseley was able to show that this claim was unfounded since the sample provided by Ogawa did not show the required atomic number when subjected to Moseley's spectral analysis. Similarly, coronium, nebullium, casseopeium, and asterium, which appeared on many early periodic tables, often between hydrogen and lithium, could all be dismissed as spurious elements.

Moseley's work was also used to settle the question of the placement of the rare earth elements, a task that had eluded Mendeleev and other early pioneers of the periodic table. Mendeleev had stated that the placement of the rare earths was one of the most difficult problems of all those confronting the periodic law. The rare earths were notoriously difficult to separate chemically. Since they appeared to differ only slightly in atomic weight and properties, no one had been able to find a satisfactory way of fitting them into the periodic table. According to William Crookes,

The rare earths perplex us in our researches, baffle us in our speculations, and haunt us in our very dreams. They stretch like an unknown sea before us, mocking, mystifying, and murmuring strange revelations and possibilities.

Georges Urbain, a French chemist known for his work on the isolation of rare earth elements, traveled to Oxford in order to meet Moseley after hearing of his groundbreaking work. As the story goes, Urbain handed Moseley a sample containing a mixture of rare earths and challenged him to identify which elements were present. After a matter of about one hour, Moseley is said to have surprised Urbain by correctly identifying the presence of erbium, thulium, ytterbium, and lutetium in the Frenchman's sample. The same feat had taken Urbain several months to achieve by chemical means. Urbain then asked Moseley to tell him the relative amounts of the various elements in the sample and was again astonished to receive an answer that coincided almost exactly with his own laborious chemical analysis.

Moseley's work clearly showed that successive elements in the periodic table have an atomic number greater by one unit. From this fact, Moseley and others could identify which gaps remained to be filled in the periodic system and found that there were a total of seven such cases still waiting to be discovered. Unlike previous lists of gaps, this list was now completely definitive and included the precise atomic numbers of the still elusive elements, which were 43, 61, 72, 75, 85, 87, and 91.

The clarification that Moseley brought to the periodic table represents one of the finest examples of the reductive power of physics in the field of chemistry. Most lingering problems regarding pair reversals, such as those concerning tellurium and iodine, which had plagued Mendeleev throughout his career, were thereby resolved. Furthermore, Moseley's work made it easier to deal with the profusion of apparent new "elements" that emerged as a result of research on radioactive phenomena. Two substances could be regarded as being the same element if, and only if, they showed the same value of atomic number, which could be clearly measured by Moseley's method.

### FILLING THE REMAINING GAPS

The seven remaining gaps in the periodic table were gradually filled, although not without further controversy in spite of the conclusive nature of Moseley's atomic number method. The first of these was element 91, discovered by Otto Hahn and Lise Meitner in 1917. The element behaved in the manner described by Mendeleev, who had given it the provisional name eka-tantalum. It now became known as protactinium but was not isolated until the year 1934 by Aristide Grosse in Germany.

Element 72, or hafnium, has a rich and controversial story associated with its discovery. Several researchers, including Urbain, independently claimed to have discovered the element but were later found to have been mistaken. In 1923 Dirk Coster and György von Hevesy, working in the Niels Bohr Institute in Copenhagen, finally succeeded in isolating the element, naming it for _Hafnia_ , Latin for Copenhagen. According to most accounts, Bohr had first made a theoretical prediction that the element would be a transition metal rather than a rare earth. In fact, some chemists already shared this opinion. As discussed in chapter 8, Charles Bury had also predicted that the element would be a transition metal and had even arrived at its electronic configuration before Bohr.

Element 75, called rhenium, was first discovered in Berlin in 1925 by the husband and wife team of Walter and Ida Noddack, who isolated it and used Moseley's X-ray method to confirm the presence of the new element. The Noddacks were also looking for element 43, Mendeleev's eka-manganese, and claimed to have found it in the same ores, calling the new element masurium after Walter Noddack's native region of Prussia. The Noddacks published X-ray data for masurium, but it was discredited by others for a variety of reasons. The distinction of discovering element 43 went to Carlo Perrier and Segre, who obtained it 12 years later, in 1937, at the University of California-Berkeley. They named the new element technetium to reflect the fact that it had been artificially synthesized as a byproduct in a nuclear reaction.

Recently, it has come to light that technetium may indeed have been isolated by the Noddacks and Walter Berg. This reassessment was carried out by the Dutch physicist Pieter Van Assche in the late 1980s on the basis of a careful reanalysis of the German team's X-ray data. The evidence marshaled by Van Assche is rather convincing and implies that the first isolation of element 43 involved a naturally occurring element. Had the discovery been recognized at the time, there would have been no need to name the element technetium since it seems that it does occur naturally.

In 1939, an element subsequently named francium, number 87, was discovered in Paris by Marguerite Perey, and in 1940 Segre discovered astatine, element 85. The final piece of the jigsaw puzzle, element 61, promethium, was finally obtained as a byproduct in a nuclear reaction. The discoverers on this occasion were Jacob Marinsky, Lawrence Glendenin, and Charles Coryell.

### WHAT MOSELEY DID NOT ACHIEVE

As with so many scientific heroes, perhaps more so in this case because of his early death, the claims for what Moseley is supposed to have achieved far outpace the truth. The hagiography of Moseley is constantly propagated by science textbooks, sometimes in sincere attempt to simplify the account, but it also occurs in more detailed historical treatments. Contrary to most accounts, Moseley did not personally settle the question of how many naturally occurring elements exist. Nor did he even definitively resolve the question of how many elements exist between aluminum (13) and gold (79), which marked the boundaries of his own studies. By assuming that aluminum is the 13th element, Moseley argued that there could be only 79 elements up to and including gold.

Limiting the elements to 79 left only three remaining gaps in the periodic table, located at atomic numbers 43, 61, and 75. But Moseley could not be confident of this prediction since he did not have pure samples of some of the rare earths. X-ray spectra were not available for terbium (65), dysprosium (66), thulium (69), ytterbium (70), and lutetium (71), and this led him to assert incorrectly the existence of three forms of thulium, named thulium, thulium I, and thulium II.

This assignment in turn meant that such elements as ytterbium and lutetium were advanced by one place, so no vacant space was left at element 72. Moseley was unable to place Urbain's keltium, which eventually turned out to be the same as lutetium, discovered by Urbain a few years previously. When matters were resolved, after Moseley's early death, only one form of thulium remained and ytterbium and lutetium were found to have atomic numbers of 70 and 71, respectively. This meant that there was a vacant gap at 72 for a new element between lutetium and tantalum, the element that would eventually be named hafnium.

Since his experiments did not go beyond gold, or atomic number 79, Moseley certainly did not show that uranium is element 92, as is often claimed. This honor went to the spectroscopist Manne Siegbahn, working in Sweden, in 1916. Finally, even the central achievement invariably associated with Moseley, the realization that atomic number is equal to the number of positive charges in the nucleus, was not conclusively settled until some time later.

In 1920, James Chadwick, who 12 years later would discover the neutron, reanalyzed Moseley's work. He discovered that the choice of value for the constant _b_ = 7.4 was not as inevitable as Moseley had claimed. It was still possible in principle for an atomic number not to equal the number of positive charges in the nucleus, and this in turn would have implied that there might be more than 13 elements from hydrogen to aluminum inclusive. Chadwick therefore decided to make some independent measurements of the charges on various nuclei using a refined version of Geiger and Marsden's experiment with alpha rays. Only after this work had been carried out and atomic charges been successfully measured by a second method did Chadwick announce the confirmation of Moseley's simple idea. Atomic number does indeed equal the number of positive charges in the nucleus of any atom.

### PHILOSOPHICAL DEBATES REOPENED

Van den Broek's suggestion, and Moseley's experimental work on atomic number, had the effect of rehabilitating Prout's hypothesis, which had proposed that all elements were composites of hydrogen. The atomic numbers of all the elements were indeed exact multiples of the atomic number for hydrogen, which is 1. More generally, the work of van den Broek and Moseley revitalized some philosophical notions of the unity of all matter that had been so harshly criticized by Mendeleev, among others. By now, Thomson had shown that the electron was common to all elements and Rutherford had established that electric particles were present in the nuclei of all elements. Moseley had added the fact that all nuclei seemed to consist of an integral number of positive charges. There clearly seemed to be some form of underlying unity behind the apparent diversity of the elements. This view was strengthened further when Rutherford discovered that elements could be transmuted into each other through the use of radioactive techniques, thus once again recalling the ancient alchemical notion of the fundamental unity of all matter.

Nevertheless, the cause of the initial rejection of Prout's hypothesis, in its original form, had not been resolved. As described in chapter 2, this was the fact that certain elements such as chlorine (35.46) and lead (207.20) had nonintegral atomic weights. This particular puzzle had to await the discovery of isotopy, which is generally attributed to the chemist Soddy.

### ISOTOPY

The idea that any element can consist of different kinds of atoms can be traced to a remark made by Crookes in 1886:

I conceive that when we say the atomic weight of calcium is 40, we really explain the fact, while the _majority_ of calcium atoms have an actual atomic weight of 40, there are not a few which are represented by 39 or 41, a less number by 38 or 42, and so on.

The first clear elaboration of isotopy, however, came much later and belongs to the English chemist Soddy, who began as one of Rutherford's collaborators, like so many others who made important contributions to atomic science. After research in chemistry at Oxford, Soddy joined Rutherford at McGill University in Montreal in 1900 and participated in much of the work that established the concept of radioactive half-lives and the reality of radioactive transmutation.

During this time, other scientists were also exploring radioactivity and in the process were discovering new elements. The first of these were polonium, radium, actinium, and radon, followed by another 30 or so suspected new elements, most of which would turn out to be isotopes of existing elements. Some, like van den Broek, tried desperately to incorporate all these new species into the periodic table. Others, including the Swedes Daniel Strömholm and Theodor Svedberg, realized that there were great similarities among many of these new species. As Jan van Spronsen notes in his book on the periodic table, Strömholm and Svedberg can also be regarded as having anticipated the existence of isotopes. For example, they grouped together radium emanation, actinium emanation, and thorium emanation into one single place in their periodic system (table 6.1). Similarly, radium, actinium X, and thorium X were all made to occupy a single place. Without explicitly stating the concept and drawing out its full consequences, Stromholm and Svedberg had realized that several species can occupy a single space in the periodic table, a concept Soddy was soon to name isotopy from the Greek _iso_ (same) and _topos_ (place).

D. Stromholf, T. Svedberg, Untersuchungen über die Chemie der radioaktiven Grundstoffe. II. Die Aktiniumreihe _Zeitschrift für anorganische Chemie_ ,, 63, 197-206, 1909, table on p. 204. The abbreviation Rad stands for radio, a prefix used to denote suspected new elements, such as radio-thorium, most of which turned out to be isotopes. Em denotes the term emanation meaning substances emanating from a particular element. Akt was the German abbreviation for the modern symbol Ac for actinium.

Another strand of development came from several attempts to separate some of these new radio-elements chemically, which ended in failure. First of all, in 1907 Herbert McCoy and William Ross concluded that, in the case of thorium and radiothorium, "Our experiments strongly indicate that radiothorium is entirely inseparable from thorium by chemical processes," a comment Soddy considered the first definitive statement of the chemical inseparability of what were soon to be called isotopes. Soddy himself wrote in the same year that there seemed to be no known method of separating thorium X from mesothorium. They were in fact two isotopes of thorium. Similar cases began to multiply. Bertram Boltwood discovered the radio-element ionium, which could not be chemically separated from thorium. In another famous case, Hevesy and Paneth were asked by Rutherford to try to separate radio-lead from ordinary lead and likewise failed to do so, in spite of using 20 different chemical methods. Their work was not entirely in vain, however, since it led to the development of the use of radioactive tracers, which have become an indispensable tool in modern chemistry and biochemistry.

In 1911, Soddy wrote the following comments regarding the various series of very similar radioactive elements that had recently been discovered:

The conclusion is scarcely to be resisted that we have in these examples no mere chemical analogues but chemical identities. . . . Chemical homogeneity is no longer a guarantee that any supposed element is not a mixture of several different atomic weights, or that any atomic weight is not merely a mean number. The constancy of atomic weight, whatever the source of the material, is not a complete proof of homogeneity.

The first time Soddy actually used the term "isotope" was in an article in 1913, where he wrote,

The same algebraic sum of positive and negative charges in the nucleus, when the arithmetic sum is different, gives what I call "isotopes" or isotopic elements, because they occupy the same place in the periodic table. They are chemically identical, and save only as regards the relatively few physical properties which depend upon atomic mass directly, physically identical also.

The first sentence in this quotation might appear to be a mistake, and in a sense it is since there are no negative charges in the nucleus. What Soddy was referring to was beta particles, which are identical to electrons but are created in the nucleus. In modern terms beta decay involves the transformation of a neutron into a proton, accompanied by the emission of a beta particle. Interestingly, the notion that beta particles originate in the nucleus was first proposed by van den Broek and later supported by several others, including Soddy.

Many aspects of the problem of inseparable elements were clarified when Soddy and Fajans independently suggested what became known as the group displacement laws. They stated that the emission of an alpha particle from the atom of an element produces an element located two places to the left, while the emission of a beta particle resulted in a movement of one position to the right in the periodic table. It followed that the elements between lead and uranium in the periodic table could exist as more than one kind of atom, differing in mass but displaying the same chemical behavior. For example, if an atom of uranium-235 ( _Z_ = 92) undergoes alpha decay, it forms an atom of thorium-231 ( _Z_ = 91). Meanwhile an atom of actinium-230 (Z = 89) can undergo beta decay to form an atom of thorium-230 (Z = 90). The products of both radioactive decays are atoms of the same element but have different atomic weights. Fajans coined the term "pleiad" to mean a group of chemically identical atoms with different atomic masses, but his term was not generally adopted.

Only now did it become clear why such elements as tellurium and iodine, and other pair reversals, had caused so much trouble for the pioneers of the periodic system. Tellurium has a lower atomic number than iodine and so should genuinely be placed before iodine, as Mendeleev and others had guessed. In addition, it was now clear that the higher atomic weight of tellurium was due to a higher average mass of the various isotopes that made up a terrestrial sample of this element.

The final piece of evidence that completed this episode regarding isotopes and the periodic table was provided by the Harvard chemist Theodore W. Richards in 1914. Although the idea that isotopes of the same element, arising from different mineral sources, might have different atomic weights had been discussed for a few years, it had not been directly examined. Richards, an acknowledged expert on atomic weight determination, was ideally placed to undertake this research. Since the element lead had been found to be the end point in several radioactive decay series, it was reasonable to expect this element to show some variation in atomic weight. Any such variation would depend on the mineral source used, since any lead found in earth might have resulted from one of several different elements by a process of natural transmutation brought about by radioactive decay.

Fajans' and Soddy's independent work on the displacement series had shown that the stable end products of all three radioactive decay series, as well as common lead, were chemically indistinguishable or, in the new terminology, were all isotopes of lead. What Richards set out to discover was whether different naturally occurring mixtures of these isotopes might show different atomic weights, as one might expect. In the report by Richards and a young German student Max Lembert, they called their results "amazing." They had found atomic weights of lead differing from that of common lead by as much as 0.75 of an atomic weight unit, an amount that was several times larger than the error associated with their experimental method. Repeated purification of lead samples from various radioactive origins produced no changes in their atomic weights. Encouraged by this research, others tried to find other ores of lead in the hope of showing an even greater variation in atomic weights. These efforts eventually produced a lowest value of 207.05 and a highest value of 207.90.

### POSTSCRIPT ON TRIADS

The discoveries discussed in this chapter effectively revived Prout's hypothesis as well as the related notion of the unity of matter, two philosophical ideas discussed in chapter 2. The other main theoretical notion discussed in chapter 2, that of triads, also received a form of rehabilitation. The discovery of triads had given the very first hint that groups of three elements were related to each other. These relationships were not just in chemical similarities but were also numerical, in that the atomic weight of one of the three elements in a triad was shown to be approximately the arithmetic mean of the weights of the other two.

This idea had been at the root of Döbereiner's work, which is often taken as marking the birth of the modern periodic system. However, there were limits to the applicability of the triad concept, and it is probably fair to say that much time was wasted by other researchers in trying to uncover triads where they simply did not exist. Some pioneers, including Mendeleev, made it a point to turn their backs on the two original concepts of Prout's hypothesis and the existence of numerical triads. This attitude certainly seems to have paid dividends for Mendeleev in that he made progress where others had failed to do so.

The problem with triads and, indeed, Prout's hypothesis is easy to discern in retrospect. It is simply that atomic weight, which both concepts draw upon, is not the most fundamental quantity that can be used to systematize the elements. Atomic weight such as that of lead, as just discussed, depend on the particular geological origin of the sample examined. In addition, the measured weight is an average of several isotopes of the particular element. Atomic number, on the other hand, is fundamental and correctly characterizes, as far as presently known, the distinction between one element and the next. Prout's hypothesis is brought back to life if one considers that all the elements are composites of the atomic number, or charge, of the element hydrogen, which has a value of 1.

In the case of triads, the adoption of atomic number has an intriguing consequence that has seldom been discussed: About 50% of all vertical triads based on atomic number, rather than atomic weight, are absolutely exact  This remarkable result is quite easy to appreciate by referring to the long form of the modern periodic table (figure 6.7).

By considering elements from rows 1, 2, and 3, such as helium, neon, and argon, a perfect atomic number triad is obtained:

Or, from rows 3, 4, and 5:

Or, from rows 5, 6, and 7:

Alternatively, any triads taken from combinations of elements in rows 2, 3, 4 or from rows 4, 5, 6, and so on, do not give perfect triads.

The reason why this works so perfectly, albeit in only 50% of possible triads, is because the length of each period repeats just once in the long-form periodic table, with the exception of the very first short period. The full sequence is 2, 8, 8, 18, 18, 32, 32, and so on. So, if one selects any element, then there is a 50% chance that the element above and below the selected element, in the same column of the periodic table, will have atomic numbers lying at an equal distance away from the original element. If this is the case, then it follows trivially that the second element in the sequence will lie exactly midway between the first and third elements. In numerical terms, its atomic number will be the exact mean of the first and third elements, or in other words, the atomic number triad will hold perfectly. All one needs to do is to pick a middle element from the first of a repeating pair of periods. Thus, half of all the elements are good candidates. This phenomenon falls out mathematically from the fact that all periods repeat (except for the first one) and that the elements are characterized by whole number integers. It would appear that the original discoverers had accidentally stumbled upon the fact that some periods of elements repeat twice. What held them back was that these repeat distances vary in length and, of course, the fact that they were operating with the vagaries of atomic weight data.

FIGURE 6.7 Slightly modified long-form table showing that about 50% of all atomic number triads are exact. The heavily outlined elements represent examples of perfect atomic number triads.

It is somewhat amusing to think that the ancient notions of Prout's hypothesis and triads of elements, which were initially so productive and later so strongly criticized, have been shown to be essentially correct, and that the reason for their being essentially correct is now fully understood. In fact, the philosopher of science Imre Lakatos used the example of Prout's hypothesis to illustrate a theory making a "comeback" after being apparently refuted.

### CONCLUSION

This chapter examines the various lines of research on the nucleus of the atom that contributed to the evolution of the periodic system. This represents the first time that work in physics began to have a profound impact on the way the periodic system was understood. Perhaps the most important of these contributions has been the concept of atomic number, first argued for by van den Broek and first experimentally demonstrated by Moseley. The importance of this work is that, for the first time, chemists now had an unambiguous method for determining exactly how many elements were present and where in the periodic system any gaps might still remain to be occupied by new elements.

## **CHAPTER 7  
THE ELECTRON AND CHEMICAL PERIODICITY**

J.J. Thomson's discovery of the electron is one of the most celebrated events in the history of physics. What is not so well known is that Thomson had a deep interest in chemistry, which, among other things, motivated him to put forward the first explanation for the periodic table of elements in terms of electrons. Today, it is still generally believed that the electron holds the key to explaining the existence of the periodic table and the form it takes. This explanation has undergone a number of subtle changes. The extent to which the modern explanation is purely deductive or whether it is semiempirical is examined in this chapter.

While Dimitri Mendeleev had remained strongly opposed to any attempts to reduce, or explain, the periodic table in terms of atomic structure, Julius Lothar Meyer was not so averse to the reduction of the periodic system. The latter strongly believed in the existence of primary matter and also supported William Prout's hypothesis. Lothar Meyer did not hesitate to draw curves through the numerical properties of atoms, whereas Mendeleev believed this to be a mistake, since it conflicted with his own belief in the individuality of the elements.

This is how matters stood before the discovery of the electron, three years prior to the turn of the twentieth century. The atom's existence was still very much a matter of dispute, and its substructure had not yet been discovered. There appeared to be no way of explaining the periodic system theoretically.

### THE DISCOVERY OF THE ELECTRON AND EARLY MODELS OF THE ATOM

Johnston Stoney first proposed the existence and name for the electron in 1891, although he did not believe that it existed as a free particle. Several researchers discovered the physical electron, including Emil Wiechert in Köningsberg, who was the first to publish his findings. Because these early researchers did not seriously follow up on their results, it was left to the British physicist Thomson to capitalize upon and establish the initial observations. These false starts show an interesting parallel with the discovery of the periodic system, where the essential idea of periodicity occurred to a number of scientists, including Emile De Chancourtois, John Newlands, and William Odling, none of whom was able to make much headway in establishing his insights.

While Wilhelm Röntgen discovered X-rays by experimenting with cathode rays, Thomson was one of several physicists who set out to explain the very nature of these cathode rays. The experiments he and others were carrying out typically involved the passage of an electric discharge of about 1,000V through a gas held in a glass tube of about 300 cm in length and 3 cm wide at a pressure of about 0.01 mm of mercury. In 1869, the year of Mendeleev's famous periodic table, Johann Hittorf in Germany had observed that glowing rays were emitted from the cathode, or negative pole, of such an experimental apparatus. Some early workers, such as William Crookes, supported the notion that these "cathode rays" were particles projected from the negative pole and were themselves negatively charged. A number of others working in Germany, such as Heinrich Hertz, came to believe that the cathode rays were a form of radiation. In 1897, Wiechert interpreted his own experiments by concluding, "We are not dealing with atoms known from chemistry, because the mass of the moving particles turned out to be 2000-4000 times smaller than the one of the hydrogen atom, the lightest of the known chemical atoms." In the same year, Walter Kaufmann measured the charge-to-mass ratio of cathode rays and found it to be the same in every gas, a fact that puzzled him but did not lead him to draw the conclusion that the particle might be a universal constituent of all substances.

It was in this context that Thomson conducted his own research, which, according to the traditional account, led to the discovery of the electron and the realization that it was indeed a constituent of all matter. By now, it was known that cathode rays were negatively charged, and they appeared to be particulate. But there was yet no confirmation of their particle nature. This would be forthcoming only if it could be shown that cathode rays could be deflected by an electric field, something that had eluded all previous attempts. Thomson succeeded where others had failed by using an extremely high electric charge as well as by ensuring that the glass tube was under vacuum conditions. Under these conditions, the cathode rays finally showed a deflection due to an electric field in 1897.

Moreover, Thomson was able to measure the charge-to-mass ratio of cathode rays and found a value of 770 for cathode rays emanating from hydrogen atoms. This finding suggested three possibilities: the particles making up the cathode rays bore a very large charge, or they had a very small mass, or possibly a combination of the two effects. It was later found that cathode rays, or electrons, as they became known, had the same charge as hydrogen ions, although of opposite sign, but had a much smaller mass. Last but not least, Thomson went beyond Wiechert in that he repeated his experiments with cathode rays produced from various different elements, concluding that the same particle was produced in each case, and that this particle was therefore a fundamental constituent of all matter. Thomson seems to have disliked Stoney's name for the particle, although it had been popularly adopted. He insisted on calling it the "corpuscle," only later capitulating to the popular usage of "electron."

### MODELS OF THE ATOM

The newly discovered electron began to feature in several postulated models of the atom. The French physicist Jean Perrin, like Thomson in England, had conducted experiments on cathode rays. In fact, Perrin had been the first to obtain direct proof that the electron was negatively charged. This was carried out in experiments in which a metal cylinder was placed inside a vacuum tube in order to collect the charge. By drawing on this finding, in addition to the experimental evidence gathered by Thomson, Perrin suggested the first planetary conception of the atom in 1901. He proposed that each atom consisted of one or more highly charged positive bodies, much like a positive sun around which small negative planets, or electrons, were in orbit. Perrin also believed that the total negative charge in the atom would be exactly equal to the total positive charge, in apparent anticipation of current views on the structure of the atom. He stated his hypothesis thus:

Each atom will consist of one or more highly charged positive bodies, a kind of positive sun whose charge is much higher than that of a corpuscle (electron), and also of a kind of small negative planets, all these bodies gravitating under the action of electrical forces, and with total negative charge exactly equal to the total positive charge, so that the atom is electrically neutral.

A further proposal by Perrin in the same paper seems to foreshadow later work on the connection between the structure of the atom and spectral frequencies: "The gravitational periods of the different masses in the atom might correspond to the different wavelengths of light revealed in the rays of the emission spectrum." In modern terms, the wavelengths of light revealed in the atomic spectra are not related to gravitational periods but to transitions between energy levels, which are characteristic of the various orbitals that the electrons can occupy. In 1903, Han-taro Nagaoka in Japan independently proposed a Saturnian atom in which electrons move in one or more rings around a central body. A translation of one of his lectures was published in 1904 in the _Philosophical_ Magazine and was subsequently quoted by leading physicists such as Ernest Rutherford and Henri Poincare.

In that same year, Thomson began to think specifically about how the electrons might be arranged in the atom. He concluded that the solar system-like atoms of Perrin and Nagaoka would be unstable because the orbiting electrons would continuously radiate energy, eventually falling into the center of the atom. He suggested an alternative model in which the electrons were embedded in the nucleus, circulating within its positive charge. This became known as the "plum pudding" model of the atom. In a paper of 1904, Thomson also published the first set of electronic arrangements, or what today would be called electronic configurations. In taking this step, Thomson went beyond Perrin and Nagaoka in conceiving of the electrons not just as moving around the atom but doing so in a structured manner.

Thomson based his configurations of electrons on the work of an American physicist Alfred Mayer, who had experimented with magnets that were attached to corks and floated in a circular basin of water above which was placed a current-bearing metal coil (figure 7.1). Meyer had found that when up to five magnets were floated, they would form a single ring, but that on the addition of a sixth magnet a new ring would be formed. As more magnets were added, the phenomenon repeated: When a certain number of magnets was reached, the addition of a new magnet caused the formation of yet another ring, thus producing an arrangement of concentric rings. Thomson believed that the same kind of principle might operate in the case of electrons circulating in the atom and began to develop these views in an attempt to explain the periodic table in terms of the electron.

In many respects, Thomson can therefore be regarded as the originator of electronic configurations and of attempts to explain the periodic table in terms of them. Table 7.1 is an extract from one of Thomson's later articles showing how his electron rings were arranged. As with Mayer's cork rings, the presence of five electrons in an atom results in the formation of one electron ring in Thomson's account. A second ring begins to form once the number of electrons reaches six, although after this happens, new electrons continue to be added to the first ring, just as in the case of the floating needles and corks. On reaching 10 electrons, a new electron suddenly appears in the second ring, and on reaching 17 electrons, a third ring begins to form. In each case, the additional, or differentiating, electron is generally being added to an inner ring rather than to an outer one.

FIGURE 7.1 Mayer's floating magnets. From Alfred M. Mayer, On the Morphological Laws of the Configurations Formed by Magnets Floating Vertically and Subjected to the Attraction of a Superposed Magnet; With Notes on Some of the Phenomena in Molecular Structure Which These Experiments May Serve to Explain, _American Journal of Science_ , 15, 276-277, 1878. This image from the original paper is reproduced from J.J. Thomson, _The Corpuscular Theory of Matter_ , Archibald Constable, London, 1907, p. 111.

TABLE 7.1  
J.J. Thomson's Electron Rings

From a modern point of view, these electronic arrangements have little merit in chemical terms since they suggest a nonexistent analogy between, for example, element 5, boron, and element 16, sulfur. It would be expected that, since they are assigned five electrons in their outermost shells according to this scheme, boron and sulfur would display similar chemical properties, which is not in fact the case. But it would be a mistake to criticize Thomson on this point, since in 1904 he and his contemporaries were not aware of the number of electrons in any particular atom. Not until Henry Moseley's work with atomic number was published 10 years later would it become clear that the serial number of an element in the periodic table, its atomic number, corresponds to the number of positive charges in the atom. In proposing his new scheme of electron rings, J.J. Thomson was merely suggesting the plausibility of explaining periodicity through similarities in electronic structures among different elements, something that remains valid to this day.

Although Thomson's atomic model would soon be discarded by Rutherford when he introduced his nuclear model of the atom, it did succeed in establishing two important concepts. One was that the electron held the key to chemical periodicity, and the other was the notion that the atoms of successive elements in the periodic table differ by the addition of a single electron. Both of these ideas were to become important aspects of Niels Bohr's atomic theory of periodicity, which would soon be published.

### THE QUANTUM THEORY OF THE ATOM

When Rutherford revived Perrin's and Nagaoka's planetary model of the atom following Hans Geiger and Ernest Marsden's alpha particle scattering experiments, he left the problem of the model's stability unresolved. According to James Clerk Maxwell's electromagnetic theory, any circulating charged body should lose energy through radiation, so the orbiting electrons would be expected to spiral into the nucleus. The nuclear model implied that any atom, and consequently all matter, would thus be unstable, contrary to the obvious facts of experience. Furthermore, Rutherford's model could not explain the discrete nature of the optical spectra of atoms that had been accurately recorded since the development of the spectroscope in 1859 and that had been used to identify many new elements.

The pattern observed following the dispersion of light emitted from excited atoms is quite different from that of white light. Instead of a continuous spectrum ranging from red to violet frequencies, one observes a series of discrete lines of various colors. Some particular color frequencies are simply missing compared with the spectrum from a source of white light. The discrete nature of the spectrum in the case of atoms could not be explained by any of the atomic models that have been reviewed so far. In Rutherford's model, for example, the energies of the electrons are not restricted to particular values; consequently, all possible transition energies would be expected to occur, and the optical spectrum of any element would be continuous rather than discrete.

Both of these problems, the stability of atoms and the discrete nature of atomic spectra, were resolved by the Danish physicist Bohr (figure 7.2), who also provided the first successful explanation of the periodic system in terms of arrangements of electrons in the atom. Bohr obtained a Ph.D. in theoretical physics of the study of metals before undertaking a one-year postdoctoral fellowship with Rutherford at Manchester. Although other physicists had begun to establish the quantum theory in physics, Bohr was the first to apply these ideas in the context of atomic physics.

Bohr first came to prominence in 1913 when he published his quantum theory of the hydrogen atom. The notion of quanta, or packets of energy, had been introduced by Max Planck in 1900 to explain the details of observations made on the black-body radiation. Bohr adopted Planck's notion of quantization and applied it to the physics of atoms. His calculations led him to conclude that, in the planetary model of the atom, additional rings of electrons are formed outside already full rings, correcting Thomson's model of electron rings, in which electrons are added to inner rings. Most important, Bohr proposed that electrons would be stable if they remained in certain quantized orbits and would lose energy only on undergoing transitions from one orbit to another, more stable orbit. Electrons in a discrete set of stable orbits around the nucleus of an atom were said to be in stationary states that would not radiate energy:

FIGURE 7.2 Niels Bohr. Photo and permission from Emilio Segré Collection.

An atomic system can only exist permanently in certain series of states corresponding to a discontinuous series of values for its energy, and that consequently any change of the energy of the system, including emission and absorption of electromagnetic radiation, must take place by a complete transition between two such states. These states are denoted as "stationary states" of the system.

Bohr was following Planck's lead in departing from classical electromagnetic theory. In studying black-body radiation, which occurs at very short frequencies, Planck had found it necessary to introduce a constant, h, also called the elementary quantum of action, to explain its discontinuous nature. Such radiation could be emitted or absorbed only in packets, or quanta, described by the formula _h_ ν, where ν is the frequency of the radiation and _h_ is Planck's constant. Bohr was suggesting that the atom could likewise not be described adequately by the laws of classical mechanics but that it required a quantum description.

Applying Planck's idea of how electrons move from one stationary state to another, Bohr proposed that for the atom to pass from one energy state to another it must emit or absorb one quantum, _h_ **v,** of energy:

The radiation absorbed or emitted during a transition between two stationary states is "unifrequentic" and possesses a frequency V given by the relationship,

_E'_ – _E_ = _hv_

where _h_ is Planck's constant, and _E'_ and _E_ are the values of the energy in the two states under consideration.

But this theory was limited in its application in that it gave an exact account only of the spectrum of hydrogen, the simplest case. Atoms with more than one electron are much more complicated, since the various electrons exert influences on each other. Nevertheless, Bohr had sufficient confidence in his quantum theory of the atom to try to apply it to multielectron atoms in an approximate manner.

Although he first applied his quantum theory of the atom to the spectrum of the hydrogen atom, historians of physics John Heilbron and Thomas Kuhn have shown rather conclusively that the initial motivation for Bohr's theory was more comprehensive. Bohr was rather attempting to gain an understanding of the periodic table through electronic configurations and to examine the stability of the electron rings with which Thomson had tried to explain the periodic table. In this same article of 1913, Bohr produced his first version of an electronic periodic table. He assigned electronic configurations to the atoms of various elements in terms of the principal quantum number of each electron, which could be used to characterize its stationary or nonradiating states (table 7.2).

Bohr's general method, called the _aufbauprinzip_ (which translates as "building up"), consisted in building up atoms of successive elements in the periodic table by the addition of an electron to the previous atom. On moving from one element to the next in the periodic table, Bohr supposed that an additional electron was added to the outermost shell, although there were exceptions to this rule, as discussed below. At specific stages in this process, a shell would become full, at which point a new shell would begin to fill. Contrary to the impression that he created in his published articles, however, Bohr was unable to deduce the maximum capacity of each electron shell, and he allowed himself to be guided almost entirely by chemical and spectroscopic data rather than theoretical calculations.

The fact that Bohr used essentially chemical considerations in producing these configurations can be seen clearly in his choice of configuration for certain elements. The population of electrons in the outermost ring is determined by chemical valence. These electrons are the most loosely bound to the nucleus and thus the most likely to bond with another atom. In the case of nitrogen, for example, Bohr was forced to rearrange an inner shell in order to make the configuration correspond to the element's known trivalence. This can be seen in table 7.2. Whereas from helium to carbon the atoms have two inner electrons and a varying number of outer electrons, once nitrogen is reached the inner electron shell abruptly doubles in its number of electrons. This move appears a little odd until it is realized that it is made precisely to obtain the three outer electrons needed to correspond with the fact nitrogen forms three chemical bonds.

In altering his configurations to make them agree with experimental evidence, Bohr gave no theoretical arguments for why such a rearrangement should occur. Such abrupt rearrangements can be seen in a number of places even just among the 24 configurations shown in the table 7.2, such as for the atoms of phosphorus and nitrogen. The atoms of both of these elements show valences of 3, while oxygen and sulfur display valences of 2 and fluorine and chlorine display valences of 1, in accordance with the chosen configurations. Instead of rigorously deriving his atomic model from quantum theory, Bohr relied on intuition as well as spectroscopic and purely chemical considerations.

TABLE 7.2  
Bohr's Original Scheme for Electronic Configurations of Atoms. Numbers of electrons is consecutive energy levels, beginning closest to the nucleus.

Nevertheless, Bohr achieved two things with his theory. One was that he introduced the important idea that the differentiating electron should, in most cases, occupy an outer shell and not an inner one, as Thomson had thought was the case. Second, in spite of some arbitrary aspects, Bohr's scheme provided at least some correlation between electronic configurations and chemical periodicity. For example, the configuration of lithium is 2, 1, while that of sodium, which lies in the same group chemically, is 8, 2, 1. Similarly, beryllium and magnesium, which are found together in group II of the periodic table, share the property of having two outer-shell electrons. This is the origin of the modern notion that atoms fall into the same group of the periodic table if they possess the same numbers of outer-shell electrons, something that had already been hinted at by Thomson.

Following this work, Bohr abandoned the question of periodicity for about a decade, and it was left to various chemists to try to improve upon the electronic version of the periodic table. As discussed in chapter 8, there are some grounds for thinking that Bohr's later tables were directly influenced by the more detailed electronic configurations given by the chemist Charles Bury and that insufficient credit has been given to this pioneer of electronic configurations.

### BOHR'S SECOND THEORY OF THE PERIODIC SYSTEM

In 1921, Bohr returned to the problem of atomic structure and the periodic table. In 1922 and 1923, he announced a new, improved version of the electronic periodic table. Again he employed the _aufbauprinzip_ to build up successive atoms in the periodic table, but this time he used two quantum numbers: _n_ , the principal quantum number, and _k_ , the second or azimuthal quantum number, which later became labeled as _l_ (table 7.3). The second quantum number had recently been discovered by Arnold Sommerfeld, a theoretical physicist in Munich.

Whereas Bohr had assumed the orbit of the hydrogen electron to be circular, Sommerfeld realized that it was elliptical. Since the angular momentum of an electron moving in an elliptical orbit would change continually, the orbit itself would precess, independently of the motion of the electron in its ellipse. Thus, the electron would have two degrees of freedom: the orbiting motion of the electron, and its precession. To describe the latter motion, Sommerfeld introduced a second quantum number, _l_ , the azimuthal quantum number, which depended on the principal quantum number and could adopt values of _n_ – 1, _n_ – 2, . . ., 0.

When Bohr became aware of this discovery, he applied it to many-electron atoms and produced the set of more detailed electronic configurations shown in table 7.3. These numbers emerged from the quantization that was imposed mathematically on the system and served to identify the stationary states of the system, as they had in his earlier theory. According to this scheme, an atom of nitrogen, for example, with seven electrons, would have an electronic configuration of 2, 4, 1. It is interesting to see that in the case of nitrogen and a few other elements, Bohr's more detailed theory of 1922 seems to have taken a retrograde step, since contrary to the configuration he had given in 1913, the newer version did not accord well with the experimental fact that nitrogen forms three chemical bonds, a point taken up further below.

TABLE 7.3  
Bohr's 1923 Electronic Configurations Based on Two Quantum Numbers. Numbers of electrons is consecutive energy levels, beginning closest to the nucleus.

Following the early success of his theory of the hydrogen atom, Bohr was invited to give a series of seven lectures in 1922 at the University of Göttingen. Some of the physicists present in the audience for these lectures, which became known as the Bohrfest, included Werner Heisenberg, Wolfgang Pauli, Sommerfeld, and Max Born as well as Göttingen's leading mathematical physicist, David Hilbert. Throughout his career, Bohr was regarded more for his physical insight and his ability to synthesize ideas in atomic physics rather than for any special mathematical prowess, which he left to others like Heisenberg, Erwin Schrödinger, Pauli, and Paul Dirac. This lack of a formal mathematical approach was evident in Bohr's lectures at Göttingen, which produced questions from the audience regarding the mathematical justification for what Bohr was doing. It would appear that in many cases there were no such justifications.

As several of the Göttingen physicists who were exposed to these ideas by Bohr's own lectures later commented, the work rested on a mixture of ad hoc arguments and chemical facts without any derivations from the principles of quantum theory, to which Bohr frequently alluded. According to the German physicist Heisenberg,

It could very distinctly be felt that Bohr had not reached his results through calculations and proofs but through empathy and inspiration and it was now difficult for him to defend them in front of the advanced school of mathematics in Göttingen.

Friederich Hund wrote:

After he had explained a simple spectrum he came to his crucial review of the structure of atoms with regard to their positions in the periodic system. In some respects this turned out to be obscure and not always easy to understand.

In a book containing Bohr's famous 1923 paper on the _aufbauprinzip_ , Pauli made a revealing marginal remark. In discussing the adding of the 11th electron to the closed shell of 10 electrons, Bohr says, "We must expect the eleventh electron to go into the third orbit." Pauli, obviously annoyed by this statement, writes hastily in the margin with an exclamation mark, "How do you know this? You only get it from the very spectra you are trying to explain!" The notion that the periodic table was deduced from quantum theory by Bohr is thus something of an exaggeration.

Bohr claimed that his _aufbauprinzip_ , by which he applied his theory of the atom to multielectron atoms, was based on an important principle of quantum theory called the adiabatic principle:

Suppose that for some class of motions we for the first time, introduce the quanta. In some cases the hypothesis fixes completely which special motions are to be considered as allowed. This occurs if the new class of motions are derived by means of an adiabatic transformation from some class of motions already known.

Introduced by Paul Ehrenfest in 1917, the adiabatic principle allows one to find the quantum conditions when an adiabatic or gradual change is imposed on a system. However, it depends on the possibility of deriving the new motion from the known one by means of an adiabatic transformation. For example, if the quantum states of a particular system are known, the new quantum states that result from a gradual change, such as the application of an electric or a magnetic field, can be calculated. The quantities that preserve their values after such a transformation are known as adiabatic invariants. Ehrenfest showed that for any arbitrary periodic motion, the following quantity is an adiabatic invariant:

2T/n,

where _T_ is the time average of the kinetic energy and _n_ is the frequency of motion.

There are stringent restrictions on the applicability of the adiabatic principle. Ehrenfest himself showed that it was applicable to simply periodic systems. These are systems having two or more frequencies that are rational fractions of each other. In such systems, the motion will necessarily repeat itself after a fixed interval of time. Later, J.M. Burgers, a student of Ehrenfest, showed that it was also applicable to multiply periodic systems. In these more general systems, the various frequencies are not rational fractions of each other, such that the motion does not necessarily repeat itself. The hydrogen atom provides an example of a multiply periodic system, with its two degrees of freedom.

An even more general class of systems is termed aperiodic, and as far as is known, the adiabatic principle does not apply in such cases. Unfortunately for the field of atomic physics, all atoms larger than that of hydrogen constitute aperiodic systems. In the helium atom, for example, the motion of each of the two orbiting electrons changes according to the varying interaction with the other electron as their distance apart changes (in terms of the early Bohr theory). We may no longer speak of a constant period for either of the electrons.

Bohr was well aware of this limitation of the adiabatic principle but continued to use it even for many-electron atoms in the hope that it might still remain valid for such aperiodic systems. He repeatedly acknowledged this point in his writings:

For the purposes of fixing the stationary states we have up to this point only considered simply or multiply periodic systems. However the general solution of the equations frequently yield motions of a more complicated character. In such a case the considerations previously discussed are not consistent with the existence and stability of stationary states whose energy is fixed with the same exactness as in multiply periodic systems. But now in order to give an account of the properties of the elements, we are forced to assume that the atoms, in the absence of external forces at any rate always possess sharp stationary states, although the general solution of the equations of motion for the atoms with several electrons exhibits no simple periodic properties of the type mentioned.

Later in his 1923 article, he states:

We shall try to show that not withstanding the uncertainty which the preceding conditions contain, it yet seems possible even for atoms with several electrons to characterize their motion in a rational manner by the introduction of quantum numbers. The demand for the presence of sharp, stable, stationary states can be referred to in the language of quantum theory as a general principle of the existence and permanence of quantum numbers.

Bohr's attitude as expressed in these writings does not seem to be very rigorous, but more akin to the obscurantism that characterized some of his scientific work. In the two above-quoted passages he appears to ignore the problems he himself elaborates and merely expresses the hope of retaining the quantum numbers even though one is no longer dealing with multiply periodic systems.

The main feature of the building-up procedure, as mentioned above, was Bohr's assumption that the stationary states would also exist in the next atom in the periodic table, obtained by the addition of a further electron. Bohr also assumed that the number of stationary states would remain unchanged from the atom of one element to the next, apart from any additional states pertaining to the newly introduced electron. He thus envisaged the existence of sharp stationary states, and their retention on adding both an electron and a proton to an atom.

Bohr's hypothesis of the permanence of quantum numbers came under attack from the analysis of the spectral lines under the influence of a magnetic field. As is generally the case, the application of a magnetic field on the atoms results in a splitting, to produce more lines than occur in the absence of such a field. An atomic core consisting of the nucleus and inner-shell electrons showed a total of _N_ spectroscopic terms in a magnetic field. If an additional electron having an azimuthal quantum number _k_ were to be added, the new composite system would be expected to show N(2k – 1) states, since the additional electron was associated with 2 _k_ – 1 states. However, experiments revealed more terms. In general, the terms split into one type consisting of (N + 1)(2k – 1) components and a second type consisting of (N – 1)(2k – 1) components, giving a total number of 2N(2k – 1) components. This represents a violation of the number of quantum states, since a twofold increase seems to occur in the number of atomic states on the introduction of an additional electron. Bohr's response was to maintain adherence to the permanence of quantum numbers even in the face of this evidence. He merely alluded to a mysterious device, which he called a nonmechanical "constraint," to save the quantum numbers.

Bohr's account of the periodic table also came under attack from chemical evidence. The element nitrogen, for example, was attributed an electronic configuration of 2, 4, 1, as noted above. This grouping of electrons suggested that 1 or 5 electrons were more loosely bound than the others and implied either penta- or univalence, neither of which is the case in practice, as nitrogen is predominantly trivalent.

Despite the problems with his quantum theory, however, Bohr went on to make numerous other contributions to atomic physics and quantum mechanics in the course of his long life. Indeed, Bohr is probably the best-known physicist of the twentieth century, eclipsed only by Albert Einstein. After Bohr's theories of 1913 and 1922–1923, he remained at the heart of developments in quantum theory, although specific steps were often taken by others, including Heisenberg, Schrödinger, and Pauli. But throughout this period, and for many years later, Bohr played the role of godfather to quantum theory by founding an international institute in Copenhagen, which hosted many of the world's leading physicists as they continued to shape the new quantum mechanics. In addition, he served as the focal point for the discussions on the nature of quantum mechanics and had a profound influence on many of the physicists of his generation through his willingness to engage in debate.

### EDMUND STONER

Shortly after introducing his second theory of the periodic system, Bohr began to believe that the assumptions on which it was based might be unfounded, but it was not until the work of Pauli a little later that the situation would begin to be clarified. In the meantime, another physicist, Edmund Stoner, was to provide the next missing piece of the puzzle of quantum numbers and the periodic table.

In 1924, British-born Stoner (figure 7.3), then a graduate student at Cambridge University, took the next step in using electronic configurations to explain the periodic table. His approach was based on using not merely two quantum numbers, but also a third one introduced by Sommerfeld shortly before. The third, or inner, quantum number, _j_ , refers to the precession of the orbital motion in the presence of a magnetic field. Its value is tied to the second quantum number such that _j_ can take all values ranging from _-k_ to _+k_ , increasing in integral steps.

The occurrence of this third quantum number suggested additional stationary states in the atom, but Bohr did not extend his electronic configuration scheme accordingly. As mentioned above, Bohr was becoming increasingly interested in the deeper question of the existence of stationary states for individual electrons in many-electron atoms. That is, he was concerned about the fact that, strictly speaking, the electrons in many-electron atom are not in stationary states. It is rather the atom as a whole that possesses stationary states. This "holistic" property denies the validity of the independent electron approximation wherein each electron is in a stationary state and can be characterized by its own set of quantum numbers.

FIGURE 7.3 Edmund Stoner. Photo and permission from University of Leeds.

TABLE 7.4  
Stoner's Scheme for Assignment of Electronic Configurations

The young Stoner, undaunted by these theoretical problems, reexamined the experimental evidence on optical as well as X-ray spectra of atoms. Based on his studies, he suggested that the number of electrons in each completed level should equal twice the inner quantum number of that particular shell. This produced the scheme shown in table 7.4 for ascribing electrons to shells.

When Stoner applied this relationship to the three quantum numbers, he deduced the set of electron configurations shown in table 7.5. According to Stoner's scheme, the electronic configuration for the element nitrogen is 2, 2, 2, 1, where the last three numbers represent the outer-shell electrons. This configuration could account successfully for the valence state of 3 shown by nitrogen, whereas Bohr's scheme could not. However, this new scheme could not resolve the above-mentioned problem of the violation of number of quantum states as was seen in the splitting of spectral lines in a magnetic field.

As the problems with what became known as Bohr's "old quantum theory" began to deepen, some physicists, such as Heisenberg and Pauli, started to question the reality of electron orbits. For example, in Pauli's correspondence with Bohr there is the following passage on this issue: "The most important question seems to be this: to what extent may definite orbits in the sense of electrons in stationary states be spoken of at all."

TABLE 7.5  
Stoner's Configurations of 1924 Based on Three Quantum Numbers

### THE PAULI EXCLUSION PRINCIPLE

In 1923 Bohr wrote to Pauli (figure 7.4), asking him to try to bring order to the increasingly complicated situation in atomic physics and to attempt to save the quantum numbers. Pauli responded with two papers that seemed to clarify matters, and in the process he developed his exclusion principle, which has become one of the central pillars of modern physics. Once again, the motivation for this work was partly an attempt to explain the periodic table of the elements.

Pauli's first main contribution was to challenge the view held at the time that the core of an atom possesses an angular momentum. Alfred Landé had proposed that the core of the atom, consisting of the nucleus plus the inner electrons, would explain the origin of the complex structure of atomic spectra. Pauli rejected this hypothesis and suggested that the spectral lines and their shifts in the presence of magnetic fields were due entirely to the presence of outer electrons. He went on to propose the assignment of a fourth quantum number, _m s_, to each electron (table 7.6). This fourth number was due, according to Pauli, to a classically non-describable duplicity in the quantum theoretical properties of the optically active electron, a property now called spin angular momentum.

FIGURE 7.4 Wolfgang Pauli. Photo from Author's collection used by permission from Emilio Segré Collection.

Armed with four quantum numbers, Pauli found that he could obtain Stoner's classification of electronic configurations from the following simple assumption, which constitutes the famous exclusion principle in its original form: "It should be forbidden for more than one electron with the same value of the main quantum number n to have the same value for the other three quantum numbers k, j and m." The principle is often stated as follows: no two electrons in an atom can have the same set of four quantum numbers. Meanwhile, Pauli justified the assignment of four quantum numbers to each electron by the following apparently clever argument. He supposed that if a strong magnetic field were applied, the electrons would cease to interact and could therefore be said to be in individual stationary states.

Of course, the periodic table arrangement must also apply in the absence of a magnetic field. In order to maintain the validity of the four-quantum-number assignment for each electron even in the absence of a field, Pauli appealed to what he called a "thermodynamic argument." He proposed an adiabatic transformation in which the strength of the magnetic field was gradually reduced such that, even in the absence of the field, the characterization of stationary states for individual electrons remained valid. This argument seemed to ensure the existence of sharp stationary states for individual electrons.

TABLE 7.6  
Assignment of Electron Shells Based on Pauli's Scheme

Pauli then considered how this proposal fared with regard to the experimental evidence showing a violation in the number of quantum states. As mentioned above, the problem was that a system expected to show _N_ (2 _k_ – 1) states on the addition of a single electron to the atomic core is in fact transformed into two sets of states numbering (N + 1)(2 _k_ – 1) and (N – 1)(2k – 1) states, or a total of 2N(2k – 1).

Pauli was able to resolve this problem very simply. According to his view, the additional electron possesses 2(2k – 1) states, in contrast to the former view of only (2k – 1). The twofold increase in the number of observed states arises from the proposed duplicity of states of the new electron. The number of states of the atomic core therefore remains as N. Pauli's arguments appeared very persuasive and were received enthusiastically by the atomic physics community.

Not surprisingly, Bohr was pleased with Pauli's contribution, although both of them seemed to view it as a temporary measure. What they and everybody else failed to notice was that Pauli had committed a fallacy concerning the applicability of the adiabatic principle. A many-electron atom constitutes an aperiodic system to which the adiabatic principle does not apply, as previously emphasized by Bohr. Pauli merely changed the argument from the addition of an extra electron as in the _aufbauprinzip_ to the case of gradually reducing the strength of a magnetic field.

TABLE 7.7  
Quantum Numbers and Orbitals

This does not alter the issue, however, since the system remains aperiodic, and Pauli was using the adiabatic principle where it did not strictly apply. But as often happens in science, taking a step that is not rigorous can often pay dividends, at least temporarily, as it did in this case.

Perhaps the reason why theoretical considerations were suspended was that Pauli's new scheme resolved some major problems. First, the notion of the existence and permanence of the quantum numbers could be retained, as Bohr had hoped. Second, the long-standing problem of the "closing of electron shells" in atoms was resolved. The question had been how to explain the series of whole numbers 2, 8, 18, 32, and so on, which characterizes the lengths of the periods in the periodic system of chemical elements. These numbers also correspond to the maximum number of electrons in each shell. Now the closing of the various shells could seen to be a consequence of Pauli's exclusion principle, which prohibits any two electrons from having the same four quantum numbers together with the assumption that the fourth number itself can adopt only two possible values. Meanwhile, all the previous rules for assigning the values for the second and third quantum numbers for a given value of the first quantum number were retained.

When the first quantum number, or n, takes the value of 1, the second quantum number can only be 0, and likewise the third quantum number (table 7.7). According to Pauli's principle, the first shell can therefore contain a maximum number of two electrons that differ just in the value of the fourth quantum number.

For the _n_ = 2 shell, the situation is more complicated, since there are two possible values for the second quantum number: 0 and 1. As noted above, when the second quantum number is 0, the third quantum number also adopts a 0 value and, since the fourth quantum number can adopt two possible values, two electrons are accounted for. When the second quantum number in the second shell takes a value of 1, the third quantum number may take on three possible values: – 1, 0, and +1. Each of these possibilities can show two values for the fourth quantum number, thus accounting for a further six electrons. Considering the second shell as a whole, a total of eight electrons is therefore predicted, in accordance with the well-known short period length of eight elements.

Similar considerations for the third and fourth shells predict 18 and 32 electrons, respectively, once again in accordance with the arrangement of the elements in the periodic table.

This scheme is still widely regarded as the explanation for the periodic table, and some version of it is found in virtually every textbook in chemistry or physics. But it is only a partial explanation. It relies for its success on using experimentally observed data in order to determine at what point, in the sequence of the elements, any particular electron shell begins to be filled. The explanation provided by Pauli and most textbooks is only an explanation of the maximum number of electrons successive electron shells can accommodate. It does not explain the particular places in the periodic table at which periodicity occurs. This is to say that Pauli's explanation alone does not explain the lengths of _periods_ , which is the really crucial property of the periodic table.

The more important aspect of the periodic system, namely, the lengths of the periods, and their explanation, is taken up again in chapter 9. Just to anticipate matters a little, it will emerge that even present-day physics has not provided a deductive explanation of the closing of the periods, although some promising candidate explanations are becoming available. This is a situation that is seldom acknowledged in textbooks or even in the research literature. Such sources give the impression that quantum physics provides a fully deductive explanation of the closing of the periods, or the particular atomic numbers at which each period is terminated.

## **CHAPTER 8  
ELECTRONIC EXPLANATIONS OF THE PERIODIC SYSTEM DEVELOPED BY CHEMISTS**

Given the advances in explanations of the periodic system provided by physicists in the first quarter of the twentieth century, described in chapter 7, it is interesting to consider what advances, if any, were achieved by chemists during the same period. Unlike physicists, chemists were working largely inductively with experimental data on the elements and not via any theoretical arguments.

However, in many instances, the electronic configurations proposed by chemists were superior to those postulated by such physicists as Niels Bohr and Edmund Stoner. This is not entirely surprising given the chemist's familiarity with the properties of the elements. Inductive arguments based on macroscopic behavior of elements were often more fruitful than the deductive arguments based on physical principles. Moreover, as described in chapter 7, even physicists' routes to electronic configurations were not always as deductive as they were claimed to be by their authors.

The starting point for the chemical contributions to the assignment of electronic configurations can be regarded as J.J. Thomson's discovery of the electron in 1897, since without the existence of this particle there could be no electronic configurations. In 1902, the American chemist Gilbert Newton Lewis (figure 8.1) began speculating about the electronic structure of atoms, although he did not publish his views due to the prevailing empiricist climate in U.S. chemistry, which was rather hostile toward theoretical approaches. Considerably later, Lewis recalled his early thoughts on the constitution of atoms:

In the year 1902 (while I was attempting to explain to an elementary class in chemistry some of the ideas involved in the periodic law) becoming interested in the new theory of the electron, and combining this idea with those implied in the periodic classification, I formed an idea of the inner structure of the atom which, although it contained certain crudities, I have ever since regarded as representing essentially the arrangement of electrons in the atom.

FIGURE 8.1 Gilbert Newton Lewis. Photo and permission from Edgar Fahs Smith Collection.

Some dated fragments of this work still survive, including a diagram in which Lewis depicts the electronic structures of the elements from helium up to fluorine (figure 8.2). Lewis envisaged the electrons as being arranged at the corners of a cube and that when the number eight was exceeded, another cube would be formed to build up a series of concentric cubes around the nucleus of any element.

It should be realized that from purely chemical evidence Lewis had succeeded in deducing the correct number of electrons for all but one (helium) of the first dozen or so elements in the periodic system, whereas, as discussed in chapter 7, this had been a major stumbling block for the physicist Thomson. The latter's electronic account of the periodic table showed only that it might be possible to relate elements in the same group in terms of analogous configurations. Lewis succeeded in explaining the formation of polar or, as more commonly termed, ionic compounds such as sodium chloride by means of his cubic atom concept. According to his model, the sodium atom, which possessed one electron on the corner of a cube, could lose this electron to form a positive sodium ion with no outer electrons on any of the corners. Meanwhile, the cube around a chlorine atom would begin with seven of its eight corners occupied with electrons and would gain the spare electron from sodium. This would give the chlorine a full complement of eight electrons, thereby forming a negative chlorine ion, which would be attracted to the positive sodium ion.

However, while this model could explain the formation of polar compounds, it could not address how nonpolar organic compounds, such as methane, might be formed. This serious limitation may have been another reason why Lewis did not publish his early ideas on the cubic atom. It was only in 1916 that Lewis did so.

FIGURE 8.2 Lewis's sketch in his unpublished memorandum of March 28, 1902. Lewis Archive, University of California-Berkeley.

FIGURE 8.3 The formation of a covalent bond between cubes representing fluoride atoms. Reproduced from A. Stranges, _Electrons and Valence_ , Texas A&M University Press, College Station, TX, 1982, p. 212, with permission from the publisher.

These ideas on the cubic atom and pairs of electrons were to lead Lewis to formulate one of the most influential ideas in the whole of modern chemistry: the notion of a covalent bond as a shared pair of electrons. Until this time, chemical bonds had been regarded exclusively as involving the transfer of electrons and the formation of ionic bonds. It is interesting to realize that the concept of a covalent bond thus began, like so many important developments in modern science, with research connected to the periodic system of the elements. Moreover, Lewis's 1916 article, titled "The Atom and the Molecule," has turned out to be one of the most influential works in modern chemistry. What Lewis also suggested was that the two kinds of bonding were essentially forms of the same behavior, namely, the sharing of electrons between atoms. In the case of polar compounds, this sharing could be regarded as being very uneven, whereas in nonpolar compounds the electrons could be more or less equally shared by adjacent atoms of different elements.

In this chapter I concentrate on what Lewis had to say on the periodic system and the structure of atoms. Lewis began by paying tribute to the work of German chemist Richard Abegg, who in 1902 had proposed a rule of valence and contravalence:

_The total between the maximum positive and negative valences of an element is frequently eight and in no cases more than eight_.

Abegg's maximum positive valence corresponds to the group number of the element in question in the periodic table. The normal valence is whichever of these two valences is less than 4 while the contravalence, or "other valence," is displayed less commonly and gives rise to less stable compounds. The elements in group IV of the periodic table show no natural preference with respect to valency and were called amphoteric, a term that was first coined by Abegg and is still in chemical use today, although with a somewhat different meaning.

Abegg explained why the sum of the valence and contravalence was eight by assuming that this number represented the number of electron attachment sites on any atom. However, he did not venture to speculate why each atom could attach precisely this number of electrons. This step was provided by Lewis, who devised his cubical atom on the basis of Abegg's rule. Each of the eight corners of a cube represented a site at which an electron could be attached. Indeed, whereas Abegg merely accepted the stability of eight electrons to an atom, for Lewis it was a simple consequence of the cubic structure of his hypothetical atom. As historian Anthony Stranges has suggested, Lewis's cubic atom appears to be a geometric representation of Abegg's arithmetical rule.

Lewis gave a number of postulates:

1. In every atom is an essential kernel which remains unaltered in all ordinary chemical changes and which possesses an excess of positive charges corresponding in number to the ordinal number of the group in the periodic table to which the element belongs.

2. The atom is composed of a kernel and an outer atom or shell, which, in the case of the neutral atom, contains negative electrons equal in number to the excess of positive charges of the kernel, but the number of electrons in the shell may vary during chemical change between 0 and 8.

3. The atom tends to hold an even number of electrons in the shell, and especially to hold eight electrons which are normally arranged at the eight corners of a cube.

4. Two atomic shells are mutually interpenetrable.

5. Electrons may ordinarily pass with readiness from one position in the outer shell to another. Nevertheless they are held in position by more or less rigid constraints, and these positions and the magnitude of the constraints are determined by the nature of the atom and of such other atoms as are combined with it.

6. Electric forces between particles which are very close together do not obey the simple law of inverse squares which holds at greater distances.

As a comment on postulate 3, Lewis points out that among the "tens of thousands of known compounds," only a few of them do not have an even number of electrons in their valence shells. In every compound in which the element uses either its highest or lowest valence, the total number of valence electrons is a multiple of eight. Examples given by Lewis include ammonia (NH3), water (H2O), and potassium hydroxide (KOH), all of which show a total of eight valence electrons, and magnesium chloride (MgCl2), where the total is 16, and sodium nitrate (NaNO3), where it is 24. The few exceptions to the notion of even numbers of valence electrons include NO (11), N02 (17), and ClO2 (19), but Lewis adds that these molecules are highly reactive, forming more stable molecules where the number of valence electrons is once again even, such as in the case of the dimerization of N02 to form N204.

Postulate 4, which allows cubic atoms to interpenetrate, forms the basis of the electron sharing mechanism. In this way, one electron or more could belong to two atoms simultaneously without being gained or lost by either of the atoms. This simple idea, stemming directly from cubic arrangements of electrons, seems to be the origin of the now ubiquitous concept of electron sharing in chemistry. Lewis illustrated the interpenetration of cubes with the formation of a diatomic molecule held together by a single bond (figure 8.4). The concept could be extended to explain double bonds in such molecules as diatomic oxygen, which Lewis represented as two cubes sharing a common face (figure 8.5).

Postulate 6 implies an abandonment of Coulombic repulsion in the case of two closely lying electrons and is essential if one is to contemplate the existence of pairs of electrons as an integral part of the model. Interestingly, Lewis qualifies this postulate further by saying that electrons can act as small magnets that, when correctly oriented, can account for the stability of the shared pair of electrons. This statement, and later elaborations, have been interpreted by many as an anticipation of the concept of electron spin, which, as discussed in chapter 7, was not formally introduced until 1925.

What is curious about this article of 1916 is that Lewis begins with a detailed account of his cubic atom but in the very same article shows that it is necessary to go beyond this model. One of the shortcomings of the simple model is its inability to explain the formation of triple bonds such as in a molecule of ethyne (acetylene), with formula H-C=C-H, or the diatomic nitrogen molecule N=N. There seems to be no way that two cubes of electrons can share three pairs of electrons, and Lewis concludes that he needs to assume a somewhat different way of arranging the electrons in order to overcome this problem. The solution he offers is to place the electrons on the four corners of a tetrahedron that has been superimposed on the earlier cubic structure (figure 8.6). This new tetrahedral atom can accommodate the formation of a triple bond by assuming that two adjacent atoms share a common tetrahedral face.

FIGURE 8.4 Single bond formation with cubic atoms. Reproduced from A. Stranges, _Electrons and Valence_ , Texas A&M University Press, College Station, TX, 1982, p. 212, with permission from the publisher.

FIGURE 8.5 Double bond formation with cubic atoms. Reproduced from A. Stranges, _Electrons and Valence_ , Texas A&M University Press, College Station, TX, 1982, p. 213, with permission from the publisher.

FIGURE 8.6 Lewis's tetrahedral atom. The electron pairs are now on the corners of a tetrahedron that has been superimposed on the earlier cubic structure.

TABLE 8.1  
Lewis's Outer Electronic Structures for 29 Elements

Lewis's article also introduces the use of a pair of dots to denote the shared pair of electrons, a form of notation that survives to this day:

Whereas in 1902 Lewis had thought that helium possessed a complete cube of eight electrons, he corrected its electronic structure in his 1916 paper to include just two electrons, as had been revealed by the work of Henry Moseley. Table 8.1 is based on the positive charges on the atomic kernels of a number of elements as given by Lewis in the same article.

### IRVING LANGMUIR

The next step in the evolution of chemically motivated electronic configurations was taken by another American, Irving Langmuir, who spent his life as an industrial research chemist and was responsible for making many of Lewis's ideas widely known. In 1919, Langmuir published an article that begins with an insightful comment, especially in view of the kinds of questions raised in the present book, regarding the relationship between chemistry and physics in the evolution of the periodic system:

The problem of the structure of atoms has been attacked mainly by physicists who have given little consideration to the chemical properties, which must ultimately be explained by a theory of atomic structure. The vast store of knowledge of chemical properties and relationships, such as is summarized in the periodic table, should serve as a better foundation for a theory of atomic structure than the relatively meager experimental data along purely physical lines.

Langmuir remarks that Lewis confines his attention to only 35 of the 88 known elements and that his theory does not apply at all satisfactorily to the remaining elements, thus highlighting the limitations of Lewis's scheme especially for the transition elements. Langmuir then briefly reviews the work of Walther Kossel in which electrons are regarded as being in concentric rings and comments on the fact that while Kossel's theory considers elements up to cerium, that is, a total of 57 elements, just like Lewis's theory, it is unable to deal with the transition metals.

Langmuir bases his own theory on the number of electrons in the atoms of the noble gases:

He = 2, Ne = 10, Ar = 18, Kr = 36, Xe = 54, niton = 86.

By means of "constant checking against the periodic table and the specific properties of the elements," Langmuir proceeds to elaborate seven postulates, which enable him to assign electronic configurations for all the naturally occurring elements up to uranium or _Z_ = 92. He then provides a classification of the elements according to their arrangement of electrons in what is essentially a short-form periodic table in which the numbers of outer-shell electrons are displayed for each element along with their atomic number (figure 8.7).

Unlike Lewis, and Kossel before him, Langmuir does not hesitate to assign configurations to the transition element atoms. For example, the first transition series is depicted as follows:

where the numbers denote the number of outermost electrons.

The 10th postulate given by Langmuir is significant for two reasons. It includes the statement that there can be no electrons in the outer shell of an atom until all the inner shells contain the maximum number of electrons that each one can accommodate. In addition, he states that a second outer-shell electron can occupy a cell only when all other cells contain at least one electron. The first of these statements requiring that electron shells be filled in a strictly sequential order was subsequently abandoned. Indeed, the precise order of shell and subshell filling has become an important question to assess the degree to which modern physics can explain the periodic system.

But while, in the light of current knowledge, Langmuir's first statement appears to be incorrect, the second statement seems to anticipate an important aspect of modern quantum mechanical configurations, namely, the existence of Hund's rule. This rule states that when electrons are distributed among a number of orbitals with equal energies, they are placed in separate orbitals until the pairing of electrons into single orbitals becomes unavoidable.

FIGURE 8.7 Langmuir's periodic table of electronic configurations. W. Langmuir, Arrangement of Electrons in Atoms and Molecules, _Journal of the American Chemical Society_ , 41, 868-934, 1919, p. 874.

Langmuir's configurations appeared in pictorial form a couple of years later in a chemistry textbook written by Washburn as shown in figure 8.8.

### CONTRIBUTIONS OF CHARLES BURY

As mentioned above, Langmuir assumed that electron shells fill in a strictly sequential order. The first chemist to challenge this idea was Charles Bury, working at the University College of Wales in Aberystwyth. In his article, Bury states that the configurations he is proposing give a better explanation of the chemical properties of the elements than do those of Langmuir. He also notes that his own configurations dispense with the need to postulate cells as Langmuir does.

FIGURE 8.8 Langmuir's extended cubical atom models. From E.W. Washburn, _Introduction to the Principles of Physical Chemistry_ , 2nd ed., McGraw-Hill, New York, 1921, p. 470.

TABLE 8.2  
Bury's Configurations for Some First Transition Series Atoms

Contrary to Langmuir, Bury suggests that the number of electrons in the outer shell cannot be more than eight. Furthermore, he claims that an inner stable group of eight electrons can change into one containing 18 electrons, or that one of 18 can change into one of 32, in the course of the development of a transition series of elements (table 8.2). These transition elements are supposed by Bury to have more than one electronic structure depending on their state of chemical combination. Although Bury's postulates do not lead to any disagreement with Langmuir's regarding the first few configurations, differences begin to appear in the first long period ranging from potassium to krypton.

Bury clearly states that electron shells do not fill sequentially when he writes, "Since eight is the maximum number of electrons in an outer layer K, Ca and Sc must form a fourth layer although their third is not complete. Their structures will be 2, 8, 8, 1, 2, 8, 8, 2, 2, 8, 8, 3." Furthermore, he infers that the elements from titanium to copper "form a transition series in which the incomplete group of eight in the third layer is changed to a saturated group of eighteen." However, as mentioned above, Bury considers the elements from titanium to copper to possess more than one configuration, depending on what compounds they find themselves in, a suggestion that has not survived the test of time.

### THE CASE OF HAFNIUM (ELEMENT 72)

The prediction and eventual confirmation that element 72 is not a rare earth element is widely regarded as a triumph for Bohr's theory of the periodic system. It is often argued that, while chemists believed that this element was a rare earth, Bohr drew on quantum theory to suggest otherwise. This is therefore presented as an early case of reduction of chemistry by quantum theory as distinct from the later quantum mechanics.

However, both parts of this commonly held view are partly mistaken. First, only a minority of chemists believed that hafnium should be a rare earth, and second, Bohr's prediction was not very conclusive and was based on a highly empirical theory of electron shells rather than on any deep theoretical principles. According to Bohr's theory, the rare earths are characterized by the building up of the N group or the fourth electron shell from the nucleus. On this view, the first rare earth is cerium with a fourth shell of the following configuration:

cerium (58): (41)6 (42)6 (43)6 (44)1

And the last rare earth is lutetium with the following configuration:

lutetium (71): (41)8 (42)8 (43)8 (44)8

The completion of the fourth shell represents the end of the rare earth series, and the next, as yet undiscovered, element is expected to be a transition metal and a homologue of zirconium, showing a valence of 4. The general approach used by Bohr in his assignment of electron shells is to ensure an overall agreement with the known periodic table. The form of the periodic table in fact guided Bohr to electronic configurations, as he sometimes admitted.

It emerges that the notion that element 72 was not a rare earth was the commonly held view among a number of chemists. Element 72, or at least the vacant space that it was supposed to fill, was often placed beyond the rare earth block in published periodic tables prior to Bohr's theory, for example, by Bury. In fact, the prediction that hafnium is not a rare earth element can be obtained quite simply by counting and is by no means dependent on assuming the existence of electron shells. This can be illustrated as follows: It had been known for some time that the number of elements in each period follows a definite sequence given by 2, 8, 8, 18, 18, 32 (probably followed by 32), and so on. By adding the first six of these numbers, one arrives at the conclusion that the sixth period terminates with a noble gas of atomic number 86. It is a simple matter to work backward from this number to discover that element 72 should be a transition metal and a homologue of zirconium, which shows a valence of 4. This procedure depends on the plausible assumption that the third transition series should consist of 10 elements, as do the first and second transition series:

The only chemists who did indeed believe that element 72 was a rare earth were the few who specialized in obtaining these types of elements by painstaking separation of some mineral ores that were first found in Sweden. In 1879, Charles Marignac showed that the rare earth erbia could be separated into two rare earths, ytterbia and another element later called holmium (figure 8.9). A year later, ytterbia was separated into two distinct elements named scandium and ytterbium. The next step was taken by Georges Urbain and Auer von Welsbach, who independently found that ytterbium itself could be separated into neo-ytterbium and lutetium. It was only natural that these workers should suspect the possibility of discovering further new elements by repeated separations of the same minerals.

FIGURE 8.9 Sequence of discovery of some rare earth elements.

Urbain and von Welsbach both believed that ytterbium contained small amounts of a third rare earth that would possibly turn out to be element 72. Indeed, Urbain announced what he believed to be a positive spectroscopic identification of element 72 in 1911, although this claim could not be confirmed by Moseley using his X-ray method. Urbain then abandoned his claim for 11 years, after which time he announced that together with Alexandre Dauvillier that he had used a more accurate X-ray experiment and had detected two weak lines whose frequencies corresponded approximately to those expected for element 72 on the basis of Moseley's law. But this claim, too, turned out to be unfounded.

### BACK TO BOHR

As mentioned in chapter 7, when Bohr presented his method for ascribing electron shells, most physicists were puzzled by the manner in which he obtained his results. Letters to Bohr following the publication of his theory of the periodic system in _Nature_ magazine contain passages such Ernest Rutherford's: "Everybody is eager to know whether you can fix the rings of electrons by the correspondence principle or whether you have recourse to the chemical facts to do so." And from Paul Ehrenfest: "I have read your article in Nature with eager interest....Of course I am now even more interested to know how you saw it all in terms of correspondence." Several years later, Hendrik Kramers wrote:

It is interesting to recollect how many physicists abroad thought, at the time of the appearance of Bohr's theory of the periodic system, that it was extensively supported by unpublished calculations which dealt in detail with the structure of individual atoms, whereas the truth was, in fact, that Bohr had created and elaborated with a divine glance a synthesis between results of a spectroscopical nature and of a chemical nature.

This remark seems to be particularly true regarding element 72, for which Bohr never produced any mathematical arguments or any other form of argument resting specifically on quantum theory. Bohr's predictions regarding the electronic arrangements of the rare earths and that of hafnium were as follows.

First of all there are vague arguments based on "harmonic interaction," correspondence, and symmetry, such as the following:

Even though it has not yet been possible to follow the development of the group [rare earths] step by step, we can even here give some theoretical evidence in favour of the occurrence of a symmetrical configuration of exactly this number of electrons. I shall simply mention that it is not possible without coincidence of the planes of the orbits to arrive at an interaction between four sub-groups of six electrons each in a configuration of simple trigonal symmetry, which is equally simple as that shown by these sub-groups. These difficulties make it probable that a harmonic interaction can be attained precisely by four groups containing eight electrons the orbital configurations of which exhibit axial symmetry.

In a somewhat less obscure fashion, Bohr uses a counting argument not unlike one mentioned above in order to arrive at the conclusion that element 72 should not be a rare earth:

As in the case of the transformation and completion of the 3-quanta orbits in the fourth period and the partial completion of the 4-quanta orbits in the fifth period, we may immediately deduce from the length of the sixth period the number of electrons, namely 32, which are finally contained in the 4-quanta group of orbits. Analogous to what applied to the group of 3-quanta orbits it is probable that, when the group is completed, it will contain eight electrons in each of the four subgroups.

According to Bohr, the element that represents the completion of the four-quanta groups and therefore marks the end of the rare earths is lutetium, with the following grouping of four-quanta electrons:

lutetium (71) (41)8 (42)8 (43)8 (44)8

Bohr writes:

This element therefore ought to be the last in the sequence of consecutive elements with similar properties in the first half of the sixth period, and at the place 72 an element must be expected which in its chemical and physical properties is homologous with zirconium and thorium.

He then adds: "This which is already indicated on Julius Thomsen's old table, has also been pointed out by Bury."

In his Göttingen lectures on the periodic table, Bohr alluded to a calculation concerning the rare earth configurations. But this form of calculation was never produced by Bohr, nor has anything of the sort ever been found in the Bohr archives. Bohr also expressed a certain amount of doubt over his prediction that hafnium would not be a rare earth. Having explained the filling of the four-quanta groups as described above, he says: "However the reasons for indicating this arrangement are still weaker than in the case of the 3-quantic group and the preliminary closure of the 4-quantic group in silver."

When Urbain and Dauvillier claimed to have discovered element 72 and that it was a rare earth, Bohr's initial response was to doubt his own prediction that it lay beyond the rare earths. This wavering was expressed in letters to colleagues as well as in the appendix of a book on atomic constitution. He wrote to James Franck:

The only thing I know for sure about my lectures in Göttingen is that several of the results communicated are already wrong. A first point is the constitution of element 72, which, as shown by Urbain and Dauvillier, contrary to expectations has turned out to be a rare earth element after all.

And to Dirk Coster: "The question is apparently rather clear but one must of course always be prepared for complications. These may arise from the circumstance that we have to do with a simultaneous development of two inner electron rings."

Bohr soon returned to his original claim about element 72. In doing so, he provided further examples of his essentially chemical arguments for his views on the missing element. In referring to the claim by Urbain and Dauvillier, Bohr points out that if element 72 is a rare earth, it should have a valence of 3 in common with other members of this group. Moreover, Bohr mentions that element 73, tantalum, is known to have a valence of 5: "This would mean an exception to the otherwise general rule, that the valency never increases by more than one unit when passing from one element to the next in the periodic table."

Meanwhile, in response to the claims of Urbain and Dauvillier, which they believed to be unfounded, Georg Hevesy and Coster, working at Bohr's institute in Copenhagen, began a search for element 72 in the ores of zirconium. Even their first attempt proved to be unexpectedly successful. After some further concentration of the new element, they obtained six clear X-ray lines whose frequencies were in very good agreement with Moseley's law applied to element 72. The new element was named hafnium after _Hafnia_ , Latin for Copenhagen, where the element had been discovered. The commonly cited story that Bohr instructed his colleagues to look for the new element in the ores of zirconium, where they discovered hafnium, is simply untrue. The suggestion to search for the new element within zirconium ores was made by a chemist, Fritz Paneth, based on purely chemical arguments.

No doubt the controversy over Urbain's claim and Bohr's theory stimulated this eventual true discovery of element 72, but in view of all the factors described above, it can still be doubted whether this development represents a successful chemical prediction on the basis of quantum theory. Had Bohr's theory been correct in making a prediction that had been contrary to the beliefs of the chemists of the day, this would have made Bohr's triumph all the greater, but this was not the case.

It might be more accurate to say that the view held by most chemists that hafnium would not be a rare earth was rationalized by Bohr's quantum theory of periodicity, which was partly empirical in origin. In addition, as noted above, Bury had already obtained the same correct prediction that hafnium was a transition metal, and not a rare earth, on the basis of purely chemical arguments.

### JOHN DAVID MAIN SMITH

John David Main Smith is another chemist who succeeded in producing more detailed electronic configurations and a more accurate explanation of the periodic system than did Bohr, but without receiving much credit at the time or in subsequent accounts of the development of the periodic system.

In March 1924, Main Smith, at Birmingham University in England, published an article in the somewhat obscure journal _Chemistry and Industry_ , in which he corrected an important feature in Bohr's electronic configurations, discussed in chapter 7. Bohr's scheme of 1923 assumed that all subgroups of electrons were equally populated when full. For example, Bohr assumed that the second shell consisted of a total of eight electrons distributed equally into two subgroups, each containing four electrons (table 8.3). Main Smith challenged this notion on the basis of chemical, as well as X-ray diffraction, evidence.

Let us pause to consider the chemical arguments, especially in view of the general theme of the present book. In his 1924 book _Chemistry and Atomic Structure_ , Main Smith begins a chapter titled "Atomic Structure and the Chemical Properties of Elements" with the following remark, which may seem obvious to chemists but perhaps not to physicists:

Bohr's theory of atomic structure is strictly a theory relating to single atoms, neutral or ionised, far removed from the influence of other atoms. The fact that it is an interpretation of the periodic classification of the elements, largely based on the properties of atoms in combination, indicates that it must be valid for atoms in combination, at least so far as the broad outlines of the theory are concerned.

He then proceeds to mount a sustained critique of the electronic configurations as assigned by Bohr on the basis that they do not take into account the chemical behavior of many of the elements. Main Smith points out that the elements of group III of the periodic table commonly display two distinct valences, a fact that cannot be explained from Bohr's configurations. He points out that the elements in group IV, and to some extent those of groups V, VI, and VII, commonly show two different valences. Main Smith remarked:

TABLE 8.3  
Bohr's Subgroups Consisting of Equal Subdivisions of Electrons

N. Bohr, _Theory of Spectra and Atomic Constitution_ , Cambridge University Press, Cambridge, UK, 1924, table based on p. 113.

This may be interpreted as evidence that all elements containing more than two valency electrons have two electrons, which, further interpreted in terms of orbits, indicates that that two electrons in the outer structure of atoms are in quantum orbits the energies of which are different from that of other outer electrons.

From the point of view of our current knowledge, Main Smith had discovered that every main shell begins with an orbital containing just two electrons. However, another conclusion that is apparently equally drawn from chemical facts has turned out to be incorrect in the light of contemporary knowledge of electronic configurations. Main Smith argued that all the elements of groups V, VI, and VII have a marked tendency to form compounds with a coordination number of four and that this suggests that valence electrons in excess of four are "equally feebly attached to atoms." He interpreted this behavior to mean that any valence electrons in excess of four are all in similar quantum orbits. In fact, it is the six electrons in excess of two that form another shell in the atoms of successive elements, or in modern terminology, the following six electrons enter into three equivalent p orbitals.

Be that as it may, Main Smith concludes that the subgroups, in the second main shell, for example, should contain 2, 2, and 4 electrons, respectively, starting with the subgroup closest to the nucleus (table 8.3). He also states categorically that "This evidence shows conclusively that Bohr's subgroup scheme, of two subgroups of four electrons for the two-quanta group, cannot be maintained."

According to Bohr's set of configurations, the third shell consists of three subgroups, each of which contain six electrons. If this were indeed the case, Main Smith reasoned, we should expect to observe a single transition between levels 31 and 32, for example, in the X-ray spectrum of any element that possesses outer electrons in these levels. In fact, the X-ray evidence in the sodium atom spectrum, which is associated with the transition between these levels, is not a single line but the well-known sodium doublet. Main Smith concluded that there were additional levels between Bohr's levels 31 and 32. The subgroups of electrons for the elements in the second period according to Bohr and Main Smith, respectively, are compared in table 8.4. Main Smith proceeds to extend his list of configurations (figure 8.10), and with far greater detail than Bohr had published, for many of the elements up to gold ( _Z_ = 79).

TABLE 8.4  
Subgroups of Electrons in the Second Main Shell for Elements in the Second Period According to Main Smith and Bohr

Not surprisingly, these configurations have not withstood the test of time, since subgroups of four or eight electrons are not admitted in the modern scheme, which contains 2, 6, 10, or 14 in successive subshells of electrons. However, these little known articles by Main Smith are of great historical interest because they show that some chemists not only understood Bohr's theory of periodicity but were prepared to grapple with its details, including the physical evidence such as that obtained from X-ray spectroscopy. Moreover, several chemists were able to deduce more comprehensive explanations of the periodic system in terms of electronic configurations, as in the case of Main Smith.

As mentioned in chapter 7, the next major step after Bohr's two-quantum-number account was given by Stoner. It emerges that Stoner's scheme is almost identical to the one by Main Smith just described. The two scientists arrived at their respective versions independently, although Main Smith was the first to publish. Both of them drew upon a detailed analysis of X-ray spectra to arrive at their electron subgroups.

FIGURE 8.10 Configurations of some transition elements, extracted from more complete tables of configurations. J.D. Main Smith, _Chemistry and Atomic Structure_ , Ernest Benn Ltd., London, 1924, p. 196.

Main Smith correctly considered that his contributions had not been properly acknowledged and wrote the following published letter to the editor of _Philosophical Magazine:_

[A]ttention to the fact that the distribution of electrons in atoms characterized by the subgroupings 2; 2,2,4; 2,2,4,4,6; 2,2,4,4,6,6,8 did not originate with Mr. E. Stoner, as within recent months various papers published in your journal have suggested.

It is gratifying to note that Stoner fully conceded Main Smith's priority when, a couple of years later in a textbook of atomic physics, he wrote,

I have since found that my distribution had already been proposed, primarily on the basis of chemical arguments by Main Smith. It is very satisfactory that two different lines of attack should have led to the same conclusions.

This is a fitting conclusion to this chapter, which has demonstrated how chemistry was by no means eclipsed by the discoveries in atomic physics, as is sometimes implied. The cases of Main Smith and Bury, in particular, show that chemists not only were able to compete with the atomic physicists on their own terms but also arrived at more detailed configurations before the physicists could do so.

### CONCLUSION

In a matter of a few years, several chemists, including Lewis, Langmuir, and Bury, had obtained detailed electronic configurations for all the known elements, including the more complicated transition elements. Bury had realized that the atoms of the transition elements do not fill their electron shells in sequential order and had predicted that element 72 would be a transition metal that would show chemical similarities with zirconium. All this work was achieved without any arguments based on theoretical physics or, more specifically, without using quantum theory. The chemists' configurations were obtained inductively on the basis of the chemical properties of the elements. This aspect of the history of the periodic system is seldom emphasized, with most accounts promoting the view that electronic configurations resulted entirely from the work of theoretical physicists such as Bohr. In truth, Bohr had also reached electronic configurations inductively, frequently drawing on chemical evidence, as the chemists themselves had done. Bohr's configurations were frequently less detailed in that he specified only those of the closed-shell atoms of the noble gases and did not cite those of the intervening series of elements in each period of the table.

The popular story according to which Bohr predicted the chemical nature of element 72, subsequently named hafnium, has been criticized and can no longer be sustained by anyone who examines the historical evidence surrounding this case. Indeed, Bohr seems to have arrived at many configurations by appeal to chemical as well as other experimental data that he then dressed up in quantum mechanical language through his characteristically obscure style of writing.

It is also quite possible that Bohr could have relied quite heavily on the work of Bury, who had predicted that element 72 would be a transition element. Bury's priority in this matter is even conceded by Bohr himself in his articles, although he does not seem to attach much significance to Bury's prediction, presumably because it is not couched in terms of the quantum theory. In addition, whereas Bohr initially gave configurations only for the noble gases, he appears to have begun listing those of the intervening elements only after the appearance of Bury's detailed versions published in 1921.

The case for Bury's priority over Bohr in these matters has been valiantly argued by one of Bury's former students, Mansel Davies, who published a number of articles to this effect. This claim has been taken up and amplified by Keith Laidler, the distinguished chemical kineticist and historian. While it may be that Bury's work has been highly neglected, perhaps a more conservative conclusion may be more appropriate. The reason for the neglect of Bury's work may not be due to any duplicity by Bohr, or his supporters, but rather because Bury gave chemical arguments for his own assignment of configurations, whereas the prevailing reductionist climate implied that quantum mechanics inevitably provides a more fundamental explanation for the periodic system.52 A fuller discussion of this issue is given in chapter 9, which includes an analysis of the reduction of the periodic system using quantum mechanics.

And finally, the chemist Main Smith, drawing on the same X-ray data as the atomic physicist Stoner, as well as chemical evidence, was able to arrive at the conclusion that the number of electrons in each subgroup was twice the value of the inner quantum number. He thus obtained the same electron subgrouping several months before Stoner, whose discovery of the same concept is far better acknowledged by historians of science.

## **CHAPTER 9  
QUANTUM MECHANICS AND THE PERIODIC TABLE**

In chapter 7, the influence of the old quantum theory on the periodic system was considered. Although the development of this theory provided a way of reexpressing the periodic table in terms of the number of outer–shell electrons, it did not yield anything essentially new to the understanding of chemistry. Indeed, in several cases, chemists such as Irving Langmuir, J.D. Main Smith, and Charles Bury were able to go further than physicists in assigning electronic configurations, as described in chapter 8, because they were more familiar with the chemical properties of individual elements. Moreover, despite the rhetoric in favor of quantum mechanics that was propagated by Niels Bohr and others, the discovery that hafnium was a transition metal and not a rare earth was not made deductively from the quantum theory. It was essentially a chemical fact that was accommodated in terms of the quantum mechanical understanding of the periodic table.

The old quantum theory was quantitatively impotent in the context of the periodic table since it was not possible to even set up the necessary equations to begin to obtain solutions for the atoms with more than one electron. An explanation could be given for the periodic table in terms of numbers of electrons in the outer shells of atoms, but generally only after the facts. But when it came to trying to predict quantitative aspects of atoms, such as the ground–state energy of the helium atom, the old quantum theory was quite hopeless. As one physicist stated, "We should not be surprised . . . even the astronomers have not yet satisfactorily solved the three–body problem in spite of efforts over the centuries." A succession of the best minds in physics, including Hendrik Kramers, Werner Heisenberg, and Arnold Sommerfeld, made strenuous attempts to calculate the spectrum of helium but to no avail.

It was only following the introduction of the Pauli exclusion principle and the development of the new quantum mechanics that Heisenberg succeeded where everyone else had failed. In fact, Heisenberg performed the calculation using both his own matrix mechanics and Erwin Schrödinger's wave mechanics as discussed below. In terms of wave mechanics, Heisenberg interpreted his result as showing the need for the overlap between the wavefunctions of the two electrons in helium. This overlap, which he called an "exchange term," was due entirely to the indistinguishability of the two electrons. This meant that the terms in the equation had to be written in two ways, the second of which involved the exchange of labels to account for the fact that both electrons are identical. Such exchange terms are highly nonclassical and follow from Wolfgang Pauli's discovery of the exclusion principle.

This discovery was to be the beginning of the use of exchange terms in the quantum mechanics of atoms and molecules. It became the key factor that shortly afterward allowed Walter Heitler and Fritz London to obtain the first successful quantum mechanical calculation of the covalent bond in the simplest case of a diatomic hydrogen molecule. Exchange terms would also pave the way for the notion of quantum mechanical resonance and the development of the quantum mechanical theories of bonding by Linus Pauling and many others.

Perhaps the key advance that quantum mechanics provided, compared with the old quantum theory, was that the quantization itself seemed to arise in a more natural manner. In the old quantum theory, Bohr had been forced to postulate that the angular momentum of electrons was quantized, while the advent of quantum mechanics showed that this condition was provided by the theory itself and did not have to be introduced by fiat. For example, in Schrödinger's version of quantum mechanics, the differential equation is written, and certain boundary conditions are applied, with the result that quantization emerges automatically.

A conceptual grasp for how the application of boundary conditions to waves leads naturally to quantization can be obtained from the following analogy. Suppose that a string is tied at both ends and made to vibrate. It turns out that the string can adopt one of many possible standing wave patterns where certain points along the string remain stationary. As shown in figure 9.1, the string can vibrate either as a whole or with a number of so–called nodes, each of which represents a stationary point along the string.

FIGURE 9.1 The imposition of boundary conditions produces quantization in a vibrating wave. From R. Chang, _Physical Chemistry for the Chemical and Biological Sciences_ , University Science Books, Sausalito, CA, 2000, p. 576. By permission from the publisher.

In other words, the mere presence of waves that are bound at both ends immediately implies quantization of the form described above. The string can vibrate only in a number of well–defined ways that have 0, 1, 2, 3, and so on, nodes. No other intermediate vibrational nodes can exist, and this is the essence of quantization associated with any kind of standing wave phenomenon.

### FROM BOHR'S OLD QUANTUM THEORY TO QUANTUM MECHANICS

What Bohr had been doing in his explanations of the periodic table was not deducing electronic configurations from first principles, as he led his readers to believe; rather, he was essentially working backward from chemical and spectroscopic facts and showing that these facts were consistent with a quantum theoretical description.

But the old quantum theory was only the beginning of quantum mechanics, which is the most powerful physical theory that has ever been devised. The transition between the old quantum theory and the new quantum mechanics is examined in this chapter, as is the impact that the updated theory had on attempts to understand the periodic table. As I argue here, the effect has been considerable, but surprisingly still incomplete, from the fundamental point of view of trying to provide a deeper explanation of the periodic system. Nevertheless, many forms of more accurate calculations can now be carried out in quantum chemistry than were even dreamt of at the time of the old quantum theory.

Although it is not my intention to give a history of the transition between Bohr's old quantum theory and the later quantum mechanics, it is necessary to sketch some of the steps that were taken. In fact, one of the connecting steps between the old and the new versions of quantum theory is mentioned in chapter 7, because it provided the culminating step in the explanation of the periodic system as it is still generally understood. This was the introduction by Pauli of the fourth quantum number and his subsequent discovery of the Pauli exclusion principle, which dictates that no two electrons in an atom can possess the same four quantum numbers. What follows from this assumption is an elegant explanation of the possible lengths of any period but only provided that one is willing to admit some experimental information into the explanation.

As noted in chapter 7, an explanation can be given for the maximum possible number of electrons in any shell around the nucleus. The formula 2n _2_ , which had been recognized for some time as summarizing the number of elements in any particular period, is thus given an apparent theoretical underpinning. But there is one aspect, the order of shell filling, that has not yet been deduced from first principles. This issue cannot be avoided if one is to really ask whether quantum mechanics explains the periodic system in a fundamental manner.

### THE ADVENT OF QUANTUM MECHANICS

The old quantum theory reached a crisis point around 1924–1925, at which time it was realized that a more radical theory would be needed in order to settle a number of outstanding problems in physics. One of these problems of particular importance to the story of the periodic table was the attempt to calculate the properties of helium, the second atom in the periodic table following hydrogen. Whereas the old quantum theory provided a means of obtaining an exact solution to the calculation of the energy of the hydrogen atom, the move to considering helium appeared to cause insurmountable problems. It was not that the solution of this problem was just difficult in the old quantum theory. It was not even possible to formulate the necessary equations adequately.

Only following the advent of quantum mechanics, as distinct from the old quantum theory, was there a possibility of calculating the energy of helium, and even then only approximately. Developments initially occurred along two distinct lines. First of all, Heisenberg, a very young German, developed an approach that eventually became known as matrix mechanics. Heisenberg's original motivation appears to have been the complete abandonment of unobservable features of the world, such as atomic orbits. This followed the realization that atomic orbits were quite different from the orbits of planets and other macroscopic objects. They were eventually renamed "orbitals" instead of orbits, a name intended to mean a form of motion without a definite trajectory. Unfortunately, the change in terminology is too subtle, with the result that many chemists, in particular, still seem to maintain some form of pathlike visualization.

Heisenberg intended to build a theory centered on observable quantities such as spectral frequencies. The theory that he developed was highly counterintuitive and required physicists to invest much time and effort in learning a new branch of mathematics dealing with the manipulation of matrices. In addition, the attempt to reject unobservable quantities that Heisenberg had hoped for was not realized.

At about the same time, Schrödinger developed what came to be known as wave mechanics. Already in 1924, the French physicist Prince Louis De Broglie had suggested an analogy to Albert Einstein's earlier discovery that light waves have a particulate nature as well as their expected wave nature. De Broglie made the association run in the opposite sense. Why not suppose that particles such as electrons could likewise display wavelike properties? The test for this idea would be to demonstrate experimentally that electrons produce diffraction and interference effects just like classical waves, such as waves on the surface of water.

Two physicists, Clinton Davisson and Lester Germer, successfully carried out just such an experiment in 1927, thus giving experimental support to De Broglie's proposal. With this discovery, theorists such as Schrödinger received the impetus to further pursue the mathematical analogies between classical waves and electron waves. Whereas Heisenberg's approach was mathematically abstract, that of Schrödinger was more familiar to physicists because it dealt principally with wave motion. Unlike Heisenberg, Schrödinger had not originally tried to break with realistic notions of the microscopic world and, in fact, had hoped that his method would retain strong connections with classical physics and physical visualization.

As it turned out, neither Heisenberg's nor Schrödinger's hopes materialized fully. The quantum mechanics that emerged after a few years of intense debate was not based solely on observable properties, nor was it possible to retain a realistic view of matter waves as Schrödinger had originally hoped. Moreover, the two forms of quantum mechanics were shown to be equivalent.

The new theory became centered on the wavefunction for an atom or molecule. This wavefunction could be expressed with a number of terms called "atomic orbitals." As mentioned above, the name was derived from atomic orbits of the old quantum theory but without any intended connection with a definite trajectory for the electron. Such orbitals inhabit a multidimensional Hilbert space in quantum mechanics, thus further denying their visualizability in familiar three–dimensional space. Moreover, wavefunctions and their component building blocks consisting of such orbitals are themselves complex mathematical functions in the sense that they contain factors involving the square root of –1.

What is observable in the case of wavefunctions, as it emerged a little later, is the square of the wavefunction, which is called the electron density. In addition, even the square of the wavefunction cannot be obtained for a single electron at a specific point. The interpretation of quantum mechanics calls for a statistical view in which one can know only the probability of an electron residing in a certain region of space.

### HARTREE–FOCK METHOD

When it comes to calculating the properties of atoms, the new quantum mechanics provides a way in which the problem can be attacked by means of approximation methods. The basis of the most widely used approximation for solving quantum mechanical equations for atoms is called the Hartree–Fock method after Douglas Hartree (figure 9.2) and Vladimir Fock, an English and a Russian physicist, respectively.

The main assumption made in the Hartree–Fock model is that any given electron moves in a field resulting from the attraction of the nucleus added to the field that results from the sum of all the remaining electrons. This approach avoids dealing directly with individual electron–electron repulsion terms, and instead, one recovers a situation not altogether unlike that of the hydrogen atom in which one electron is moving in a spherically symmetrical field. In the many–electron case, the field consists of those of the nucleus and of all the other electrons lumped together. The only difference is that instead of one equation for one electron, there are now as many equations as there are electrons in the atom. In addition, the solution for each electron must be consistent with those for all the other electrons, thus requiring a self–consistent iteration procedure that is typically carried out on a computer.

FIGURE 9.2 Douglas Hartree. Photo and permission from Emilio Segré Collection.

But let us return to the question the explanation of periodicity, which opened this chapter. The Pauli exclusion principle and the use of four quantum numbers only provide a deductive explanation of the total number of electrons that any electron shell can hold. The correspondence of these values with the number of elements that occur in any particular period is something of a coincidence. The lengths of successive periods have not yet been strictly deduced from the theory. However, most chemistry and physics textbook authors do not emphasize or even mention this point. As a result, they imply that quantum mechanics does indeed provide a perfectly satisfactory deductive explanation of the periodic system. This, in turn, fuels the general impression that chemistry is fully explained by quantum physics and has a negative effect on chemical education. Instead of starting from chemical facts, and the properties of the elements, the modern tendency is to expose students to the rules for electronic configurations in the belief that the chemistry will somehow follow. Nevertheless, the number of electrons contained in any shell, as opposed to the lengths of periods, does emerge directly from the rules for combining the four quantum numbers. This part of the explanation for periodicity is completely satisfactory, as shown in the next section.

### WRITING ELECTRONIC CONFIGURATIONS FOR ATOMS

The assignment of electronic configurations to the atoms in the periodic table proceeds according to three principles:

1. The _aufbau_ principle _(aufbauprinzip_ in chapter 7): Orbitals are occupied in order of increasing values of _n_ \+ ℓ For example, the 4s orbital for which _n_ \+ ℓ = 4 is filled before the 3d orbital for which _n_ \+ ℓ = 5. This rule is often accompanied by a diagram like the one shown in figure 9.3, which represents the Madelung or _n_ \+ ℓ rule.

2. The Hund principle: When electrons fill orbitals of equal energies, they occupy as many different orbitals as possible.

3. The Pauli exclusion principle: Only two electrons can occupy a single orbital, and if they do so they must orient their spin angular momenta in opposite directions.

Several points need to be made about these principles. The first principle does not, in fact, refer to the ordering of energies of atomic orbitals. What it really refers to is the order of filling of the various orbitals. These are related but separate issues. But there is more involved in the occupation of orbitals than their individual energies, as discussed further below. The _n_ \+ ℓ rule has not yet been derived from the principles of quantum mechanics. This failure has been described as one of the outstanding problems in quantum mechanics by the leading quantum chemist Per–Olov Löwdin.

It emerges that all three of these principles are essentially empirical, and none of them has been strictly derived from the principles of quantum mechanics. Pauli's principle, for example, takes the form of an additional postulate to the main postulates of quantum mechanics. Despite strenuous efforts on the part of many physicists, including Pauli himself, it has never been possible to derive the principle from the postulates of quantum mechanics and / or relativity theory. So, rather than providing an explanation for electronic configurations, the three commonly used rules are really statements that summarize what is known to happen from experimental data on atomic spectra.

FIGURE 9.3 Madelung (or _n_ \+ ℓrule) for the order of filling of orbitals. From R. Chang, _Physical Chemistry for the Chemical and Biological Sciences_ , University Science Books, Sausalito, CA, 2000, p. 601. By permission from the publisher.

And now let us turn to the explanation for the number of electrons in each shell and its connection to the number of elements in each subsequent period of the periodic table. These facts are usually explained in terms of the relationship between the four quantum numbers, which can be assigned to any electron in a many–electron atom. The relationship between the first three quantum numbers is rigorously deduced from the Schrödinger equation for the hydrogen atom. The first quantum number, n, can adopt any integral value starting with 1. The second quantum number, which is given the label ℓ, can have any of the following values related to the values of n:

ℓ = _n_ – 1,... 0

In the case when _n_ = 3, for example, ℓ can take the values 2, 1, or 0. The third quantum number, labeled _m ℓ_, can adopt values related to those of the second quantum numbers:

_m ℓ = –ℓ, –(ℓ + 1),... 0... (ℓ – 1),ℓ_

For example, if ℓ = 2 the possible values of _m ℓ_ are –2, –1, 0, +1, and +2. Finally, the fourth quantum number, labeled _m s_ can take only two possible values, either +1/2 or –1/2 units of spin angular momentum. There is therefore a hierarchy of related values for the four quantum numbers, which are used to describe any particular electron in an atom.

As a result of this scheme, it is clear why the third shell, for example, can contain a total of 18 electrons. If the first quantum number, given by the shell number, is 3, there will be a total of 2 **X** (3)2 or 18 electrons in the third shell. The second quantum number, ℓ, can take values of 2, 1, or 0. Each of these values of ℓ will generate a number of possible values of _m ℓ_, and each of these values will be multiplied by a factor of 2 since the fourth quantum number can adopt values of 1/2 or –1/2.

But the fact that the third shell can contain 18 electrons does not strictly explain why it is that some of the periods in the periodic system contain 18 places. It would be a rigorous explanation of this fact only if electron shells were filled in a strictly sequential manner. Although electron shells begin by filling in a sequential manner, this ceases to be the case starting with element 19, potassium. Since the configuration of element 18, argon, is

1s2, 2s2, 2p6, 3s2, 3p6,

one might expect the configuration for element 19, potassium, would be

1s2, 2s2, 2p6, 3s2, 3p6, 3d1.

FIGURE 9.4 The relative ordering of the 3d and 4s energy levels. L.G. Vanquickenborne, K. Pierloot, D. Devoghel, _Journal of Chemical Education_ , 71, 469–471, 1994, p. 469. By permission from the publisher.

This would be expected because up to this point the pattern has been one of adding the differentiating electron to the next available orbital at increasing distances from the nucleus. However, experimental evidence shows that the configuration of potassium should be denoted as

1s2, 2s2, 2p6, 3s2, 3p6, 4s1.

As many textbooks explain, this can result from the fact that the 4s orbital has a lower energy than the 3d orbital for the atoms of potassium and calcium (see figure 9.4).

In the case of element 20, calcium, the new electron also enters the 4s orbital. But in the case of element 21, scandium, the orbital energies have reversed so that the 3d orbital has a lower energy. Textbooks typically claim that since the 4s orbital is already full, the next electron necessarily begins to occupy the 3d orbital. This pattern is supposed to continue across the first transition series of elements, apart from the elements chromium and copper, where further anomalies occur (table 9.1).

In fact, this explanation for the configuration of the scandium atom, and most other first transition elements, is inconsistent. If the 3d orbital has a lower energy than 4s starting at scandium, and if one were indeed filling the orbitals with electrons in order of increasing energy, one would expect that all three of the final electrons would enter 3d orbitals. The argument that most textbooks present is incorrect since it should be possible to predict the configuration of an element from a knowledge of the order of its own orbital energies. One should not have to consider the configuration of the previous element and assume that this configuration is somehow carried over intact on moving to the next element.

TABLE 9.1 Electronic Configurations for First Transition Metals

What seems to make this issue more mysterious is that, whereas all transition elements show a preferential occupation for an s orbital, it appears that the s electrons are also the easiest to ionize. This situation may be represented by two diagrams, one for relative occupation and one for relative ionization of orbitals in the first transition series, to give the sets of ordered levels shown in figure 9.5.

The apparent paradox is as follows: If the 4s orbital is preferentially occupied by electrons, this suggests that it has greater stability after all interactions have been properly taken into account. However, the right diagram in figure 9.5, which depicts the relative ease of losing electrons, suggests that the 4s electrons are overall less stable since they, rather than the 3d electrons, are more easily removed. Many complicated analyses of this situation have been published in recent years in order to try to resolve the apparent paradox.

There is perhaps a simple solution, or perhaps a dissolution, of the problem. In posing the paradox regarding the 4s and 3d orbitals, many authors appear to have overlooked one very important feature, which makes the comparison problematic. In considering the buildup of atoms across the periodic table, one is concerned with the successive addition of one proton and one electron to each previous atom. However, in considering the ionization of any particular atom, one is concerned only with the successive removal of electrons and not the removal of protons. As a result, the comparison of the two diagrams in figure 9.5 does not constitute a comparison of like with like. The long–standing puzzle, which has exercised the minds of generations of students and their instructors, can be dissolved at a stroke. The question of why 4s fills first but also empties first is an illegitimate question in some respects.

FIGURE 9.5 Ordering of orbital energies as implied by relative filling and relative ionization. The lower the level, the more stable the atom.

### AN EXPLANATION FOR SHELL CLOSING BUT NOT FOR PERIOD CLOSING

As suggested above, there is a problem with the claim that the periodic table is deductively explained by quantum mechanics. A feature that seems to generally go unnoticed is the need to assume the empirical order of shell filling rather than trying to derive it from the theory. The order in which orbitals are occupied with electrons is not derived from first principles. It is justified _post facto_ and by some complex calculations.

Suppose, for example, that the Hartree–Fock method is used to compare the energies of the scandium atom with two alternative configurations: [Ar] 4s2 3d1 and [Ar] 4s1 3d2. This can be carried out using ordinary nonrelativistic quantum mechanics or, alternatively, by including relativistic effects. The results obtained are as shown in table 9.2. In each case, the more negative the calculated value of the energy, the more stable the configuration. Clearly, the inclusion of relativistic effects serves to reduce the energy from the nonrelativistic value, as one would expect. In the case of scandium, it appears that both nonrelativistic and relativistic ab initio calculations correctly compute that the 4s2 configuration has the lower energy, in accordance with experimental data. Similar calculations do not fare so well in the case of the chromium atom, however (table 9.3). In this case, it appears that both nonrelativistic and relativistic calculations fail to predict an explanation for shell closing which of these two configurations is the correct experimentally observed ground state, namely, 4s1 3d5.

TABLE 9.2  
Nonrelativistic and Relativistic Calculated Energies for Two Configurations of Scandium (in Hartree units)

TABLE 9.3  
Nonrelativistic and Relativistic Calculated Energies for Two Configurations of Chromium (in Hartree units)

Looking at the calculated energies for the copper atom in table 9.4 shows that a nonrelativistic calculation sometimes gives the correct result for the lowest energy configuration. However, it also emerges that by carrying out the calculation to a greater degree of accuracy by including relativistic effects the prediction can in some cases deteriorate in that one predicts the opposite order of stabilities than observed experimentally. The lowest energy configuration for copper cannot yet be successfully calculated from first principles, at least at this level of approximation.

TABLE 9.4 Nonrelativistic and Relativistic Calculated Energies for Two Configurations of Copper (in Hartree units)

The fact that copper has a 4s13d10 configuration rather than 4s23d9 is an experimental fact. The theory is, strictly speaking, accommodating what is already known experimentally. For example, the first of the two periods of 18 elements is not due to the successive filling of 3s, 3p, and 3d electrons but due to the filling of 4s, 3d, and 4p. It just so happens that both of these sets of orbitals are filled by a total of 18 electrons. This coincidence is what gives the generally given explanation its apparent credence. It does not seem to be appreciated that these are not the same 18 electrons that are "doing the occupying" as one traverses the periodic table.

#### The Nickel Atom

The case of nickel turns out to be more interesting (table 9.5). According to nearly every chemistry and physics textbook, the configuration of this element is given as 4s2 3d8. However, the research literature on atomic calculations invariably quotes the configuration of nickel as 4s1 3d9. The difference occurs because in more accurate work one considers not just the lowest possible component of the ground–state term but the average of all the components arising from a particular configuration. Nickel is somewhat unusual in that, although the lowest energy term arises from the 4s2 3d8 configuration, the average energy of all the components arising from this configuration is higher than the average energy of all the components arising from the 4s1 3d9 configuration. As a consequence, the 4s1 3d8 configuration is regarded as the ground state, and it is this average energy that is compared with experimental energies. When this comparison is made, it emerges that the quantum mechanical calculations using a relativistic Hartree-Fock approach give an incorrect ground state.

TABLE 9.5 Nonrelativistic and Relativistic Calculated Energies for Two Configurations of Nickel (in Hartree units)

Of course, the calculations can be improved by adding extra terms until this failure is eventually corrected, but these additional measures are taken only after the fact. Moreover, the lengths to which theoreticians are forced to go to in order to obtain the correct experimental ordering of terms does not give one too much confidence in the strictly predictive power of quantum mechanical calculations in this context.

#### Back To Hund's Rule

Let us now consider the Hund principle and the manner in which it is used to try to justify the configurations of elements in the first, second, and third transitions. The elements in the first transition series are generally believed to show two "anomalous" configurations, which include a 4s1 orbital occupation, rather than the more common 4s2 configuration. These atoms are those of chromium and copper, which are taken to have respective configurations of 4s1 3d5 and 4s1 3d10. The justification for the adoption of the first of these configurations is frequently given by appeal to Hund's rule of maximum spin multiplicity. It is argued that this configuration is more stable than any alternatives because it involves a half–filled d subshell. However, if the configurations of the elements in the second transition series are considered, it is clear that this form of explanation is rather ad hoc in the sense that it cannot be generalized to other transition series.

For example, the configurations of the elements in the second transition series are shown in table 9.6. Once again, this set of configurations is primarily arrived at from experimental data, although these ground–state configurations are supported by theoretical calculations in most cases. But if the possession of half–filled orbitals is the explanation for why chromium adopts a 4s1 configuration in the first transition series, some other factors must be operating in many cases of the second transition series. This is because many of these atoms likewise show an s1 configuration even though they do not possess a half filled d subshell. Hund's principle is essentially an empirical result. In spite of many attempts, nobody has yet succeeded in deriving the principle from quantum mechanics. Of course, some plausible arguments can be given for its effectiveness, such as the claim that one is thereby minimizing the contribution from exchange terms involving repulsions between electrons. For example, a calculation can be carried out to show that, in the case of the helium atom, the triplet state (one involving two unpaired electrons) has lower energy than the singlet state where the two electrons are paired. But contrary to the standard account one encounters in textbooks, it has been shown that the reason for the greater stability of the helium triplet state is not reduced electron–electron repulsion but the greater electron–nucleus attraction that occurs in the triplet state.

TABLE 9.6 Configurations of Outermost Two Orbitals of Elements in Second Transition Series

#### Choice Of Basis Set

There is yet another general problem that mars any hope of claiming that electronic configurations can be predicted theoretically and that quantum mechanics thereby provides a purely deductive explanation of what was previously only obtained from experiments. In most of the configurations considered above, it has been possible to use quantum mechanics to calculate the particular configuration that possesses the lowest energy. However, in performing such calculations, the candidate configurations that are subjected to the calculation are themselves obtained from the _aufbau_ principle and other rules of thumb such as Hund's principle, or by straightforward appeal to experimental data. Theoretical calculations cannot actually predict the electronic configuration for any element. There is a very simple reason for this state of affairs, which is often overlooked. The quantum mechanical calculations on ground–state energies involve the initial selection of a basis set, which in simple terms is the electronic configuration of the atom in question. Quantum mechanical calculations do not actually generate their own basis sets. So, whereas the correct ground–state electronic configurations can in many cases be correctly calculated among a number of plausible options, the options themselves are not provided by the theory. This is another weakness of the present claims to the effect that quantum mechanics fully explains the periodic system, although this limitation is being addressed in some recent work.

### THREE POSSIBLE APPROACHES TO THE REDUCTION OF THE PERIODIC TABLE

This section attempts to take stock of the various senses of the claim that the periodic system is reduced, or fully explained, by quantum mechanics.

#### Qualitative Reduction/Explanation of Periodic Table in Terms of Electrons in Shells

In broad terms, the approximate recurrence of elements after certain regular intervals is explained by the possession of a certain number of outer–shell electrons. This form of explanation appears to be quantitative because it deals in number of electrons but, in fact, turns out to be rather qualitative in nature. It cannot be used to predict quantitative data such as the ground–state energy of any particular atom. In order to do so, one needs to go beyond the ground–state configuration of the atom in question, and it is essential to assume that electrons also find themselves in higher energy orbitals that are not considered in the textbook configuration of the element.

In addition, it emerges that the possession of a particular number of outer–shell electrons is neither a necessary nor a sufficient condition for an element's being in any particular group. It is possible for two elements to possess exactly the same outer electronic configuration and yet not to be in the same group of the periodic system. For example, the inert gas helium has two outer–shell electrons and yet is not generally placed among the alkaline earth elements such as magnesium, calcium, and barium, all of which also display two outer–shell electrons.

Conversely, there are cases of elements that do belong in the same group of the periodic table even though they do not have the same outer–shell configuration. In fact, this occurrence is rather common among the transition metal series. Consider this interesting example:

Ni [Ar] 4s2 3d8

Pd [Kr] 5s0 4d10

Pt [Xe] 6s1 4f14 5d9

In addition, the very notion of a particular number of electrons in a particular shell stands in violation of the Pauli exclusion principle, which states that electrons cannot be distinguished. The indistinguishability of electrons implies that one can never state that a particular number of electrons are in any particular shell, although it is frequently useful to make this approximation. Indeed, the independent–electron approximation, as it is known, represents one of the central paradigms in modern chemistry and physics. To state the electronic configuration of an atom is to operate within this level of approximation. For example, one might state that the configurations of two randomly chosen elements are as follows:

Carbon 1s2, 2s2, 2p2

Fluorine 1s2, 2s2, 2p5

This kind of activity could only be considered as fully satisfactory and as indicating a theoretical deduction if such configurations themselves could be derived from quantum mechanics. However, as discussed above, electronic configurations such as those for carbon and fluorine are arrived at essentially by means of the _aufbau_ principle, which is experimentally based. The configurations can be justified in terms of calculations in some cases, but they cannot be derived from first principles because the basis set, consisting of a particular set of atomic orbitals, is generally selected before any calculation can be carried out.

#### Ab Initio Calculations

The second approach to be considered is a far better candidate for the claim to explain the periodic table from quantum mechanics. Even if the crude notion of a particular number of outer–shell electrons for any particular atom fails to give a fundamental explanation, it should be possible to carry out detailed calculations that allow atoms to have more complicated configurations. Going to such a deeper level than the notion of a particular number of electrons in shells might thus provide a more successful explanation of the periodic system.

Ab initio calculations aim to calculate the properties of atoms and molecules starting from the fundamental equation of quantum mechanics, the Schrödinger equation for the system. The various methods utilized vary in the extent to which they are genuinely ab initio. In some cases, the methods incorporate semiempirical aspects. For example, certain integration terms that are too difficult to evaluate are replaced by quantities derived from experimental data. But the type of approach considered here is the purer variety of such calculations, where no semiempirical aspects are incorporated. My aim is to examine the extent to which such ab initio approaches provide a reduction of the periodic system.

Such an approach represents an improvement and is a better contender for the claim of a full explanation of the periodic system. In order to illustrate both the power and the pitfalls of the method, I focus on the ab initio calculation of ionization energies of atoms. In this approach, the notion of electrons in shells is used instrumentally with the knowledge that such an approximation represents only a first–order approach to calculations. If one wishes to still think in terms of electrons in orbitals, these calculations can be thought of as regarding the atom as existing in many different electronic configurations simultaneously. The ground–state configuration, so beloved of chemistry and physics textbooks, is just the leading term in an algebraic expansion for the wavefunction of the atom in question.

At this level of approximation, the fact that certain elements fall into the same group of the periodic table is not explained by recourse to the number of outer–shell electrons. Instead, the explanation lies in calculating the magnitude of a property such as the first ionization energy and seeing whether the expected periodicity is recovered in the calculations. Figure 9.6 shows schematically the experimental first–ionization energies for elements 3–53 in the periodic table, along with the values calculated using ab initio quantum mechanical methods. As is readily apparent from the figure, the periodicity is captured remarkably well, even down to portions of the graph occurring between elements in groups II and III and between groups V and VI in each period of the table. Clearly, the calculation of atomic properties can be achieved by the theory to a high degree of accuracy. The quantum mechanical explanation of the periodic system within this approach represents a far more impressive achievement than merely claiming that elements fall into similar groups because they share the same number of outer electrons.

And yet in spite of these remarkable successes, such an ab initio approach may still be considered to be semiempirical in a rather specific sense. In order to obtain the calculated points shown in figure 9.6, the Schrödinger equation must be solved separately for each of the 50 atoms concerned. The approach therefore represents a form of "empirical mathematics," where one solves 50 individual Schrödinger equations in order to reproduce the well–known pattern in the periodicities of ionization energies. It is as if one had performed 50 individual experiments, although the "experiments" in this case are all iterative mathematical computations. This is still, therefore, not a general solution to the problem of the electronic structure of atoms.

FIGURE 9.6 Calculated and observed first ionization energies of elements 3–53. Ionization energy is plotted against atomic number. Circles represent experimental values; triangles are calculated values From E. Clementi, _Computational Aspects of Large Chemical Systems, Lecture Notes in Chemistry_ , vol. 19, Springer–Verlag, Berlin, 1980, p. 12. By permission from the publisher.

#### Density Functional Approach

The third kind of approach to reducing the periodic table does not suffer from the drawback just mentioned in the case of ab initio calculations, at least not in principle. In 1926, the physicist Llewellyn Thomas proposed treating the electrons in an atom by analogy to a statistical gas of particles. No electron shells are envisaged in this model, although electrons still possess angular momentum values as they do in the electron–shell model. This method was independently rediscovered by Italian physicist Enrico Fermi two years later, and is now called the Thomas–Fermi method. For many years, it was regarded as a mathematical curiosity without applications since the results it yielded were inferior to those obtained by the method based on electron orbitals. The appeal of the Thomas–Fermi method comes from the fact that it treats the electrons around the nucleus as a perfectly homogeneous electron gas and that the mathematical solution for this system is "universal" in the sense that it can be solved once and for all. This represents an improvement over any method in which one seeks to solve a Schrödinger equation for every separate atom as in the wavefunction approach illustrated in figure 9.6.

Gradually, the Thomas–Fermi method or its modern descendants, which are known as density functional theories, have become equally powerful compared to methods based on orbitals and wavefunctions and in many cases can outstrip the wavefunction approaches in terms of computational accuracy. The solution is expressed in terms of the variable **Z,** which represents atomic number, the crucial feature that distinguishes one kind of atom from any other element. One does not need to repeat the calculation separately for each atom, but this advantage applies only in principle, as discussed below.

There is another important conceptual, or even philosophical, difference between the orbital/wavefunction methods and the required density functional methods. In the case of orbitals, the theoretical entities are completely unobservable, whereas electron density, which is featured in density functional theories, is a genuine observable. Experiments to observe electron densities have been routinely conducted since the development of X–ray and other diffraction tech–niques. Orbitals cannot be observed either directly or indirectly since they have no physical reality, a state of affairs dictated by quantum mechanics. The orbitals used in ab initio calculations are just mathematical constructs that exist in a multidimensional Hilbert space, while electron density is altogether different, as indicated, since it is a well–defined observable and exists in real three–dimensional space.

### DENSITY FUNCTIONAL THEORY IN PRACTICE

Most of what has been described so far concerning density theory applies in theory rather than in practice. The fact that the Thomas–Fermi method is capable of yielding a universal solution for all atoms in the periodic table is a potentially attractive feature but has not been realized in practice. Because of various technical difficulties, which are not described here, the attempts to implement the ideas originally due to Thomas and Fermi have not materialized. This has meant a return to the need to solve a number of equations separately for each individual atom as one does in the Hartree–Fock method and other ab initio methods using atomic orbitals. In addition, most of the more tractable approaches in density functional theory also involve a return to the use of atomic orbitals in carrying out quantum mechanical calculations since there is no known means of obtaining the functional based directly on electron density. Researchers therefore fall back on using basis sets of atomic orbitals that yield the electron density when squared.

To make matters worse, the use of a uniform gas model for electron density does not enable one to carry out accurate calculations. Instead, "ripples" must be introduced into the uniform electron gas distribution. The way in which this has been implemented has typically been in a semiempirical manner by working backward from the known results on a particular system, usually taken to be the helium atom. In this way, it has been possible to obtain an approximate set of functions that also give successful approximate calculations in many other atoms and molecules. By carrying out this combination of a semiempirical approach and retreating from the pure Thomas–Fermi ideal of a uniform gas, it has actually been possible to obtain computationally better results, in many cases, than with conventional ab initio methods using orbitals and wavefunctions.

If anything, the early promise and hope offered by quantum mechanics and Paul Dirac's famous dictum that all of chemistry can be calculated from first principles has turned out to be only partly fulfilled. Although calculations have become increasingly accurate, one realizes that they include considerable semiempirical elements at various levels. From the purist philosophical point of view, this implies that not everything is being explained from first principles.

As time has progressed, the best of both approaches have been blended together with the result that many computations are now performed using a mixture of wavefunction and density approaches within the same computations. This feature brings with it advantages as well as disadvantages. The unfortunate fact is that, as yet, there are no pure density functional methods that are tractable for performing calculations. The philosophical appeal of a universal solution for all the atoms of the periodic system, based on electron density rather than fictitious orbitals, has not yet borne fruit.

### CONCLUSION

The aim of this chapter has not been trying to decide whether or not the periodic system is explained by quantum mechanics _tout court_ , since the situation is more subtle. It is more a question of the extent of reduction or extent of explanation that has been provided by quantum mechanics.

Whereas most chemists and educators seem to believe that the reduction is complete, perhaps there is some benefit in pursuing the question of how much is strictly explained from the theory. After all, it is hardly surprising that quantum mechanics cannot yet fully deduce the details of the periodic table, which gathers together a host of empirical data from a level far removed from the microscopic world of quantum mechanics.

It is indeed something of a miracle that quantum mechanics explains the periodic table to the extent that it does at present. But we should not let this fact seduce us into believing that it is a deductive explanation. One thing that is clear is that the attempt to explain the details of the periodic table continues to challenge the ingenuity of quantum physicists and quantum chemists and that the periodic table will continue to present a test case for the adequacy of new methods developed in quantum chemistry.

Our story has now been brought up to date. From its humble beginnings as a set of isolated triads of elements, the periodic system has grown to embody more than 100 elements and has survived various discoveries such as that of isotopes and the quantum mechanical revolution in the study of matter. Rather than being swept aside, it has continued to provide a challenge to the development of ever more accurate means of calculating the basic properties of the atoms of the chemical elements. The central role of the periodic system in modern chemistry has been consolidated rather than eroded.

The reduction of chemistry to quantum mechanics has neither failed completely, as some philosophers of science have claimed, nor has it been a complete success, as some contemporary historians have claimed. The reductive enterprise has been highly successful but not to the extent of deposing the chemical facts or the quintessential discovery of chemical periodicity made by De Chancourtois, Newlands, Odling, Hinrichs, Lothar Meyer, and most significantly, Mendeleev. Rather than undermining chemical periodicity, modern quantum physics has literally re–presented the periodic system and has provided it with a theoretical justification. More important, quantum physics has achieved this feat without assuming the imperialistic role that it is sometimes attributed.

## **CHAPTER 10  
ASTROPHYSICS, NUCLEOSYNTHESIS, AND MORE CHEMISTRY**

Having now examined attempts to explain the nature of the elements and the periodic system in a theoretical manner, it is necessary to backtrack a little in order to pick up a number of important issues not yet addressed. As in the preceding chapters, several contributions from fields outside of chemistry are encountered, and the treatment proceeds historically.

So far in this book, the elements have been treated as if they have always existed, fully formed. Nothing has yet been said about how the elements have evolved or about the relative abundance of the isotopes of the elements. These questions form the contents of the first part of this chapter. It also emerges that different isotopes show different stabilities, a feature that can be explained to a considerable extent by appeal to theories from nuclear physics.

The study of nucleosynthesis, and especially the development of this field, is intimately connected to the development of the field of cosmology as a branch of physical science. In a number of instances, different cosmological theories have been judged according to the degree to which they could explain the observed universal abundances of the various elements. Perhaps the most controversial cosmological debate has been over the rival theories of the big bang and the steady–state models of the universe. The proponents of these theories frequently appealed to relative abundance data, and indeed, the eventual capitulation of the steady–state theorists, or at least some of them, was crucially dependent upon the observed ratio of hydrogen to helium in the universe.

Later parts of this chapter go on to examine further aspects of the chemistry of the elements and, in particular, the aspects that do not fit neatly into the simple idea that trends occur just within groups and within periods of the periodic system. The complexity that is seen on examining these more esoteric yet, in many cases, well–known effects raises new questions for the overall understanding of the periodic system. Finally, the fact that scientists working in many different fields such as geology, metallurgy, physics, and chemistry have developed their own versions of the periodic table is a feature that is discussed in a quest to reach a global or philosophical understanding of the periodic system.

#### EVOLUTION OF THE ELEMENTS

Chapters 2, , and  discussed Prout's hypothesis, according to which all the elements are essentially made out of hydrogen. Although the hypothesis was initially rejected on the basis of accurate atomic weight determinations, it underwent a revival in the twentieth century. As mentioned in chapter 6, the discoveries of Anton van den Broek, Henry Moseley, and others showed that there is a sense in which all elements are indeed composites of hydrogen. This is so if one focuses on the fact that hydrogen contains one proton while all other elements contain a particular number of protons bound together in their nuclei. In this chapter I concentrate on the second sense in which Prout's hypothesis may be said to have made a comeback. The elements are now believed to have literally evolved from hydrogen by various mechanisms. One of the first people to take this possibility seriously was the English scientist William Crookes, who was also the founder and editor of the influential journal _Chemical News_.

Crookes belongs among the pioneers of the periodic system, although his name is less frequently encountered in this context than are those of precursors such as Johann Döbereiner or discoverers such as John Newlands and Dimitri Mendeleev. Crookes began by studying chemistry under A. W. Hoffmann at the Royal College of Chemistry and then under Michael Faraday at the Royal Institution, while initially working in the field of spectroscopy. Among other accomplishments, Crookes seems to have anticipated the discovery of isotopes, as demonstrated in a quotation from him in chapter 6.

In 1861, Crookes announced the discovery of a new element, thallium, which he identified through a prominent green line in its spectrum. But the most important contribution made by Crookes, for the purposes of the present chapter, was his advocating the inorganic evolution of the elements:

In the very words selected to denote the subject that I have the honour of bringing before you, I have raised a question which may be regarded as heretical. At the time when our modern conception of chemistry first dawned upon the scientific mind, the average chemist as a matter of course accepted the elements as ultimate facts.

I venture to say that our commonly received elements are not simple or primordial, that they have not arisen by chance and have not been created in a desultory and mechanical manner but have been evolved from, simple matters—or perhaps indeed from one sole kind of matter. . . .

Crookes made a spectroscopic study of gases at low pressure that were subjected to high–voltage electric discharges. In 1879, he speculated that the plasma present in the gases treated in this manner, as well as in the stars, consisted of a fourth state of matter. Under such conditions, Crookes argued, the atoms of the elements existed as primary matter that he identified with William Prout's protyle. Seven years later, at a meeting of the British Association for the Advancement of Science, Crookes announced his theory that the chemical elements had evolved in the stars, as they cooled from such a plasma state, through the oscillation of giant electrical forces analogous to those he had studied in discharge tubes (figure 10.1). He claimed that the main oscillating electrical force had an amplitude that corresponded to a period in Mendeleev's periodic system, for example, from hydrogen to fluorine and beyond it. A subsidiary oscillation would act in such a manner as to separate the electropositive elements from the electronegative ones. According to Crookes, the elements were formed in increasing order of atomic weight as the cosmic plasma cooled down. Such giant electrical oscillations would recur to form all the elements in the periodic table, including some that occupied new vacant spaces for elements that were still not known. Each successive amplitude became smaller, with further cooling and with increasing atomic weight, with the result that heavier elements would have more similar properties among each other than would the lighter ones.

This mechanism was illustrated by a three–dimensional pretzel–shaped periodic system, created after the discovery of the noble gases, which is still displayed at the Science Museum in London. This double helical model shows hydrogen at the top and moves downward toward the final element, uranium (figure 10.2). When the noble gases were discovered in the 1890s Crookes was quick to point out that these elements were all implied by his periodic system since they represented the centers of the giant electrical oscillations that he had published in 1886, such as the place between fluorine and sodium on his diagram (figure 10.1).

Mendeleev, however, was critical of evolutionary schemes such as these, declaring in his Faraday lecture of 1889, "The periods of the elements have a character very different from those which are so simply represented by the geometers. . . . T]hey correspond to points, to numbers, to sudden changes of the masses, and not to a continuous evolution." A large number of chemists were involved in founding the field of nucleosynthesis in addition to Crookes. Among them was Richard Tolman, a Caltech chemist who was also an expert in the theory of relativity and statistical mechanics. Another was Jean Perrin, a physical chemist who contributed crucially to the acceptance of atoms as real physical entities and whose early atomic model was mentioned in [chapter 7. Svante Arrhenius was a Nobel Prize–winning chemist and one of the founders of physical chemistry at the turn of the twentieth century. He developed a cosmological theory in which he speculated, unsuccessfully as it turned out, that the universe would not have to suffer a heat death.

FIGURE 10.1 Crookes's electrical oscillations generating the elements. W. Crookes, _Chemical News_ , 45, 115–126, 1886, figure on p. 120.

Similarly, Walther Nernst, another of the founding figures of physical chemistry and the discoverer of the third law of thermodynamics, speculated that radioactive atoms could be created in the ether, which was in turn associated with the zero–point energy that had recently been discovered through the new quantum mechanics. He hoped that a mechanism of continuous recycling would prevent the dreaded heat death of the universe that is generally predicted from thermodynamics.

FIGURE 10.2 Crookes's periodic system. W. Crookes, Proceedings of the Royal Society of London, 63, 408-411, 1898, figure on p. 409.

The idea of the evolution of the elements was seriously taken up again by the astronomer Arthur Eddington, who was intrigued by Prout's hypothesis. Eddington started by suggesting that four hydrogen atoms could combine together to form atoms of helium. In an article published in _Nature_ in 1920, Eddington speculated that the artificial transmutation of elements, which Rutherford had recently discovered by bombarding nuclei with protons, might also take place in the interiors of stars: "What is possible in the Cavendish Laboratory [to make atomic nuclei react] may not be too difficult in the sun."

Big bang cosmology, although it did not originally bear this name, originated with the Belgian priest Georges Lemaître, who was the first to discuss the universe as having been created at a particular moment in time. At first his theory was not taken seriously because it seemed to conflict with Albert Einstein's view of a static universe and because, as some suggested, it seemed to border on theology, especially given Lemaître's declared religious affiliations.

Gradually, astronomical observations showed that the universe was indeed expanding, but whether this was occurring as a result of an initial moment of creation remained controversial. The person who placed the big bang theory on a more secure foundation and, coincidentally for our story, a physicist who made the first major contribution to the theory of nucleosynthesis was the Ukrainian born George Gamow. Gamow was also the first to bring a knowledge of nuclear physics into cosmology and, as it turned out, to some considerable advantage. Broadly speaking, Gamow, along with colleagues Ralph Alpher and Hans Bethe, was able to show that the hypothesized conditions, which prevailed just after the big bang, were consistent with the synthesis of the light elements from hydrogen to beryllium. They argued that the birth of the elements did not take place under equilibrium conditions but as a result of what subsequently became known as the big bang creation of the universe. The mechanism that the authors appealed to was one of neutron absorption by hydrogen atoms followed by beta decay, which could in principle be repeated to form all the elements successively. This notion depends on the fact that beta decay involves the conversion of a neutron into a proton and a beta particle, which is essentially a fast–moving electron created in the nucleus. The absorption of a neutron thus results in the formation of an element with one more proton than the previous one:

In spite of some early successes, Gamow's theory quickly encountered a couple of major stumbling blocks concerning the formation of nuclei of masses 5 and 8. The abundance of both of these nuclei is almost completely negligible. This fact may seem harmless enough until it is appreciated that it puts a bottleneck on the formation of nuclei larger than4 He by the absorption of neutrons or even protons. And if the possibility of forming successive elements by the addition of protons to lighter nuclei in the sequence is interrupted, it becomes difficult to explain the occurrence of any nuclei whatsoever with a mass heavier than 4. In addition, the nonoccurrence of nuclei of mass 8 suggests that it is impossible for two helium nuclei (mass 4) to combine together to form a composite nucleus. Of course, the gaps at mass 5 and mass 8 leave open the possibility of completely different mechanisms for the formation of heavier nuclei, but none that were even contemplated by Gamov's theory.

This impasse was partly surmounted in 1952 by Edwin Saltpeter at Cornell University. His suggestion was that a "triple alpha" mechanism could provide a means of building nuclei beyond mass number 4, as summarized in the following equation:

3 4He → 12C + 2 γ + 7.3 MeV

Saltpeter argued that this process could very well take place in the interior of stars. In addition, he deduced that even if 8Be could exist only for a small fraction of a second, this would be enough time to enable the formation of 12C by an additional mechanism:

2 4He → 8Be

4He + 8Be →12C* → 12C + 2γ

FIGURE 10.3 From left to right, Margaret and Geoffrey Burbidge, William Fowler, and Fred Hoyle, coauthors of the B2FH paper (see text).

Saltpeter also suggested that the 12C formed by both mechanisms (triple alpha and double alpha) could then go on to capture some further alpha particles to yield 16O and 20Ne in accordance with the observed higher abundances of these two particular isotopes. However, Saltpeter did not have much to say on the nature of what he labeled as 12C ***** , and his theory created little impression in the astrophysical community.

The problem of how 12C is formed was solved by the enigmatic British physicist Fred Hoyle (figure 10.3), who perhaps has made the greatest contributions to the question of nucleosynthesis of any person to date, as well as being one of the three architects of the steady–state cosmological theory. Before describing how Hoyle solved the missing link in the triple alpha mechanism, it is necessary to return to an influential article that he published in 1946.

Although Eddington had suggested that element formation could take place in the interior of stars, the temperatures for such processes were far higher than the temperatures that were assumed to exist inside of most typical stars. For example, our sun has a core temperature of a few million degrees. While these conditions can support the burning of hydrogen to form helium, they cannot begin to support the fusion of helium atoms (helium burning), which requires temperatures in the billions of degrees.

Another way to appreciate the situation is to consider the following argument: In order for two nuclei to fuse together, they must approach each other to a distance approximately equal to the sum of their radii. However, such an approach is counteracted by a strongly repulsive Coulomb force, which would seem to render this process impossible. Only following the advent of quantum mechanics was it realized that such a close encounter between nuclei could still occur by means of the phenomenon of quantum mechanical tunneling, which is now believed to take place in stars. In a paper published in 1946, Hoyle sketched the essential pathways through which stellar nucleosynthesis takes place.

In the course of this work, Hoyle also uncovered many important features of how stars change in the course of their lifetimes. For example, a middle–age star fuses hydrogen into helium and, in the process, loses heat as radiant light energy. Two effects then compete to determine the eventual fate of the star. On one hand, the star contracts due to the effect of the gravitational force, while on the other hand, the high temperature generated at the core of the star opposes the contraction. As the star loses its hydrogen fuel, less hydrogen burning can occur, and consequently, the temperature starts to decrease. At this point, the gravitational force begins to dominate and causes the star to contract. However, the compression that occurs causes a new increase in temperature, which acts to halt the further collapse of the star. In addition, the newly established temperature, which is invariably higher than it was previously, allows for new fusion reactions to take place. This reestablished equilibrium is only temporary, however, since the new nuclear reactions eventually run out of fuel, leading to a further contraction phase and consequently another increase in temperature.

This cycle repeats itself many times over, and each time the temperature is higher such that increasingly heavier nuclei can be made to fuse together. The essential details of Hoyle's scheme are shown in table 10.1 for a star of approximately 25 solar masses, although his calculations extended to various types of stars. In this way, different elements could be formed at different stages in the course of a star's life, culminating with the formation of the most stable nuclei of them all, those of iron.

When all the nuclear fuel is consumed, the core collapses in a very short time, followed by an explosion of the star in the form of a supernova. The explosion and the conditions generated by it lead to the formation of many heavy elements and the expulsion of this material into space. All this takes place in the outer parts of the star, while the inner core undergoes an implosion or collapse. During the collapse phase, the nuclei of iron are broken down to form neutrons and the entire star forms a neutron star in cases where the mass is up to two to three solar masses. In heavier stars, not even the Pauli exclusion principle can halt the further collapse of the star to form a black hole.

Hoyle thus obtained an almost complete solution to the problem of nucleosynthesis. What remained was to find an explanation of the second step shown in table 10.1. How could helium atoms fuse together to form carbon? As mentioned above, this was a problem that had already been confronted by Gamov and later by Saltpeter: the lack of any plausible mechanism to form atoms of 12C. Without such a mechanism, all the subsequent steps in Hoyle's table would have remained in the realm of wishful thinking.

TABLE 10.1 Conditions Needed for Different Stages in Nucleosynthesis According to Hoyle's Calculations

But Hoyle succeeded in solving even this problem in an unequivocal and dramatic fashion. He predicted that a 4He nucleus would combine with a nucleus of 8Be to form a high-energy state (or resonance) of the carbon nucleus, contrary to all the then–known evidence on the resonance states of carbon. Hoyle was able to predict the mass and hence the energy of this new excited state by means of a wonderfully simple argument: If the mass of a 4He nucleus is added to that of 8Be, one obtains the mass of the hypothetical new state of carbon that can subsequently decay to form the more common ground state of carbon. The result of this calculation yields an energy of 7.68 MeV above the carbon ground state. While on a sabbatical leave at Caltech, Hoyle eventually persuaded the experimental nuclear physicist William Fowler to try to detect the new resonance state. When the experiments were conducted, they indeed revealed a new state at energy at precisely 7.68 ± 0.03 MeV above the carbon ground state  Hoyle's triumph was complete and became further solidified when he published an even more widely cited article along with Fowler and the husband and wife team of Margaret and Geoffrey Burbidge, which became subsequently known as the B2FH paper (figure 10.3).

Returning to the formation of elements heavier than iron, these authors found that they formed through two main processes. First, there is a slow process of neutron capture, known appropriately as the s–process, which takes place over thousands of years, typically in red giant stars. Nuclei of zinc, for example, absorb neutrons and, following beta decay, produce nuclei of higher atomic numbers:

Nuclei with masses of 230 and greater, however, are formed in the course of multiple neutron absorptions followed by multiple beta decays. This so–called r–process occurs very rapidly and in the course of supernova explosions. Elements that are ejected in supernova explosions are later incorporated into new stars, generation after generation. In fact, the presence of certain heavy elements in the sun, and the fact that solar conditions cannot support the formation of these elements, has led to the conclusion that the sun is at least a second–generation star.

### ASTROPHYSICS AND COSMOLOGY: THE CURRENT VIEW

The universe is now generally believed to have come into being about 13.7 billion years ago in the course of a cataclysmic explosion, involving matter of density 1,070 g/cm3 and whose temperature has been set at 1023 K (table 10.2). This hot big bang produced matter and energy, of which just 4% is ordinary matter and the rest is present as "dark energy" and "dark matter." Of the 4% of ordinary matter, 75% consists of hydrogen and 24% of helium; just 1% consists of all the other elements put together. It is therefore a remarkable fact that all the elements other than hydrogen and helium make up just 0.04% of the universe. Seen from this perspective, the periodic system appears to be rather insignificant. But the fact remains that we live on the earth, which consists entirely of ordinary matter, as far as we know, and where the relative abundance of elements is quite different from the overall cosmic abundance. But before coming to the elements on the earth, it is interesting to consider solar abundances for a moment.

The sun is a good deal younger than the universe as a whole, being 4.55 billion years old. The percentage of hydrogen in the sun is a little less than for the entire universe at 70%, while helium is a little higher at 28%; all the remaining elements account for 2% of the sun. The planets, including the earth, vary widely in chemical composition. While the inner planets have lost most of their gaseous atmospheres, the outer, more massive ones continue to exert an attraction on their gaseous envelopes. Jupiter, Saturn, and Neptune are often called the "gas giants" due to their predominantly gaseous compositions. On earth, hydrogen ranks as only the 11th element in terms of abundance, or just 0.12% by mass, while helium is present only in trace amounts.

TABLE 10.2 Stages in Big Bang Cosmology

### STABILITY OF NUCLEI AND COSMIC ABUNDANCE OF ELEMENTS

The stability of nuclei can be estimated through their binding energy, a quantity given by the difference between their masses and the masses of their constituent particles. This difference in mass gives a measure of the energy released any particular nucleus is formed, via Einstein's famous equation _E_ = mc2. If the binding energy is divided by the mass number of any particular nucleus, one obtains the binding energy per nucleon, which provides a better means of comparing the stability of nuclei. A plot of this quantity against mass number is shown in figure 10.4. Attempts to understand this curve theoretically have been made by appealing to theories from nuclear physics.

An approximate understanding can be gained through the liquid drop model of the nucleus, as developed by Bethe, Carl Friedrich von Weizächer, Niels Bohr, and others. In this model, the nucleus is assumed to be of uniform density like any drop of a uniform liquid. The objective is to explain the rapid rise in binding energy per nucleon, up to a maximum value of between 8.7 and 8.8 MeV, which occurs for iron, the most stable of all nuclei. Beyond this mass number of _A_ = 56, a slow decrease occurs, indicating that nuclei become progressively less stable. Indeed, the formation of nuclei lighter than iron proceeds via exothermic processes in which energy is released. This is why it is favorable for stars to form progressively heavier elements starting from hydrogen and helium, since the energy evolved provides energy to sustain the star. Beyond iron, however, the formation of heavier nuclei occurs via endothermic processes that do not contribute to the power output of the stars.

A nucleus is stable only if the attractive nuclear force within it outweighs the repulsive force between the positive protons. The strong nuclear force, unlike the repulsive Coulomb force, operates equally between protons and neutrons and has a short range with an effect that does not exceed about 2 X 10 –15m. The observed curve in figure 10.4 can be explained in qualitative terms as the net result of combining the strong force (a) and the repulsive Coulomb force (b) in any nucleus, as shown in figure 10.5.

FIGURE 10.4 Binding energy per nucleon as a function of mass number for stable nuclei. Reproduced from G. Friedlander, J.W. Kennedy, E.S. Macias, J.M. Miller, Nuclear and Radiochemistry, John Wiley & Sons, New York, 1981, pp. 26, 27 (with permission).

FIGURE 10.5 Separate and combined effects of strong nuclear force and repulsive Coulomb force in the nucleus. Reproduced from P.A. Cox, The Elements, Oxford University Press, Oxford, 1989, figure from p. 33 (with permission).

However, the liquid drop model is powerless to explain the more detailed features within the binding energy per nucleon curve, such as the various discontinuities that are superimposed on it, reflecting the enhanced stabilities of nuclei of 4He, 12C, 16O, 20Ne, and 24Mg. To explain these more subtle features, we need to consider the quantum mechanical nuclear–shell model, which bears a number of similarities to the electron–shell model as described in chapters 7 and .

The irregularities shown in figure 10.4 can be more easily appreciated by plotting a curve of the difference in binding energy between successive nuclei. This is carried out in a separation energy plot, which gives the energy required to remove a nucleon from any nucleus (figure 10.6). Such plots can be separately drawn for protons or neutrons and show similar general characteristics. They provide plots analogous to those of first–ionization energy plotted against atomic number, as shown in figure 9.6.

FIGURE 10.6 Separation energy plot giving energy required to remove a nucleon from any nucleus. Reproduced from P.A. Cox, _The Elements_ , Oxford University Press, Oxford, 1989, p. 38 (with permission).

FIGURE 10.7 Relative abundance of elements in the solar system, including contributions from meteorites. Reproduced from P.A. Cox, _The Elements_ , Oxford University Press, Oxford, 1989, figure from p. 17 (with permission).

The separation energy curve for a number of nuclei, all having 70 neutrons in this case, shows a distinctive sawtooth pattern with nuclei displaying alternately more or less stable values depending on whether the number of protons is even or odd, respectively. In addition to the sawtooth pattern, there is an overall decrease in stability following the value of _Z_ = 50 as atomic number increases. If this diagram is extended to all known nuclei, it reveals a series of maxima corresponding to especially stable nuclei at _Z_ or _N_ = 2, 8, 20, 28, 50, 82, and 126, the so–called magic numbers. To some extent, the magic numbers for protons also correspond to the maxima in the plot of solar system abundance of elements (figure 10.7). These elements are 2He, 8O,20Ca, 28Ni, 50Sn, 82Pb.

The nuclear–shell model approaches this problem by approximating the forces present in the nucleus by means of a central–field potential. As in the case of electrons in an atom, solving the Schrödinger equation for the nucleus yields a number of distinct energy–level solutions. The labels used for the nuclear levels are similar to those for electrons: s, p, d, and f. But there are also a number of differences in that, for example, the lowest p and d levels in the nuclear case are labeled 1p and 1d, respectively, although such combinations do not occur in the case of electrons. The nuclear energy levels can be thought of as being progressively occupied by nucleons just like the electronic levels are progressively occupied with electrons. However, the energy levels predicted by using only the central field approximation starting with 1s <1p < 1d <2s, and so on, do not explain the occurrence of the magic numbers. The latter feat was achieved by Maria Goeppert–Mayer, Hans Suess, and Hans Jensen in the 1950s by taking into account the effect of spin–orbit coupling present between all nucleons (figure 10.8).

FIGURE 10.8 Energy levels obtained in nuclear–shell theory with inclusion of spinorbit coupling as given by the Goeppert–Mayer–Jensen–Suess model. Numbers on the right represent the number of protons or neutrons in each level, with cumulative totals on extreme right. Reproduced from L. Pauling, _General Chemistry_ , Dover, New York, 1970, p. 855 (with permission).

The introduction of spin–orbit coupling between nucleons results in the splitting of energy levels. In addition, there is considerable overlap in these newly formed levels to produce the sequence shown on the right side of figure 10.8. The filling of nuclear energy levels thus proceeds in the order 1s1/2 < 1p3/2 < 1p1/2 < 1d5/2< and so on. Finally, the number of nucleons that can fill any particular level is 2 _j_ \+ 1 for any given angular momentum _j_ value.

In both the electronic and nuclear–shell theories, one is dealing with a many–body problem for which there is no analytical solution. As a result, the explanations provided in both cases are approximate and rely to some extent on empirical evidence, such as the precise ordering of levels. These relative orderings of levels have not been deduced from first principles, contrary to the impression created by some presentations. Indeed, problems are more severe in the nuclear case, in view of the greater complexity of the nucleus. Just as the _n_ \+ _l_ rule is obtained empirically in the electronic case, as described in chapter 9, so the nuclear ordering by the _aufbau_ principle is also obtained by appeal to empirical data.

The explanation of the magic numbers by nuclear–shell theory is nevertheless a remarkable achievement in that the number of nucleons per level as well as the relationship between the various quantum numbers is deduced from first principles even if the ordering of levels is not.

### MORE CHEMISTRY

The trends within rows and columns of the periodic table are quite well known and are not repeated here. Instead, I concentrate on a number of other chemical trends, some of which challenge the form of reductionism that attempts to provide explanations based on electronic configurations alone. In the case of one particular trend described here, the knight's move, the chemical behavior defies any theoretical understanding whatsoever, at least at the present time.

##### Diagonal Behavior

As is well known to students of inorganic chemistry, a small number of elements display what is termed diagonal behavior where, in apparent violation of group trends, two elements from adjacent groups show greater similarity than is observed between these elements and the members of their own respective groups (figure 10.9). Of these three classic examples of diagonal behavior, let us concentrate on the first one to the left in the periodic table, that between lithium and magnesium. The similarities between these two elements are as follows:

1. Whereas the alkali metals form peroxides and superoxides, lithium behaves like a typical alkaline earth in forming only a normal oxide with formula Li2O.

2. Unlike the other alkali metals, lithium forms a nitride, Li3N, as do the alkaline earths.

FIGURE 10.9 Elements that display diagonal behavior: lithium and magnesium, beryllium and aluminum, and boron and silicon.

3. Although the salts of most alkali metals are soluble, the carbonate, sulfate, and fluorides of lithium are insoluble, as in the case of the alkaline earth elements.

4. Lithium and magnesium both form organometallic compounds that act as useful reagents in organic chemistry. Lithium typically forms such compounds as LiC(CH3)Br, while magnesium forms such compounds as CH3MgBr, a typical Grignard reagent that catalyzes nucleophilic addition reactions. Organolithium and organomagnesium compounds are very strong bases that react with water to form alkanes.

5. Lithium salts display considerable covalent character, unlike their alkali metal homologues but in common with many alkaline earth salts.

6. Whereas the carbonates of the alkali metals do not decompose on heating, that of lithium behaves like the carbonates of the alkaline earths in forming the oxide and carbon dioxide gas.

7. Lithium is a considerably harder metal than other alkali metals and similar in hardness to the alkaline earths.

Although some good explanations for this behavior are available, they serve to undermine the simplistic physicist's notion that chemical behavior is governed just by the electronic configuration of atoms.

The diagonal effect can be explained as the outcome of several opposing trends. As one moves down any group, electronegativity, to consider just one property, decreases. But, as one moves across the table, the same quantity increases. If one moves diagonally the two trends cancel each other out, and there is little change in electronegativity. Similarly, ionization energy and atomic radii trends are such that a diagonal movement results in little change in these properties that, like electronegativity, govern a great deal of the chemistry of the elements. The broader implication is that the electronic configurations of the gas–phase atoms are of little relevance in trying to understand chemical properties. Or to state matters a little differently, the influence of any particular configuration seems to be outweighed by other properties such as those that have just been mentioned, for example, electronegativity and ionization energy.

A rather useful means of discussing the diagonal effect is to appeal to the charge density of the ions of the elements in question, a property that consists of the charge of an ion divided by its volume. The ions of elements that show a diagonal relationship typically have similar charge densities. However, in the case of the boron–silicon relationship, that option is not even available since these elements do not typically form cations.

##### Similarities between Group ( _n_ ) and Group ( _n_ \+ 10)

The chemical similarities of this type have already been mentioned in passing in chapters 1 and . They are similarities that were well known to the pioneers of the periodic table in the nineteenth century and that were embodied in the short–form periodic table (figure 1.6). Unfortunately, many of these trends have been forgotten as a result of the widespread adoption of the medium–long–form table, which does not point to them in any obvious manner.

The first significant example of an _n_ , _n_ \+ 10 effect is observed in the elements magnesium and zinc, which belong respectively in groups 2 and 12 according to the modern International Union of Pure and Applied Chemistry (IUPAC) numbering scheme. Both elements form water–soluble sulfates and water–insoluble hydroxides as well as carbonates. Also, their chlorides are hygroscopic and predominantly covalent.

Moving one step to the right across the periodic table one comes to an even more pronounced example of this kind of behavior in the case of aluminum and scandium. In fact, the Canadian chemist and metallurgist Fathi Habashi has suggested that there are grounds for moving the position of aluminum from group 13– into the scandium group or group 3–. Indeed, one can even make a good argument for this repositioning on electronic grounds. A comparison of the +3 ions of the elements aluminum, scandium, and gallium suggests that the first two of these elements might be grouped together since they share a noble gas configuration, whereas Ga3+ does not.

Some similarities between aluminum and scandium can be seen in table 10.3. The standard electrode potential for aluminum and the other elements would seem to point clearly in favor of a repositioning to the scandium group. The implications from the melting point data are not quite as suggestive, but it does appear as though the high melting–point value of 660°C for aluminum is somewhat anomalous for an element in this group but not so out of place in the scandium group.In addition, Al3+ and Sc3+ both hydrolyze to produce acidic solutions, both of which contain unusual polymeric hydroxo species. Yet another similarity concerns the reactions of Al3+ and Sc3+ with hydroxide ions, resulting in the formation of gelatinous precipitates that redissolve in excess hydroxide ions to form such anions as [Al(OH)4]–. Also, both aluminum and scandium form isomorphous compounds of the general type Na3MF6, where M is aluminum or scandium.

TABLE 10.3 Comparison of Melting Points and Standard Electrode Potentials (E°) of Elements in Groups 3 and 13

Meanwhile, aluminum differs significantly from gallium, the element lying directly below it in group 13. Whereas aluminum forms a polymeric solid hydride with a formula (AlH3) _x_ , gallium forms the gaseous and monomeric hydride Ga2H6. Nevertheless, it must also be recognized that the halides of aluminum resemble those of gallium more than they do those of scandium. Nothing is ever simple as far as the elements are concerned.

The case of tin and titanium is interesting for a somewhat different reason (table 10.4). Here, the similarity is greatest between elements that are related as _n_ and _n_ \+ 10 but that belong to different periods (3 and 4). Moreover, these two elements provide one of the closest similarities between any two elements in different groups, even more so than the classic cases of diagonal relationships mentioned above.

The same kinds of similarities can be seen in cases where _n_ = 5, 6, 7, and 8, although these are not all examined here. The case of groups 8 and 18, for example, is interesting since it is surprising that an element like xenon among the noble gases (group 18–) should bear any resemblance to any other elements in the periodic table. And yet both osmium and xenon, from group 8– and 18–, respectively, form covalent compounds in which they show the +8 oxidation state such as in the cases of OsO4 and XeO4, both of which occur as yellow solids. Furthermore, both elements form other sets of analogous compounds, including OsO2F4 and XeO2O4 as well as OsO3F2 and XeO3F2.

In fact, the only case in which there are no similarities between elements in group _n_ and _n_ \+ 10 are those of group 1– and 11–. The alkali metals (group 1) such as sodium and potassium show pronounced _dissimilarities_ from such elements as copper, silver, and gold (group 11–). The alkali metals are soft, low–density metals that react vigorously with water, whereas the so–called noble metals of group 11–are hard, display high density, and, particularly in the legendary case of gold, show a great reluctance to react with water and many other reagents.

TABLE 10.4 Comparison of Titanium (Group 4) with Tin (Group 14)

The fact that these two particular groups should display such an anomaly regarding _n, n_ \+ 10 behavior serves to highlight further the complexity of the elements, which, as described here, sometimes defies the reductionist's desire for regimentation. In many of these cases, the reductionist can point to the obvious similarity in electronic configurations between an atom from group _n_ and one from group _n_ \+ 10, such as the example of magnesium and zinc discussed above. However, as Geoffrey Rayner Canham, a leading advocate of teaching inorganic chemistry in a qualitative manner, has written, the similarities shown far exceed any expectations on electronic grounds.

##### Early Actinoid Relationships

The relationship concerning members of the actinide series was mentioned is passing in chapter 1. Prior to the work of Glenn Seaborg, the similarities between the transition elements and the early actinides were used to determine the placement of the early actinides in the periodic table (figure 1.9). The modern tendency to separate out the actinides has its merits in terms of electronic configurations but serves, not for the first time, to obscure some undeniable chemical similarities among a number of pairs of elements.

FIGURE 10.10 Early actinides that show analogies with transition metals. Numbers denote the IUPAC group labels.

A number of analogies have been noted between thorium and the members of group 4– headed by titanium, between protactinium and members of group 5– headed by vanadium, and between uranium and the members of group 6-headed by chromium (figure 10.10). For example, uranium, which is assigned to the actinide series and not regarded as a transition metal these days, forms a yellow ion, U2O72–, while chromium forms the well–known oxidizing ion with an orange color of formula Cr2O72–. The analogy with chromium is further displayed in the compounds UO2Cl2 and CrO2Cl2, respectively. But in other respects, uranium resembles tungsten, such as in the formation of the hexachlorides UCl6 and WCl6, neither of which is analogously formed by chromium or molybdenum.

Although relativistic effects may well play a role in these matters, they must be outweighed by other factors since these analogies cease quite abruptly beyond group 6, whereas the influence of relativistic effects is known to increase regularly as a function of atomic number. On the other hand, a comparison of the actinides with respective lanthanides lying directly above in the medium–long–form or long–form periodic table reveals little similarity, except for thorium and cerium, in spite of similarities in electronic configurations between members of these two series.

##### Secondary Periodicity

This behavior was first described in a 25–page paper by the Russian chemist Evgenii Biron. He noted that various chemical and physical properties show a zigzag or alternating behavior instead of the expected regular trend as one descends any group of elements. For example, the elements in group 15 display the zigzag pattern in their common oxidation states, as shown in table 10.5. Whereas the elements in rows 3 and 5, phosphorus and antimony, show a valence of 5, the other three elements predominantly show trivalence.

TABLE 10.5 Secondary Periodicity among Elements in Group 15

The traditional explanation for this behavior has been to invoke the additional electron screening due to the 3d10 electrons in the case of atoms in row 4, such as arsenic, and the even greater screening in atoms in row 6, such as bismuth. The notion is that whereas phosphorus can readily lose five electrons, at least formally, to form a +5 ion, arsenic cannot do so because of d electron screening, which acts to "separate" the outermost p electrons from the outermost s electrons. A similar argument can be made for the change from antimony to bismuth. The removal of the five outermost electrons in bismuth is prevented by the even greater separation in energy between the 6s and 6p outer–shell electrons due to the intervening 4f14 electrons, which are absent in the atoms of antimony.

The drop in the sum of the first five ionization energies between arsenic and antimony is at first sight surprising since both sets of outermost p and s electrons are screened to the same extent by 10 d-orbital electrons in each case. But an overall decrease in ionization is the normal behavior observed on descending most groups in the periodic table.

Ralph Sanderson, an author who has published extensively on the periodic system, has listed some further interesting examples of secondary periodicity:

_Group 13_

B2H6 and Ga2H6 are volatile, whereas the intervening (AlH3) _x_ is not. Stable borohydrides are formed by aluminum but not by boron itself or gallium.

Al(CH3)3 and Al(C2H5)3 are both dimeric in the vapor phase, whereas the analogous boron and gallium compounds are monomeric.

_Group 14_

Germanium resembles carbon more than silicon does. For example, SiH4 is far more readily oxidized than is either GeH4 or CH4.

TABLE 10.6 Variation in Atomic Radii (Å) of Free Atoms for Transition Metal Groups

_Group 15_

Phosphorus and antimony form a pentachloride, whereas arsenic does not. While N(+5) and As(+5) compounds act as good oxidizing agents, P(+5) does not.

N(+3) and As(+3) compounds are far weaker reducing agents than are compounds of P(+3).

Interestingly, secondary periodicity is not confined to main–group elements but occurs even more consistently among transition metals, so much so that this behavior has been used to argue for an alternative placement of lutetium and lawrencium in the periodic table. In 1968, VM. Chistyakov presented data showing that secondary periodicity occurs in most transition metal groups (table 10.6), suggesting that the scandium group should consist of scandium, yttrium, and lutetium, rather than scandium, yttrium, and lanthanum, as is more frequently assumed in published periodic tables.

Finally, several authors who seek to provide group–theoretical explanations for the periodic system have claimed that their approaches also "predict" secondary periodicity.

##### Knight's Move Relationship

The knight's move relationship is perhaps the most mysterious one among all the unusual relationships involving the periodic table (figure 10.11). It takes its name from the knight's move in the game of chess, meaning a move of one step in any direction followed by two steps in a direction at right angles to the first movement. The South African chemist Michael Laing discovered such a relationship among the elements and has described it in detail in a number of articles.

FIGURE 10.11 Elements that show knight's move relationships. For example, zinc and tin or silver and thallium.

The examples of the knight's move relationship so far discovered are located at the heart of the medium–long–form table among metallic elements. Consider the elements zinc and tin. Both are commonly used for plating steel such as in the case of food cans. Not only do layers of both metals successfully delay the onset of corrosion in the iron, but they are also nonpoisonous, unlike many other metals lying close to them in the periodic table. Zinc and tin are not merely nonpoisonous but also appear to be biologically important. Zinc is an essential element for many living organisms because it occurs in a variety of important enzymes. Tin is not essential to humans although it may be so for some living organisms, a fact that has yet to be settled. The compounds of tin are generally regarded as being nontoxic with the exception of organotin compounds such as trimethyl tin. Nevertheless, tin is found in many medicines and even in toothpaste in the form of stannous fluoride, which it is claimed can prevent tooth cavities.

Zinc and tin share another important property: their ability to form alloys with the element copper. Whereas they fail to form an alloy with each other and do not form any intermetallic compounds, zinc alloys with copper to form brass and tin alloys with copper to form bronze, both of which have been known since antiquity.

Cadmium and lead, on the other hand, are both poisonous, which is not too surprising when it is realized that they, too, stand in a knight's move relationship to one another. Further similarities include some closely lying boiling and melting points among their chlorides, bromides, and iodides, as shown in table 10.7. There is also a striking similarity between PbCrO4 and CdCrO4, both of which are yellow substances that are insoluble in water. Table 10.7 also shows aspects of the knight's move relationship between silver and thallium as well as between gallium and antimony and provides further evidence for the zinc–tin relationship discussed above. The elements silver and thallium form another knight's move pair. Among their similarities is the fact that their monochlorides AgCl and TlCl are both photosensitive and insoluble in water.

TABLE 10.7 Melting and Boiling Points That Support Knight's Move Relationships Among Pairs of Elements

Laing has considered possible theoretical explanations of the knight's move relationship but concludes that none is forthcoming. He ends one of his articles by making predictions concerning element 114, which has been observed in trace amounts but has yet to be named. The significance of this element is that, lies in the middle of the so–called "island of stability" among the superheavy nuclei, and this leads one to suppose that it may eventually be possible to synthesize enough of the element to examine its macroscopic properties. Given the knight's move relation to mercury, Laing has predicted that element 114, or eka–lead, should possess a moderate density of around 16 g/cm3, will have a very low melting point, and will possibly be a liquid at room temperature.

##### First–Member Anomaly

It has long been recognized that the first members of groups, especially main–group elements, are anomalous with respect to other members of their groups. This applies equally to physical and chemical properties. For example, hydrogen is a gas, unlike the other members of group 1. Similarly, nitrogen and oxygen occur as gases at room temperature, whereas all the remaining members of their respective groups are found as solids.

In chemical terms, the first members of each group fail to achieve higher oxidation states; that is, they fail to expand their octet of electrons. For example, oxygen shows a maximum oxidation state of just +2 by contrast to the following members, starting with sulfur, which commonly display oxidation states of +4 and +6. Such behavior in the higher members has usually been explained in electronic terms by invoking available d orbitals that allow the atoms to expand their octets. While nitrogen forms only NCl3, phosphorus is said to form PCl5 as a result of promotion of two electrons into available d orbitals and the associated hybridization of the five unpaired electrons. More recently, such explanations have been called into doubt, however. Following some theoretical calculations, it has been argued that the d orbital contribution to the bonding in compounds in which octet expansion occurs is highly insignificant.

In addition to the kind of first–member anomaly that has just been described, there is a more specific observation that has independently been made by William Jensen and Henry Bent, two inorganic chemists and chemical educators. This effect is such that the extent of the first–member anomaly is greatest in the s block of the periodic table, followed by a moderate effect in the p block, and progressively less noticeable in the d and f blocks, respectively. Thus, hydrogen is vastly different from its analogues in group 1, namely, the alkali metals, such as sodium and potassium. The first–member anomalies in the case of the p block elements include the well–known cases mentioned above and involving such elements as nitrogen, oxygen, and fluorine. In the d block, the first members of each group, such as scandium and titanium, show less pronounced anomalies compared to the other elements in their groups, and finally in the case of the f block, the lanthanides show even less difference from the actinides.

But whereas Bent and Jensen have agreed to share the credit for the discovery of this more detailed aspect of first–member anomaly, they draw surprisingly different conclusions regarding the noble gases. For Jensen, helium remains a noble gas, whereas Bent takes the radical step of moving helium to the alkaline earth group and champions the use of the left–step table, as discussed below.

##### Other Relationships

Aluminum and iron in their +3 oxidation states show a number of curious similarities. They are especially curious from the point of view of their electronic configurations, which show no hint of any similarity:

Aluminum [Ne] 3s2 3p1 iron [Ar]4s23d6

And yet both of these elements form analogous hydrated ammonium sulfates: (NH4)Al(SO4)2·12H2O and (NH4)Fe(SO4)2·12H2O. Their chlorides exist as dimers in the gas phase with formulas Al2Cl6 and Fe2Cl6. Their anhydrous chlorides act as Friedel–Crafts catalysts to introduce alkyl groups into aromatic compounds. The active species have been identified as AlCl4– and FeCl4–, respectively. Finally, the cation of both elements hydrolyzes in water to produce acidic solutions.

Another unexpected behavior consists in the close similarity between the combination of boron and nitrogen in certain compounds and compounds consisting of carbon bonded to itself. First of all, boron nitride has a structure analogous to graphite. In addition, as in the case of graphite, the application of very high pressure to boron nitride produces an extremely hard substance that behaves like diamond. Even more intriguing is the analogy between the benzene ring with its characteristic aromatic chemistry and the chemistry of the boron–nitrogen analogue consisting of B3N3H6, called borazine. A post hoc explanation for these similarities is that the sum of the number of outer electrons in an atom of boron plus those from an atom of nitrogen is eight. Similarly, the total number of outer electrons in two carbon atoms is also eight. One wonders, however, whether such similarities, or others like it, could have been predicted.

##### Ions That Imitate Elements

There are some examples of polyatomic ions whose behavior mimics that of an ion of a group of elements in the periodic table. This is the case with the ammonium ion, NH4+, which in some respects behaves like an alkali metal ion. On the one hand, this may be explained by the remarkable similarity between the charge densities of NH4+, which is 151 C/m3, and K+ at 152 C/m3. Nevertheless, the chemistry of the ammonium ion more closely resembles that of Rb+ and Cs+. Among the similarities are reactions with the [Co(NO2)6]3– anion, which give precipitates in the case of NH4+, K+, Rb+, and Cs+.

##### Superatom Clusters

The recent discovery of superatom clusters threatens to disturb the peaceful order of the periodic table in a radical manner. Some chemical elements present in the form of clusters or "superatoms" can take on the properties of entirely different elements that are completely unrelated in terms of their grouping. Indeed, there are cases of a single element that can be made to mimic several different elements according to the precise number of atoms present in its cluster. In the 1980s, Thomas Upton at Caltech discovered that a cluster of six aluminum atoms could catalyze the splitting of hydrogen molecules, thus mimicking the behavior of the element ruthenium. Moreover, a superatom consisting of 13 atoms of aluminum behaves as the analogue of noble gas atoms with their full outer shell of electrons. If an electron is removed to form Al13+, the properties of this superatom ion are similar to those of halogen ions. More specifically, Al13+ behaves like Br–. Furthermore, just as Br– can react with I2 to form BrI2–, the analogous reaction occurs between Al13+ and I2 to form Al13I2–. Even more curiously, a cluster of 14 aluminum atoms mimics the behavior of alkaline earth atoms such as calcium and magnesium. It has been suggested that there might be a new kind of periodic table waiting to be discovered and that the customary two–dimensional table that has been known since the 1860s might require another dimension to take atomic clusters into account.

### VARIETY OF PERIODIC TABLES: IS THERE ONE MOST FUNDAMENTAL PERIODIC TABLE?

It would be a pity to conclude a book on the periodic table without broaching the subject of the variety of tables and systems currently on offer. In addition, this final section serves to revisit some philosophical strands that may have been left hanging in preceding chapters, such as the question of elements as basic substances.

The number of periodic systems that has been proposed probably exceeds 1,000, and are certainly more than the 700 that were carefully analyzed by Edward Mazurs in his classic book of 1974. The rapid proliferation and growth of the Internet and new means of representing data and information on the elements has also fueled the development of what may be called the "periodic table industry." There are now dozens of websites devoted to all aspects of the periodic table, from its history to etymological derivations of the names of elements and tabulations of chemical and physical data.

There seems to be considerable agreement among chemists, in particular, that there is no one "best" periodic table and that one's choice depends on what particular aspect of periodicity or of the elements one is most interested in depicting. In the present account, I subject this view to further analysis and suggest that there may, in fact, be a most fundamental table, regardless of the immediate utility that such a table might possess.

In 2003, the geologist Bruce Railsback published what he termed "An Earth Scientist's Periodic Table" of the elements and their ions. He claims that such a table arranges lithophiles, siderophiles, and chalcophiles into distinct groups unlike the conventional chemist's periodic table. Railsback also seeks to group elements together into naturally occurring sets depending on whether they might be concentrated in the mantle, in seawater, or in soil.

Meanwhile, as mentioned above, the metallurgist Habashi has proposed a periodic table in which the element aluminum is moved to the top of the scandium group. Moving to chemists, Rayner Canham has published an "Inorganic Chemist's Table" (see figure 10.12), in which he highlights a number of unusual relationships, several of which have been reviewed in this chapter. One particularly unusual feature of his table is the inclusion of the ions CN– and NH4+ because of their similarities to certain elements.

Of course, one would not want to deny the utility of these and dozens of other tables that could have been mentioned. But from a philosophical point of view, there is value in asking whether there might be one periodic table that represents the truth about the elements and how they are related to each other, rather than focusing only on the utility of tables to any particular discipline. Pursuing this line of thought raises the question of realism about the elements and realism about grouping them together into columns, at least as far as the conventional representation is concerned. Is the grouping of the elements a matter of objective fact, or is it merely a matter of convention? Should one be a realist or an antirealist about the periodic system and the grouping of elements? My suggestion is that one should adopt a realistic attitude. It is proposed that the arrangement of elements into chemically similar groups is a matter of fact and not a question of choice. If this is indeed the case, then in addition to the huge variety of tables that may be useful to geologists, metallurgists, chemists, and so on, there might nevertheless be one objective periodic system that most closely approximates the truth about the elements.

##### Back to Elements as Basic Substances

In some preceding chapters, the subject of elements as basic substances compared with elements as simple substances is discussed. As described in chapter 4, Mendeleev placed greater emphasis on the elements as basic substances than on elements as simple substances when he produced his periodic classification. The main criterion of basic substances was their atomic weight. When atomic number took over the role as the ordering criterion for the elements, Fritz Paneth in particular took it upon himself to redefine basic substances as being characterized by their atomic numbers.

FIGURE 10.12 The inorganic chemist's periodic table, designed by G. Rayner Canham. Shadings indicate relationships: ( _n_ ) and ( _n_ \+ 10) relationships; diagonal relationships; knight's move relationships; aluminum–iron link; actinoid relationship; lanthanide–actinide relationship; combination elements; pseudoelements.

Moreover, in the 1920s, Paneth drew on the metaphysical essence of elements as basic substances in order to save the periodic system from a major crisis. Over a short period of time, many new isotopes of the elements had been discovered, such that the number of "atoms" or most fundamental units suddenly seemed to have multiplied. The question was whether the periodic system should continue to accommodate the traditionally regarded atoms of each element or whether it would be restructured to accommodate the more elementary isotopes that might now be taken to constitute the true "atoms." Paneth's response was that the periodic system should continue as it had before, in that it should accommodate the traditional chemical atoms and not the individual isotopes of the elements. Paneth regarded isotopes as simple substances in that they are characterized by their atomic weights, while elements as basic substances are characterized in his scheme by atomic number alone.

Moreover, Paneth, along with Georgy Hevesy, provided experimental evidence in support of this choice for chemists. They showed that the chemical properties of isotopes of the same element were, for all intents and purposes, identical. As a result, chemists could regard the isotopes of any element as being the same simple substance even though such atoms might occur in different isotopic forms.

It is worth noting that, in the case of this isotope controversy, Paneth's recommendation for the retention of the chemist's periodic table depended on the notion of elements as basic substances and not as simple substances. If the chemists had focused on simple substances, they would have been forced to recognize the new "elements" in the form of isotopes that were being discovered in rapid succession. By choosing to ignore these "elements" in favor of the elements as basic substances, chemists could continue to uphold that the fundamental units of chemistry, or its natural kinds, remained as the entities that occupied a single place in the periodic system.

##### Elements and Groups of Elements as Natural Kinds?

Elements defined by their atomic numbers are frequently assumed to represent "natural kinds" in chemistry. The general idea is that the elements represent the manner in which nature has been "carved at the joints." On this view, the distinction between an element and another one is not a matter of convention. The question arises as to whether groups of elements appearing in the periodic table might also represent natural kinds. Could it be that there is some objective feature that connects all the elements that share membership to a particular group in the periodic system?

It would seem that the criterion for membership to a group is by no means as clear–cut as that which distinguishes one element from another. In the case of groups of the periodic table, it is the electronic configuration of gas–phase atoms that seems to provide a criterion, although in neither a necessary nor a sufficient manner. However, one may also argue that the placement of the elements into groups is not a matter of convention. If periodic relationships are indeed objective properties, as I argue here, it would seem to suggest that there is one ideal periodic classification, regardless of whether or not this may have been discovered. This in turn would have a bearing on some recent questions regarding the placement of some elements within the periodic system. And if electronic configurations do not perfectly capture the fact that groups are natural kinds, this may merely indicate the limitations of the concept of electronic configurations.

##### The Placement of Hydrogen and Helium in the Periodic System

There has been considerable debate within chemistry in recent years as to the placement of the elements hydrogen and helium within the periodic system. For example, hydrogen is similar to the alkali metals in its ability to form single positive ions. However, hydrogen can also form single negative ions, thus suggesting that the element might be placed among the halogens, which also display this type of ion formation. Helium is traditionally regarded as a noble gas in view of its extreme inertness and is thus placed among the other inert gases in group 18 of the periodic system. However, in terms of its electronic configuration, helium has just two outer electrons and might therefore be placed among the alkaline earth metals such as magnesium and calcium. Many periodic tables appearing in physics books do just that, as do many spectroscopic periodic systems.

Peter Atkins and Herbert Kaesz have proposed a modification to the periodic table concerning the placement of the element hydrogen. Contrary to its usual placement at the top of the alkali metals, and its occasional placement among the halogens, Atkins and Kaesz choose to position hydrogen on its own, floating above the table. In addition, they place helium alongside hydrogen, thus also removing it from the main body of the periodic table.

Rather than considering the relative virtues of these placements in chemical terms, the argument for the removal of hydrogen and helium from the main body of the table can be examined from the perspective of the elements as basic substances. The widely held belief among chemists is that the periodic system is a classification of the elements as simple substances that can be isolated and whose properties can be examined experimentally. However, as emphasized in the present book, there is a long–standing metaphysical tradition of also regarding the elements as unobservable basic substances.

I suggest that our current inability to place hydrogen and helium in the periodic table in an unambiguous manner should not lead us to exclude them from the periodic law altogether, as Atkins and Kaesz seem to imply. Hydrogen and helium are surely as subject to the periodic law as are all the other elements. Perhaps there is a "fact of the matter" as to the optimum placement of hydrogen and helium in the main body of the table. Perhaps this question is not a matter of utility or convention that can be legislated, as most authors have argued.

Surprising as it may seem, some chemists have even proposed chemical evidence for placing helium in this manner. Such arguments are based on the first–element rule, as discussed above, which in its simplest form states that the first element in any group of the periodic system tends to show several anomalies when compared with successive members of its group. For example, in the p block, all the first–member elements show a reluctance to expand their octets of outer–shell electrons while subsequent group members do so quite readily. In addition, there is a more sophisticated version of this first–member rule that also specifies the extent to which the first elements in the various blocks of the periodic table display anomalies.

But once again, rather than relying on specific properties of the elements as simple substances, I suggest that we should concentrate on elements as basic substances. Perhaps one should seek some form of underlying regularity in order to settle the question of the placement of any element. Such a possibility is discussed below, along with the question of the best possible form for the periodic system.

### IS THERE A BEST FORM FOR THE PERIODIC TABLE?

The periods in the currently most popular representation of the periodic system, the so–called medium–long form, are arranged so that each one begins with a new value of _n_ , or the first quantum number (figure 1.4). This value denotes the main shell of the most energetic electron in each case, in terms of the _aufbau_ principle, that is used to "build up" the configuration of any particular atom. In more macroscopic chemical terms, the medium–long–form table places the reactive metals such as the alkalis and alkaline earths on the left side of the periodic table and the reactive nonmetals on the right side.

The conventional medium–long form displays the periods as though the main–shell number is the dominant criterion for the buildup of successive periods. But, as is well known, this form of display leads to a somewhat confusing layout whereby in several cases a main shell begins to fill, followed by an interruption due to a transition metal series in which a penultimate shell is filled. Only after such interruptions, which are more pronounced in the case of periods that also include inner transition elements, does the filling of the main shell resume.

Many authors have suggested that a more satisfactory representation can be obtained by basing the start of periods on _n_ \+ _l_ instead of n. Such a table requires that the s block be shifted to the right of the p block elements, which leads more specifically to at least two particular periodic tables. The first one is the so–called left–step periodic table (figure 10.13). The second is a modified form of the pyramidal periodic system that likewise places the s block elements on the right–hand edge of a pyramid (figure 10.14). Both of these tables display two short periods of two elements, thus satisfying the desire for regularity that many authors, including some group theorists, believe might lie at the heart of the periodic system.

Both of these alternative representations of the periodic system display the elements in a continuous manner with no break between any sets of elements, contrary to what is encountered in the currently accepted medium–long form. But these tables also contain a feature that causes many chemists some concern, in that the element helium is firmly located among the alkaline earth elements.

However, as I argued in the preceding section, such worries are alleviated once one acknowledges that the periodic system is primarily intended to classify the elements as basic substances and not simple substances. Although one can partly agree with the view that different representations can help to convey different forms of information, I believe that one may still maintain that one particular representation reflects chemical periodicity, regarded as an objective fact, in the best possible manner.

It may seem odd to the reader that the suggested periodic systems are ones that appear to rest rather heavily on a reductionist view in favor of the importance of electronic configurations of atoms. In addition, these considerations, and more specifically the _n_ \+ _l_ rule concerning the order of filling of atomic orbitals, are being placed above current wisdom concerning the chemical nature of helium, which dictates that it should be regarded as a noble gas par excellence and not as an alkaline earth element.

FIGURE 10.13 The left-step or Janet table. Numbers on the right represent values of _n_ \+ _l_.

FIGURE 10.14 A modified pyramidal version of the periodic table. This form has bilateral symmetry.

My response to such worries is to point out that throughout this book I have sought to examine the limits of reductionism in chemistry and have not been critical of reductionism as a general approach. As mentioned at the outset, reductionism has provided an undeniably successful approach to the acquisition of scientific knowledge. The thrust of this book has been directed against exaggerated claims made on behalf of reductionism, for example, Bohr's claim that he had predicted the chemical nature of the element hafnium from first principles or the claim that all aspects of the periodic table have been strictly deduced from the later quantum mechanics. It is rather the limitations of reductionism that are of interest to philosophers of science and that should be taken more seriously by science educators.

### A CONTINUUM OF PERIODIC TABLES?

The metaphysical notion of the elements as basic substances and as the bearers of properties has been historically important in the case of Mendeleev's establishment of the periodic system and Paneth's resolution of the fate of the periodic system in light of the discovery of isotopes.

I have suggested that the notion of elements as basic substances can cast some light on the question of the optimal representation of the periodic system. As in the case of the distinction between elements as basic substances and as simple substances, the aim should be to obtain a classification that primarily classifies elements as basic substances, while also recognizing aspects of the elements as simple substances. This optimal classification will not be obtained by behaving as naive inductivists and agonizing over the minutiae of the properties of hydrogen, helium, or other problematic elements. It is suggested that an optimal classification can be obtained by identifying the deepest and most general principles that govern the atoms of the elements, such as the _n_ \+ _ℓ_ rule, and by basing the representation of the elements on such principles.

But I conclude with a less controversial proposal. Let us imagine that the various representations of the periodic system lie on a continuum. At one end of this continuum is the "unruly" Rayner Canham table (figure 10.12) that attempts to do justice to many unusual relationships of the kind that have been highlighted in this chapter. At the other end of the continuum lies what I call the Platonic periodic table, or what is usually called the left–step or Janet periodic table (figure 10.12). Somewhere near the middle of this continuum of representations, one can locate the currently popular medium–long representation. It is not altogether surprising that this form has been so popular since it appears to capture the correct balance between utility and the display of order and regularity. While it sacrifices many of the unusual chemical and physical relationships that Rayner Canham's table features, it embodies the physics and chemistry of the elements as simple substances as well as basic substances. At the same time, the medium–long form stops short of adopting a fully reductionist approach that puts the highest premium on electronic configurations, which would commit one to the placement of helium among the alkaline earths.

FIGURE 10.15 Dufour's 3–D periodic tree. Photo and permission from Fernando Dufour.

The left–step table, I suggest, embodies the elements entirely as basic substances since it relegates the chemical and physical properties of elements such as helium and places greater importance upon more fundamental aspects. From a philosophical point of view, I believe that the left–step table may provide an optimal periodic system in showing the greatest degree of regularity while also adhering to the deepest available principles relating to the elements as basic substances.

It would be gratifying to think that principles of beauty and elegance as embodied in the system shown in figure 10.15, for example, or indeed, a philosophical version of the periodic table may eventually become the standard form of the periodic system. But the argument between the relative virtues of utility and beauty in science is not an easy one to resolve, and I do not propose to do so here. It is with some trepidation that I advocate the general adoption of the left–step periodic system since I am well aware of the resistance that this proposal will meet, especially from the chemical community, which, rightly or wrongly, regards itself as the sole proprietor of the periodic system.

## **N OTES**

### Acknowledgments

. M.P. Melrose, E.R. Scerri, Why the 4s Orbital Is Occupied before the 3d, _Journal of Chemical Education_ , 73, 498–503, 1996; E.R. Scerri, J. Worrall, Prediction and the Periodic Table, _Studies in the History and Philosophy of Science_ , 32, 407–452, 2001.

. At about the same time, the official journal of the society, _Foundations of Chemistry_ was also started.

### Introduction

. There have only ever been two conferences specifically on the periodic table. The first was in 1969 as part of the celebrations commemorating the centenary of Mendeleev's famous table of 1869 [M. Verde (ed.), _Atti del Convegno Mendeleeviano_ , Accademia delle Scienze di Torino, 1971]. The second was held as recently as 2003 in Banff, Canada [D. Rouvray, R.B. King, _The Periodic Table: Into the 21st Century_ , Science Studies Press, Bristol, 2004].

. J. van Spronsen, _The Periodic System of the Chemical Elements, the First One Hundred Years_ , Elsevier, Amsterdam, 1969. I find it embarrassing to make this criticism given the enormous debt I owe to Van Spronsen's wonderful book on the periodic system.

. F.P. Venable, _The Development of the Periodic Law_ , Chemical Publishing Co., Easton, PA, 1896.

. E. Mazurs, _The Graphic Representation of the Periodic System During 100 Years_ , University of Alabama Press, Tuscaloosa, 1974. In addition, Mazurs has given some arguments for the adoption of a symmetrical representation of the periodic system.

. For a bibliography of secondary articles on the periodic system, which emphasizes philosophical works, see E.R. Scerri, J. Edwards, Bibliography of Literature on the Periodic System, _Foundations of Chemistry_ , 3, 183-196, 2001.

. P.W. Atkins, _The Periodic Kingdom_ , Basic Books, New York, 1995. Also see E.R. Scerri, A Critique of Atkins' Periodic Kingdom and Some Writings on Electronic Structure, _Foundations of Chemistry_ , 1, 287-296, 1999.

. R.J. Puddephatt, P.K. Monaghan, _The Periodic Table of the Elements_ , Oxford University Press, Oxford, 1985.

. D.G. Cooper, _The Periodic Table_ , Plenum Press, New York, 1968.

. J.S.F. Pode, _The Periodic Table; Experiment and Theory_ , Wiley, New York, 1973.

. R.T. Sanderson, _The Periodic Table of the Chemical Elements_ , School Technical Publishers, Ann Arbor, MI, 1971.

. P. Strathern, _Mendeleyev's Dream_ , Thomas Dune Books, New York, 2001; O. Sacks, _Uncle Tungsten_ , Alfred Kopf, NewYork, 2001; R. Morris, _The Last Sorcerers:Atoms, Quarks and the Periodic Table_ , Walker & Co., New York, 2003.

. M. Gordin, _A Well-Ordered Thing_ , Basic Books, New York, 2004.

. B.J.T. Dobbs, M.C. Jacob, _Newton and the Culture of Newtonianism_ , Humanity Books, Amherst, NY, 1998.

. L. Principe, _The Aspiring Adept: Robert Boyle and His Alchemical Quest: Including Boyle's "Lost" Dialogue on the Transmutation of Metals_ , Princeton University Press, Princeton, NJ, 1998, quoted from p. 220.

. A number of detailed studies on philosophical aspects of scientific experiments now exist, including David Gooding, Trevor Pinch, Simon Schaffer, _The Uses of Experiment: Studies in the Natural Sciences_ , Cambridge University Press, New York, 1989; and Allan Franklin, _The Neglect of Experiment_ , New York, Cambridge University Press, 1986.

. E.g., the book on scientific models by the philosopher Nancy Cartwright, _How the Laws of Physics Lie_ , Oxford University Press, Oxford, 1983.

. D. Shapere, Scientific Theories and their Domains, in F. Suppe (ed.), _The Structure of Scientific Theories_ , Illinois University Press, Urbana, 518-599.

. The literature in this area has grown tremendously in recent years. For discussions, see P.R. Gross, N. Levitt, _Higher Superstition_ , Johns Hopkins University Press, Baltimore, MD, 1994; A. Sokal, Transgressing the Boundaries: Towards a Transformative Hermaneutics of Quantum Gravity, _Social Text_ , 46-47, 217-252, 1996; J.A. Labinger, H. Collins, _The One Culture?_ University of Chicago Press, Chicago, 2001.

. G. Bodner, M. Klobuchar, D. Geelan, The Many Forms of Constructivism, _Journal of Chemical Education_ , 78, 1107-1134, 2001. For a critical appraisal, see E.R. Scerri, Philosophical Confusion in Chemical Education Research, _Journal of Chemical Education_ , 80, 468-474, 2003.

. This is not to imply that Kuhn himself or anyone else that I am aware of has argued that the development of the periodic system _did_ represent a scientific revolution.

. Related claims about Kuhn's conservatism are made in Steve Fuller, _Thomas Kuhn: A Philosophical History for Our Times_ , University of Chicago Press, Chicago, 2000; and Mara Beller, _Quantum Dialogue: The Making of a Revolution_ , University of Chicago Press, Chicago, 1999.

. Readers interested in scholarly research on Mendeleev in particular should consult the work of a number of excellent contemporary historians of science, including N. Brookes, Developing the Periodic Law: Mendeleev's Work during 1869-1871, _Foundations of Chemistry_ , 4, 127-147, 2002; M. Gordin, _A Well-Ordered Thing_ , Basic Books, New York, 2004; M. Kaji, Mendeleev's Discovery of the Periodic Table, _Foundations of Chemistry_ , 5, 189-214, 2003.

. Over the past 20-30 years, there has been a great deal of debate among historians of chemistry regarding Lavoisier's role in the chemical revolution and whether this was indeed a revolution or just the culmination of previous work begun by the likes of Georg Stahl. See articles by Gough, Siegfried, Perrin, and Holmes in A. Donovan (ed.), Chemical Revolution, Essays in Reinterpretation, _Osiris_ , 2nd series, vol. 4, 1988.

. The popular story found in most books is that Bohr was primarily concerned with explaining the spectrum of the hydrogen atom. But as Kuhn and Heilbron have convincingly argued, Bohr was not even aware of the problems with atomic spectra when he began applying quantum theory to the structure of the atom. T.S. Kuhn, J. Heilbron, The Genesis of the Bohr Atom, _Historical Studies in the Physical Sciences_ , 3, 160-184, 1969.

. J.D. Trout, in R. Boyd, P. Gaspar, J.D. Trout (eds.), Reduction and the Unity of Science, _The Philosophy of Science_ , MIT Press, Cambridge, MA, 1992, 387-392.

. A few modern commentators appear to disagree in this respect and regularly advertise their support for the "dis-unity of science": J. Dupré, _The Disorder of Things, Metaphysical Foundations of the Disunity of Science_ , Harvard University Press, Cambridge, MA, 1993; N. Cartwright, _How the Laws of Physics Lie_ , Clarendon Press, Oxford, 1983; N. Cartwright, _Nature's Capacities and Their Measurement_ , Oxford University Press, Oxford, 1989; P. Galison, D. Stump, _The Disunity of Science_ , Stanford University Press, Palo Alto, CA, 1996.

. For a more detailed treatment of this modern approach to the reduction of chemistry, see E.R. Scerri, Popper's Naturalized Approach to the Reduction of Chemistry, _International Studies in Philosophy of Science_ , 12, 33-44, 1998.

. K.R. Popper, Scientific Reduction and the Essential Incompleteness of All Science, in F.L. Ayala, T. Dobzhansky (eds.), _Studies in the Philosophy of Biology_ , Berkeley University Press, Berkeley, CA, 1974, pp. 259-284.

. J. LaPorte, Chemical Kind Terms, Reference and the Discovery of Essence, _Nous_ , 30, 112-132, 1996; J. LaPorte, _Natural Kinds and Conceptual Change_ , Cambridge University Press, New York, 2004.

. J. van Brakel, _Philosophy of Chemistry_ , Leuven University Press, Leuven, Belgium, 2000.

. I believe that this criticism can be countered by appeal to the elements as basic substances in the sense used by Mendeleev. E.R. Scerri, Some Aspects of the Metaphysics of Chemistry and the Nature of the Elements, _Hyle_ , 11, 127-145, 2005.

. P. Bernal, Foundations of Chemistry: Special Issue on the Periodic System (editor-in-chief Eric R. Scerri), _Journal of Chemical Education_ , 79, 1420, 2002.

. E.g., see an editorial in _Foundations of Chemistry_ for the special issue on the Periodic System, vol. 3, 97-104, 2001.

### Chapter 1

. There has been some debate concerning the precise criteria used by Lavoisier, given that several of the entries fail to meet his stipulation that simple substances are the final products of chemical analysis. R. Siegfried, B.J. Dobbs, Composition, A Neglected Aspect of the Chemical Revolution, _Annals of Science_ , 29, 29–48, 1982.

. With the exception of fire, which is a process rather than a substance.

. Lavoisier's simple substances were defined in opposition to the classical view of the elements as abstract entities or principles. However, Lavoisier was not entirely consistent in that some of his simple substances appear to be more akin to the older principles. This issue concerning the dual nature of elements is resumed in later chapters.

. Until recently, it was believed that the element technetium with atomic number 43 does not occur naturally. It has now been established that this element does occur terrestrially and that the initial reports of its discovery by the Noddacks in 1925 may have been correct. I. Noddack, W. Noddack, Darstellung und Einige Chemische Eigenschaften des Rheniums, _Zeitschrift für Physikalishe Chemie_ , 125, 264–274, 1927. Promethium is therefore the only element within the first 92 that does not occur naturally.

. M.E. Weeks, H. Leicester, _The Discovery of the Elements_ , 7th ed., Journal of Chemical Education, Easton, PA, 1968.

. H.M. Van Assche, The Ignored Discovery of Element Z = 43, _Nuclear Physics_ A, A480, 205–214, 1988. See also note 4.

. For a very informative article on the naming of compounds, from which I have drawn liberally for this section, see V. Ringnes, Origin of the Names of Chemical Elements, _Journal of Chemical Education_ , 66, 731–738, 1989.

. Primo Levi, _The Periodic Table_ , 1st American ed., Schocken Books, New York, 1984.

. Levi took his own life after surviving the holocaust and after writing several books, the best known of which remains _The Periodic Table_. He is believed to have acted out of survivor guilt.

. O. Sacks, _Uncle Tungsten_ , Alfred Knopf, New York, 2001.

. The classic book on the discovery of the individual elements remains M.E. Weeks, H. Leicester, _The Discovery of the Elements_ , 7th ed., Journal of Chemical Education, Easton, PA, 1968.

. Other elements that take their names from mythology are vanadium, niobium, and tantalum.

. The element names of rubidium, indium, and thallium are also derived from colors.

. These scientists were all famous physicists, with the exception of Mendeleev and Seaborg, who were chemists.

. The most recently approved names, at the time of writing, are darmstadtium and roentgenium for elements 110 and 111, respectively.

. The unofficial reason is that many members of the IUPAC committee objected to the idea of naming an element after the person who had synthesized such deadly substances as plutonium, which was used in one of the atomic bombs dropped on Japan during the Second World War.

. The modern author Ruth Sime has written several articles and a book about the way in which the Nobel Prize committee overlooked Lise Meitner's work. R.L. Sime, _Lise Meitner: A Life in Physics_ , University of California Press, Berkeley, 1996.

. The others are potassium (K), iodine (I), yttrium (Y), phosphorus (P), and tungsten (W).

. These Latin names are _cuprum_ (Cu), _natrium_ (Na), _ferrum_ (Fe), _plumbum_ (Pb), _hydrargyrum_ (Hg), _argentum_ (Ag), and _aurum_ (Au).

. An excellent and detailed account of the discovery and properties of all the individual elements can be found in John Emsley, _Nature's Building Blocks:An A-Z Guide to the Elements_ , Oxford University Press, Oxford, 2001.

. The story of this development is mentioned by the discoverer of the compound, Paul Chu, in the article, Yttrium, _Chemical & Engineering News_, Special Issue on the Elements, September 8, 2003, p. 102.

. The groups headed by copper and zinc are labeled as IB and IIB, respectively, in both the U.S. and European systems. Also note that in the US and European systems three groups are collectively labeled as VIIIB and VIIIA respectively.

. According to some observers, the IUPAC recommendation is really the European system in disguise since it numbers the groups sequentially from left to right regardless of whether they might be main-group elements or transition elements. The IUPAC numbering proposal also raises the question of what should be done if the rare earth elements are incorporated into the periodic table rather than being displayed as a footnote. This would strictly necessitate a numbering of all groups from 1 to 32.

. In chapter 10, however, the IUPAC system is used.

. With the exception of the first member of the group, lithium, which is rather unreactive, although it, too, forms an alkaline solution and even reacts vigorously with nitrogen when heated.

. One example of a loss is the correspondence between the numbers in the group labels and the maximum oxidation state of the element in question.

. Fullerenes, also known as buckyballs or buckminsterfullerenes are a recently discovered form of carbon. The best-known such molecule contains a total of 60 carbon atoms arranged in the shape of a soccer ball, that is, a set of interlocking hexagons and pentagons.

. But there are variations, in that the valence of 2 is increasingly the more predominant one as the group is descended. In the case of lead, compounds displaying a valence of 2 such as PbCl2 are actually more stable than their 4-valent analogues such as PbCl4 in this case.

. However, in many countries cesium (melting point 28.5°C) and gallium (melting point 29.8°C) are also liquid at room temperature.

. One further element in this group, astatine, has been discovered but only a handful of atoms of it have ever been isolated. Its macroscopic properties, such as the color of the element, therefore remain unknown.

. It is the abstract element that survives when elements form compounds, and so there are more similarities among the compounds of the elements than in the isolated elements or elements as simple substances.

. The actual dates are helium, 1895; neon, 1898; argon, 1894; krypton, 1898; xenon, 1898; and radon, 1900.

. Hundreds of chemical compounds of krypton and xenon are now known. Only helium and neon still resist all attempts at making them combine with other elements.

. This way of counting period length counts the first element up to and including the element that represents the approximate repetition of the first one.

. D.W. Theobald, Some Considerations on the Philosophy of Chemistry, _Chemical Society Reviews_ , 5, 203–213, 1976.

. The growing interest in the philosophy of chemistry, and specifically in the autonomy of chemistry, makes holding such views increasingly more plausible. E.R. Scerri, L. McIntyre, The Case for Philosophy of Chemistry, _Synthese_ , 111, 213–232, 1997.

. Whether or not a circular-shaped display would count as a table is debatable, although one sometimes encounters the term "circular periodic table."

. Some time ago, in his highly popular book _The Tao of Physics_ (Shambala, Berkeley, CA, 1975), F. Capra argued that modern physics shares many similarities with the Taoist philosophy of complementary opposites. It has been suggested that chemistry lends itself far more directly to such analogies. E.R. Scerri, The Tao of Chemistry, _Journal of Chemical Education_ , 63, 100–101, 1986.

. Much chemical history has been condensed into this sentence. The quantities used were first equivalent weight, then followed by a period of confusion in which atomic weights and equivalent weights (confusingly defined in several different ways) were used. After the Karlsruhe conference in 1860, atomic weights began to be used more exclusively, and finally atomic weight was replaced by atomic number as the main ordering criterion for the elements.

. I am greatly oversimplifying the situation. As Alan Rocke and many others before him have argued, the use of equivalent weights in preference to atomic weights carried out by William Wollaston and others was motivated by the notion of avoiding theoretical assumptions as well as the existence of atoms. However, these chemists still needed to assume formulas for the compounds they were considering, and as a result, what they were calling equivalent weights were operationally equivalent to atomic weights. A. Rocke, Atoms and Equivalents, The Early Development of Atomic Theory, _Historical Studies in the Physical Sciences_ , 9, 225–263, 1978; A.J. Rocke, _Chemical Atomism in the Nineteenth Century_ , Ohio State Press, Columbus, 1984.

. Historian Alan Rocke argues that this change was already in the air at the time and would have taken place regardless of the Karlsruhe meeting. A. Rocke, _Chemical Atomism in the Nineteenth Century_ , Ohio State Press, Columbus, 1984.

. This is a generalization. E.g., it is not clear that Gustav Hinrichs's system followed this form of ordering. Also, some of the discoverers of the periodic system such as John Newlands began by using equivalent weights and later changed to using atomic weights.

. The fact that atoms contain protons and neutrons also explains the concept of isotopes, which is of crucial importance in the story of the periodic table. Atoms of an element that differ in the number of neutrons they contain are said to represent different isotopes of that element. E.g., the element carbon has three most common isotopes: carbon-12, carbon-13, and carbon-14. Each of these contains six protons (which identifies them as carbon) but also six, seven, or eight neutrons, respectively. Each is said to have a different mass number given by the sum of protons and neutrons. The atomic weight of carbon is given by a weighted average of the masses of all the isotopes of the element, meaning an average, which takes account of how much of each isotope occurs in any given natural sample. Until atomic number was understood, the existence of isotopes made it difficult to fit some elements into a periodic scheme in what would appear to be the proper order based on their chemical properties.

. E.g., see F. Habashi, A New Look at the Periodic Table, _Interdisciplinary Science Reviews_ , 22, 53–60, 1997. This article presents a periodic table from the point of view of metallurgy. An interesting geologist's table can be found in L.B. Railsback, An earth scientist's periodic table of the elements and their ions, _Geology_ , 31, 737–740, 2003.

. After publishing articles in _American Scientist_ and _Scientific American_ on the development of the system, the author received about 50 models, diagrams, and letters outlining new designs from passionate advocates of some particular version. He still frequently receives messages and letters from well-meaning enthusiasts asking him to comment on a new theory or a new form of representation of the periodic table.

. The final comment is rather controversial, with many chemists believing that there is no one best representation. These authors consider representation to be a secondary issue, which is dictated by convention. The present author takes issue with this view and supports a more realist interpretation whereby the grouping of troublesome elements such as hydrogen has an objective aspect and is not merely a manner of convenience. See E.R. Scerri, The Best Representation of the Periodic System: The Role of the n + 1 Rule and the Concept of an Element as a Basic Substance, in D. Rouvrary, R.B. King (eds.), _The Periodic Table: Into the 21st Century_ , Science Studies Press, Bristol, 2004, 143–160.

. P. Armbruster, F.P. Hessberger, Making New Elements, _Scientific American_ , 72–77, September 1998. This article is followed by one on the history of the periodic system: E.R. Scerri, The Evolution of the Periodic System, _Scientific American_ , 78–83, September 1998.

. W.B. Jensen, Classification, Symmetry and the Periodic Table, _Computers and Mathematics with Applications_ , 12B, 487–509, 1986; H. Merz, K. Ulmer, Position of lanthanum and lutetium in the Periodic Table, _Physics Letters_ , 26A, 6–7, 1967; D.C. Hamilton, M.A. Jensen, Mechanism for Superconductivity in lanthanum and uranium, _Physical Review Letters_ , 11, 205–207, 1963; D.C. Hamilton, Position of lanthanum in the Periodic Table, _American Journal of Physics_ , 33, 637–640, 1965.

. The contemporary author on the periodic system, W.B. Jensen, uses the terms primary and secondary kinship, which should not be confused with the terms primary and secondary classification as used by the present author. A primary kinship as termed by Jensen results from secondary classification according to the terminology used in this book. W.B. Jensen, _Computers and Mathematics with Applications_ , 12B, 487–509, 1986.

. This is an important issue. The helium question is at the center of recent attempts to revolutionize the way in which the periodic system should be represented. See, e.g., Gary Katz, The Periodic Table: An Eight Period Table for the 21st Century, _The Chemical Educator_ , 6, 324–332, 2001.

. Evidence for higher elements is not yet conclusive, and some claims have, in fact, been withdrawn.

. Strictly speaking, the electron is regarded as much as a delocalized wave as an orbiting particle, as explained a little later in the text. The use of the phrase "rapidly moving electrons" should therefore be regarded as a classical approximation in this context.

. There are several relatively accessible articles on relativistic effects in atoms. L.J. Norrby, Why Is Mercury Liquid? _Journal of Chemical Education_ , 68, 110–113, 1991; M.S. Banna, Relativistic Effects at the Freshman Level, _Journal of Chemical Education_ , 62, 197–198, 1985; D.R. McKelvey, Relativistic Effects on Chemical Properties, _Journal of Chemical Education_ , 60, 112–116, 1983. For a more technical account, see P. Pyykkö, Relativistic Effects in Structural Chemistry, _Chemical Reviews_ , 88, 563–594, 1988.

. This idea was first proposed by the discoverer of the electron, J.J. Thomson.

. The change in terminology from orbit to orbital is considered to be rather unfortunate by many, since the similarity in the two words does not begin to convey the radical change in the way that electron motion is regarded in the new quantum mechanics.

. The detailed evolution of the concept of electronic configurations is given in chapter 7.

. I am not disputing the approximate nature of the current explanation of the periodic system, as B. Friederich seems to believe, but am rather referring to the fact that the important _n_ \+ _l_ rule has not yet been deduced from first principles. B. Friederich, _Foundations of Chemistry_ , 6, 117–132, 2004; this is a response to the present author's article Just How Ab Initio is Ab Initio Quantum Chemistry?, _Foundations of Chemistry_ , 6, 93–116, 2004.

. R. Hefferlin, H. Kuhlman, The Periodic System for Free Diatomic Molecules III, _Journal of Quantitative Spectroscopy and Radiation Transfer_ , 24, 379–383, 1980. Hefferlin, who is named in the text, is also the author of a book on the subject, R. Hefferlin, _Periodic Systems of Molecules and their Relation to the Systematic Analysis of Molecular Data_ , Edwin Mellin Press, Lewiston, New York, 1989.

. At the time of writing, only 111 of these elements have been confirmed, although preliminary reports claiming the synthesis of the heavier elements have been published. Elements 116, 117, and 118 have yet to be synthesized. Early reports of the synthesis of elements 116 and 118 were withdrawn about a year after their initial announcement. In addition, a member of the research team that had initially made the claim was dismissed on the grounds that he had fabricated data.

### Chapter 2

. The role of physics cannot be eliminated, however. John Dalton was concerned with the physics of the air in the early research that led to his atomic theory.

. B. Bensaude-Vincent, A Founder Myth in the History of Sciences? The Lavoisier Case in L. Graham, W. Lepenies, P. Weingart (eds.), _Functions and Uses of Disciplinary Histories_ , Reidel, Dordrecht, 1983, pp. 53–78.

. This is not to suggest that Lavoisier was the first to use the chemical balance, as some popular accounts would have it. There is some evidence that the balance was already being used by Johann Baptista van Helmont, one of the leading alchemists of his day. W.R. Newman, L.M. Principe, _Alchemy Tried in the Fire: Starkey, Boyle and the Fate of Helmontian Chemistry_ , Chicago University Press, Chicago, 2002.

. However, Lavoisier seems to have regarded oxygen as a principle rather than a simple substance, thus diminishing his break with the past.

. These aspects have been stressed by J.B. Gough, Lavoisier and the Fulfillment of the Stahlian Revolution, _Osiris_ , 2nd series, vol. 4, 15–33, 1988.

. R. Siegfried, M.J. Dobbs, Composition, A Neglected Aspect of the Chemical Revolution, _Annals of Science_ , 24, 275–293, 1968.

. But as I describe in chapter 4, Dmitri Mendeleev was to later resuscitate the notion of abstract elements, which would serve a crucial role in his periodic classification.

. E.g., several of Lavoisier's alleged simple substances appear to be more akin to abstract elements, or principles, even by Lavoisier's own descriptions. This is true of _lumière_ and _calorique_ , as described in chapter 1, and even _oxygène, azote_ (nitrogen), and _hydrogène_.

. For a short account of atomism and its origins in Greek philosophy, see William R. Everdell's review of Bernard Pullman's book _The Atom in the History of Human Thought_ , In _Foundations of Chemistry_ , 1, 305–309, 1999.

. B. Pullman, _The Atom in the History of Human Thought_ , Oxford University Press, New York, 1998.

. I. Newton, _Opticks_ , Query 31, London, 1704; also see A.R. Hall, _An Introduction to Newton's Opticks_ , Clarendon Press, Oxford, 1993.

. Some authors use the term "positivist" to describe Lavoisier's philosophical approach. I will avoid this in view of the more technical sense of the word positivism, which followed Auguste Comte's later usage of the term.

. As discussed in chapter 4, the Russian chemist Mendeleev held a similar view of the existence of distinct elements, whereas his leading competitor, Julius Lothar Meyer, believed in the essential unity of matter.

. Dalton's reasons for arriving at his atomic theory have a complicated and incomplete history. This is because many of his papers were lost in a fire during the Second World War.

. F. Greenaway, _John Dalton and the Atom_ , Heinemann, London, 1966; A.J. Rocke, _Chemical Atomism in the Nineteenth Century_ , Ohio State University Press, Columbus, 1984.

. Dalton's assumption of binary formulas for water and ammonia is taken up later in this chapter.

. This conclusion is not quite as inevitable as I imply here, however. For a different opinion, see, e.g., P. Needham, Has Daltonian Atomism Provided Chemistry with Any Explanations? _Philosophy of Science_ , 71 (2004), 1038–1047. A closely related article is P. Needham, Paul, When did Atoms Begin to do any Explanatory Work in Chemistry?, _International Studies in the Philosophy of Science_ , 18 (2004), 199–219. Needham's view is based, in part, on that of Pierre Duhem. See Needham's translation of Duhem's article, Atomic Notation and Atomistic Hypotheses Translated by Paul Needham _Foundations of Chemistry_ , 2, 127–180, 2000.

. As mentioned in chapter 1, the notion that equivalent weights are purely empirical is problematic, although perhaps more true of Richter's early tables involving just reactions between acids and metals.

. This statement is not quite true since two oxygen atoms can also combine with two atoms of hydrogen to form hydrogen peroxide. Fortunately, this complication did not arise in Dalton's time, since hydrogen peroxide had not yet been discovered when he began his work. The value of 8 for the atomic weight of oxygen is more in keeping with the modern value. Dalton's original estimate of the atomic weight of oxygen was 7 rather than 8 because of experimental inaccuracies. Nevertheless, he soon corrected it from 7 to 8 when better experimental became available.

. Dalton was well aware of the arbitrary nature of his rule of simplicity. In 1810, he discussed the possibility that water could be a compound of three atoms, two of hydrogen and one of oxygen, in which case the atomic weight of oxygen would be 14. In fact, water does consist of these three atoms, and the modern atomic weight of oxygen is closer to 16 than 14. At the same time, Dalton also discussed the possibility that water might consist of two atoms of oxygen and one of hydrogen, which would give oxygen an atomic weight of 3.5. As mentioned in note 19, Dalton originally believed that the atomic weight of oxygen was 7 rather than 8, hence explaining his estimate of 14 rather than 16 for the atomic weight of oxygen when using the correct formula for water.

. J.F. Gay-Lussac, _Alembic Club Reprints_ , No. 4, Edinburgh, reprinted 1923.

. In modern terms we would write the reaction as

2H2 \+ O2 → 2H2O

Since the right-hand side includes a substance containing a single oxygen atom, it appears that the oxygen molecule on the left side must be divisible; hence, it is written as O2. Up to this point the notion of 'diatomic molecules' that we have today had not been envisaged.

. It appears that Dalton had implicitly used the EVEN hypothesis in estimating the relative weights of the atoms of different gaseous elements from their relative densities.

. Anonymous, On the Relation between the Specific Gravities of Bodies in the Gaseous State and the Weights of Their Atoms, _Annals of Philosophy (Thomson)_ , 11, 321–330, 1815.

. Anonymous, Correction of a Mistake in the Essay on the Relation between the Specific Gravities etc., _Annals of Philosophy (Thomson)_ , 12, 111, 1816.

. The classic historical and philosophical study on Prout is William Brock, _From Protyle to Proton_ , Adam Hilger, Boston, 1985.

. _Collected Works of Sir Humphry Davy_ , edited by his brother John Davy, Smith, Elder & Co., London, 1839–1840, vol. 5, p. 163.

. Berzelius's own values underwent many revisions in successive published versions. E.g., the following selected elements show how his later values contained many nonintegral values:

. Berzelius's weights are relative to the oxygen standard, whereby O = 16.

. J. Berzelius, Tafel über die Atomengewichte der elementaren Körper und deren hauptsächlichsten binairen Vebindungen, _Annalen der physikalishe Chemie_ , 14, 566–590, 1828.

. L. Gmelin, _Handbuch der theoretischen Chemie_ , Frankfurt, 1827, as cited on p. 23 of F.P. Venable, _The Development of the Periodic Law_ , Chemical Publishing Co., Easton, PA, 1896.

. These whole number coincidences involving carbon, oxygen, and nitrogen were not evident from the early published values of equivalent and atomic weights. Carbon initially showed values of 12.2 and 12.3, and it was not until 1843 that a value of 12 was obtained. Oxygen was assigned values of 5.5, 7, and 7.6 in various early tables. The value of 16 emerged in 1815. Finally, nitrogen appeared as 14.2 until 1843, when Charles Gerhard's table gave the value of 14.

. J.S. Stas, Researches on the Mutual Relations of Atomic Weights _Bulletin de l'Académie Royale de Belgique_ , 10, 208–350, 1860.

. J.S. Stas, Sur les Lois des Proportions Chimiques, _MemoiresAcademiques de L'Académie Royale de Belgique_ , 35, 24–26, 1865.

. R.J. Strutt, On the Tendency of the Atomic Weights to Approximate to Whole Numbers, _Philosophical Magazine_ , 1, 311–314, 1901.

. Many common elements show one predominant isotope, and as a result, their atomic weights are very close to integral multiples of the weight of the hydrogen atom. Hydrogen itself consists of about 99.99% one particular isotope. Carbon is 98.89% carbon-12, nitrogen is 99.64% nitrogen-14, oxygen is 99.76% oxygen-16, sulfur is 95.0% sulfur-32, and fluorine is 100% fluorine-19.

. Modern writers on the periodic system have tended to downplay Prout's hypothesis, perhaps due to Whiggish tendencies and the fact that it has turned out to be incorrect. One exception is F.P. Venable's classic history of the early stages of the periodic system, in which he makes the following highly laudatory remark about Prout's idea: "Probably no hypothesis in chemistry has been so fruitful of excellent research as this much discussed hypothesis of Prout" _(The Development of the Periodic Law_ , Chemical Publishing Co., Easton, PA, 1896, p. 3).

. Why Döbereiner chose to begin his work with oxides is not known. These compounds had recently been isolated in England by Davy and might thus have aroused general interest. In addition, working with the oxides would not have required the isolation of the elements and would therefore present an easier experimental option.

. It is worth emphasizing that, contrary to the accounts still found in many chemistry textbooks, Döbereiner's discovery of triads, whose middle member has approximately the mean weight of the two flanking members, did not in fact concern elements but instead their compounds.

. These values were recalculated by Johannes van Spronsen using a correct atomic weight for oxygen of 16 instead of the value of 7.5 that Döbereiner used.

. This also tends to be omitted from accounts of the evolution of the periodic system, presumably because transmutation is now known not to occur. In fact, nuclear reactions _can_ result in transmutation of elements, in a different sense, as first discovered in the twentieth century by the physicist Ernest Rutherford.

. A printer's error was probably responsible for this small error in the calculated mean, which should be 80.97.

. Döbereiner was working with incorrect formulas for the oxides of these elements, MO instead of M2O, with the result that his atomic weights appear to be about twice the currently accepted values.

. This seems to be another printer's error and more serious this time since the mean should be 84.241.

. There is a sense in which the chemical properties can be regarded as more basic since the purpose of the exercise is to obtain a chemical classification. Numerical data serve to formalize the system and to sometimes resolve cases that may be difficult to decide on the basis of chemical properties. Nevertheless, this question of the relative importance to be attached to chemical and numerical properties is in itself an important issue that will recur in our story.

. I am not claiming that this system is unknown to other authors, only that it has been highly neglected.

. Rather than being literally a "hand" book, this work amounted to a massive 18 volumes.

. Gmelin obtained a value of 20.5 for calcium by direct determination.

. If one examines the later system of John Hall Gladstone, which is almost exclusively based on Gmelin's system under discussion, this reveals that Gmelin did in fact order most elements according to trends in their atomic weights. J.H. Gladstone, On the Relations Between the Atomic Weights of Analogous Elements, _Philosophical Magazine_ , 5(4), 313–320, 1853.

. Nevertheless, Gmelin's ordering within a family of chemically similar elements is explicitly based on the earlier concept of electronegativity.

. Whether to present chemistry inductively or deductively ultimately depends on each author's philosophical taste. It is by no means clear that Mendeleev's apparent decision to proceed inductively is the only correct option.

. Several subsequent volumes continue this detailed survey of the chemical properties of the elements.

. This placement cannot be blamed just on Gmelin since it recurs in many later periodic systems.

. Surprisingly, the excellent book on the early history of the periodic system written by F.P. Venable (The _Development of the Periodic Law_ , Chemical Publishing Co., Easton, PA, 1896) fails to even mention Gmelin's system.

. J. van Spronsen, _The Periodic System of the Chemical Elements, the First 100 Years_ , Elsevier, Amsterdam, 1969, p. 70.

. This is all the more surprising given that van Spronsen even mentions this fact himself on the same page, although in a different context. Van Spronsen also criticizes Gmelin for not seeming to arrange the elements in order of increasing atomic weight. But Gmelin may well have based his system on atomic weights, although perhaps a little erratically. It is difficult to see how he can be said to have "demoted" atomic weight in producing his system, as van Spronsen claims.

. Helga Hartwig (chief ed.), _Gmelin Handbook of Inorganic Chemistry_ , 8th ed., Springer-Verlag, Berlin, 1988.

. For a detailed historical account of the evolution of the concept of electronegativity, see W.B. Jensen, Electronegativity from Avogadro to Pauling: Part 1: Origins of the Electronegativity Concept, _Journal of Chemical Education_ , 73, 11–20, 1996; and Jensen, Electronegativity from Avogadro to Pauling: II. Late Nineteenth-and Early Twentieth-Century Developments, _Journal of Chemical Education_ , 80, 279–287, 2003.

. Chlorine forms acids, which Gmelin gives as ClO3 and ClO4 in addition to ClO5 and ClO7. The fact that all mineral acids contain hydrogen had not yet been realized.

. In contemporary terms, one might also see the differences between fluorine and the other halogens as resulting from the phenomenon of first-member anomaly, whereby the uppermost element in the main-group elements shows anomalous behavior when compared with other group members.

. The question of the placement of tellurium takes on some importance in view of its being one of the few elements that belong to a reversed pair, the other element in this case being iodine. Many pioneers of the periodic system reversed the positions of tellurium and iodine in order to better reflect their respective chemical analogies. It would appear that this was more easily decided for iodine than for tellurium, given Gmelin's apparent uncertainty in the chemical analogies of tellurium.

. The omission of nitrogen from the group that includes phosphorus, arsenic, and antimony may be because nitrogen alone occurs as a gas while the other three elements mentioned are all solids at room temperature. In addition, the properties of nitrogen are somewhat anomalous, in keeping with the phenomenon of first-member anomalies, once again from the perspective of contemporary knowledge. Similarly, Gmelin did not include oxygen, a gas at room temperature, with sulfur and selenium, two solids with which it is grouped in the modern periodic table.

. The other elements that would eventually join this trio of elements are rubidium and cesium, discovered in 1860 and 1861, respectively.

. Gmelin places beryllium in a neighboring group along with cerium and lanthanum. This would be regarded as a mistake from the perspective of the modern table, in which beryllium is a group II main-group element while the other two are rare earths. Radium had not yet been discovered.

. As noted above, Gmelin himself had discovered that magnesium, calcium, and barium form a triad.

. Formulas given by Gmelin for the oxides were LiO, NaO, CaO, and BaO. In modern terms, only the third and fourth of these are correct. The first two should read Li2O and Na2O, respectively.

. For some interesting remarks on the nature of predictions and its relationship to scientific laws as seen by Mendeleev, see M. Gordin, _A Well-Ordered Thing_ , Basic Books, New York, 2004.

. This lecture was subsequently published in the scientific journals of various European countries and thus exerted considerable influence on chemists worldwide.

. Michael Faraday, _A Course of Six Lectures on the Non-metallic Elements. Before the Royal Institution_ , Royal Institution, London, 1852.

. Of course, _some_ of these elements do have things in common, namely O, S, and Se, all of which are grouped together in group 16 of the modern periodic table.

. The subject of secondary relationships is taken up in chapter 10. This is a feature that is revealed in the older short-form tables as well as pyramidal displays of the periodic system but not, unfortunately, in the currently popular medium-long form.

. E. Lenssen, Uber die gruppirung der elemente nach ihrem chemisch-physikalischen charakter, _Annalen der Chemie Justus Liebig_ , 103, 121–131, 1857.

. Many articles have appeared on this issue, including S.J. Brush, The Reception of Mendeleev's Periodic Law in America and Britain, _Isis_ , 87, 595–628, 1996; R. Campbell, T. Vinci, Novel Confirmation, _British Journal for the Philosophy of Science_ , 34, 315–341, 1983; P. Maher Prediction, Accommodation and the Logic of Discovery, in A. Fine, J. Leplin (eds.), _PSA 1988_ , vol. 1, Philosophy of Science Association, East Lansing, MI, 1988, 273–285; J. Worrall Fresnel, Poisson and the White Spot: The Role of Successful Prediction in the Acceptance of Scientific Theories, in D. Gooding, T. Pinch, S. Schaffer (eds.): _The Uses of Experiment_ , Cambridge University Press, Cambridge, 1989, pp. 135–157; E.R. Scerri, J. Worrall, Prediction and the Periodic Table, _Studies in History and Philosophy of Science_ , 32, 407–452, 2001.

. This could be regarded as a form nonrational development in science, but not in the sense implied by Thomas Kuhn, for whom rival scientific theories cannot be strictly compared because they speak different languages such that translation is never quite possible.

. There are 21 elements that show just one single isotope. They include sodium, cesium, beryllium, aluminum, phosphorus, arsenic, bismuth, fluorine, iodine, manganese, cobalt, and gold. Also see note 36. (Throughout this book I use the American spelling for the elements whose symbols are Al and Cs rather than the official IUPAC spelling of aluminium and caesium.)

. In addition, hydrides did not lend themselves to very accurate analysis. E.g., for several years water was reported to contain 13.27% hydrogen until Pierre Dulong corrected this measurement to 11.1%.

. The following four chemists used four different values: Thomas Thomson, 1; William Wollaston, 10; Berzelius, 100; Stas, 16. The final value most closely approximates the modern value and is consistent with an approximate value of 1 for hydrogen.

. The law of Dulong and Petit failed for a number of elements such as carbon, silicon, and boron due to variations in their specific heats with increasing temperature. This issue is taken up again in chapter 5, where the determination of the atomic weight of beryllium is discussed in more detail.

. S. Mauskopf, Crystals and Compounds: Molecular Structure in Nineteenth Century Century French Science, _Transactions of the American Philosophical Society_ , 66, pt 3, 5–82, 1976.

. Dalton had incorrectly assigned an atomic weight of 40 to selenium, while Berzelius and others did not venture any value whatsoever in their early tables of atomic weights. In 1927, Berzelius adopted Mitscherlich's value, which he cited as 79.1.

. J.B.A. Dumas, Mémoire sur Quelques Points de la Theorie Atomique, _Annales de Chimie et Physique_ , 33(2), 334–414, 1826.

. J.B.A. Dumas, _Leçons sur la philosophie chimique_ , 1837 (reprint, Editions Culture et Civilization, Brussels, 1972), p. 249.

. The problem with the anomalous elements was solved by Gaudin, who suggested that molecules of different elements might contain different numbers of atoms. E.g., sulfur would be hexa-atomic while mercury was monoatomic. M.A.A. Gaudin, _Annales de Chimie et Physique_ , 52(2), 113, 1833. A discussion of a more recent method of determining atomicity using the kinetic theory is given in chapter 5 in connection with the noble gases.

### Chapter 3

. In saying this, I am essentially agreeing with Jan van Spronsen's analysis of the developments (chapter 5). I am also following van Spronsen rather faithfully in saying that there were six discoverers. However, I would _not_ want to emphasize the occurrence of definite periods in the history of the discovery of the periodic system, as van Spronsen seems to favor. Nevertheless, I have accepted van Spronsen's terms "precursors" and "discoverers" partly as a means of presenting the material in a more coherent fashion. It must be realized that this is something of a conventionalist strategy and not meant to be taken too literally.

. L.M. Ampère, Lettre de M. Ampère à M. le comte Berthollet, sur la détermination des proportions dans lesquelles les corps se combinent d'aprés le nombre et la disposition respective des molécules don't leurs particules intégrantes sont composées, _Annales de Chimie_ , 90, 43–86, 1814.

. C. Gerhardt, Recherches sur la Classification Chimique des Substances Organiques, _Comptes Rendus_ , 15, 498–500, 1842.

. The importance of the Karlsruhe conference in connection with the rationalization of atomic weights and the concept of the molecule is disputed by historian Alan Rocke, who claims that even without this meeting the changes would have occurred quite quickly. A. Rocke, _Chemical Atomism in the Nineteenth Century_ , Ohio State Press, Columbus, 1984.

. The question of whether Cannizzaro was committed to chemical or physical atomism is the subject of Alan Chalmers, Cannizzaro's Course of Chemical Philosophy Revisited (forthcoming). Chalmers believes that Cannizzaro would only be committed to the former.

. For a detailed exposition of Cannizzaro's method see, J. Bradley, _Before and after Cannizzaro_ , Whittles Publishing Services, North Humberside, UK, 1992.

. S. Cannizzaro, _Il Nuovo Cimento_ , 7, 321–366, 1858 (English translation, Alembic Club Reprints, no. 18, Ediburgh, 1923), quoted from p. 11.

. A. Naquet, _Principes de Chimie_ , F. Savy, Paris, 1867.

. The further inclusion of uranium in this group is incorrect in the light of modern knowledge.

. The modern medium-long form of the periodic system separates out the transition metals even though they show the same valence of 4, as in the case of zirconium and titanium.

. It would also be possible to make a case for simultaneous discovery by these six researchers.

. Inquirer, Numerical Relations of Equivalent Numbers, _Chemical News_ , 10, 156, 1864; Studiosus, Numerical Relations of Equivalent Numbers, _Chemical News_ , 10, 11, 1864; Studiosus, Numerical Relations of Equivalent Numbers, _Chemical News_ , 10, 95, 1864.

. P.J. Hartog, A First Foreshadowing of the Periodic Law, _Nature_ , 41, 186–188, 1889; P.E. Lecoq De Boisbaudran, A. Lapparent, A Reclamation of Priority on Behalf of M. De Chancourtois Referring to the Numerical Relations of the Atomic Weights, _Chemical News_ , 63, 51–52, 1891.

. A.E. Bégueyer De Chancourtois, _Comptes Rendus de l'Academie des Sciences_ , 54, 1862, 757, 840, 967.

. Among the recipients of De Chancourtois's privately published system was Prince Napoleon.

. A.E. Béguyer De Chancourtois, Mémoire sur un Classement Naturel des Corps Simples ou Radicaux Apelé Vis Tellurique, _Comptes Rendus de l'Académie des Sciences_ , 54, 757–761, 840–843, and 967–971, 1862.

. P.J. Hartog, A First Foreshadowing of the Periodic Law, _Nature_ , 41, 186–188, 1889 186–188, quoted from p. 187.

. J.A.R. Newlands, _Journal of the Chemical Society_ , 15, 1862, 36.

. C.J. Giunta, J.A.R. Newlands, Classification of the Elements: Periodicity, but No System (1), _Bulletin for the History of Chemistry_ , 24, 24–31, 1999.

. As described below, Mendeleev repeated the first of Newlands's incorrect predictions concerning an element with an atomic weight in the region of about 170, along with making a number of other failed predictions of his own.

. The chemical association of tellurium with sulfur and selenium and that of iodine with the halogen elements were well known on qualitative chemical grounds.

. Newlands beat Odling by just four months in terms of publication dates: July 1864, as compared with October 1864 for Odling. I disagree with Carmen Giunta's denial of this anticipation and especially with the reasons that he gives for taking this stance. C. Giunta, J.A.R. Newlands'; Classification of the Elements: Periodicity But No System, _Bulletin for the History of Chemistry_ , 24, 24–31, 1999. A response to this article is E.R. Scerri, A Philosophical Commentary on Giunta's Critique of Newlands' Classification of the Elements, _Bulletin for the History of Chemistry_ , 26, 124–129, 2001.

. Both of the qualitatively based systems of families of Gmelin and Naquet, described earlier in this chapter, grouped lithium and sodium together.

. A periodicity of 8 was correct for the chemistry known at the time. Today the periodicity is actually 9, counting from the first element up to and including the first analogous element (e.g., from lithium to sodium), as discussed in chapter 1.

. J.A.R. Newlands, On the Law of Octaves, _Chemical News_ , 12, 83, August 18, 1865, emphasis original.

. Wendell H. Taylor, J.A.R. Newlands: A Pioneer in Atomic Numbers, _Journal of Chemical Education_ , 26, 152–157, 1949.

. W. Odling, On the Proportional Numbers of the Elements, _Quarterly Journal of Science_ , 1, 642–648, October 1864, quoted from p. 648.

. J.A.R. Newlands, On the Law of Octaves, _Chemical News_ , 13, 130–130, 1866.

. On the other hand, Newlands can be faulted for omitting gaps for as yet undiscovered elements in the manner that Mendeleev later did.

. Here I am considering the distance between the number of successive similar elements to be consistent with the Newlands quotation and not as in other parts of this book when considering one element up to and including its analogue.

. J.A.R. Newlands, _On the Discovery of the Periodic System and on Relations among the Atomic Weights_ , Spon, E&FN, London, 1884. Many copies of this book were published, and the copy owned by the Science Museum in London is still displayed on open shelves and signed by Newlands himself.

. W. Odling, On the Proportional Numbers of the Elements, _Quarterly Journal of Science_ , 1, 642–648, October 1864, quoted from p. 642.

. Ibid, quoted from p. 643.

. W. Odling, On the Proportional Numbers of the Elements, _Quarterly Journal of Science_ , 1, 642–648, 1864, quoted from p. 644.

. Van Spronsen correctly praises Odling (pp. 112–116) in my view, for being the first to recognize this feature, although I differ somewhat regarding the details, as I argue in the main text.

. Van Spronsen's claim (p. 113) that Odling had anticipated the separation of transition metals in the modern table would therefore need to be qualified somewhat.

. Carl A. Zapffe, Hinrichs, Precursor of Mendeleev, _Isis_ , 60, 461–476, 1969.

. Ibid, p. 464.

. In conversation with Bill Jensen, one very rainy evening in a Cincinnati restaurant, the author's car having broken down while en route to a conference in South Carolina.

. H. Cassebaum, G. Kauffman, The Periodic System of the Chemical Elements: The Search for Its Discoverer, _Isis_ , 62, 314–327, 1971.

. The connection is altogether different from that postulated by Hinrichs, however.

. Clearly, the correspondence with the astronomical distances is only approximate.

. Isaac Newton is credited with first performing a similar experiment with sunlight, which he dispersed into its component colors, also by means of a glass prism.

. It is said that Bunsen never once referred to the work of his former students Mendeleev and Lothar Meyer, either in writings or in lectures. This was in spite of the fact that both of these former students acquired considerable fame for their respective systems of classifying the elements.

. According to the atomic weights used by Hinrichs, calcium has a weight of 20 and barium a weight of 68.5.

. One cannot exclude the possibility that he designed his system to fit the known facts.

. The element didymium (Di) was included in many systems, including several of Mendeleev's tables. It eventually turned out to be a mixture of rare earth elements praseodymium and neodymium.

. In many ways, the earlier table of Newlands, published in 1863, is more similar to that of Hinrichs in terms of groupings. The table of 1864 by Odling also shows very similar groupings to Hinrichs's spiral table.

. Admittedly, Newlands's grouping of all these elements together makes sense in terms of secondary periodicity relationships as embodied in many short-form periodic tables. E.g., each of these elements shows a valence of 1.

. G. Hinrichs, _The Elements of Chemistry and Mineralogy_ , Davenport, Iowa; Day, Egbert & Fidlar, 1871; G. Hinrichs, _The Principles of Chemistry and Molecular Mechanics_ , Davenport, Iowa, Day, Egbert & Fidlar, 1874.

. G. Hinrichs, _The Pharmacist_ , 2, 1869, 10.

. K. Hentschel, _Why Not One More Imponderable? John William Draper's Tithonic Rays, Foundations of Chemistry_ , 4, 5–59, 2002.

. Part of the motivation for Cannizzaro's work on atomic weights lies with the earlier work of Avogadro, as mentioned above.

. Lothar Meyer in his editorial on the papers of Cannizzaro in Oswald's _Klassiker der Exacten Wissenschaften_ , vol. 30, Abriss eines Lehrganges der theoretischen Chemie, vorgetragen von Prof. S. Cannizzaro, Leipzig, 1891.

. Thus, the compounds in any homologous series can be defined by a formula, and the molecular weight of successive members of such a series varies by a characteristic constant value. E.g., the compounds CH4, C2H6, C3H8, C4H10, etc., are members of the alkane homologous series, and they all conform to the general formula of C _n_ H2 _n_ +2. The radicals of this series, CH3 = 15, C2H5 = 29, C3H7 = 43, and C4H9 = 57, increase in weight in intervals of 14, as do the compounds themselves.

. Given the subsequent discovery of atomic substructure, this view may be considered one of the instances in which Lothar Meyer's thinking was more advanced than that of Mendeleev.

. The modern atom may be said to be composite in the sense that it consists of smaller parts such as protons, neutrons, and electrons.

. The term "horizontal relationship" may be a little ambiguous given that some tables show chemical groups vertically and others horizontally. I am using the term here in the sense mentioned in connection with Ernst Lenssen (see chapter 2) to mean relationships between elements that are not chemically analogous, or elements with steadily increasing atomic weights. These relationships appear horizontally as periods in the modern table and, indeed, in many but not all tables of the Lothar Meyer-Mendeleev period.

. In the modern table, one sees an initial increase from valence 1 to valence 4 followed by a decrease down to 1 again once the halogens are reached. Lothar Meyer's table differs from the modern one simply in that he chooses to begin with the modern group 14. In addition, the noble gases had not yet been discovered in 1864, and the modern group 13 had not yet been recognized as a separate group.

. E.g., van Spronsen makes this criticism (page 126).

. The main reason for separating these elements must also be the valency relationships among them as well as more specific chemical similarities.

. The original sense of the term "transition metal" referred to elements such as iron, cobalt, and nickel, which represented a "transition" between successive periods in the short-form table. In the modern sense, the term denotes a transition between the s and p blocks of the long-form tables, either medium-long or long forms. There are a total of 54 transition metals in the modern sense, up to and including element 112.

. In his famous table of 1969, Mendeleev wrongly placed mercury with copper and silver, he misplaced lead with calcium, strontium, and barium, and he also misplaced thallium among the alkali metals. For a more detailed set of comparisons, see J. van Spronsen, _The Periodic System of the Chemical Elements, the First One Hundred Years_ , Elsevier, Amsterdam, 1969, pp. 127–131. The misplacement of mercury with silver is perhaps not altogether surprising given that _hydrargyrum_ , the Latin name for mercury, means "liquid silver."

### Chapter 4

1. In an earlier article in _Scientific American_ , I implied that Mendeleev had spent the remainder of his life in elaborating the periodic system. This view has now been corrected by Michael Gordin. See M. Gordin, _A Well Ordered Thing_ , Basic Books, New York, 2004.

2. M. Gordin, _Historical Studies in the Physical Sciences_ , 32, 183-196, 2001; M. Gordin, _A Well Ordered Thing_ , Basic Books, New York, 2004; N.M. Brookes, Dimitrii Mendeleev's _Principles of Chemistry and the Periodic Law of the Elements_ , in B. Bensaude Vincent, A. Lundgren (eds.), _Communicating Chemistry:Textbooks and Their Audiences 1789-1939_ , Science History-Publications, Canton, MA, 2000, pp. 295–309.

3. Not being a reader of the Russian language, I have not been able to consult the primary literature, as have contemporary Mendeleev scholars.

4. The question of the nature of elements is mentioned in Jan van Spronsen's book _The Periodic System of the Chemical Elements, the First One Hundred Years_ , Elsevier, Amsterdam, 1969. One of the few articles to examine the issue is a two-part paper by F.A. Paneth, The Epistemological Status of the Chemical Concept of Element, _British Journal for the Philosophy of Science_ , 13, 1–14, 144–160, 1962. Another analysis has been given in an unpublished Ph.D. thesis written in French by Bernadette Vincent-Bensaude, _Les Piéges de l'Elémentaire_ , Université de Paris, 1981 (I am grateful to the author for sending me a copy).

5. D.C. Rawson, The Process of Discovery: Mendeleev and the Periodic Law, _Annals of Science_ , 31, 181–193, 1974.

6. Rawson refers to a letter from Mendeleev to his mentor, Aleksandr Voskresenskii, in which he describes how he is impressed by Cannizzaro's system, which is based on Amedeo Avagadro's hypothesis.

7. The Russian expert on the periodic table, Bonifatii Kedrov, has made this claim.

8. It may even be that Mendeleev consciously avoided mentioning his immediate precursors and competitors, although I have no evidence to support this notion.

9. For a more detailed account, see M. Gordin's recent book, _A Well Ordered Thing_ , Basic Books, New York, 2004.

10. At this date, Russia was still using the Julian calendar of the Roman Empire. Most other European countries had switched to the Gregorian or reformed calendar, according to which the date would have been March 1st.

11. As mentioned in chapter 2, Kremers also did something of this kind, but it appears that the comparison was not made consciously.

12. D.I. Mendeleev, Sootnoshenie svoistv s atomnym vesom elementov, _Zhurnal Russkeo Fiziko-Khimicheskoe Obshchestvo_ , 1, 60–77, 1869.

13. The German abstract of Mendeleev's famous first paper on the periodic system appeared in the _Journal für praktische Chemie_ , 1, 251, 1869, and a longer article summarizing Mendeleev's first article appeared in _Berichte der deutschen chemischen Gesellschaft_ , 2, 553, 1869.

14. Mendeleev, Manuscript Table 19 (M13) dating from summer-early fall of 1870 (the numbering denotes the 13th manuscript table and the 19th table in the overall sequence of 65 tables of all forms).

15. D. Mendeleev, The Periodic Law of the Chemical Elements, _Chemical News_ , 40, 243–244, November 21, 1879, quoted from p. 243. Mendeleev specifically mentions combination with oxygen and hydrogen. The quote appears in one of 18 sections of a serialization which appeared in Chemical News, 1879, 40, 231–232, 243–244, 255–256, 267–268, 279–280, 291–292, 303–304, ibid. 1880, 41, 2–3, 27–28, 39–40, 49–50, 61–62, 71–72, 83–84, 93–94, 106–108, 113–114, 125–126.

16. D.I. Mendeleev, Über dem die Stellung des Ceriums in System der Elemente, _Bulletin of the Academy of Imperial Science (St. Petersburg)_ , 16, 45–51, 1870.

17. The basis on which Mendeleev carried out this change is analyzed in chapter 5.

18. Lothar Meyer had also moved indium in this way.

19. Mendeleev's grounds for making these changes varied considerably. E.g., his moving the element uranium from the boron group to the chromium group is discussed in detail in chapter 5.

20. See E.R. Scerri, Realism, Reduction and the Intermediate Position, in N. Bhushan, S. Rosenfeld (eds.), _Of Minds and Molecules_ , Oxford University Press, 2000, pp. 51–72.

21. In using the word "metaphysical," I am following the work of Fritz Paneth on this question. Some contemporary philosophers of chemistry, e.g., Paul Needham and Robin Hendry, deny any metaphysical notion when discussing the question of basic substances.

22. The more prosaic explanation given in contemporary chemistry is that what survives of each of the elements is the number of protons, in other words, the nuclear charge of the atoms of sodium and chorine. This would also be the case in rather extreme examples, e.g., the Na11+ and Cl17+ ions. Although this response is correct, it also seems a little unsatisfactory for the identity of chemical elements to depend on the nucleus of their atoms given that all the chemical properties are supposed to be determined by the configurations and exchanges in the electrons around the nucleus.

23. This is perhaps why Mendeleev, a great defender of the nineteenth-century element scheme, was so reluctant to accept the notion of the transmutation of the elements discovered by Ernest Rutherford at the turn of the twentieth century.

24. The term refers to substance in the philosophical sense as discussed by Aristotle and then as recently as Spinoza and Kant, although each of there authors has rather different views on the question.

25. This is despite the fact that our present element scheme, which we owe to Paneth, was arrived at partly by his insistence on the distinction between abstract element and simple substance.

26. There is a certain irony here in that Mendeleev is really breaking away from Lavoisier in upholding the importance of the elements as basic substances, something that Lavoisier considered a sterile concept.

27. For a discussion of this point, see F.A. Paneth, The Epistemological Status of the Chemical Concept of Element, _British Journal for the Philosophy of Science_ , 13, 1–14, 144–160, 1962. Also, the mere fact that Mendeleev and considerably later Paneth continue to maintain a dual nature for the elements attests to the fact that the chemical revolution did not eliminate the metaphysical view of elements.

28. My comments apply specifically to the first English translation of Mendeleev's book, or the fifth Russian edition.

29. The French translation lends itself more readily to making the distinction between element and simple substance, whereas in the English translation the word "element" is frequently used to mean simple body. It is not surprising, therefore, that the only extensive philosophical analysis of this distinction has been made by the French philosopher-historian Bernadette Bensaude Vincent. The only other such analysis in modern times has been by Paneth, who used the German translation of Mendeleev's book, which likewise preserves the spirit of the distinction by speaking of simple body rather than using the word "element" indiscriminately.

30. D.I. Mendeleev, _The Principles of Chemistry_ , 5th Russian ed., vol. 1, 1889 (1st English trans., by G. Kemensky, Collier, New York, 1891), p. 23.

31. The phrase "elements as principles" is also frequently used in the literature on the nature of elements.

32. It is worth noting that this question has taken on a rather mundane sense in today's chemistry, namely, that every element, by which one actually means simple body, is characterized by a particular atomic weight or atomic number.

33. The dates of the eight Russian editions published during Mendeleev's lifetime are as follows: 1st ed., 1868–1871; 2nd ed., 1872–1873; 3rd ed., 1877; 4th ed., 1881–1882; 5th ed., 1889; 6th ed., 1895; 7th ed., 1903; 8th ed., 1906. A further five posthumous editions have been published in Russian, with some additions to cover more recent discoveries. The translations of Mendeleev's book are as follows: 1st English trans., 1891 (of the 5th Russian ed.); 2nd English trans., 1897 (of the 6th Russian ed.); 3rd English trans., 1905 (of the 7th Russian ed.). In addition, the fifth Russian edition was translated into German in 1890 and the sixth Russian edition into French in 1895.

34. M. Kaji, Mendeleev's Conception of the Chemical Elements and the Principles of Chemistry, _Bulletin for the History of Chemistry_ , 27, 4-16, 2002; M. Kaji, Mendeleev's Discovery of the Periodic Law: The Origin and the Reception, _Foundations of Chemistry_ , 5, 189–214, 2003. Of course, many Russian scholars have conducted such surveys before Kaji, but I am not aware of any that have been translated into English.

35. It is interesting to note that this is the first time in his book that Mendeleev actually treats a group of elements together in the same chapter, namely, chapter 11.

36. Even on this point, there were precursors, as mentioned in chapter 2. The first person to consider what might be termed horizontal relationships was Kremers.

37. Mendeleev, 1869, quoted in translation in H.M. Leicester and H.S. Klickstein, Dmitrii Ivanovich Mendeleev, _A Sourcebook in Chemistry, 1400–1900_ , Harvard University Press, Cambridge, MA, 1952, pp. 439–444, quoted from p. 442.

38. Kaji cites Henry Leicester, William Brock, and Bernadette Bensaude.

39. E.R. Scerri, J.W. Worrall, Prediction and the Periodic Table, _Studies in History and Philosophy of Science_ , 32, 407–452, 2001.

40. I do not mean to imply that the weights of individual atoms can be directly observed. I intend this remark in the chemist's sense that stoichiometric reactions can be rationalized by appeal to atomic weights of participating elements.

41. As a matter of fact, the grouping together of the halogens had already been anticipated on chemical grounds in spite of their obvious visual differences. I merely cite this as an example of the unreliability, in general, of classification based on simple substances. J.H. Kultgen, one of very few philosophers to try to analyze Mendeleev's underlying assumptions, has supported the general philosophical approach I am emphasizing, in some respects. J.H. Kultgen, Philosophical Conceptions in Mendeleev's Principles of Chemistry, _Philosophy of Science_ , 25, 177–183, 1958.

42. Many other chemists had already realized that chlorine, bromine, and iodine belong together in one group.

43. M. Gordin, _A Well Ordered Thing_ , Basic Books, New York, 2004, p. 228.

44. D.I. Mendeleev, The Periodic Law of the Chemical Elements, Journal _of the Chemical Society_ , 55, 634–658, 1889, Quoted from p. 644.

45. D.I. Mendeleev, _The Principles of Chemistry_ , 3rd English translation, of 7th Russian edition, 1905, vol. 1, Longmans, London, p. 20.

46. F.A. Paneth, Chemical Elements and Primordial Matter, in H. Dingle, G.R. Martin (eds.), _Chemistry and Beyond_ , Wiley, New York, 1965, pp. 53–72, quoted from pp. 56–57.

47. Of course, modern chemists are constantly referring to protons, neutrons, and electrons. I am making a more general point here that pertains more to the discovery of subnuclear structure, which can generally be ignored by the chemist.

48. G. Bachelard, _Le Pluralisme Coherent de la Chimie Moderne_ , Vrin, Paris, 1932 (translation of quotation provided by the present author).

49. For further discussion of these issues, see E.R. Scerri, Realism, Reduction and the Intermediate Position, in N. Bhushan, S. Rosenfeld, _Of Minds and Molecules_ , Oxford University Press, New York, 2000, pp. 51–72.

50. E.R. Scerri, Response to Vollmer's Review of Minds and Molecules, _Philosophy of Science_ , 70, 391–398, 2003.

### Chapter 5

. As previously mentioned, Mendeleev was not, in fact, the first to predict unknown elements. William Odling, John Newlands, and Julius Lothar Meyer all did so before him. E.g., Newlands left spaces for yttrium, indium, and germanium. For germanium, he predicted an atomic weight of 73, which compares very favorably with the current value of 72.59.

. W. Brock, _The Norton History of Chemistry_ , Norton, New York, 1992, pp. 324–325.

. For general references to the prediction/accommodation debate, see chapter 2, note 73.

. S.G. Brush, The Reception of Mendeleev's Periodic Law in America and Britain, _Isis_ , 87, 595–628, 1996.

. Posing such questions is complicated by the fact that, in some cases, the successful accommodation of an element relied on Mendeleev's correction of the atomic weights of some elements.

. None of these comments should be taken to contradict what has already been said regarding Mendeleev putting more emphasis on the elements as unobservable basic substances.

. These days, chemists can be associated with a single element. When I taught chemistry at Purdue University, I worked in the Brown building, named after H.C. Brown, who won a Nobel Prize in 1979 for his pioneering work in boron chemistry, which he continued to do until his death in December 2004 (at age 92). Similarly, the chair of chemistry during my days at Purdue was Richard Walton, who is the world's expert on the chemistry of rhenium. Few people, if any, are still being considered experts on the chemistry of all the elements.

. The myths are explored and debunked in some detail in M. Gordin, _A Well-Ordered Thing_ , Basic Books, New York, 2004.

. This is not to say that chemical aspects were absent from Lothar Meyer's system. E.g., the headings for the various groups in his system consisted of different valences, as mentioned in chapter 3.

. Not to be confused with group VIII in the modern table, the noble gases, which had not yet been discovered when Mendeleev discovered his periodic system. It was these elements, e.g., iron, cobalt, and nickel, that were termed transition metals in the sense of providing a transition between successive periods in the short-form table.

. These elements were originally called the transition elements, whereas the term has now come to mean the elements in the central block of the medium-long form table as well as the elements placed under the table as a footnote. In modern terminology these elements from the d and f blocks, respectively.

. He may have reached this conclusion after seeing Lothar Meyer's published system of 1870, which already incorporated this improvement.

. In fact, uranium is now known to form compounds with hydrogen, although they tend to nonstoichiometric, their formulas being written as UH _x_ , where _x_ varies.

. As is the case of Mendeleev's claimed interpolations to obtain the atomic weights of gallium, scandium, and germanium, his predicted values were not exactly as prescribed in his explanations.

. Unlike in chapter 2, where the original version was given, relative to the O = 1 standard, the form given here is the more common one based on O = 16, hence, the difference in the constant cited in each chapter.

. L.F. Nilson, O. Petterson, _Berichte_ , 11, 381–386, 1878.

. T.S. Humpidge, On the Atomic Weight of Glucinium (Beryllium) [Abstract], _Proceedings of the Royal Society_ , 38, 188–191, 1884; Humpidge, On the Atomic Weight of Glucinum (Beryllium) Second Paper, _Proceedings of the Royal Society_ , 39, 1–19, 1885.

. More generally, the change in valence across the second and third periods shows a smooth increase from 1 to 4, followed by an equally uniform decrease down to 0 for the noble gases.

. In 1946, Seaborg discovered that a major change was needed in the periodic table. Several elements that had been regarded as belonging to a fourth transition metal series were separated out from the main body of the periodic table to form the lanthanide and actinide series. Uranium is among these elements and is no longer regarded as a transition metal.

. The prefix "eka-" is Sanskrit for the numeral one. Mendeleev also used "dvi-," or two, on some occasions to describe a second element that was like a particular known element, or a double of it.

. Once again, this irregularity occurs because many elements consist of mixtures of various isotopes, and their atomic weights are thus averages of their values.

. D.I. Mendeleev, Über die Beziehungen der Eigenschaften zu den Atomgewichten der Elemente, _Zeitschrift für Chemie_ , 12, 405–406, 1869, quoted from p. 406.

. Ibid., p. 42, note 16.

. Strictly speaking, these provisional names were coined in the following year of 1871.

. I thank Michael Gordin for this information. The article is D.I. Mendeleev, Die periodische Gessetzmässigkeit der chemischen Elements, _Annalen der Chemie und Pharmacie_ , 8, 133–229, 1871.

. The first person to present such tables of comparison for Mendeleev's predictions was Per-Teodor Clève.

. P. E. Lecoq De Boisbaudran, Charactères Chimiques et Spectroscopiques d'un Nouveau Métal, le Gallium, Decouvert Dans un Blende de la Mine de Pierrefitte, Valée d'Argèles (Pyrénées), _Comptes Rendus de l'Academie des Sciences, Paris_ , 81, 493–495, 1875.

. De Boisbaudran originally stated that the density of the element was 4.7 g/cm3. Mendeleev had predicted a value of 5.9 g/cm3 and wrote to De Boisbaudran asking him to redetermine the value, which he did, obtaining a value close to the present value of 5.904 g/cm3.

. Others maintain that he was really naming the element after himself in view of "Lecoq" contained in his own name. The Latin for cock is _gallus_.

. D.I. Mendeleev, Remarques à Propos de la Découverte du Gallium, _Comptes Rendus de l'Academié des Sciences, Paris_ , 81, 969–972, 1876.

. D. Mendeleev, La Loi Périodique des Éléments Chimiques, _Moniteur Scientifique_ , 21, 691–735, quoted from p. 692.

. D.I. Mendeleev, The Periodic Law of the Chemical Elements, Journal _of the Chemical Society_ , 55, 634–656, 1889.

. The optical ether was a medium that had been invoked as the carrier of the electromagnetic force, although it had never been detected experimentally. Nevertheless, this concept served a mathematical purpose in the theory of electromagnetism until it was conclusively demolished by Albert Einstein's 1905 theory of special relativity.

. Since the present book is primarily about the development of the periodic system and not about Mendeleev, very little has been said on the latter's view on the ether. Mendeleev's interest on this issue began early on in his career and was the motivation for his work on deviations from the gas laws carried out in the 1870s. Although he failed to uncover any evidence for the ether, he maintained a theoretical interest in it, which formed the basis for his speculations aimed at counteracting the discoveries of radioactivity and transmutation, which Mendeleev remained opposed to almost until his death in 1907. More information on Mendeleev and the ether can be found in Gordin's book, _A Well-Ordered Thing_ , Basic Books, New York, 2004.

. D.C. Rawson, The Process of Discovery: Mendeleef and the Periodic Law, _Annals of Science_ , 31, 181–204, 1974.

. D.I. Mendeleev, _Perioicheskii Zakon. Osnovye Stat'I, Compilation and Commentary of articles on the Periodic Law_ , by B.M. Kedrov, Klassiki Nauk, Soyuz sovietskikh sotsial'sticheskikh respublik, Leningrad, 1958, p. 316, note 16 (emphasis added).

. For fuller details of Mendeleev on magnesium and beryllium, see J.R. Smith, _Persistence and Periodicity_ , unpublished Ph.D. thesis, University of London, 1975.

. J. van Spronsen, _The Periodic System of the Chemical Elements, the First One Hundred Years_ , Elsevier, Amsterdam, 1969, p. 215.

. Although it must be acknowledged that the dramatic successes came first.

. A similar table, although containing far fewer entries and only Mendeleev's later predictions, is given by W. Brock, _The Norton History of Chemistry_ , Norton, New York, 1992, p. 325. It is interesting to also note that this author remarks, "[H]is predictions of eka-manganese, tri-manganese, dvi-tellurium, dvi-caesium and eka-tantalum were fortuitous guesses rather than predictions based upon a firm and accurate placing of their homologues in the table."

. Entry under a section entitled Chemical Notices from Foreign Sources, _Chemical News_ , 23, 1871, p. 252, mentioning Mendeleev's paper published in German in _Berichte der Deutschen Chemischen Gesellschaft zu Berlin_ , 6, 1871.

. P. Lipton, Prediction and Prejudice, _International Studies in Philosophy of Science_ , 4, 51–60, 1990.

. P. Lipton, _Inference to the Best Explanation_ , Routledge, London, 1991.

. See P. Lipton, Prediction and Prejudice, _International Studies in Philosophy of Science_ , 4, 51–60, 1990.

. Contemporary historians have begun to redress this imbalance. For example, S.J. Brush, The Reception of Mendeleev's Periodic Law in America and Britain, _Isis_ , 87, 595–628, 1996.

. W. Spottiswode, "President's Address," _Proceedings of Royal Society of London_ , 34, 303–329, 1883, quoted from p. 392.

. On this issue, unlike the alleged time lag, as I have called it, Maher cannot be exonerated on the basis of any mistake reported by his cited source on the history of chemistry, namely, the book by Ihde, since the latter does not mention the award of the Davy Medal. A.J. Ihde, The Development of Modern Chemistry, Dover Publications, New York, 1984, as cited in chapter 6, note 37.

. P.T. Clève, Sur le Scandium, _Comptes Rendus de l'Académie des Sciences_ , 89, 419–422, 1879, quoted from p. 421.

. Editorial by W. Crookes, _Chemical News_ , 1879.

. D.I. Mendeleev, On the History of the Periodic Law, _Chemical News_ , 43, 15, 1881.

. Nevertheless, I note that Gordin argues that Mendeleev regarded predictions very seriously. M. Gordin, _A Well-Ordered Thing_ , Basic Books, New York, 2004.

. A. Wurtz, _The Atomic Theory_ , translated by E. Cleminshaw, Appleton, New York, 1881.

. This latter turned out to be another case of "pair reversal."

. A. Wurtz, _The Atomic Theory_ , translated by E. Cleminshaw, Appleton, New York, 1881, p. 16.

. Marcellin Berthelot, _Les Origines de L'Alchimie_ , Steinheil, Paris, 1885, p. 311.

. D. Mendeleev, The Periodic Law of the Chemical Elements, _Journal of the Chemical Society_ , 55, 634–656, 1889. This is Mendeleev's Faraday lecture. See the comments on p. 644.

. W. Brock, _The Norton History of Chemistry_ , Norton, New York, 1992, p. 324–325.

. But to be more accurate, at least two authors, William Sedgwick and Jörgen Thomsen, had independently predicted the possibility of a group of completely unreactive elements. W. Sedgwick, The Existence of an Atom Without Valency of the Atomic Weight of "Argon" Anticipated Before the Discovery of "Argon" by Lord Rayleigh and Prof. Ramsay, _Chemical News_ , 71, 139–140, 1895; J. Thomsen, _Anorganische Chemie_ , 9, 282, 1895.

. Recall that at the time the argon problem arose only one pair reversal had yet come to light, that of iodine and tellurium, and that its explanation would not be obtained until nearly 20 years later with the discovery of isotopes and the work of Moseley.

. W. Ramsay and Lord Rayleigh, Argon a New Constituent of the Atmosphere, _Chemical News_ , 71(1836), 51–63, 1895.

. Since rotational motion can occur only about the common center of mass of a polyatomic system, its absence is an indication that the molecules in the gas are not polyatomic. Isolated atoms are perfectly spherical, so any rotational motion they might exhibit is undetectable. Similarly, vibrational motion can exist only between any two or more atoms in a polyatomic molecule, so its absence would also accord with monoatomicity.

. This is the same Fitzgerald who anticipated, to some extent, Einstein's special relativistic length contraction.

. W. Ramsay and Lord Rayleigh, Argon a New Constituent of the Atmosphere, _Chemical News_ , 71, 51–63, 1895, quoted from p. 62.

. Lord Kelvin, Argon a New Constituent of the Atmosphere, _Chemical News_ , 71 51–63, 1895, quoted from p. 63.

. Professor Mendeleev on Argon, (Report of the Russian Chemical Society Meeting), March 14, 1895, _Nature_ , 51, 543, 1895.

. Professor Mendeleev on Argon, (Report of the Russian Chemical Society Meeting), March 14, 1895, _Nature_ , 51, 543, 1895.

. As cited by J.R. Smith, _Persistence and Periodicity_ , unpublished Ph.D. thesis, University of London, 1975, p. 456.

. It has since been discovered, in work beginning in the 1960s, that the noble gases do in fact form stable compounds, with the exception of helium and neon, which still appear to be completely unreactive.

. It should be remembered that even Newlands had anticipated this possibility, which would in no way destroy the periodicity of the remaining elements in the table.

. As cited by J.R. Smith, _Persistence and Periodicity_ , unpublished Ph.D. thesis, University of London, 1975, p. 460. Also see D. Mendeleev, _An Attempt Towards a Chemical Conception of the Ether_. This statement appears in the Russian edition of 1902 as a footnote.

. S.J. Brush, Prediction and Theory Evaluation, _Science_ , 246, 1124–1129, 1989.

### Chapter 6

. An interesting semipopular book on the life and work of Boltzmann is D. Lindley, _Boltzmann's Atom_ , Free Press, New York, 2001.

. Whether or not, or to what extent, Thomson discovered the electron has been the focus of much historical research. See various articles in J. Buchwald, A. Warwick (eds.), _Histories of the Electron: The Birth of Microphysics_ , MIT Press, Cambridge, MA, 2001.

. This is not exactly case. Isotopes of hydrogen, e.g., give rise to compounds that do show chemical differences. Nevertheless, for most purposes, chemical differences between the isotopes of an element may be taken to be insignificant.

. It is by no means clear that Becquerel was the first to discover radioactivity, contrary to most accounts and, indeed, the one given here. See T. Rothman, _Everything's Relative_ , Wiley, Hoboken, NJ, 2003, pp. 46-52. Rothman makes a very good case for the prior discovery by Abel Niépce de Saint-Victor, who was the brother of Joseph-Nicéphore Niépce, who made the first ever photographic image.

. The story of her early education, which has been told many times, is truly heroic, especially given the difficulties experienced by women wishing to study in universities at the turn of the nineteenth century. Curie was forced to go to Paris because Polish universities simply did not admit women at that time. After working for about six years as a governess and teacher she had saved enough money to undertake a trip to Paris to enroll at the Sorbonne in 1891. While living under very meager conditions she began by attending physics lectures and succeeded in graduating first in her class only two years later. She was immediately taken on to do some research on the magnetic properties of steels in the nearby laboratory of Pierre Curie, who was already a prominent French physicist. Eventually they would marry. During this period she also undertook another undergraduate degree in mathematics, finishing second in her class. She registered for a doctoral degree, which would be the first such degree awarded to a woman anywhere in Europe. The research she did for this degree would win her the first of her two Nobel Prizes. There are a number of detailed historical studies of Madame Curie, including S. Quinn, _Marie Curie, A Life_ , Simon & Schuster, New York, 1995.

. B. Bensaude, I. Stengers, _A History of Chemistry_ , Harvard University Press, Cambridge, MA, 1996, quoted from p. 227.

. In any case, the same authors are surely mistaken when they wrote, "In each place in Mendeleev's table there was no longer just an element, but a certain number of distinct atoms, all having the same chemical properties, but distinguished by their atomic weights and the instability of their nuclei. . . ." B. Bensaude, I. Stengers, _A History of Chemistry_ , Harvard University Press, Cambridge, MA, 1996, p. 230.

. J. Perrin, Le Mouvement Brownien de Rotation, _Comptes Rendus_ , 149, 549-551, 1909; H. Nagaoka, Motion of Particles in an Ideal Atom Illustrating the Line and Band Spectra and the Phenomena of Radioactivity, _Bulletin of the Mathematical and Physical Society of Tokyo_ , 2, 140-141, 1904.

. C.G. Barkla, Note on the Energy of Scattered X-radiation, _Philosophical Magazine_ , 21, 648–652, 1911. This relationship held true for elements with atomic weights equal to or less than 32 ( _A_ ≤ 32). In terms of atomic number, this is equivalent to the first 16 elements, or hydrogen to sulfur. It should also be noted that by this time it was understood that X-rays were produced by electrons.

. A.J. van den Broek, The α Particle and the Periodic System of the Elements, _Annalen der Physik_ , 23, 199–203, 1907.

. In fact, the α particle is a helium atom that has been stripped of both of its orbiting electrons. It has a mass of 4 and a charge of +2.

. A.J. van den Broek, Das Mendelejeffsche 'kubische" periodische System der Elemente und die Einordnuung der Radioelemente in dieses System, _Physikalische Zeitschrift_ , 12, 490–497, 1911.

. A.J. van den Broek, The Number of Possible Elements and Mendeléeff's "Cubic" Periodic System, _Nature_ , 87, 78, 1911.

. Van den Broek did not make this connection explicit, with the result that most writers on the periodic table and in history of science generally have failed to notice it. They merely state that van den Broek drew on the work of Rutherford and Barkla and went on to hint at the concept of atomic number. The point is that he had prior grounds for latching onto the work of Rutherford and Barkla.

. A. Pais, _Inward Bound_ , Oxford University Press, New York, 1986, p. 227.

. A. van den Broek, _Physikalische Zeitschrift_ , 14, 32–41, 1913.

. N. Bohr, On the Constitution of Atoms and Molecules, _Philosophical Magazine_ , 26, 1–25, 476–502, 857–875, 1913 (known as the trilogy paper). Van den Broek is cited on p. 14.

. A.J. Van den Broek, Intra-atomic Charge, _Nature_ , 92, 372–373, 1913.

. E. Rutherford, The Structure of the Atom, _Nature_ , 92, 423, 1913.

. Many accounts incorrectly state or imply that Moseley achieved this feat himself.

. Moseley's ancestors had all been prominent scientists. His father was a professor of comparative anatomy at Oxford. His grandfather, also called Henry, had been a famous mathematician and physicist at King's College, London. Henry Moseley the younger followed a rather typical aristocratic academic career in attending the public school Eton and going on to undergraduate studies at Trinity College Oxford.

Moseley's appetite for hard work is shown by the following anecdote: Charles Darwin the younger, the grandson of Charles Darwin of evolution fame and a good friend of Moseley's in Manchester, was later quoted as saying that one of Moseley's many talents was the knowledge of where one could find a meal at three o'clock in the morning in the streets of Manchester.

. Fajans was visiting Rutherford's lab from Heidelberg at the time.

. Strictly speaking, the planes in such substances as sodium chloride consist of ions and not atoms.

. Barkla had actually distinguished two types of characteristic emissions, one more penetrating than the other. These he called K and L series, respectively.

. As discussed in chapter 7, Bohr was to take the physical explanation of the periodic system to new levels when he began to use quantum theory to write electronic configurations for atoms and to relate these to the periodic table.

. Moseley conducted the final stages of these experiments in Oxford in the laboratory of his former undergraduate professor John SealyTownsend, who was able to provide him with space.

. Three elements were missing between the first and last in the sequence that Moseley examined: phosphorus, sulfur, and scandium.

. H.G.J. Moseley, Atomic Models and X-Ray Spectra, _Nature_ , 92, 554, 1913.

. Eka-manganese was eventually discovered and named technetium.

. For further accounts of the discovery of elements and those that turned out to be spurious, see V. Karpenko, The Discovery of Supposed new Elements, _Ambix_ , 27, 77–102 1980; and E. Rancke-Madsen, The Discovery of an Element, _Centaurus_ , 19, 299–313, 1976.

. As cited in B. Jaffe, _Crucibles: The Story of Chemistry from Ancient Alchemy to Nuclear Fission_ , Simon & Schuster, New York, 1948.

. As emphasized further below, Moseley himself did not conclude that seven gaps remained. In fact, his first estimate, based on the available evidence, was that there were just three.

. Hahn would go on to discover the enormously important process of nuclear fission, along with colleagues Hans Strassman and Lise Meitner, thus paving the way to the development of atomic weapons and the later peaceful use of radioactivity in the generation of nuclear power.

. According to M.E. Weeks and H.M. Leicester, _Discovery of the Elements_ (7th ed., Journal of Chemical Education, Easton, PA, 1968), perhaps the most authoritative book on the discovery of the elements, protactinium was also independently discovered by Fajans and Soddy and independently by John Arnold Cranston and Alexander Fleck in the same year.

. E.R. Scerri, Prediction of the Nature of Hafnium from Chemistry, Bohr's Theory and Quantum Theory, _Annals of Science_ , 51, 137–150, 1994.

. P.H.M. van Assche, The Ignored Discovery of Element Z = 43, _Nuclear Physics_ , A480, 205–214, 1988.

. Several earlier claims for the detection of naturally occurring element 61 were eventually refuted. Among the names in the course of the early claims were illinium (after Illinois), florentium (after Florence, Italy), and cyclonium (after the use of the cyclotron accelerator). Even the last claim was incorrect, although the eventual discovery was indeed made in a particle accelerator experiment.

. W. Crookes, Address to the Chemical Section of the British Association, _Chemical News_ , 56, 115–126, 1886.

. A complete list of these radio-elements, including their eventual classification as isotopes of existing elements, can be found in the appendices of A.J. Ihde, _The Development of Modern Chemistry_ , Dover Publications, New York, 1984.

. J.W. van Spronsen, _The Periodic System of the Chemical Elements, the First One Hundred Years_ , Elsevier, Amsterdam, 1969, p. 309.

. The symbol X was used in the mathematical sense of "unknown" since it was not known whether in fact these were new elements.

. H.N. McCoy, W.H. Ross, The Specific Radioactivity of Thorium and the Variation of the Activity with Chemical Treatment, _Journal of the American Chemical Society_ , 29, 1709–1718, 1907, quoted from p. 1711.

. F. Soddy, _Annual Reports to the London Chemical Society_ 285, 1910.

. According to Alexander Fleck, a former student of Soddy's, the term "isotope" was suggested to Soddy by a family friend, Margaret Todd.

. F. Soddy, Intra-atomic Charge, _Nature_ , 92, 399–400, 1913.

. This explanation is somewhat ahistorical in the use of mass numbers to characterize particular isotopes, e.g., uranium-235 or thorium-231.

. To anticipate our current knowledge, chemical properties are governed by the number of electrons in an atom and not by its atomic weight. Two or more isotopes of the same element can therefore differ in mass, while having the same atomic number (number of protons) as well as the same number of electrons. The different weights that two or more isotopes of the same element display are due to their having different numbers of neutrons while sharing exactly the same number of protons. In approximate terms, the weight of an atom is given by the sum of the protons, neutrons, and electrons. The neutron was not actually discovered until 1932.

. Placing hydrogen among the halogens is not so unlikely given that hydrogen can form a singly charged negative ion, as do the halogen elements. Many periodic tables position hydrogen among the halogens, although not always for the same reason.

. I. Lakatos, _The Methodology of Scientific Research Programmes_ , edited by J. Worrall, G. Currie, Cambridge University Press, Cambridge, 1978. The pages dealing with Prout's hypothesis are 43, 53–55, 118–119, and 223.

### Chapter 7

. As mentioned in chapter 6, the notion that Thomson alone discovered the electron is hotly debated among historians of science.

. M. Chayut, J.J Thomson, The Discovery of the Electron and the Chemists, _Annals of Science_ , 48, 527–544, 1991.

. There has been debate in the literature regarding the extent to which chemical or physical atomism was supported by various developments starting from John Dalton's theory. See, e.g., A. Chalmers, forthcoming.

. As cited in A. Pais, _Inward Bound_ , Clarendon Press, Oxford, 1986, p. 82.

. Contrary to Thomson's original finding of a charge-to-mass ratio of 770 for cathode rays emanating from hydrogen ions, the electron was found to have a mass of 1,836 times less than that of the hydrogen atom.

. J. Perrin, Les Hypotheses Moleculaires, _Revue Scientifique_ , 15, 449–461, 1901.

. Ibid., quoted from p. 460.

. The concept of electron orbitals, or the earlier notion of electron orbits, began with Niels Bohr's theory of the atom, which is examined further below. Electronic orbitals have become perhaps the most important concept in the modern explanation of the periodic system, as discussed in chapters 8–.

. H. Nagaoka, Motion of Particles in an Ideal Atom Illustrating the Line and Band Spectra and the Phenomena of Radioactivity, _Bulletin of the Mathematics and Physics Society of Tokyo_ , 2, 140–141, 1904.

. H. Nagaoka, Kinetics of a System of Particles Illustrating the Line and the Band Spectrum and the Phenomena of Radioactivity, _Philosophical Magazine_ , 7, 445–455, 1905.

. J.J. Thomson, On the Structure of the Atom: an Investigation of the Stability and Periods of Oscillation of a number of Corpuscles arranged at equal intervals around the Circumference of a Circle; with Application of the Results to the Theory of Atomic Structure, _Philosophical Magazine_ , 7, 237–265, 1904.

. A.M. Meyer, A Note on Experiments With Floating Magnets, _American Journal of Physics_ , 15, 276–277, 1878.

. Rutherford described Thomson's plum pudding model as being like old lumber fit only for a museum of scientific curiosities. Source unknown to present author.

. Optical spectra result from outer or valence electrons and should not be confused with the spectra obtained by Moseley using an X-ray source rather than visible light. X-ray spectra involve the excitation of inner electrons.

. Another underrated contributor to this project was the British physicist John Nicholson. See T. Rothman, _Everything's Relative_ , Wiley, Hoboken, NJ, 2003.

. Experiments on incandescent objects inside a perfectly absorbing cavity produced a set of spectral distributions depending on the temperature of the heated object and the wavelength of light emitted by the object. The classical theory available to describe these spectral distributions appeared to be applicable only at high wavelengths; at lower wavelengths the theory predicted infinite emission intensities for the same heated objects, which did not agree with the experimental facts. Planck succeeded in explaining the experimental curves by assuming that, contrary to previous thinking, the energy of particles in the heated object, and consequently the energy emitted in such experiments, is not continuous but in the form of discrete units.

. Strictly speaking, Planck's work revealed the quantization of "action," that is to say, energy divided by frequency. This quantity is now of historical interest only, and it is more common to refer to the quantization of energy, which is given by the action of a particular system multiplied by its frequency.

. Conversely, electrons could undergo transitions to less stable orbits following the absorption of specific quanta of energy.

. As many authors note, the quantization of angular momentum assumed by Bohr as well as the notion that electrons in stationary states do not radiate was somewhat ad hoc and only justified later by Erwin Schrödinger's approach to calculating the energy of the hydrogen atom.

. N. Bohr, On the Constitution of Atoms and Molecules, Part III. Systems Containing Several Nuclei, _Philosophical Magazine_ , 26, 857–875, 1913. Quoted from p. 874

. Ibid, quoted from p. 875.

. Bohr's atomic theory also provided an approximate explanation for the spectra of alkali metals, which have one unpaired outer-shell electron.

. J.L. Heilbron, T.S. Kuhn, The Genesis of the Bohr Atom, _Historical Studies in the Physical Sciences_ , 1, 211–290, 1969.

. N. Bohr, On the Constitution of Atoms and Molecules, _Philosophical Magazine_ , 26, 476–502, 1913 (table on p. 497).

. E.R. Scerri, Prediction of the Nature of Hafnium from Chemistry, Bohr's Theory and Quantum Theory, _Annals of Science_ , 51, 137–150, 1994.

. For discussions of how Bohr argued as a chemist, see H. Kragh, Chemical Aspects of Bohr's 1913 Theory, _Journal of Chemical Education_ , 54, 208–210, 1977.

. This statement is a simplification and is only correct for the main-group, or representative, elements in the periodic table. In the case of the transition elements, the members of a group of elements have the same number of electrons in the same penultimate shell. In the rare earths, the elements in the same group have the same number of electrons in a shell located two shells from the outer shell. And there are further deviations given that about 20 elements have "anomalous" configurations, as discussed in chapter 9.

. I. Langmuir, Arrangement of Electrons in Atoms and Molecules, _Journal of the American Chemical Society_ , 41, 868–934, 1919; C.R. Bury, Langmuir's Theory of the Arrangement of Electrons in Atoms and Molecules, Journal _of the American Chemical Society_ , 43, 1602–1609, 1921.

. N. Bohr, Über die Anwendung der Quantumtheorie auf den Atombau. I. Die Grundpostulate der Quantumtheorie, _Zeitschrift für Physik_ , 13, 117–165, 1923, English trans lation in _Collected Papers of Niels Bohr_ , edited by J. Rud Nielsen, vol. 3, North-Holland Publishing, Amsterdam, 1981.

. Quoted in H. Kragh, The Theory of the Periodic System, in A.P. French, P.J. Kennedy (eds.), _Niels Bohr, A Centenary Volume_ , Harvard University Press, Cambridge, MA, 1985, 50–67, quote from p. 61.

. Quoted in J. Mehra, H. Rechenberg, _The Discovery of Quantum Mechanics, 1925_ , vol. 2 of _Historical Development of Quantum Theory_ , Springer-Verlag, New York, 1982.

. Quoted in Victor F. Weisskopf, _The Privilege of Being a Physicist, W.H_. Freeman, New York, 1970. quoted from p. 164.

. N. Bohr, Über die Anwendung der Quantumtherie auf den Atombau I, _Zeitschrift für Physik_ , 13, 117–165, 1923.

. P. Ehrenfest, Adiabatic Invariants and the Theory of Quanta, _Philosophical Magazine_ , 33, 500–513, 1917, quoted from p. 501.

. The term "adiabatic" has a different sense in thermodynamics than it does in quantum mechanics. In thermodynamics, it refers to a change carried out very quickly so that the system in question does not undergo any heat change. In quantum mechanics, an adiabatic change must be gradual so that the quantum states of the system are maintained following the change.

. P. Ehrenfest, Adiabatic Invariants and the Theory of Quanta, _Philosophical Magazine_ , 33, 500–513, 1917.

. J.M. Burgers, Adiabatic Invariants of Mechanical Systems, _Philosophical Magazine_ , 33, 514–520, 1917.

. H. Goldstein, _Classical Mechanics_ , 2nd ed., Addison-Wesley, Reading, MA, 1980.

. N. Bohr, Über die Anwendung der Quantumtheorie auf den Atombau I, _Zeitschrift für Physik_ , 13, 117–165, 1923, quoted from p.129.

. Ibid. Quoted from p. 130.

. J. Honner, Niels Bohr and the Mysticism of Nature, _Zygon_ , 17, 243–253, 1982.

. A. Landé, Termstruktur und Zeemaneffekt der Multipletts, _Zeitschrift für Physik_ , 15, 189–205, 1923.

. A. Sommerfeld, _Wave Mechanics_ , E.P. Dutton & Co., New York, 1930.

. E. Stoner, The Distribution of Electrons Among Atomic Levels, _Philosophical Magazine_ , 48, 719–736, 1924.

. In modern notation, the third quantum number is labeled _m l_, and the second quantum number is 1. Thus, if 1 = 2, _m_ l can take values of –2, –1, 0, +1, and +2. The second or 1 quantum number, in turn, is related to the first quantum number _n_ as 1 = _n_ – 1, . . . 0. E.g., if _n_ = 3, 1 can assume values of 2, 1, or 0.

. For a philosophical discussion of the nature of atomic orbitals, see E.R. Scerri, _British Journal for the Philosophy of Science_ , 42, 309–325, 1991.

. W. Pauli, letter to N. Bohr, February 21, 1924, quoted in Bohr-Pauli Correspondence, _Collected Papers of Niels Bohr_ , edited by J. Rud Nielsen, vol. 5, North-Holland Publishing, Amsterdam, 1981. Translation on p. 412–414. This quotation is all the more remarkable because, as argued below, it was Pauli's own exclusion principle, formulated a few months later, that seemed to reinstate the notion of individual electrons in stationary states. The notion of individual electrons in individual stationary states was finally refuted with the advent of quantum mechanics. Only the atom as a whole possesses stationary states. The distinction is rather important for the physics of many-electron systems.

. Complications included the occurrence of half quantum numbers, the problem of the anomalous Zeeman effect, and the doublet riddle. P. Forman, The Doublet Riddle and Atomic Physics _circa_ 1924, _Isis_ , 59, 156–174, 1968.

. W. Pauli, Über den Einfluss der Geschwindigkeitsabhängigkeit der Elektronmasse auf den Zeemaneffekt, _Zeitschrift für Physik_ , 31, 373–385, 1925.

. A. Landé, Termstruktur und Zeemaneffekt der Multipletts, _Zeitschrift für Physik_ , 15, 189–205, 1923.

. W. Pauli, Über den Zusammenhang des Abschlusses der Elektrongruppen im Atom mit Complexstruktur der Spektren, _Zeitschrift für Physik_ , 31, 765–783, 1925, quoted from p. 765.

52. Ibid. Quoted from p. 778.

### Chapter 8

. The following is a quotation from Lewis:

I went from the Middle-west to study at Harvard, believing that at the time it represented the highest scientific ideals. But now I very much doubt whether either the physics or the chemistry department at that time furnished real incentive to research.... A few years later [1902] I had very much the same ideas of atomic and molecular structure as I now hold, and I had a much greater desire to expound them, but I could not find a soul sufficiently interested to hear the theory. There was a great deal of research being done at the university, but as I see it now the spirit of research was dead.

G.N. Lewis to R. Millikan, October 28, 1919, Lewis Archive, University of California, Berkeley, as cited in R.E. Kohler, The Origin of G.N. Lewis's Theory of the Shared Pair Bond, _Historical Studies in the Physical Sciences_ , 3, 343-376, 1971, which is the definitive study on Lewis.

. In addition, Thomson had not been able to deduce the correct number of electrons even in atoms as simple as oxygen.

. The notion of a shared pair of electrons survives, to some extent, in the quantum mechanical treatment of the atom. In the current model, a bond consists of two antiparallel electrons within the same molecular orbital.

. G.N. Lewis, The Atom and the Molecule, _Journal of the American Chemical Society_ , 38, 762–785, 1916.

. The term "amphoteric" is now taken to mean an oxide or hydroxide that can dissolve in acids to give salts and can also dissolve in alkalis to give metallates; i.e., it can show both basic and acidic properties. Examples include the oxides and hydroxides of boron and aluminum.

. A. Stranges, _Electrons and Valence: Development of the Theory 1900–1925_ , Texas A&M University Press, College Station, 1982. p. 204

. G.N. Lewis, The Atom and the Molecule, _Journal of the American Chemical Society_ , 38, 762–785, 1916, quoted from p. 768.

. The notion of magnetic properties in electrons did not originate with Lewis but had been previously discussed by Alfred Parsons and William Ramsay. A. Parsons, A Magneton Theory of the Atom, _Smithsonian Miscellaneous Publications_ , 65, 1–80, 1915; W. Ramsay, A Hypothesis of Molecular Configuration, _Proceedings of the Royal Society_ A., 92, 451–462, 1916.

. See, e.g., J. Servos, _Physical Chemistry from Ostwald to Pauling_ , Princeton University Press, Princeton, NJ, 1990.

. This forms the basis of numerous examples used to this day to torment the lives of chemistry students attempting to write Lewis structures for any given number of molecules.

. As discussed in chapter 6, Moseley provided a method of determining the nuclear charge and consequently the number of electrons in any atom.

. This is true of the octet rule, e.g., which Lewis himself was not so keen on.

. I. Langmuir, The Arrangement of Electrons in Atoms and Molecules" in the _Journal of the American Chemical Society_ , 43, 969–934, 1921, quoted from p. 868.

. Kossel was a physicist who published a theory of ionic bonding in 1916. W. Kossel, Über Molekülbildung als Frage des Atombaus, _Annalen der Physik_ , 49, 229–362, 1916.

. Niton is now called radon.

. The inclusion of Niβ and other elements followed by Greek letters is somewhat mysterious and not explained in Langmuir's text. It would appear that he is attempting to avoid any gaps in the periodic table, although gaps do occur in later parts of his table.

. A cell can contain up to two electrons and, as such, can be thought of as analogous to the modern concept of an orbital, which can also accommodate a maximum of two electrons.

. In the modern version of electronic configurations, there are several places in the periodic table where a new shell begins to fill even though the previous shell is not yet completely full. The attempts to explain such features are resumed in chapters 9.

. This analogy depends on identifying one of Langmuir's cells, which can hold two electrons, with the modern notion of an atomic orbital.

. This time, only some of the closed shell atoms appear twice in the table, namely, nickel and palladium, but not the noble gases.

. Actually, Saul Dushman, one of Langmuir's colleagues at the General Electric Company in Schenectady, New York, had been the first to publish ideas on incomplete shells in transition metal atoms at the suggestion of Langmuir himself. S. Dushman, The Structure of the Atom, _General Electric Review_ , 20, 186–196, 397–411, 1917.

. C.R. Bury, Langmuir's Theory on the Arrangement of Electrons in Atoms and Molecules, Journal of the American Chemical Society, 43, 1602–1609, 1921.

. Modern configurations differ slightly in that the transition metals are supposed to begin one element earlier, namely at scandium which is the first element where the filling of the third shell is resumed.

. Superscripts denote the number of electrons in each quantum level.

. C.R. Bury, Langmuir's Theory on the Arrangement of Electrons in Atoms and Molecules, _Journal of the American Chemical Society_ , 43, 1602–1609, 1921.

. M.E. Weeks, _Discovery of the Elements_ , 6th ed., Easton, PA, 1956.

. G. Urbain, Sur un Nouvel Élément qui Accompagne le lutécium et le scandium dans les terres de la gadolinite: le celtium, _Comptes Rendus_ , 152, 141–143, 1911.

. N. Bohr, Atomic Structure, _Nature_ , 107, 104–107, 1921.

. E. Rutherford, letter to N. Bohr, September 26, 1921, in _Collected Papers of Niels Bohr_ , edited by J. Rud Nielsen, vol. 4, North-Holland Publishing Company, Amsterdam, 1981.

. P. Ehrenfest, letter to N. Bohr, September 27, 1921, in _Collected Papers of Niels Bohr_ , edited by J. Rud Nielsen, vol. 4, North-Holland Publishing Company, Amsterdam, 1981.

. H. Kramers, quoted in H. Kragh, The Theory of the Periodic System, in A.P. French, P.J. Kennedy (eds.), _Niels Bohr, A Centenary Volume_ , Harvard University Press, Cambridge, MA, 1985, 50–67, quote from p. 60.

. N. Bohr, _The Theory of Spectra and Atomic Constitution_ , 2nd ed., Cambridge University Press, Cambridge, 1924, p. 110

. Ibid., p. 114.

. Ibid., p. 110.

. Lecture Six of Seven Lectures on the Theory of Atomic Structure (Göttingen, 1922), in _Collected Papers of Niels Bohr_ , edited by J. Rud Nielsen, vol. 4, North-Holland Publishing Company, Amsterdam, 1981 p. 397–406, quoted from p. 404.

. N. Bohr, _The Theory of Spectra and Atomic Constitution_ , 2nd ed., Cambridge University Press, Cambridge, 1924, appendix.

. N. Bohr, letter to J. Franck, July 15, 1922, in _Collected Papers of Niels Bohr_ , edited by J. Rud Nielsen, vol. 4, North-Holland Publishing Company, Amsterdam, 1981, p. 675, translation on p. 676.

. N. Bohr, letter to D. Coster, July 3, 1922, in _Collected Papers of Niels Bohr_ , edited by J. Rud Nielsen, vol. 4, North-Holland Publishing Company, Amsterdam, 1981, as quoted in H. Kragh, Niels Bohr's Second Atomic Theory, _Historical Studies in the Physical Sciences_ , 10, 123–186, 1979.

. N. Bohr, _The Theory of Spectra and Atomic Constitution_ , 2nd ed., Cambridge University Press, Cambridge, 1924, quoted from p.114.

. D. Coster, G. von Hevesy, On the Missing Element of Atomic Number 72, _Nature_ , 111, 79, 1923.

. J.D. Main Smith, Atomic Structure, _Chemistry and Industry_ , 43, 323–325, 1924. Main Smith had previously published an article citing numerous criticisms of Bohr's electronic configurations but without suggesting any alternatives himself. J.D. Main Smith, The Bohr Atom, _Chemistry and Industry_ , 42, 1073–1078, 1923.

. J.D. Main Smith, _Chemistry and Atomic Structure_ , Ernest Benn Ltd., London, 1924, p. 189.

. Ibid, p. 190.

. Ibid., p. 192.

. In the sense of s, p, d, and f subshells, respectively.

. J.D. Main Smith, The Distribution of Electrons in Atoms [letter dated September 8], _Philosophical Magazine_ , 50(6), 878–879, 1925, quoted from p. 878.

. E. Stoner, _Magnetism and Atomic Structure_ , Methuen & Co., London, 1925, p. 1296 footnote.

. H. Kragh, Niels Bohr's Second Atomic Theory, _Historical Studies in the Physical Sciences_ , 10, 123–186, 1979; H. Kragh, Chemical Aspects of Bohr's 1913 Theory, _Journal of Chemical Education_ , 54, 208–210, 1977.

. Mansel Davies, Charles Rugeley Bury and his Contributions to Physical Chemistry, _Archives for the History of the Exact Sciences_ , 36, 75–90, 1986.

. K.J. Laidler, _The World of Physical Chemistry_ , Oxford University Press, New York, 1993.

. The question of the reduction of chemistry to quantum mechanics has been a central issue in the renewed interest in philosophical aspects of chemistry. L. McIntyre, The Emergence of the Philosophy of Chemistry, _Foundations of Chemistry_ , 1, 57–63, 1999; J. van Brakel, On the Neglect of the Philosophy of Chemistry _Foundations of Chemistry_ , 1, 111–174, 1999; E.R. Scerri, L. McIntyre, The Case for the Philosophy of Chemistry, _Synthese_ , 111, 305–324, 1997.

### Chapter 9

. Sir Karl Popper has claimed that Bohr's prediction of the chemical nature of hafnium was "the great moment when chemistry had been reduced to atomic physics." K.R. Popper, Scientific Reduction and the Essential Incompleteness of All Science, in F.L. Ayala, T. Dobzhansky (eds.), _Studies in the Philosophy of Biology_ , Berkeley University Press, Berkeley, CA, 1974, pp. 259–284.

. A. Sommerfeld, _Atombau und Spektrallinien_ , Vieweg & Sohn, Braunschweig, 1919, p. 70.

. It is also sometimes confusingly called the exchange force, although it does not constitute a physical force.

. Since this book is about the periodic table of the elements, rather than compounds, the quantum theory of chemical bonding is not discussed. For a historical account of developments in molecular quantum chemistry, interested readers may consult J. Servos, _Physical Chemistry from Ostwald to Pauling_ , Princeton University Press, Princeton, NJ, 1990.

. This motivation, among others, has led to the widespread view that quantum mechanics supports an antirealistic interpretation. Such a conclusion is disputed by many philosophers, including Ernan McMullin, The Case for Scientific Realism, in J. Leplin (ed.), _Scientific Realism_ , University of California Press, Berkeley, CA, 1984, pp. 8–40.

. E.R. Scerri, Have Orbitals Really Been Observed? _Journal of Chemical Education_ , 77, 1492–1494, 2000; E.R. Scerri, The Recently Claimed Observation of Atomic Orbitals and Some Related Philosophical Issues, _Philosophy of Science_ , 68 Suppl., S76-S88, 2001. See also S. Zumdahl, _Chemical Principles_ , 5th ed., Houghton-Mifflin, Boston, 2005, pp. 679–680, and W.H.E. Schwarz, Measuring Orbitals: Reality of Provocation? _Angewandte Chemie International Edition_ 45, 1508–1517, 2006.

. E.g., if two sets of concentric waveforms collide with each other, the result is a series of augmentations and reductions of the intensity of the waves. If two waves find themselves differing by a whole number of wavelengths, they produce constructive interference, leading to an additive effect. Conversely, two waves that are out of phase, differing by half a wavelength, will cancel each other out. The net result of these two effects is a series of so-called fringes consisting of alternating additions and cancellations of waves or, in the jargon, constructive and destructive interference.

. C.J. Davisson, L.H. Germer, The Scattering of Electrons by a Single Crystal of Nickel, _Nature_ , 119, 558–560, 1927.

. Although Schrödinger did not wait for any experimental support for the wave nature of electrons.

. The first to prove the equivalence of matrix mechanics and wave mechanics was Schrödinger himself. E. Schrödinger, Über das Verhältnis der Heisenberg-Born-Jordanschen Quantenmechanik zu der meinen, _Annalen der Physik_ , 79(4), 734–756, 1926; English translation in _Collected Papers on Wave Mechanics_ , translated by J.F Shearer, W.M. Deans, Chelsea, New York, 1984. A more elaborate proof was later given by J. von Neumann, _Mathematische Grundlagen der Quantenmechanik_ , Springer, Berlin, 1932.

. Just like the square of the square root of -1, which is the real number -1.

. More technically, it is the integral of the square of the wavefunction over a finite volume element that is observable, or ∫ΨΨ * δτ.

. As described above, even this step had not been possible within the old quantum theory.

. They did not publish their work together. First Hartree established the basis of the method, and later Fock made it relativistically invariant.

. Not everybody agrees with this claim, however. See B. Friedrich. . . Hasn't It? A commentary on Eric Scerri's Paper, Has Quantum Mechanics Explained the Periodic Table? _Foundations of Chemistry_ , 6, 117–132, 2004; V.N. Ostrovsky, What and How Physics Contributes to Understanding the Periodic Law, _Foundations of Chemistry_ , 3, 145–181, 2001.

. E.R. Scerri, Have Orbitals Really Been Observed? _Journal of Chemical Education_ 77, 1492–1494, 2000.

. More correctly, the principle is stated by saying that the wavefunction for a system of fermions is antisymmetric on the interchange of any two fermions. This version correctly avoids the assignment of quantum numbers to each individual electron in a many-electron system.

. Löwdin has expressed his views on the _n_ \+ _l_ rule in P.-O. Löwdin, Some Comments on the Periodic System of the Elements, _International Journal of Quantum Chemistry_ , 3 Suppl., 331–334, 1969.

. This fact is also frequently downplayed in textbook accounts of the rules for obtaining electronic configurations.

. E.R. Scerri, The Exclusion Principle, Chemistry and Hidden Variables, _Synthese_ , 102, 165–169, 1995.

. Moving to the many-electron case involves the use of analogous quantum numbers for which the usual one-electron-atom labels are retained.

. Using the equation for the maximum capacity of any main shell, namely, 2 _n 2_.

. E.R. Scerri, Transition Metal Configurations and Limitations of the Orbital Approximation, _Journal of Chemical Education_ , 66(6), 481–483, 1989; L.G. Vanquickenborne, K. Pierloot, D. Devoghel, Transition Metals and the Aufbau Principle, _Journal of Chemical Education_ , 71, 469, 1994.

. Although the 3d orbital is lower than 4s in energy, as shown in figure 9.5. The resulting total energy of the atom when a 3d orbital is preferentially occupied can still be higher than the case of preferentially occupying 4s.

. In fact, according to the more accurate treatment, it is incorrect to assume that the energy of an orbital is a fixed quantity. In effect, the energy of both the 4s and 3d orbitals depends on the relative occupation of these two orbitals. The energy of 4s, e.g., is different depending on whether it contains no electrons or one or two. A full analysis of the problem requires the comparison of five, not just two, orbital energies.

. The number of neutrons added is, of course, variable and accounts for the formation of different isotopes of the same element.

. These results were obtained using the Internet web pages designed by Charlotte Froese-Fischer, one of the leading pioneers in the field of Hartree-Fock calculations. <http:// atoms.vuse.vanderbilt.edu/>.

. This choice is made by convention. The energy corresponding to ionization is taken to be zero. All bound states have lower energies, and so the more negative, the more stable an energy level.

. Of course, I am talking loosely since electrons are indistinguishable according to quantum mechanics.

. E.g., very accurate calculations on the nickel atom include the use of basis sets that extend up to 14s, 9p, and 5d as well as f orbitals. K. Raghavachari, G.W. Trucks, Highly Correlated Systems. Ionization Energies of First Row Transition Metals Sc-Zn, Journal _of Chemical Physics_ , 91, 2457–2460, 1989.

. As I argued, nickel also has a configuration of 4s1 and not 4s2, as generally stated.

. The possession of a half-filled subshell by any atom is neither necessary nor sufficient to ensure that an s1 configuration is adopted.

. A theoretical analysis of Hund's rule is given in J. Katriel, R. Pauncz, _Advances in Quantum Chemistry_ , 10, 143–185, 1977.

. R.L. Snow, J.L. Bills, The Pauli Principle and Electronic Repulsion in Helium, Journal _of Chemical Education_ , 51, 585–586, 1974.

. With the exception of some recent work on so-called universal basis sets. E.V.R. de Castro, F.E. Gorge, Accurate universal Gaussian basis set for all atoms of the Periodic Table, _Journal of Chemical Physics_ , 108, 5225–5229, 1998; Some considerations about Dirac-Fock calculations, A. Canal Neto, P. R. Librelon, E. P. Muniz, F. E. Jorge, and R. Colistete Junior, _Theochem_ , 539, 11–15, 2001.

. However, there are several arguments that can be made in favor of the placement of helium among the alkaline earths. This is carried out in the left-step periodic table, e.g., G. Katz, The Periodic Table: An Eight Period Table For The 21st Century, _The Chemical Educator_ , 6, 324–332, 2001.

. Although, as noted above, the configuration of nickel is actually 4s1 3d9, contrary to what is stated in most textbooks. Even if one considers the total number of electrons in the two most energetic orbitals, they do not all show the same value.

. This point is disputed by V. Ostrovsky, What and How Physics Contributes to Understanding the Periodic Law, _Foundations of Chemistry_ , 3, 145–182, 2001; see p. 175.

. Of course, there are methods used in ab initio work that even go beyond the orbital approximation altogether, but this is discussed further below.

. This expression is due to philosopher of physics Michael Redhead; see M. Redhead, Models in Physics, _British Journal for the Philosophy of Science_ , 31, 154–163, 1980. A similar point is made by V. Ostrovsky, What and How Physics Contributes to Understanding the Periodic Law, _Foundations of Chemistry_ , 3, 145–182, 2001.

. There is also redundancy of information in the ab initio approach, in view of the fact that it operates in 3 _N_ dimensions rather than the familiar three-dimensional space in which density functional theory operates.

. The recent reports, starting in _Nature_ magazine in September 1999, that atomic orbitals had been directly observed are incorrect. J. Zuo, M. Kim, M. O'Keefe, J. Spence, Direct observation of d-orbital holes and Cu-Cu bonding in Cu2O, _Nature_ , 401, 49–52, 1999; P. Coppens, _X-Ray Charge Densities and Chemical Bonding_ , Oxford University Press, Oxford, 1997.

. The educational implications of the claims for the observation of orbitals are addressed in other articles, and I do not dwell on the issue here.

. This is an advantage only for a realist. The antirealist is not unduly perturbed by the fact that central scientific terms such as atomic orbitals are nonreferring.

. P.M.W. Gill, Density Functional Theory (DF), Hartree-Fock (HF), and the Self-consistent Field, in P. von Ragué Schlyer (ed.), _Encyclopedia of Computational Chemistry_ , vol. 1, Wiley, Chichester, 1998, pp. 678–689.

. The promise derives from some theorems proved by P.C. Hohenberg, L.J. Sham, and Walter Kohn, Inhomogeneous Electron Gas, _Physical Review B_ , 136, 864–71, 1964; W. Kohn, L.J. Sham, Self-Consistent Equations Including Exchange and Correlation Effects, _Physical Review_ A, 140, 1133–38, 1965.

. An excellent account of ab initio and density functional quantum chemistry calculations is provided in the Nobel Prize acceptance address by J. Pople, _Reviews of Modern Physics_ , 71, 1267–1274, 1999.

. Dirac's famous statement concerning the reduction of chemistry was "The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. P.A.M. Dirac, Quantum Mechanics of Many-Electron Systems, _Proceedings of the Royal Society of London, Series A_ , 123, 714–733, 1929, quoted from p. 714.

. Other universal approaches to the problem of the periodic table have been pursued by Dudley Herschbach and colleagues; see S. Kais, S.M. Sung, D.R. Herschbach, Large-Z and -N Dependence of Atomic Energies of the Large-Dimension Limit. _International Journal of Quantum Chemistry_ , 49, 657–674, 1994.

. As mentioned in note 18, this problem has been recognized by some leading quantum chemists, such as Löwdin. Several attempts to solve the problem have been published. See, e.g., V. Ostrovsky, What and How Physics Contributes to Understanding the Periodic Law, _Foundations of Chemistry_ , 3, 145–182, 2001. Readers may also be interested in the present author's chapter in a book based on a recent international conference on the Periodic Table: E.R. Scerri, The Best Representation of the Periodic System: The Role of the n + 1 Rule and the Concept of an Element as a Basic Substance, in D. Rouvray, R.B. King (eds.), _The Periodic Table: Into the 21st Century_ , Science Studies Press, Bristol, 2004, 143–160.

. J. Dupré, _Human Nature and the Limits of Science_ , Clarendon Press, Oxford, 2001; J. van Brakel, _The Philosophy of Chemistry_ , Leuven University Press, Leuven, Belgium, 2000 (see chapter 5 in particular).

. B. Bensaude, I. Stengers, _A History of Chemistry_ , Harvard University Press, Cambridge, MA, 1996 (see chapter 5 in particular); D. Knight, _Ideas in Chemistry_ , Rutgers University Press, New Brunswick, NJ, 1992 (see chapter 12).

### Chapter 10

. The reader is referred to Helge Kragh, _Cosmology and Controversy_ , Princeton University Press, Princeton, NJ, 1996, an excellent historical account of cosmology from which I have drawn liberally in the course of writing this section. Other good sources on nucleosynthesis are E.B. Norman, Stellar Alchemy: The Origin of the Chemical Elements, _Journal of Chemical Education_ , 71, 813–820, 1994; P.A. Cox, _The Elements_ , Oxford University Press, Oxford, 1989; and S.F. Mason, _Chemical Evolution_ , Clarendon Press, Oxford, 1991.

. One of the triumphs of the big bang theory is the successful prediction of the relative abundance of the two main isotopes of hydrogen: protium and deuterium. See chapter 20 of J.S. Rigden, _Hydrogen, The Essential Element_ , Harvard University Press, Cambridge, MA, 2002.

. Herman Bondi, one of the three founders of the steady-state theory, admitted defeat after learning of the hydrogen:helium ratio, which was interpreted as a "fossil" of the big bang. This is contrary to the popular story that it was the observation of the 3K cosmic background radiation in the 1960s that caused the steady-state theorists to throw in the towel. I am grateful to George Gale for pointing this out to me. He learned this through a series of interviews which he carried out with Bondi. Not all cosmologists have given up the steady-state theory, however. The husband and wife team of Geoffrey and Margaret Burbidge continue to support that theory, as reported in a recent article. R. Panek, Two Against the Big Bang, _Discover_ , 26, 48–53, 2005.

. This represents an example of simultaneous discovery, as thallium was independently isolated by C.A. Lamy working in France in the same year.

. W. Crooke's, The Genesis of the Elements, _Chemical News_ , 55, 83–99, 1887; quoted from p. 83.

. For a fuller account of Crooke's periodic system, see S.F. Mason, _Chemical Evolution_ , Clarendon Press, Oxford, 1991. This is also an excellent source for the history of nucleosynthesis and the study of the origin of life.

. D.I. Mendeleev, The Periodic Law of the Chemical Elements, _Journal of the Chemical Society_ , 55, 634–656, 1889 (Faraday lecture), quoted from p. 641.

. Whether Crookes can rightly be said to have been a chemist is debatable given his numerous interests, including spectroscopy, physics, and paranormal phenomena. The fact remains that he was initially trained as a chemist and retained a strong interest in chemistry throughout his life, including acting as the editor of _Chemical News_ from when he founded it in 1859 up to the time of his death in 1919. See W. Brock, William Crookes, in C. Gillispie (ed.), _Dictionary of Scientific Biography_ , vol. 3, Charles Scribner's, New York, 1981, pp. 474–482. Brock is currently writing a scientific biography of the life of Crookes.

. The heat death had become widely accepted on the basis of the second law of thermodynamics and the associated increase in entropy of the universe.

. A. Eddington, The Internal Constitution of the Stars, _Nature_ , 106, 14–20, 1920.

. Lemaître was more careful and went to some length to separate his scientific beliefs from his religious ones. J.D. North, Cosmology, Creation, and the Force of History, _Interdisciplinary Science Reviews_ , 25, 261–266, 2000.

. A further early contribution to the big bang theory was provided by the work of A. Friedmann, Über die Krümmung des Raumes, _Zeitschrift für Physik_ , 10, 377–386, 1922.

. Bethe had not really participated in this research, but Gamow asked him to join the authors because the names of Alpher, Bethe, and Gamow would make for a nice prank. The paper has indeed become rather famous as the αβγ paper. R.A. Alpher, H. Bethe, G. Gamov, The Origin of the Chemical Elements, Physical review, 73, 803–804, 1948.

. Two interesting biographies of the life of Hoyle have recently been published: Simon Mitton, _Conflict in the Cosmos: Fred hoyle's Life in Science_ , Joseph Henry, Washington D.C., NJ, 2005; Jane Gregory, _Fred Hoyle's Universe_ , Oxford University Press, Oxford, 2005.

. More recently, some direct evidence for hydrogen burning in the sun has become available through the study of solar neutrinos. K.S. Hirata et al., Observation of Neutrino Burst from the Supernova SN1987A, _Physical Review D_ , 44, 2241–2260, 1991.

. F. Hoyle, The Synthesis of the Elements from Hydrogen, _Monthly Notices of the Royal Astronomical Society_ , 106, 343–383, 1946.

. The term "black hole" was coined some time later by the physicist J.A. Wheeler.

. F. Hoyle, D.N.F. Dunbar, W.A. Wenzel, W. Whaling, A State in C12 Predicted from Astrophysical Evidence, _Physical Review_ , 92, 1095, 1953. This much-cited paper was in fact a brief announcement made at a conference and took up a mere 16 lines in a page arranged in two columns, the equivalent therefore of just eight lines of text. Hoyle's prediction is widely regarded as the only successful application of the anthropic principle, the notion that nature is the way that it is because this allows us to exist. Hoyle had reasoned that the resonant state of carbon had to exist since beings like us are made largely of carbon and are able to pose the question as to the formation of the element carbon.

. Only Fowler was awarded the Nobel Prize for his work in nucleosynthesis, although it is generally agreed that the core of the discovery belonged to Hoyle. Many observers believe that Hoyle's combative style cost him a share in the Nobel Prize.

. C. Seife, What is the Universe Made Of?, _Science_ , 309, 78, 2005.

. Strong nuclear forces are due to nearest-neighbor interactions. In the case of the light nuclei, a greater proportion of nucleons are at the surface, and so the overall force is of greater magnitude. In the case of heavy nuclei, however, the contribution is almost constant since most nucleons can be considered as being in the "interior" of the nucleus, and so they experience the maximum number of 12 nearest-neighbor interactions.

. The value of 126 is only experimentally realized for neutrons given that the largest stable nuclei formed thus far have Z-values in the 110s.

. In addition four of these elements have "doubly magic" nuclei since they have magic numbers with respect to both protons and neutrons. The doubly magic nuclei are 4He, 16O,40Ca, 208Pb.

. In the case of electrons in an atom, the force can be considered to be literally centrally directed, since it results from the attraction due to the central nucleus. In the nuclear analogue, each nucleon acts on every other one, and yet one can usefully assume a centrally directed field even though this is physically not the case.

. Spin-orbit coupling also occurs in atoms but to a far lesser extent and is significant only for heavy atoms.

. There are several more sophisticated approaches than nuclear-shell theory, but the empirical nature of the ordering of levels is a common feature among them.

. Readers may wish to consult any of a number of excellent sources on inorganic chemistry, including F.A. Cotton, G. Wilkinson, C.A. Murillo, M. Bochmann, _Advanced Inorganic Chemistry_ , 6th ed., Wiley, New York, 1999; N.N. Greenwood, A. Earnshaw, _Chemistry of the Elements_ , Pergamon Press, Oxford, 1984.

. Another unusual relationship, which is not discussed here, is the inert pair effect, whereby the lower members of many groups form stable compounds with a lower oxidation state than do the higher members. E.g., tin and lead form stable dichlorides compared to carbon and silicon, which produce only tetrachlorides. The electrons in the outermost s orbital of the lower members of these groups are said to be inert since they typically do not participate in bonding. A fuller explanation of the inert pair effect requires the application of relativistic quantum mechanics.

. For further information on the diagonal relationship, see T.P. Hanusa, Reexamining the diagonal relationships, _Journal of Chemical Education_ , 64, 686–687, 1987.

. F. Habashi, A New Look at the Periodic Table, _Interdisciplinary Science Reviews_ , 22, 53–60, 1997. Also note that IUPAC numbering for groups is used here and in the remainder of this chapter.

. Ga3+ nonetheless shows a closed shell configuration given that the 3d subshell is filled.

. Nor can the anomalous values for aluminum be attributed to the phenomenon of first-member anomaly for the simple reason that aluminum is the second member of group 13 as matters currently stand.

. For a fuller discussion of these cases, the reader is referred the writings of Geoffrey Rayner Canham, which have been drawn on extensively in the writing of this section: The Richness of Periodic Patterns, G. Rayner Canham, _The Periodic Table: Into the 21st Century_ , D. Rouvray, R.B. King, Research Studies Press, Bristol, UK, 2004, pp. 161–187; G. Rayner Canham, T. Overton, _Descriptive Inorganic Chemistry_ , 3rd ed., W.H. Freeman, New York, 2003.

. G.H. Lander, J. Fuger, Actinides: The Unusual World of the 5f Electrons _Endeavour_ , 13, 8–14, 1989.

. AsCl5 has now actually been prepared, but the difficulty in doing so is shown by the fact that this feat was achieved only in 1977, compared with PCl5 and SbCl5, which have been known since 1834. On a separate point, the screening explanations have been confirmed by relativistic quantum mechanical calculations carried out by P. Pyykkö, On the Interpretation of 'Secondary Periodicity' in the Periodic System, _Journal of Chemical Research_ (Sweden), (S), 380–381, 1979.

. One explanation is that, as the group is descended, the effective nuclear charge (protons minus inner-shell electrons) remains constant whereas the distance of the outermost electron increases, thus producing an overall decrease in ionization energy.

. R.T. Sanderson, _Chemical Periodicity_ , Reinhold, New York, 1960.

. E.R. Scerri, Chemistry, Spectroscopy and the Question of Reduction, _Journal of Chemical Education_ , 68, 122–126, 1991.

. H. Obadasi, Some Evidence About the Dynamical Group SO (4, 2): Symmetries of the Periodic Table of the Elements, _International Journal of Quantum Chemistry, Symposium_ 7, 23–33, 1973; V. Ostrovsky, What and How Physics Contributes to Understanding the Periodic Law, _Foundations of Chemistry_ , 3, 145–182, 2001.

. Of the eight possible knight's moves available in the game of chess, it appears that the chemical knight's move represents just one of these. In all cases, it involves a movement of one step down in the periodic table, followed by two steps to the right.

. Laing made the discovery of the knight's move relationship in the course of teaching a chemistry course for engineers that caused him to emphasize the similarity between zinc and tin (M. Laing, personal communication).

. M. Laing, The Knight's Move in the Periodic Table, _Education in Chemistry_ , 36, 160–161, November 1999; M. Laing, chapter 4, in D. Rouvray, R.B. King, Patterns in the Periodic Table, _The Periodic Table: Into the 21st Century_ , Research Studies Press, Bristol, UK, 2004, pp. 123–141

. E.g., cadmium, which lies directly below zinc, and lead, which lies directly below tin, are both highly toxic. However, cadmium appears to be an essential element for at least one organism, a marine diatom that produces a cadmium-specific enzyme that catalyzes the conversion of carbon dioxide and carbonic acid, as discovered in the year 2000. For further biological information on this element, see J. Emsley, _Nature's Building Blocks_ , Oxford University Press, Oxford, 2001, pp. 74–76. This book is the standard reference for the detailed properties of all the elements, including their human, medical, economic, historical, environmental aspects.

. Further information on the toxicity of organotin compounds is also to be found in Emsley, ibid.

. For brass, the earliest regular production appears to date from the fourth century B.C. or perhaps earlier. From textual sources and actual artifacts, Taxila, in modern Pakistan, has produced the earliest brass, dated from that time. Bronze is far earlier. Copper began to be smelted in the late fifth millennium B.C. in the Near East. The first copper "alloy" was arsenical copper, where the arsenic had the same useful effect as did tin: hardening the metal, improving the casting quality, and lowering the melting temperature. P.T. Craddock (ed.), _2000 Years of Zinc and Brass_ , British Museum Occasional paper No. 50, London, 1990.

. M. Laing, The Knight's Move in the Periodic Table, _Education in Chemistry_ , 36, 160–161, 1999.

. More recently, Laing has noted even further possible knight's move connections between technetium and iridium (M. Laing, personal communication).

. L. Suidan, J. Badenhoop, E.D. Glendening, F. Weinhold, Common Textbook and Teaching Misrepresentations of Lewis Structures, Journal _of Chemical Education_ , 72, 583–586, 1995.

. W.B. Jensen, Classification, Symmetry and the Periodic Table, _Computers and Mathematics with Applications_ , 12B, 487–510, 1986; H. Bent, The Left-Step Periodic Table, _Journal of Chemical Education_ , forthcoming.

. I am assuming that hydrogen is indeed placed among the alkali metals, something that has been disputed, for example, by P. Atkins, H. Kaesz, The Placement of Hydrogen in Periodic System, _Chemistry International_ , 25, 14–14, 2003. See also a response to this paper, E.R. Scerri, The Placement of Hydrogen in Periodic System, _Chemistry International_ , 26, 21–22, 2004.

. In any case, there are only two elements in each f block group, which makes it more difficult to establish whether there is any anomaly whatsoever.

. An excellent and detailed account of boron-nitrogen compounds and their similarities with carbon is given in N.N. Greenwood and A. Earnshaw, _The Chemistry of the Elements_ , Pergamon Press, Oxford, 1997 pp. 234–240. The question of whether borazine displays aromatic characteristics is a matter of some debate in the literature. A.K. Phukan, E.D. Jemmis, Is Borazine Aromatic? _Inorganic Chemistry_ , 40, 3615–3618, 2001.

. Another example is the cyanide ion, CN–, which behaves like a halide ion. See G. Rayner Canham, The Richness of Periodic Patterns, in D. Rouvray, R.B. King (eds.), _The Periodic Table: Into the 21st Century_ , Research Studies Press, Bristol, UK, 2004, pp. 161–187. This author goes as far as to include NH4+ and CN– in a newly designed periodic table, a tendency that seems to recapitulate some of the early periodic systems and earlier lists of elements, which also included ions and radicals.

. D.E. Bergeron, A.W. Castleman, T. Morisato, S.N. Khanna, The Formation of Al13I: Evidence for the Superhalogen Character of Al13, _Science_ , 231–235, 2004.

. Anonymous, Evidence that Superatoms Exist Could Unsettle the Periodic Table, _The Economist_ , 37, 475, 2005.

. E.G. Mazurs, Graphical Representations of the Periodic System During One Hundred Years, University of Alabama Press, Tuscaloosa, AL, 1974.

. The most authoritative website is by the inorganic chemist Mark Winter, WebElements™ Periodic Table, University of Sheffield and WebElements Ltd., 2006, available at http://www.webelements.com/.

. Lithophiles are "rock-loving" elements found predominantly in oxide minerals or as halides. Siderophiles or "boron-loving" elements are found mostly in the earth's core, and chalcophiles are elements found in the earth's crust in combination with nonmetals, including sulfur, selenium, and arsenic.

. B. Railsback, An Earth Scientist's Periodic Table of the Elements and their Ions, _Geology_ , 31, 737–740, 2003.

. F. Habashi, A New Look at the Periodic Table, _Interdisciplinary Science Reviews_ , 22, 53–60, 1997.

. In the 1960s and 1970s, philosophers of language, including Saul Kripke and Hilary Putnam, reanalyzed the question of sense and reference. They argued that reference was not fixed by the description of a natural kind term, such as "tiger," "quark," or "element," but by what they called its "essence," for which they appeal to the latest scientific knowledge. On this view, the reference of a particular element such as gold is given by its atomic number of 79 rather than by describing the properties of gold. I have argued that there are some parallels between the chemist's discussion of elements as basic and simple substances and the analogous discussion by philosophers in terms of sense and reference. Whereas the sense of an element is provided broadly speaking by the properties of the elements, its reference is defined through just one criterion: atomic number. E.R. Scerri, Some Aspects of the Metaphysics of Chemistry and the Nature of the Elements, _Hyle_ , 11, 127–145, 2005.

. Another radiochemist, Kasimir Fajans, was Paneth's leading opponent in believing that the periodic system would _not_ survive the discovery of isotopes.

. F.A. Paneth, The Epistemological Status of the Concept of Element, _British Journal for the Philosophy of Science_ , 13, 1–14, 144–160, 1962, reprinted in _Foundations of Chemistry_ , 5, 113–145, 2003.

. Paneth and Hevesy showed that the electrochemical potential from two cells made from different isotopes of the metal bismuth was the same as far as experimental techniques of the day could distinguish. E.R. Scerri, Realism, Reduction and the Intermediate Position, in N. Bhushan, S. Rosenfeld (eds.), _Minds and Molecules_ , Oxford University Press, New York, 2000, pp. 51–72.

. The fact that more recent research has revealed some differences even in the chemical properties of isotopes does not alter the central issue under discussion.

. S. Kripke, Naming and Necessity, in D. Davidson, G. Harman (eds.), _Semantics of Natural Language_ , Reidel, Dordrecht, 1972, pp. 253–355; H. Putnam, The Meaning of Meaning, in his _Philosophical Papers_ , vol. 2, Cambridge University Press, Cambridge, 1975, pp. 215–271.

. If the possession of a particular electronic configuration were a necessary condition for membership to a particular group, this would imply that all members of a group have the same outer-shell configuration. This is violated by many groups of transition elements. If the possession of a particular electronic configuration were a sufficient condition, this would imply that elements with the same outer-shell configuration must be grouped together. This is violated by the case of helium, at least in the conventional representations of the periodic system. E.R. Scerri, How Ab Initio is Ab Initio Quantum Chemistry? _Foundations of Chemistry_ , 6, 93–116, 2004.

. Electronic configurations are known to be approximations, unlike atomic number, which can be given a clear realistic interpretation in terms of the number of protons in the nucleus of any atom. E.R. Scerri, How Ab Inito is Ab Initio Quantum Chemistry?, _Foundations of Chemistry_ , 6, 93–116, 2004.

. E.g., M.W. Cronyn, The Proper Place for Hydrogen in the Periodic Table, _Journal of Chemical Education_ , 80, 947–951, 2003.

. P.W. Atkins, H. Kaesz, A Central Position for Hydrogen in Periodic System, _Chemistry International_ , 25, 14, 2003.

. Once again, unobservable apart from their possessing an atomic number.

. C. Janet, The Helicoidal Classification of the Elements, _Chemical News_ , 138, 372–374, 388–393, 1929; L.M. Simmons, The Display of Electronic Configuration by a Periodic Table, _Journal of Chemical Education_ , 25, 658, 1948; R.T. Sanderson, A Rational Periodic Table, _Journal of Chemical Education_ , 41, 187–189, 1964; G. Katz, The Periodic Table: An Eight Period Table For The 21st Centrury, _The Chemical Educator_ , 6, 324–332, 2001; E.R. Scerri, Presenting the Left-step Periodic Table, _Education in Chemistry_ , 42, 135–136, 2005.

. From this point onward, I concentrate on the left-step table, although both representations are equally viable for what follows.

. D. Neubert, Double Shell Structure of the Periodic System of the Elements, _Zeitschrift für Naturforschung_ , 25A, 210–217, 1970.

. Of course, it may be that future chemistry might reveal that helium does indeed belong in the alkaline earths. The notions of elements as basic substances and as simple substances are complementary, not contradictory.

. As in the use of atomic number, the use of the _n_ \+ l rule appeals to elements as basic substances and not as simple substances. This rule represents a generalization concerning all the elements, although it is violated in some instances and is not concerned with any directly observable properties of the elements.

. Charles Janet seems to have been the first author to publish this form of table. C. Janet, The Helicoidal Classification of Elements, _Chemical News_ , 138, 372–374, 388–393, 1929.

. On the subject of beauty and elegance, there are now a number of three-dimensional periodic systems of which one of the finest is due to Fernando Dufour as shown in figure 10.15. See G.B. Kauffman, ElemenTree: A 3-D Periodic Table by Fernando Dufour, _The Chemical Educator_ , 4, 121–122, 1999.

. E.R. Scerri, The Tyranny of the Chemist, _Chemistry International_ , 28, 11–12, May–June, 2006.

## **I NDEX**

Abegg, Richard, 208

ab initio calculations, 237, 243–245, 321

abstract elements, 289, 291, 294

accommodation, 123, 150, 280

in Mendeleev's periodic system, 143–149

of noble gases, 151–156

versus prediction, 156

acid-base chemistry, 125

acids

formation of, 18–19

measurement of, 31

actinides, 275, 307

discovery of, 129

actinium, 143, 170, 176

placement of, 21

actinoid relationships, 269–270

ad hoc arguments, 150

"adiabatic," 315

adiabatic principle, 194–195, 200–201

affinity, chemical, xiii–xiv

air

Dalton's research on, 34

as element, 3

alchemy, xix, xvi–xvii, 3, 4, 34, 53

alkali metals, 265, 268–269, 275

formulas for, 59–60

Mendeleev's classification of, 104, 106

Newlands's grouping of, 74

similarity of hydrogen to, 281

alkaline earth elements, 265

emergence of, 69

helium as, 281

Mendeleev's classification of, 116

alloys, 273

alpha particles, 159, 164, 165, 178

alpha rays, 163, 175

Alpher, Ralph, 254, 323

alphon particles, 165–166

aluminum, 174, 271, 324

association with beryllium, 128

Mendeleev's prediction of, 106

placement of, 278

similarity to iron, 276

similarity to scandium, 267–268

splitting of hydrogen, 277

superatom clusters, 277

americium, 21

ammonia

composition of, 35

formula of, 294

valence, 209

ammonium ion, 276

"amphoteric," 316

amphoteric elements, 208

Ampère, André, 63

angular momentum, 192, 199, 228, 245, 265, 314. _See also_ spin angular momentum

anthropic principle, 323

antimony, 271, 272

equivalent weights, 51

Mendeleev's placement of, 129

similarity to gallium, 273

aperiodic systems, 195

approximations, xvii

argon, 16, 117, 309

discovery of, 151–156, 291

electronic configuration, 234

Aristotle, xix

nature of elements, 113

philosophy of substance and matter, xv

Armstrong, Henry, 153

aromatic hydrocarbons, 25, 26f

Arrhenius, Svante, 251

arsenic, 271

electronic configuration, 190

equivalent weights, 51

astatine, 143, 291

discovery of, 174

asterium, 172

astrology, 3

astronomy

application to chemistry, 87

impact on nucleosynthesis theories, 253–254

names of elements from, 8

astrophysics, 258

Atkins, Peter, xv, 281

_Atomechanik_ (Hinrichs), 86

atomic combinations, 36

atomicity, of a gas, 151

atomic mass, 64

atomic number, xviii, 20, 58, 61, 131, 278, 311, 327

anticipation of, 76

in density functional theories, 246

discovery of, 165–169

of isotopes, 313

Moseley's experiments on, 170–173

relation to charge, 171, 175

relativistic effects and, 270

stability and, 263

triads and, 179–180

atomic physics. _See_ physics

atomic radii

among transition metals, 272t

within periodic table, 266

atomic states, number of, 201

atomic theory, 37–38, 159

of Dalton, 33–37, 57, 294

atomic volume, 98

plotted against atomic weight, 97f

atomic weight, xviii, 38–39, 179, 291, 296, 311

versus atomic volume, 97f

basic unit of measurement, 41–42

Dalton's research, 34–36

in De Chancourtois's tables, 71

determination of, 57–61

in development of periodic system, 66–67

versus equivalent weight, 44, 62–64

gaps of Pettenkofer, 51t

Gmelin's use of, 45, 46

history of, 19–20

interpolation, 110

in Lothar Meyer's tables, 96

Mendeleev's use of, 104, 115–116, 120, 125–127

Newland's use of, 72

nonintegral, 176

numerical relationships among, 53–54

prediction of, 124

Prout's hypothesis and, 40

relation to atomic dimension, 89

relation to charge, 164, 167

relation to chemical properties, 68, 109, 313

relation to specific heat, 127

spectral line frequencies and, 88

atomism, Greek, 32–33

atoms, 120, 302. _See also_ atomic radii

concept of, xix, 64

dimensions, 88

formation of, 254

Lewis's postulates of structure, 208–209

models of, 183–187, 214f

_aufbau_ principle, 190, 192, 233, 242, 243, 265, 282

Austin, William, 35

Avogrado, Amedeo, 7, 38, 63, 302

Bachelhard, Gaston, 121

Balard, Antoine, 48

barium, 6

atomic weight of, 301

placement of, 50

spectral frequencies, 88

triad relationships, 42, 44

Barkla, Charles, 164, 170

bases

formation of, 18–19

measurement of, 31

basic substances, 281–283, 285, 304

basis sets, choice of, 241–242

Becquerel, Henri, 161–162, 310

Becquerel rays, discovery of, 160–162

Bent, Henry, 275

benzene rings, 276

benzenoid aromatic hydrocarbons, 25, 26f

Berthelot, Marcellin, 148–149

beryllium, 298

association with aluminum, 128

atomic weight of, 150

formation of carbon from, 257

placement of, 127–128, 156

Berzelius, Jacob, 40

determination of atomic weights, 59, 104, 295

element symbols of, 9

beta decay, 178

formation of elements by, 254

beta particles, 178, 254

beta rays, discovery of, 163

Bethe, Hans, 254, 323

big bang cosmology, 249, 253–254, 258, 322

stages in, 259t

binding energy, 259, 260f, 261

biology, philosophy of, xxii

Biron, Evgenii, 270

bismuth, 271

electrochemical potential, 327

placement of, 45

black-body radiation, 189

black holes, 256

Bohr, Niels, xix, xx, xxi, 7, 24, 199, 201, 217, 229, 312

collaboration with Moseley, 171

lecture quality and style, 193–194

prediction of hafnium, 218–220, 319

quantum theory, 188–197

second theory of periodic system, 192–197

trilogy paper, 168

work method, 224

Bohrfest, 193

bohrium, 9

boiling points, knight's move relationships and, 274t

Boisbaudran, Emile Lecoq, 135–136

Boltwood, Bertram, 177

Boltzmann, Ludwig, 159

Bondi, Herman, 322

bonding, xiii, xvi

bonds. _See also_ binding energy

covalent, 207–208, 228

interatomic, 153

ionic, 207–208

notation, 211

single, double, and triple, 209–210

Bonifatii, Kedrov, 150

borazine, 276

boron, 271

bonding with nitrogen, 276, 326

equivalent weights, 51

placement of, 45, 98

boundary conditions, 228–229

Boyle, Robert, xvi–xvii, 4, 34

brass, 325

Brauner, Bohuslav, 117, 129, 130

British Association for the Advancement of Science, 251

Brock, William, 123

Broglie, Louis de, 230

bromine, 15

discovery of, 48

placement of, 148

reactions of, 49

triad relationships, 43

bronze, 325

Brush, Stephen, 124, 150

buckyballs. _See_ fullerenes

Bunsen, Robert, 87, 301

Burbidge, Geoffrey, 257

Burbidge, Margaret, 257

Burgers, J.M., 195

Bury, Charles, 173, 192, 213, 215, 224

cadmium, 85, 273, 325

placement of, 98

calcium, 6

atomic weight, 297, 301

placement of, 50

prediction of analogue, 142

spectral frequencies, 88

triad relationships, 42, 44

_calorique_ , 5

Cannizzaro, Stanislao, 7, 38, 62, 66–67, 300, 302

atomic weights of, 104, 127

influence on Lothar Meyer, 93

influence on Odling, 82

revival of Avogrado's work, 64–65

carbon, 271

atomic weight, 65t, 296

equivalent weight, 51

formation of, 255, 257

resonant state, 323

carbon-carbon bonds, 276

Cassebaum, H., 87

casseopeium, 172

cathode rays, 184–185, 313

cells, 212, 215, 317

central-field potential, 263

cerium

electronic configuration, 216

in table of Mendeleev, 110

cesium, 291, 298

derivation of name, 8

Chadwick, James, 175

chalcophiles, 278

charge, 325

atomic number and, 171, 175

atomic weight and, 164, 167

charge density, 267, 276

_Chemical News_ , 78, 147, 148, 250

chemical properties

elucidation using triads, 43

in left-step table, 286

number of electrons and, 313

similar, 109, 267–269

in table of Lothar Meyer, 96

chemistry

education, xx. _See also_ textbooks

as inductive science, 142

international, 105

numerical aspects of, 57

philosophy of, xiii, xx, 113, 117–121

versus physics, xvii–xviii, 211–212

reduction to quantum mechanics, xiv, xxii, 247–248, 318

role of alchemy in, xvi–xvii

_Chemistry and Atomic Structure_ (Main Smith), 220

Chistyakov, V.M., 272

chlorine, 6, 15, 297

atomic weight, 41, 176

derivation of name, 8

discovery of, 48

electronic configuration, 191, 206

reactions of, 49

triad relationships, 43

chromium

electronic configuration, 240

orbital energies, 237–238

classification, xix, 65–66, 285

based on atomic weight, 125

early, of elements, xv–xvi

Gmelin's, 48–50

numerical relationships and, 57

of periodic classifications, xiv

primary versus secondary, 21–22

Prout's hypothesis and, 40

Clausius, Rudolf, 151

Cléve, Pierre, 137, 147

cobalt, 302

placement of, 148, 171

colors, names of elements from, 8

columns. _See_ groups

combustion, 30

composition, Lavoisier's analyses of, 31

compounds

formation, xvi

formulas for, 36–37, 59, 63–64

tables of, 25, 27

constant differences, discovery of, 50–51

continuous recycling, heat death and, 252

contrapredictions, 124

Cooper, D.G., xv

copper, 6, 290

alloys, 325

electronic configuration, 240

orbital energies, 238–239

symbol for, 9, 10f

coronium, 172

Coryell, Charles, 174

cosmology, 249, 258. _See also_ big bang cosmology

Coster, Dirk, 173, 219

Coulomb forces, 209, 256, 259

Courtois, Bernard, 48

covalent bonds, 207–208

quantum mechanical calculation of, 228

Crookes, William, 153, 172, 176, 184, 250–251, 323

Crookes tubes, 161

crystal planes, angles between, 60

cubic particles, 3

cults, alchemy and, xvi

cultural anthropology, xvii

Curie, Marie, 162, 310

curium, 21

cyclonium, 312

Dalton, John, 7, 31, 63, 294

atomic theory of, 33–38

atomic weights of, 19, 41t

element symbols used by, 9

incorrect conclusions of, 57

rule of simplicity, 58, 295

dark energy, 258

dark matter, 258

darmstadtium, 290

Dauvillier, Alexandre, 217, 219

Davies, Mansel, 224

Davisson, Clinton, 230

Davy, Humphry, 7, 39, 48

Davy Medal, 144–146

Döbereiner, Johann, xix, 7, 25, 42–43, 94, 179, 296

triads of, 58t

De Boisbaudran, Paul Emile Le Coq, 68, 71

De Chancourtois, Alexandre Emile Béguyer, xix, 99

role in development of periodic system, 68–72

role in discovery of periodic law, 77

De Lapparent, Albert Auguste, 68, 71

Demidov Prize, 103

density

of gases, 59, 64

Lothar Meyer's use of, 98

density functional theories, 245–247

deuterium, 322

diagonal behavior, 265–267

Dias, Jerry, 25

diatomic molecules, 63, 64

didymium, 91, 302

_Die Modernen Theorie der Chemie_ , 93–94

diffraction, by electrons, 230

diffraction techniques, 246

diffusion, Dalton's hypotheses, 35

Dirac, Paul, 247

Dobbs, Betty Jo, xvi

dodecahedral particles, 3

double bonds, 209, 210f

dubnium, 9

Dufour periodic tree, 286f

Dulong, Pierre-Louis, 59–60, 127, 299

Dumas, André, xix, 52–53, 62

atomic weights of, 40–41, 60–61

dysprosium, 174

earth, as element, 3

Eddington, Arthur, 253, 255

education, chemistry, xx. _See also_ textbooks

Ehrenfest, Paul, 194, 217

"eka-," 307

eka-aluminum, 132. _See also_ gallium

eka-boron, 132. _See also_ scandium

eka-lead, 275

eka-manganese, 172, 174

eka-silicon, 132. _See also_ germanium

eka-stibium, 138

eka-tantalum, 173

eka-tellurium, 130

electrical oscillations, formation of elements through, 251

electric forces, 209

electricity

isolation of elements and, 6

use to form compounds, 37

electrochemical potential, 327

electrode potential, 267, 268t

electrolysis, 6

electromagnetism, 188

electron clouds, 24

electron density, 231, 246, 247

electronegativity, 297

within periodic table, 266

use in classification, 48

electron gas, 246

electronic configurations, 24, 185–187, 281, 283, 317

among groups, 269, 270, 327

of Bury, 213, 214

by chemists, 205–211, 224–225, 227

concept of, 21–22

ground state, 242, 244

of Langmuir, 211–213

of Main Smith, 220–223

periodicity and, 190

rearrangements, 190–191

rules for, 232

third quantum number and, 197–198, 199t

writing, 233–237

electronmagnetism, 308

electron rings, of Thomson, 187t

electrons, xix, 160, 293, 324. See also electron density; electronic configuration; electron shells

addition of, 196

attachment sites, 208

diffraction and interference by, 230

discovery of, 159, 183–185, 205

field of movement, 231–232

magnetic properties, 209, 316

number and chemical properties, 313

repulsion, 241

shared, 209, 316

velocity, 24

waves, 230–231

electron screening, 271

electron shells, xx, 190, 198, 221–222

explanation for closing, 237–242

filling, 212, 282

number of electrons in, 198, 201, 208, 215, 229, 232, 234, 242–243

outer, 14, 24

Pauli's scheme, 200t

theories, 265

electron spin, 209

electron waves, 293

element 72. See hafnium

elements. _See also names of specific elements_

abstract, 113–115, 117–118, 289

abundance of, 258–265

as basic substances, 278, 280

chemical similarities, 29, 85, 125, 267–269

classification, xv–xvi, 22, 40

comparison of dissimilar, 54

concept of, xv–xvi, xxii, 4, 280–281

definitions of, xv–xvi

discovery of, 6, 7, 67, 172, 176

formation of, 249, 250–258

in Greek philosophy, 3

macroscopic behavior, 205

Mendeleev's evaluation of, 105–106, 112–117

names and symbols of, 6–10, 290

number of, 22, 170, 174, 293

prediction of, 74, 306, 309

reactivity and ordering, 18–20

as simple substances, 281

synthesis of, 6, 21

unknown, 96, 106, 124, 131

empiricism, xv, 4, 31, 34

energy

radiation of, 188–189

released upon nucleus formation, 259

zero-point, 252

energy states, 189

enneads, 55

equal volumes equal numbers. _See_ EVEN hypothesis

equivalent weights, 19–20, 31–32, 38–39, 291, 295

versus atomic weight, 36–37, 44, 62–64

Pettenkofer's use of, 50–51

in triads, 42–44

erbia, 217

erbium, 172

derivation of name, 8

placement by Mendeleev, 126

prediction of atomic weight, 56

essentialism, 118

ether, 3, 252, 308

ether theory, 140

European periodic system, 13f, 14

europium, gadolinium and, 21

euxenite, 137

EVEN hypothesis, 38, 59, 61, 62, 295

exchange terms, 228, 241

experimentation

beginnings of, 4

philosophy of, xvii

failures, historical recording of, xviii

Fajans, Kasimir, 170, 178, 326

Faraday, Michael, 52, 82, 250

feldspars, 72

Fermi, Enrico, 246

fire, 289

as element, 3

first-member anomaly, 275–276, 282

Fitzgerald, George, 153

florentium, 312

fluorine, 15, 297

electronic configuration, 191

placement of, 48

prediction of analogue, 141

reactions of, 49

triad relationships, 43

Fock, Vladimir, 231, 319

Foster, George Carey, 78

_Foundations of Chemistry_ , 287

Fowler, William, 257, 323

francium, discovery of, 174

Frankland, Edward, 37

Friedel-Crafts catalysts, 276

Friederich, B., 293

fullerenes, 291

fundamentalism, of scientific disciplines, xvii–xviii

fusibility, Lothar Meyer's use of, 98

fusion reactions, 256

gadolinium, europium and, 21

gallium, 267, 271, 291

discovery of, 135–137, 156

predicted and observed properties, 133–134t

prediction of, 106, 123, 132

similarity to antimony, 273

Gamow, George, 254, 323

gases

atomic weight measurement, 62

composition of, 251

relative density, 59, 64

Gaudin, M.A.A., 299

Gay-Lussac, Joseph Louis, 37–38, 63

Geiger, Hans, 164

geography, names of elements from, 8

geology

influence on atomic weight, 179

periodic table for, 278

Gerhardt, Charles, 63, 72

atomic weights of, 104

germanium, 15, 271

discovery of, 137–140, 156

predicted and observed properties, 139t

prediction of, 96, 106, 123, 132

Germer, Lester, 230

Gladstone, John Hall, 155, 297

Glendenin, Lawrence, 174

Gmelin, Leopold, xix, 7, 44–50, 297

atomic weights of, 40

chemistry textbooks of, 46–50

groupings of, 65

Goeppert-Mayer, Maria, 264

gold, 6, 174, 175

alchemy, 3

Gordin, Michael, xv, 118

graphite, 276

gravitational force, on stars, 256

Greek mythology, names of elements from, 8

Greek philosophy. _See also_ Aristotle

view of elements, 3

Grignard reagent, 266

Grosse, Aristide, 173

ground state

of carbon, 257

configurations, 242, 244

energy, 227

of nickel, 239

prediction of, 242

group displacement laws, 178

groups, 11, 14–15, 66. _See also_ periodicity

discovery of, 44–48

electronic conguration and, 190–192, 242–243, 327

of Hinrichs, 89–92

of Mendeleev, 112, 125–126

as natural kinds, 280–281

of Newlands, 72–73, 80

of Odling, 82–85

similarities between, 267–269

Habashi, F., 278

hafnium, 175, 227, 283

discovery of, 173

electronic configuration, 215–217

prediction of, 218–220, 224, 319

Hahn, Otto, 9, 173, 312

hahnium, 9

halogens, 297, 305

classification by Mendeleev, 116

equivalent weights, 51

ordering of, 48

properties of, 118

reactions of, 49

_Handbuch der Chemie_ (Gmelin), 44

harmonic interaction, 218

Hartog, Philip, 68, 71

Hartree, Douglas, 231, 319

Hartree-Fock method, 231–232

heat, as an element, 5

heat death, of universe, 251–252, 323

heat envelope, 57

Hefferlin, Ray, 25, 293

Heilbron, John, 190

Heisenberg, Werner, xix, 227–228, 230–231

Heitler, Walter, 228

helium, 16

abundance of, 258

calculation of properties, 230

calculation of spectrum, 227

derivation of name, 8

discovery of, 155, 291

electronic configuration, 211, 242

formation from hydrogen, 253

formation of carbon from, 257

placement of, xxi, 22, 275–276, 281–283, 293, 321

ratio to hydrogen, 249, 322

stablity, 241

Hentschel, Klaus, 92

Herz, Heinrich, 184

Hevesy, Georg, 177, 219, 280, 327

high-temperature superconductivity, 10–11

Hilbert space, 246

Hinrichs, Gustavus, xix, 86–92, 99, 292

periodic table of, 302

history of science, xviii

Hittorf, Johann, 184

Hoffmann, A.W, 250

holmium, 217

derivation of name, 8

homogeneity, 177

homologous series, 94

horizontal relationships, 53–54, 302

Mendeleev's analysis of, 105–106, 116

in tables of Lothar Meyer, 94

Hoyle, Fred, 255–257, 323

Humboldt, Alexander von, 37

Hund's rule, 212–213, 233, 240–241

hydrides, 299

hydrofluoric acid, 48

hydrogen, 59

abundance of, 258

first-member anomaly, 275

formation of helium from, 253

as foundational element, 250

Lavoisier's view of, 31

placement of, 149, 281–282, 313, 326

quantum theory of atom, 188

ratio to helium, 249, 322

splitting, 277

hydrogen burning, 256, 323

hydrogen peroxide, 295

hydroxides, 18

reactions, 127

hypotheses, testing, 42

icosahedral particles, 3

illinium, 312

incandescent objects, 314

independent-electron approximation, 243

indium, 132, 290

in table of Mendeleev, 110, 126

inert gases. _See_ noble gases

inertness, 281

inert pair effect, 324

infinity, 32–33

inorganic atoms, 94

integral weights, 38–42

interatomic bonding, 153

interatomic distances, 25

interference effects, of electrons, 230

International Union of Pure and Applied Chemistry, 9

naming conventions, 290

periodic system, 13f, 14

periodic table, 290

interpolation, 132, 142

of Mendeleev, 131

iodine, 300

discovery of, 48

placement of, 96, 125–126, 130–131

reactions of, 49

reversal with tellurium, 76, 109, 117, 148, 173, 178, 297–298, 309

triad relationships, 43

ionic bonds, 207–208

ionic compounds, formation of, 206

ionium, 177

ionization, 236, 281

ionization energy, 25, 244, 271, 320, 325

within periodic table, 266

ions

inclusion in periodic table, 278

that imitate elements, 276

iron, 6, 302

formation of, 256

similarity to aluminum, 276

stability of, 259

isomorphism, law of, 59–60

isotopes, 58, 292

abundance of, 249, 322

atomic weights and, 73, 296

discovery of, 41–42, 160, 176–179, 250, 326

elements with single, 299

mass, 178

periodic table and, 280

triads and, 179–182

IUPAC. _See_ International Union of Pure and Applied Chemistry

Janet, Charles, 327

Janet table. _See_ left-step table

Jensen, Hans, 264

Jensen, William, 87, 275, 293

Jupiter, 258

Kaesz, Herbert, 281

Kaji, Masanori, 115

Karlsruhe conference, 63, 64, 72, 82, 93, 103, 291, 299–300

Kauffman, George, 87

Kaufmann, Walter, 184

Kekulé, August, 37, 64

keltium, 175

Kelvin, William Thomson, 154

Khodnev, Alexei Ivanovich, 105

kinetic energy, 151, 194

Kirchoff, Gustav Robert, 87

_Klassiker der Wissenschaften_ (Cannizzaro), 93

knight's move relationships, 272–275, 325

knowledge

development of system of, xviii

validity of, xvii

Kossel, Walther, 212

Kramers, Hendrik, 217

Kremers, Peter, 53–54

Kripke, Saul, 326

Kripke-Putnam view, xxii

krypton, 16

discovery of, 155, 291

Kuhn, Thomas, xviii, 67, 190, 288, 298

Laidler, Keith, 224

Laing, Michael, 273, 274

Lakatos, Imre, 182

Landé, Alfred, 199

Langmuir, Irving, 211–213

lanthanides, 74, 270, 275, 307

lanthanum, 21, 272

placement by Mendeleev, 126

Latin names, 290

Lavoisier, Antoine, xv, 7, 34, 288, 294

nature of elements, 113

quantitative analyses of, 29–31

simple substances, 289

view of elements, 4

law of chemical combination. _See_ law of multiple proportions

law of conservation of matter, 114

law of constant proportion, 35–36

law of definite proportions by volumes, 37–38, 59

law of integers, 63

law of multiple proportions, 36

law of octaves, 76–82, 85

lawrencium, 21, 272

lead, 15, 273

atomic weight, 176

placement by Lothar Meyer, 98

radioactive decay, 178–179

separation of radio-lead, 177

transmutation, 3

valence, 291

left-step table, 283, 284f, 285–286

Lemaître, Georges, 253

Lembert, Max, 179

Lenssen, Ernst, 55–56

Levi, Primo, 6, 290

Lewis, Gilbert Newton, 7, 205–211

light

as an element, 5

dispersion from atoms, 188

Lipton, Peter, 144–145

liquid drop model, 259, 261

literary criticism, xvii

lithium, 291, 301

placement of, 50, 149

similarity to magnesium, 265–266

triad relationships, 43

lithophiles, 278, 326

logic, xxi

London, Fritz, 228

London Chemical Society, 78, 80, 82

Lothar Meyer, Julius, xix, 80, 92–98, 99

Davy Medal, 145

dispute with Mendeleev, 98, 147

prediction of germanium, 139

unity of matter, 294

view of reductionism, 183

work contrasted with Mendeleev's, 124–125

Lothar Meyer, Oskar, 92

_lumière_ , 5

lutetium, 21, 172, 174–175, 217, 272

electronic configuration, 216, 218

Löwdin, Per-Olav, 233

macroscopic properties, 3

Madelung rule, 233

magic numbers, 263–264

magnesium, 6, 85

placement of, 44, 50

similarity to lithium, 265–266

similarity to zinc, 267

magnetic fields

effect on orbital motion, 197

effect on spectral lines, 196, 199–201

Maher, Patrick, 144–145

Main Smith, John David, 225

electronic configuration schemes, 220–223

Marignac, Charles, 41, 217

Marinsky, Jacob, 174

Marsden, Ernest, 164

masses, ratio of, 36

mass number, 259, 292

masurium, 174

material ingredient, 113, 114, 118

matrix mechanics, 230

matter

behavior of, xx

composition of, 258

dark, 258

fourth state, 251

subdivision of, 32–33

maximum simplicity, 62, 295

Maxwell, James Clerk, 188

Mayer, Alfred, 186

Mazurs, Edward, xiv, 277, 287

McCoy, Herbert, 177

measurable attributes, 115

Meitner, Lise, 9, 173, 312

melting points, 267, 268t

knight's move relationships and, 274t

prediction of, 136

Mendeleev, Dimitri, xiii, xix, xv–xvi, 80, 99, 101, 278, 301

on accommodation of argon, 154

on accommodation of noble gases, 155–156

criticism of De Chancourtois, 71

criticism of nucleosynthesis, 251

development of periodic system, 67, 105–112

dispute with Lothar Meyer, 93, 98, 147

early life and work, 102–105

influence of Pettenkofer on, 51–52

misplacement of elements in table, 303

nature of elements, 112–117, 294

predictions of, 117–118, 123–124, 131–135, 140–149, 300

publications of, 143

reaction to discovery of gallium, 136

style of work, 150

triads, 179

view of reductionism, 183

views on ether, 308

mercury, 6, 15, 275

placement of, 98, 126

symbol for, 9, 10f

mesothorium, 177

metal oxides, 18

reactions, 127

metals

classification of, 50, 59, 90

knight's move relationships, 273–275

measurement of, 31

properties of, 11

metaphysical explanations, 304

of chemical phenomena, 113–114

of elements, xv, 281

meterology, 86

Middle Ages, xix

concept of elements, 3

Mitscherlich, Eilhard, 60

models, use in science, xvii

molecular tables, 25, 27

molecular weight, 66, 302

molecules, concept of, 64

molybdenum, 98

Monaghan, P.K., xv

monoatomicity, 154, 309

Morris, R., xv

Moscow Congress of the Russian Scientists and Physicians, 132

Moseley, Henry, 7, 131, 159–160, 169–175, 311

motion

frequency of, 194

repetition of, 195

multiples of constant differences, 51

Nagaoka, Hantaro, 164, 185

naphthalene, 25

Naquet, Alfred, chemistry textbook of, 65–66

natural kinds, xxii

elements as, 280–281

nearest-neighbor interactions, 323

nebullium, 172

neodymium, 302

neon, 16

discovery of, 155, 291

neo-ytterbium, 217

Neptune, 258

Nernst, Walther, 252

neutralization, 19

neutrinos, 323

neutron absorption, 254, 258

neutrons, 61, 320

beta decay of, 178

formation of, 256

Newlands, John, xix, 67, 72–82, 292, 300, 301

law of octaves, 76–82

periodic table of, 91–92, 302

suggestion of atomic number, 167

Newton, Isaac, xvi, 301

atomism, 33–34

newtonium, 140–141

nickel, 302

electronic configuration, 239–240, 320

placement of, 148, 171

Nilsen, Lars Frederick, 137

niobium, 55, 290

nipponium, 172

nitrogen, 153, 298

atomic weights, 296

bonding with boron, 276

electronic configuration, 190, 192, 196, 198

equivalent weights, 51

first-member anomaly, 275

placement of, 46, 49

noble gases, 150, 307, 310

accommodation of, 156–157

discovery of, xix

effect on law of octaves, 78, 80

electronic configurations, 224

helium as, 281

Mendeleev's analysis of, 140–141

number of electrons in, 212

prediction and accommodation, 151–156

properties of, 16

noble metals, 269

in tables of Mendeleev, 106

Noddack, Ida and Walter, 173, 289

nomenclature, 8

nonmetal oxides, reactions, 127

nonmetals

Hinrichs's classification, 90

placement of, 18

properties of, 11

nonpolar organic compounds, formation of, 206–207

nuclear fission, 6, 312

nuclear forces, 259, 323

nuclear-shell model, 261, 263

nuclear-shell theories, 265, 324

nuclei, 120, 160

discovery of, 164

fusion of, 256

stability of, 259–265

nucleons, 259, 263, 324

spin-orbit coupling, 264–265

nucleosynthesis, 21, 249, 251–258

conditions for, 257t

in stars, 255–256, 259

numerical data, 296–297

numerical relationships, xix, xxi, 29, 44

Mendeleev's use of, 141

Pettenkofer's use of, 50

observable properties, 4

observers, versus theorists, 150

octets, 275

Odling, William, xix, 72, 82–86, 99, 300

periodic table of, 74, 302

role in acceptance of Newlands's work, 78, 80

role in discovery of periodic law, 77

Ogawa, Masataka, 172

orbitals, xx, 24, 185, 231, 246, 317

energy levels, 233–238, 320

filling of, 212–213, 233, 283

versus orbits, 230, 293, 313

reliance of quantum mechanical calculations on, 247

orbits, 188

versus orbitals, 230, 293, 313

reality of, 198

shape of, 192

organic compounds, classification of, 94

organometallic compounds, 266

organotin compounds, 273

osmium, similarity to xenon, 268

Ostwald, Wilhelm, 93

outer-shell electrons

denotation of, 14

similarities between elements and, 24

oxidation states, 270, 275, 291, 324

oxides

chemical characteristics, 127

Gmelin's formulas for, 50

Lavoisier's view of, 31

triad relationships, 42

oxygen, 59, 294

atomic weights, 296

discovery of importance in combustion, 30–31

electronic configuration, 190–191

first-member anomaly, 275

placement of, 46

pair reversals

iodine and tellurium, 76, 109, 117, 130–131, 148, 173, 178, 297–298, 309

nickel and cobalt, 171

understanding of, 178

palladium, 8

Paneth, Fritz, 163, 220, 304, 326, 327

atomic numbers and basic substances, 278, 280

separation of radio-lead, 177

view of Mendeleev's work, 120

Pauli, Wolfgang, xix, xx, 7, 198, 199–201

Pauli exclusion principle, xx, 199–203, 227, 229, 232, 233, 243, 315

Peligot, Eugène, 128

Perey, Marguerite, 174

periodicity, xiii, 84, 109, 149, 184, 229, 281, 283

Bohr's theory, 222

concept of, 67

discovery of, 99

electronic configuration and, 187, 190–192

explanation of, 232, 242

of Hinrichs's system, 92

nature of, 16, 18, 71

Pauli exclusion principle and, 202

secondary, 270–272

in tables of De Chancourtois, 69

van den Broek's views, 166

periodic law, 16–18, 21–22, 76, 77, 281

conserved in tables of Mendeleev, 118

periodic systems, xiii

competing, 104–105

of Crookes, 251, 252f, 253f

development of, xv–xvi, xviii–xxii, 66–68, 99–100, 123

discovery of, 299

effect of physics on, 24–25, 229, 244

first, xix

of Mendeleev, 94, 96, 105–112, 143–145

modern, 248

numbers of, 277

versus periodic tables, 18

philosophy of, xvii–xviii

role of qualitative chemistry, 48–50

symmetrical representation, 287

periodic tables, 20–21, 277–282

best form, 282–283

books on, xiv–xv

circular, 291

conferences on, 287

contemporary reactions to, 146–149

of De Chancourtois, 68–72

format of modern, 10–16

gaps in, 84, 96, 131–132, 172–174

of Hinrich, 89–92

horizontal series, 53–54

influence of, 25, 27

inorganic chemist's, 279f

isotopes and, 160

IUPAC, U.S., and European systems, 13f

long form, 17f

of Lothar Meyer, 94

medium-long form, 12f

of Mendeleev, 106–112

modified long form, 181f

of Newlands, 91–92

versus periodic systems, 18

recent changes in, 21–24

reduction of, 242–246

short form, 14, 15f

as a teaching tool, xx

of van den Broek, 166–168

periods, 11. _See also_ horizontal relationships

beginning of, 282–283

discovery of, 44

length of, 85–86, 201–203

number of elements in, 229

Perrier, Carlo, 174

Perrin, Jean, 185, 251

Petit, Alexis-Thérèse, 59–60, 127

Pettenkofer, Max, xix, 50–52, 94

philosophy. _See also under_ chemistry

of periodic system, xvii–xviii

of science, xx–xxii

of substance and matter, xv

phlogiston, xix, 30–31

phosphorescence, 161–162

phosphorus, 6, 271, 272

electronic configuration, 190

equivalent weights, 51

Lavoisier's view of, 31

oxidation states, 275

physical properties, 120

in left-step table, 286

Lothar Meyer's use of, 98

preeminence of chemical properties over, 125

used for classification, 22

Physical Society, 154

physicists, atomic theory and, 159

physics, xxi, 195

versus chemistry, xiii, xvii–xviii, 120, 211–212

chemistry as subdiscipline of, xx

effect on periodic system, xiv, 24–25

periodic table and, xix

Taoism and, 291

pitchblende, 162

Planck, Max, 188, 314

Planck's constant, 189

planetary distances, 88t

planetary model, of atom, 87, 185–186

planets

chemical composition of, 258

names of elements from, 8

symbols for elements and, 9, 10f

plasma state, 251

Platonic solids, 3

pleiads, 178

plum pudding model, 186, 314

plutonium, 6, 290

Pode, J.S.F., xv

Poincaré, Henri, 161

polonium, 176

discovery of, 162

polyatomic molecules, 276, 309

Popper, Karl, 42, 319

positivism, xxi, 294

potassium

electronic configuration, 234–235

placement of, 50

triad relationships, 43

potassium hydroxide, valence, 209

potentiality, 4

praseodymium, 302

precession, 192, 197

predictions, 74, 309

versus accommodations, 156

importance of, 56–57

of Mendeleev, 106, 117–119, 123–124, 131–135, 143–149

of molecular properties, 25, 27

of Odling, 83

of trends in properties, 137

Priestley, Joseph, 31

primary and secondary kinship, 293

primary classification, 21–22

primary matter, 89

primary substance, Mendeleev's view of, 103

Principe, Lawrence, xvi

_Principles of Chemistry, The_ (Mendeleev), 103, 117, 143

prism, 89

proactinium, 173

promethium, discovery of, 174

protium, 322

protons, 61, 160

formation, 178

number of, 20, 42

stability and, 263

protyle, 39

Prout, William, xix, 39

Prout's hypothesis, xxi, 38–42, 61, 67, 119, 149, 253, 296

in light of isotopy, 160

Mendeleev's view of, 103

Moseley's work and, 175–176, 250

triads and, 179, 182

Puddephatt, R.J., xv

Putnam, Hilary, 326

pyramidal periodic table, 283, 285f

pyroxenes, 72

Pythagoreanism, xxi, 87, 88

qualititative chemistry, role in periodic system, 48–50

quanta, 188

quantitative analysis, 29–31

quantization, 188, 192, 228

quantum mechanical nuclear-shell model, 261

quantum mechanical tunneling, 256

quantum mechanics, xiii, xx, xxi, 120, 228–231

basis sets, 242

effect on periodic system, 24–25

failure to explain periodic table, 237

versus quantum theory, 216

realism and, 319

reductionism of, xiv, xxii, 247–248, 318

solving equations, 231–232

quantum numbers, xix, 232, 234, 320

first, 282

fourth, 199–201, 229

principal and azimuthal, 192

third, 197–198, 315

values of, 201–202

quantum states, number of, 196, 198

quantum theory, 24, 224, 230, 312

atomic, 188–192

versus quantum mechanics, 216

second, 192–197

shortcomings of, 227

quintessence, 3

radiant light energy, 256

radiation, loss of energy through, 188

radicals, inclusion in tables of De Chancourtois, 69

radioactive atoms, creation of, 252

radioactive decay, 178–179

radioactive tracers, development of, 177

radioactivity, 117, 308

discovery of, xix, 6, 159–163, 310

radiochemistry, 6

radiographs, first, 161

radiothorium, 176–177

radium, 117, 176, 298

discovery of, 162

radon, 176

discovery of, 291

Railsback, Bruce, 278

Ramsay, William, 7, 151–153

rare earth elements, 16, 150

classification by Mendeleev, 117

electronic configuration, 218–219

placement of, 172

ratio of masses, 36

Rayleigh, John William, 7, 151–153

Rayner Canham, Geoffrey, 269

Rayner Canham table. _See_ pyramidal periodic table

reactivity

of metals, 50

ordering of elements and, 18–20

patterns, 49

realism, xxi–xxii, 21, 120, 278, 292

red giants, 258

reductionism, xviii, xx–xxi, xxii, 183, 247–248, 265, 283, 318

approaches to, 242–246

of Mendeleev, 119–121

refractive index, 155

relative density, 59, 64

relativism, xvii

relativistic effects, 237, 270, 293

relativity, xiii

effect on periodic system, 24–25

Remelé, Adolf, 98–99

repetition, 76, 77. _See also_ periodicity

in chemical properties, 16

repulsion, 57, 241, 259

rhenium, discovery of, 173

rhodium, derivation of name, 8

Richards, Theodore W., 178–179

Richter, Jeremias Benjamin, 31, 36

Röntgen, Wilhelm Conrad, 161, 184

Rocke, Alan, 19

roentgenium, 290

Roscoe, Henry, 129

rotational energy, 151

rotational motion, 309

Royal Institution, 82

Royal Society of London, 152

r-process, 258

rubidium, 290, 298

Rücker, William Arthur, 154

rule of simplicity, 36, 295

Russian Chemical Society, 106

Russian Physico-Chemical Society, 155

ruthenium, 277

Rutherford, Ernest, xix, 159, 175–176, 188, 217, 314

assessment of van den Broek's work, 169

research on atomic nuclei, 164

research on Becquerel rays, 162–163

Sacks, Oliver, xv, 7

Saltpeter, Edwin, 254–255

Sanderson, Ralph, xv, 271

Saturn, 258

scandium, 217, 272

discovery of, 137, 156

electronic configuration, 235–236

orbital energies, 235, 237–238

predicted and observed properties, 138t

prediction of, 106, 123, 132, 147

similarity to aluminum, 267–268

scattering experiments, 164

_Sceptical Chymist, The_ (Boyle), xvi

Scheele, Carl, 31, 48

Schrödinger, Erwin, xix, 7, 227, 230–231, 314

Schrödinger equation, xxi, 234, 244, 263

science

philosophy of, xx–xxii

postmodern critiques of, xvii

revolutions in development of, xviii

unity of disciplines, xxi

Seaborg, Glenn, 6, 7, 9, 21, 129, 269, 307

seaborgium, 9

secondary classification, 21–22

secondary periodicity, 270–272

Sedgwick, William, 309

Segré, Emilio, 174

selenium, 300

atomic weight of, 299

deduction of atomic weight, 60

Gmelin's study of, 49

triad relationships, 43

separation, 176–177

discovery of isotopy and, 177–178

of rare earth elements, 172

separation energy plots, 261–263

Seubert, Carl, 98–99

siderophiles, 278, 326

Siegbahn, Manne, 175

silicon, 15, 271

equivalent weights, 51

Mendeleev's prediction of, 106

similarity to titanium, 268

silver, similarity to thallium, 273

simple substances, xv–xvi, 4, 5f, 117–118, 121, 289, 305

concept of, 113–114

periodic system and, 281–283

simplicity, rule of, 36, 295

single bonds, 209, 210f

single occupancy, 125

size ratios, of atomic dimensions, 88

slats, 18

social construction, science as, xvii

Soddy, Frederick, 163, 176, 177–179

sodium, 6, 301

atomic structure, 206

placement of, 50

properties of, 11

triad relationships, 43

sodium chloride, properties of, 113

Sommerfeld, Arnold, 192

specific heat, 59, 127, 151, 153–154

spectral frequencies, 25, 230

atomic structure and, 185

understanding of, 188

spectral lines

effect of magnetic fields on, 196, 199–201

spectroscopy, 5, 71, 314

role in discovery of elements, 67

use by Hinrichs, 87–88, 92

spin angular momentum, 200, 233, 234

spin multiplicity, 240

spin-orbit coupling, 264–265, 324

s-process, 258

stability

atomic, 188

of isotopes, 249

of nuclei, 259–265

of orbitals, 236, 238

Stahl, Georg, 31, 288

stars

contraction and collapse, 256

nucleosynthesis in, 251, 253–255, 259

quantum mechanical tunneling in, 256

Stas, Jean-Servais, 41, 103

stationary states, 195–198, 201, 316

steady-state models of the universe, 249, 255

stoichiometry, 42, 305

Stoner, Edmund, 197–198, 222–223

Stoney, Johnston, 183

Strassman, Hans, 312

Strathern, P., xv

Strömholm, Daniel, 176

strontium

placement of, 50

triad relationships, 42

Strutt, R.J., 41

subshells, 222

substance, 304

philosophy of, xv

Suess, Hans, 264

sulfur, 6, 300

electronic configuration, 191

Gmelin's study of, 49

Lavoisier's view of, 31

oxidation states, 275

triad relationships, 43

sun

age of, 258

heavy elements in, 258

hydrogen burning, 323

temperature of, 255

superatom clusters, 277

superconductivity, 10–11

superheavy elements, 22

supernovae, 256, 258

supertriads, 55–57

Svedberg, Theodor, 176

symbols, for elements, 9–10

synthesis, of elements. _See_ nucleosynthesis

tantalum, 175, 219, 290

teaching. _See_ education

technetium, 6, 289

discovery of, 174

Telluric Screw, 70f

tellurium, 300

Gmelin's study of, 49

placement by De Chancourtois, 69

placement by Lothar Meyer, 96

placement by Mendeleev, 125–126, 130–131

reversal with iodine, 76, 109, 117, 148, 173, 178, 297–298, 309

triad relationships, 43

temperature

effect on triad relationships, 54

needed for element formation, 255

of superconductivity, 10–11

terbium, 174

prediction of atomic weight, 56

tetrahedral particles, 3

textbooks

explanations of electronic configuration, 235

of Gmelin, 46–50

of Lothar Meyer, 93–94

of Mendeleev, 103, 115–117

of Naquet, 65–66

thallium, 290

discovery of, 250

placement of, 98, 110

similarity to silver, 273

theories, acceptance of, 123–124

theorists, versus observers, 150

theory of relativity, 153

effect on periodic system, 24–25

thermodynamics, 200

Thomas, Llewellyn, 245

Thomas-Fermi method. See density functional theories

Thomsen, Jörgen, 309

Thomson, J.J., xix, xx, 7, 159, 164, 175, 205, 293, 313, 316

discovery of electron, 183–188

Thomson, Thomas, 39–40

thorium, 176, 177, 270

formation from uranium, 178

radioactivity experiments, 162

thulium, 172, 174–175

tin, 15

placement of, 98, 129

similarity to zinc, 273

titanium

placement of, 127

similarity to silicon, 268

Tolman, Richard, 251

toxicity of elements, 273, 325

transformation. _See_ transmutation

transition elements, 21, 307

electronic configuration, 212, 215, 240–241

electron shells of, 224

occupation of orbitals, 236

in tables of De Chancourtois, 69

in tables of Lothar Meyer, 96, 98

transition metals, 302, 317

atomic radii, 272t

electronic configuration, 243

in periodic tables, 14, 85–86, 300

placement by Newlands, 77

translational energy, 151

translational motion, 153

transmutation, 43, 117, 163, 176, 253, 296, 304, 308

hypothesis of Dumas, 52

refutation of, 34

trans-uranium elements, 6, 21

naming, 8–9

triads, xxi, 53, 61, 94, 296

conjugated, 54

discovery of, 42–44

expansion of, 45

isotopy and, 179–182

Mendeleev's view of, 103–104

in modern periodic system, 57–58

Pettenkofer's view of, 50

super, 55–57

use by Dumas, 52

triple alpha mechanism, 254

triple bonds, 209–210

truth, objective, xvii

tungsten, 270

units of measurement, for atomic weight, 41–42

unity of matter, 179, 294

universe

age of, 258

heat death, 251–252, 323

steady-state models of, 249, 253

Upton, Thomas, 277

uranium, 21, 175, 270, 300, 307

alpha decay of, 178

correction of atomic weight, 128–129

determination of valence, 126

phosphorescence experiments, 161–162

placement of, 110, 304

Urbain, Georges, 172, 173, 219, 220

work with ytterbium, 217

U.S. periodic system, 13f, 14

utility, 286

valence, 19–20, 37, 190, 209, 291

change across periods, 307

determining, 126

of groups, 221

of metals, 128

relationships, 302

in tables of Lothar Meyer, 96

use by Mendeleev, 103, 109, 116

vanadium, 98, 290

placement of, 148

Van Assche, Pieter, 174

van den Broek, Anton, 7, 165–169

van Helmholt, Johann, 294

van Spronsen, Jan, 47, 87, 142, 176, 297, 299

vaporization, 61

velocity, of electrons, 24

Venable, F.P., xiv, 296

vibrational energy, 151

vibrational motion, 154, 309

Vincent, Bernadette Bensaude, 305

von Hevesy, Gyorgy, 173

von Laue, Max, 170

von Richter, Victor, 139

von Welsbach, Auer, 217

water

data on composition of, 35

as element, 3

formula of, 57, 63–64, 294

Lavoisier's view of, 31

valence, 209

water vapor, formation experiments, 37

wavefunction, 228–234, 244, 246, 319–320

wavelength, 314

weight changes, of substances in chemical reactions, 30

Whiggism, xviii

Wiechert, Emil, 183

Williamson, Alexander, 74

Winkler, Clemens, 137–139

Wollaston, William, 292

Würzburg Physical-Medical Society, 161

Wurtz, Charles-Adolphe, 148

xenon

discovery of, 155, 291

similarity to osmium, 268

X-rays

discovery of, 159–162

link with luminescence, 161–162

types, 170–171

ytterbia, 217

ytterbium, 172, 174–175, 217

derivation of name, 8

yttrium, 272

derivation of name, 8

superconductivity of, 11

Zapffe, Karl, 86

Zeno of Elea, 32

zero-point energy, 252

zinc, 85, 290

beta decay of, 258

similarity to magnesium, 267

similarity to tin, 273

zirconium, 219

zodiac, 3
