4.1: Well-orderings
In this chapter we discuss the principle of mathematical induction. Be aware that the word induction has a different meaning in mathematics than in the rest of science. The principle of mathematical induction depends on the order structure of the natural numbers, and gives us a powerful technique for proving universal mathematical claims.
DEFINITION. Well-ordering Let \(X\) be a set, and \(\preceq\) a linear ordering on \(X\) . We say that \(X\) is well-ordered with respect to \(\preceq\) (or \(\preceq\) is a wellordering of \(X\) ) if every non-empty subset of \(X\) has a least element with respect to \(\preceq\) . That is, for any non-empty subset \(Y\) of \(X\) \[(\exists a \in Y)(\forall y \in Y) a \preceq y .\] In general, linear orderings need not be well-orderings. Well-ordering is a universal property — a set \(X\) with an ordering \(\preceq\) is well-ordered if every non-empty subset of \(X\) has a least element with respect to \(\preceq\) . If there is any non-empty subset which does not have a least element, then \(\preceq\) does not well-order \(X\) .
EXAMPLE 4.1. \(\mathbb{Z}\) is not well-ordered by \(\leq\) . The integers do not have a least element, which suffices to demonstrate that \(\mathbb{Z}\) is not well-ordered by \(\leq\) .
EXAMPLE 4.2. Let \(X=\{x \in \mathbb{R} \mid x \geq 2\}\) . Let \(\leq\) be the usual ordering on \(\mathbb{R} . X\) is linearly ordered by \(\leq\) , but \(X\) is not well-ordered by \(\leq\) . In this example, \(X\) has a least element, but any open interval contained in \(X\) will fail to have a least element. The key order properties of \(\mathbb{N}\) are that it is well-ordered and every element of \(\mathbb{N}\) , except 0 , is the successor of a natural number:
WELL-ORDERING PRINCIPLE FOR THE NATURAL NUMBERS: The set \(\mathbb{N}\) is well-ordered by \(\leq\) .
SUCCESSOR PROPERTY FOR THE NATURAL NUMBERS: If \(n \in \mathbb{N}\) and \(n \neq 0\) , then there is \(m \in \mathbb{N}\) such that \(n=m+1\) .
If one accepts an intuitive understanding of the natural numbers, these principles are more or less obvious. Indeed, let \(Y\) be any nonempty subset of \(\mathbb{N}\) . Since it is non-empty, there is some \(m\) in \(Y\) . Now, consider each of the finitely many numbers \(0,1,2, \ldots, m\) in turn. If \(0 \in Y\) , then 0 is the least element. If 0 is not in \(Y\) , proceed to 1 . If this is in \(Y\) , it must be the least element; otherwise proceed to 2 . Continue in this way, and you will find some number less than or equal to \(m\) that is the least element of \(Y\) .
This argument, though convincing, does rely on the fact that we have an idea of what \(\mathbb{N}\) "is". If we wish to define \(\mathbb{N}\) in terms of set operations, as we do in Chapter 8, we essentially have to include the well-ordering principle for the natural numbers as an axiom.


5.9: Exercise- Global Field Power
-
- Last updated
- Save as PDF
Another useful reference-free transformation is mean global field power . If you have a reasonable number and spread of electrodes, any given ERP component will produce a systematic gradient in the amplitude across electrode sites that is proportional to the amplitude of the internal generator. For example, Screenshot 5.4 (which I generated with the Viewer in the Measurement Tool) overlays all 28 scalp electrodes for the unrelated-minus-related difference wave in the N400 experiment (referenced to the average of P9 and P10). The spread of voltage values across electrode sites is proportional to the amplitude of the N400. We can quantify this spread by taking the standard deviation across sites at any given time point. This standard deviation is called the global field power or GFP. Because the reference electrode contributes equally to each channel, it is effectively a constant and has no impact on the GFP.
Let’s compute the GFP for the data in the N400 data. L oad Grand_N400_diff.erp into ERPLAB if it’s not already loaded, and make sure that it’s the active ERPset. Select EEGLAB > ERPLAB > ERP Operations > ERP Channel Operations , clear out any equations that remain in the text box from the last time you used this routine, and change the Mode to Modify existing ERPset . We’re going to create a new channel (channel 31) with the GFP for the EEG channels (channels 1–28). To do this, put the following equation in the ERP Channel Operations text box:
ch31 = mgfperp(1:28) label GFP
Now click RUN , and then plot the data from Bin 5. At the bottom of the plot, you should see a channel labeled GFP (see Screenshot 5.5). This waveform is the standard deviation across channels 1–28 at each time point, and you can see that the time course matches the time course of the difference wave at the other electrode sites. However, when we look at the GFP, we no longer have to worry about that pesky reference electrode issue.
GFP has some other virtues as well. For example, it is typically cleaner than the individual-channel waveforms (because noise is typically minimized by transformations that combine the data from multiple sites). In addition, rather than having to choose which electrode site or sites to use in your statistical analyses (which can be a source of bias), you can just measure the amplitude or latency from the GFP waveform (Hamburger & Van der Burgt, 1991). However, you should keep in mind that the standard deviation across channels will increase as the noise level increases, so special methods are necessary to compare GFP amplitudes across conditions that differ in the number of trials or any other factor that might impact the noise level (Files et al., 2016).


1.3: Technology in Education - Looking at Fiction to Find Real Possibilities
-
- Last updated
- Save as PDF
In his “lost novel,” Paris in the 20th Century, science fiction author Jules Verne predicted gasoline-powered automobiles, high-speed trains, calculators, the concept of the Internet, and several other technologies invented well after 1863. Verne believed strongly that humans could realize all such predictions: “Anything one man can imagine, other men can make real” (Verne, n.d., para. 1). As scientists in various fields may have taken their cues from Jules Verne, we too can get some ideas about the future of technology and education from science fiction.
Looking at some science fiction within the past 15 years, we will start with predictions that are less farreaching than those contained within Jules Verne’s works. For example, in 1993 a low-grade action movie called Demolition Man depicted a teacher in the year 2023 talking to distance learners who attended class via individual video monitors placed around an empty table. The students’ heads, as shown on the monitors, followed the instructor’s movements as he paced around the room. Most or all aspects of this scenario are already possible with today’s videoconferencing solutions, high bandwidth connectivity, and cameras that use infrared beams to automatically follow a moving subject. Three years ago, Florence Olsen (2003) depicted immersive videoconferencing solutions with virtual students beamed into another classroom hundreds of miles away. In some cases, perhaps, Moore’s Law—computerprocessing power, measured by the number of transistors on integrated circuits, doubling every 18 months— makes it more difficult to look too far into the future because the future arrives so much more quickly.
At the same time, when we read Neal Stephenson’s The Diamond Age, we can see the potential to realize some of his predictions in less dramatic fashion. For example, when people first study sign language, they may dream about signing in full sentences, even though they cannot yet sign in the waking world. In this scenario, the brain contains the previously learned phrases in a mental “database” and stitches them together in new ways during the dream. Soon some instructional designer will put a comprehensive set of sign language video clips into an online database that will allow anyone to learn full sentences quickly by typing text and watching the dynamically generated compilation of the sign language equivalent. Additionally, education and technology have been combined to create tutoring software that learns what you know and steers you to specific lesson components that will fill your learning gaps. These “intelligent tutors” exist for math, accounting, physics, computer science, and other disciplines.
A final set of educational predictions in science fiction is too far out to tell if they are possible. In 1999, a film called The Matrix strongly contradicts William Butler Yeats, who said, “Education is not the filling of a pail, but the lighting of a fire” (Yeats, n.d., para. 1). In the film, the characters plug a cable into the back of their heads and go through “programs” that embed knowledge and skills directly into their brains. The lead character, Neo, becomes a martial arts expert in hours instead of years. Another character, Trinity, learns how to pilot a helicopter in seconds. In reality, humans have had little success linking computers to the brain. Recent developments, such as real-time brain control of a computer cursor (Hochber, Serruya, Friehs, Mukand, Saleh, Caplan, Branner, Chen, Penn & Donoghue, 2006), allow us to believe that some day Matrix-style education may be possible. By then, hopefully, we will have mastered how to teach higher level thinking skills, since this futuristic just-in-time learning presumably will let us skip over lower level skills.


4.2: What Is Consciousness?
Learning Objectives
- Understand what is meant by consciousness
- Explain how circadian rhythms are involved in regulating the sleep-wake cycle, and how circadian cycles can be disrupted
- Discuss the concept of sleep debt
Consciousness describes our awareness of internal and external stimuli. Awareness of internal stimuli includes feeling pain, hunger, thirst, sleepiness, and being aware of our thoughts and emotions. Awareness of external stimuli includes seeing the light from the sun, feeling the warmth of a room, and hearing the voice of a friend.
We experience different states of consciousness and different levels of awareness on a regular basis. We might even describe consciousness as a continuum that ranges from full awareness to a deep sleep. Sleep is a state marked by relatively low levels of physical activity and reduced sensory awareness that is distinct from periods of rest that occur during wakefulness. Wakefulness is characterized by high levels of sensory awareness, thought, and behavior. In between these extremes are states of consciousness related to daydreaming, intoxication as a result of alcohol or other drug use, meditative states, hypnotic states, and altered states of consciousness following sleep deprivation. We might also experience unconscious states of being via drug-induced anesthesia for medical purposes. Often, we are not completely aware of our surroundings, even when we are fully awake. For instance, have you ever daydreamed while driving home from work or school without really thinking about the drive itself? You were capable of engaging in the all of the complex tasks involved with operating a motor vehicle even though you were not aware of doing so. Many of these processes, like much of psychological behavior, are rooted in our biology.
Biological Rhythms
Biological rhythms are internal rhythms of biological activity. A woman’s menstrual cycle is an example of a biological rhythm—a recurring, cyclical pattern of bodily changes. One complete menstrual cycle takes about \(28\) days—a lunar month—but many biological cycles are much shorter. For example, body temperature fluctuates cyclically over a \(24\)-hour period. Alertness is associated with higher body temperatures, and sleepiness with lower body temperatures.
This pattern of temperature fluctuation, which repeats every day, is one example of a circadian rhythm. A circadian rhythm is a biological rhythm that takes place over a period of about \(24\) hours. Our sleep-wake cycle, which is linked to our environment’s natural light-dark cycle, is perhaps the most obvious example of a circadian rhythm, but we also have daily fluctuations in heart rate, blood pressure, blood sugar, and body temperature. Some circadian rhythms play a role in changes in our state of consciousness.
If we have biological rhythms, then is there some sort of biological clock ? In the brain, the hypothalamus, which lies above the pituitary gland, is a main center of homeostasis. Homeostasis is the tendency to maintain a balance, or optimal level, within a biological system.
The brain’s clock mechanism is located in an area of the hypothalamus known as the suprachiasmatic nucleus (SCN) . The axons of light-sensitive neurons in the retina provide information to the SCN based on the amount of light present, allowing this internal clock to be synchronized with the outside world (Klein, Moore, & Reppert, 1991; Welsh, Takahashi, & Kay, 2010).
Problems with Circadian Rhythms
Generally, and for most people, our circadian cycles are aligned with the outside world. For example, most people sleep during the night and are awake during the day. One important regulator of sleep-wake cycles is the hormone melatonin . The pineal gland , an endocrine structure located inside the brain that releases melatonin, is thought to be involved in the regulation of various biological rhythms and of the immune system during sleep (Hardeland, Pandi-Perumal, & Cardinali, 2006). Melatonin release is stimulated by darkness and inhibited by light.
There are individual differences with regards to our sleep-wake cycle. For instance, some people would say they are morning people, while others would consider themselves to be night owls. These individual differences in circadian patterns of activity are known as a person’s chronotype, and research demonstrates that morning larks and night owls differ with regard to sleep regulation (Taillard, Philip, Coste, Sagaspe, & Bioulac, 2003). Sleep regulation refers to the brain’s control of switching between sleep and wakefulness as well as coordinating this cycle with the outside world.
Disruptions of Normal Sleep
Whether lark, owl, or somewhere in between, there are situations in which a person’s circadian clock gets out of synchrony with the external environment. One way that this happens involves traveling across multiple time zones. When we do this, we often experience jet lag. Jet lag is a collection of symptoms that results from the mismatch between our internal circadian cycles and our environment. These symptoms include fatigue, sluggishness, irritability, and insomnia (i.e., a consistent difficulty in falling or staying asleep for at least three nights a week over a month’s time) (Roth, 2007).
Individuals who do rotating shift work are also likely to experience disruptions in circadian cycles. Rotating shift work refers to a work schedule that changes from early to late on a daily or weekly basis. For example, a person may work from 7:00 a.m. to 3:00 p.m. on Monday, 3:00 a.m. to 11:00 a.m. on Tuesday, and 11:00 a.m. to 7:00 p.m. on Wednesday. In such instances, the individual’s schedule changes so frequently that it becomes difficult for a normal circadian rhythm to be maintained. This often results in sleeping problems, and it can lead to signs of depression and anxiety. These kinds of schedules are common for individuals working in health care professions and service industries, and they are associated with persistent feelings of exhaustion and agitation that can make someone more prone to making mistakes on the job (Gold et al., 1992; Presser, 1995).
Rotating shift work has pervasive effects on the lives and experiences of individuals engaged in that kind of work, which is clearly illustrated in stories reported in a qualitative study that researched the experiences of middle-aged nurses who worked rotating shifts (West, Boughton & Byrnes, 2009). Several of the nurses interviewed commented that their work schedules affected their relationships with their family.  (West et al., 2009, p. 114)
While disruptions in circadian rhythms can have negative consequences, there are things we can do to help us realign our biological clocks with the external environment. Some of these approaches, such as using a bright light as shown in Figure \(\PageIndex{3}\), have been shown to alleviate some of the problems experienced by individuals suffering from jet lag or from the consequences of rotating shift work. Because the biological clock is driven by light, exposure to bright light during working shifts and dark exposure when not working can help combat insomnia and symptoms of anxiety and depression (Huang, Tsai, Chen, & Hsu, 2013).
Insufficient Sleep
When people have difficulty getting sleep due to their work or the demands of day-to-day life, they accumulate a sleep debt.  The consequences of sleep debt include decreased levels of alertness and mental efficiency. Interestingly, since the advent of electric light, the amount of sleep that people get has declined. While we certainly welcome the convenience of having the darkness lit up, we also suffer the consequences of reduced amounts of sleep because we are more active during the nighttime hours than our ancestors were. As a result, many of us sleep less than \(7-8\) hours a night and accrue a sleep debt. While there is tremendous variation in any given individual’s sleep needs, the National Sleep Foundation (n.d.) cites research to estimate that newborns require the most sleep (between \(12\) and \(18\) hours a night) and that this amount declines to just \(7-9\) hours by the time we are adults.
If you lie down to take a nap and fall asleep very easily, chances are you may have sleep debt. Given that college students are notorious for suffering from significant sleep debt (Hicks, Fernandez, & Pelligrini, 2001; Hicks, Johnson, & Pelligrini, 1992; Miller, Shattuck, & Matsangas, 2010), chances are you and your classmates deal with sleep debt-related issues on a regular basis. The table below shows recommended amounts of sleep at different ages.
| Age | Nightly Sleep Needs |
|---|---|
| 0–3 months | 12–18 hours |
| 3 months–1 year | 14–15 hours |
| 1–3 years | 12–14 hours |
| 3–5 years | 11–13 hours |
| 5–10 years | 10–11 hours |
| 10–18 years | 8–10 hours |
| 18 and older | 7–9 hours |
Sleep debt and sleep deprivation have significant negative psychological and physiological consequences. As mentioned earlier, lack of sleep can result in decreased mental alertness and cognitive function. In addition, sleep deprivation often results in depression-like symptoms. These effects can occur as a function of accumulated sleep debt or in response to more acute periods of sleep deprivation. It may surprise you to know that sleep deprivation is associated with obesity, increased blood pressure, increased levels of stress hormones, and reduced immune functioning (Banks & Dinges, 2007). A sleep deprived individual generally will fall asleep more quickly than if she were not sleep deprived. Some sleep-deprived individuals have difficulty staying awake when they stop moving (example sitting and watching television or driving a car). That is why individuals suffering from sleep deprivation can also put themselves and others at risk when they put themselves behind the wheel of a car or work with dangerous machinery. Some research suggests that sleep deprivation affects cognitive and motor function as much as, if not more than, alcohol intoxication (Williamson & Feyer, 2000).
The amount of sleep we get varies across the lifespan. When we are very young, we spend up to 16 hours a day sleeping. As we grow older, we sleep less. In fact, a meta-analysis , which is a study that combines the results of many related studies, conducted within the last decade indicates that by the time we are \(65\) years old, we average fewer than \(7\) hours of sleep per day (Ohayon, Carskadon, Guilleminault, & Vitiello, 2004). As the amount of time we sleep varies over our lifespan, presumably the sleep debt would adjust accordingly.
Summary
States of consciousness vary over the course of the day and throughout our lives. Important factors in these changes are the biological rhythms, and, more specifically, the circadian rhythms generated by the suprachiasmatic nucleus (SCN). Typically, our biological clocks are aligned with our external environment, and light tends to be an important cue in setting this clock. When people travel across multiple time zones or work rotating shifts, they can experience disruptions of their circadian cycles that can lead to insomnia, sleepiness, and decreased alertness. Bright light therapy has shown to be promising in dealing with circadian disruptions. If people go extended periods of time without sleep, they will accrue a sleep debt and potentially experience a number of adverse psychological and physiological consequences.
Glossary
- biological rhythm
- internal cycle of biological activity
- circadian rhythm
- biological rhythm that occurs over approximately 24 hours
- consciousness
- awareness of internal and external stimuli
- homeostasis
- tendency to maintain a balance, or optimal level, within a biological system
- insomnia
- consistent difficulty in falling or staying asleep for at least three nights a week over a month’s time
- jet lag
- collection of symptoms brought on by travel from one time zone to another that results from the mismatch between our internal circadian cycles and our environment
- melatonin
- hormone secreted by the endocrine gland that serves as an important regulator of the sleep-wake cycle
- meta-analysis
- study that combines the results of several related studies
- pineal gland
- endocrine structure located inside the brain that releases melatonin
- rotating shift work
- work schedule that changes from early to late on a daily or weekly basis
- sleep
- state marked by relatively low levels of physical activity and reduced sensory awareness that is distinct from periods of rest that occur during wakefulness
- sleep debt
- result of insufficient sleep on a chronic basis
- sleep regulation
- brain’s control of switching between sleep and wakefulness as well as coordinating this cycle with the outside world
- suprachiasmatic nucleus (SCN)
- area of the hypothalamus in which the body’s biological clock is located
- wakefulness
- characterized by high levels of sensory awareness, thought, and behavior
Contributors and Attributions
-
Rose M. Spielman with many significant contributors. The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the creative commons license and may not be reproduced without the prior and express written consent of Rice University. For questions regarding this license, please contact<EMAIL_ADDRESS>.Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>.


6.5: Choosing a Topic
- Analyze strategies for choosing a topic for a paper
How Do I Pick a Topic?
Have you ever been stressed out because you can’t think of a good topic for an important writing assignment? You’re not alone. As a student, you’d probably prefer it if professors would just assign topics rather than leave you to find one on your own. However, professors aren’t vague because they want to punish you; they usually just don’t want to constrain your creativity or discourage you from writing about topics that truly interest you. Professors also want to be surprised by their students’ ingenuity, and very few teachers want to read a big stack of essays all on the same stale topic. Unfortunately, just being told to “be creative” is unlikely to calm you down when you have a major paper due next week and still haven’t found a topic to write about.
Imagine that you are in an introductory literature course. The professor has assigned a 3-5 page essay on a Shakespearean play that requires multiple sources. You try asking the professor to be more specific or offer some suggestions. The professor responds, “No, it’s up to you. Surprise me.” What do you do?
One smart option is to go to the library and look for scholarly journals that cover Shakespearean studies. In today’s environment, much of these journals are housed electronically in databases your college library subscribes to. You might also try scholarly books about Shakespeare and his plays. Browsing these sources should give you some ideas about the aspects of Shakespeare and his plays that scholars have found worth writing about. You might find that an idea that you thought was “totally original” has already been done. However, you shouldn’t let this worry you. If every essay or book had to be 100% original, we’d have precious few to read.
If you keep reading and skimming articles and books, you will find many different discussions and possibilities for writing topics. One way to do this is to write a list of binaries, a list of opposing ideas that may represent larger discussions about the topic at hand. Choosing from these opposing ideas in the text will lead you to ideas for a more specific argument. Scholars frequently engage in complex and long-lasting arguments that span across different journal articles and books. Professor X’s article on climate change will be mentioned, discussed, or challenged by Professor Y in a book and Professor Z in another article. None of them are worried about saying things that have never been said before; the key is just to say them differently and perhaps better.
You will always have one advantage over any other scholar you read—their articles and books cannot take advantage of all the relevant scholarship that appeared after their publication date. Don’t be afraid to freshen up an old article with new supporting evidence—or challenge one whose conclusions are called into question by subsequent research.
You should also look for an issue that you can reasonably cover given the time and space (page count) you have available. After that, it’s a simple matter of supporting your argument by bringing in relevant quotations from those who agree with you. You should also identify the counter-arguments and provide pertinent background information. In essence, the easiest way to find a topic to write about is to see what other writers are writing about and join their “conversation.” The conversation metaphor is a very useful way to understand what scholarship is all about.
Rather than thinking of essays or books as isolated units of scholarship, try envisioning them as the fruits of a massive network of scholars who converse with each other via scholarly documents, conference presentations, e-mail, phone calls, and other forms of communication. Research what is available and where you can make the most valuable contribution.
The following video demonstrates the process of selecting and refining a research topic.
You can find the transcript for “Research Tutorial: Developing Your Topic” here (opens in new window) .
The Problem of Topic vs. Approach
Some instructors who assign writing projects will leave the choice of what to write about up to you. Others will have a very defined set of topics for you to write from. But even when an instructor assigns a given topic or offers a choice of assigned topics, you have a lot of opportunity for creativity.
The real issue here is the approach. When you come to an assigned essay as a project, how you first engage with it will determine your overall experience. Some students see any writing assignment as an externally imposed task—something they have to do in order to pass the course. This approach will guarantee that those students will eventually hate their assignments, possibly their instructor, and when push comes to shove the whole prospect of being in school.
Solution: Choosing an Approach to Your Topic
Deliberately choosing how you approach your topic will help you not only choose one that will satisfy the requirements, but also ensure that you enjoy the process of research and writing. After all, no one on earth can do what you do. So, only you can figure out how to write a great essay in your own voice.
It all starts with selecting a topic. How you approach that selection process is vastly important.
Look to things that interest you as a way of finding your paper topic! Use that initial fascination to twist the topic of your paper so that it becomes an excuse to wallow in whatever got you interested in that class in the first place.
Avoiding the Pit of Despair
Whatever you do, don’t fall into the trap of thinking that your work is simply a required box that needs to be checked and you can’t bring any creativity to the table. Even if the class was required for your program or degree, you still chose that program. There are ways to make almost any writing task enjoyable, or at least something you gain something interesting out of.
Narrowing a Broad Topic
Once you’ve settled on a general topic or problem to address for a writing assignment, the next step is to narrow it down to an appropriate focus.
Narrowing a topic can be done in various ways. Most of the time you will need to use two or more of the following strategies. However, the requirements and scope of your assignment will determine which ones you use.
To narrow a topic, ask yourself the following questions.
- Can you focus your project on a specific aspect of the topic?
Most issues or concepts can be subdivided into narrower issues or concepts. If you can’t subdivide your topic, then, most of the time, your topic is as narrow as it can get. In addition, it is probably better suited to a short or small project than a long or substantial one.
In some cases, you might find you need to expand, rather than narrow, a topic selection.
- Can you narrow your topic to a specific time period?
Restricting your topic to a specific time period can narrow most topics. Many activities or things exist through time. Restricting yourself to that activity or thing within a specific time period reduces the amount of material you have to cover.
For example, armies and soldiers have existed from before recorded history. Restricting yourself to “Army life during World War II” or “Army life in Ancient Egypt” reduces the scope of what you need to cover.
HINT: there is likely to be a lot more primary and secondary material on army life in World War II than there is on army life in ancient Egypt simply because more information from recent centuries has survived than from ancient centuries.
- Can you narrow your topic to a specific geographic area?
Many topics can be limited to a specific region of the country or the world. For example, “Wolves” can be limited to “Arctic Wolves.”
- Can you narrow your topic to a specific event?
Restricting your topic to a specific event is another way to narrow a topic. However, the amount of information available on a specific event will depend upon the relative importance of that event.
For example, you will find more information on the atomic bombs dropped on Hiroshima and Nagasaki than you will on the bomb used by robbers to blow up the safe of a bank.
Contributors and Attributions
- Modification, adaptation, and original content. Provided by : Lumen Learning. License : CC BY-SA: Attribution-ShareAlike
- Picking a Topic for Your Essay. Authored by : Legible Larry. Provided by : Writing Spaces. Located at : www.thepaperexperts.com/blog/2013/04/picking-a-topic-for-your-essay.html. Project : The Paper Experts Notepad. License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike
- How do I pick a topic?. Authored by : Marianne Botos, Lynn McClelland, Stephanie Polliard, Pamela Osback . Located at : https://pvccenglish.files.wordpress.com/2010/09/eng-101-inside-pages-proof2-no-pro.pdf . Project : Horse of a Different Color: English Composition and Rhetoric . License : CC BY-SA: Attribution-ShareAlike
- Strategies for narrowing a topic. Provided by : Virginia Tech University Libraries. Located at : http://info-skills.lib.vt.edu/choosing_focusing/11.html . Project : Information Skills Modules. License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike
- Research Tutorial: Developing Your Topic. Provided by : UNC Libraries. Located at : https://www.youtube.com/watch?v=x4XZxIqSuyY . License : All Rights Reserved . License Terms : Standard YouTube License


Skip to main content
7: Molecular and Solid State Structure
-
-
Last updated
-
-
Save as PDF
-
-
-
7.1: Crystal Structure
-
In any sort of discussion of crystalline materials, it is useful to begin with a discussion of crystallography: the study of the formation, structure, and properties of crystals. A crystal structure is defined as the particular repeating arrangement of atoms (molecules or ions) throughout a crystal. Structure refers to the internal arrangement of particles and not the external appearance of the crystal. However, these are not entirely independent.
-
-
7.2: Structures of Element and Compound Semiconductors
-
A single crystal of either an elemental (e.g., silicon) or compound (e.g., gallium arsenide) semiconductor forms the basis of almost all semiconductor devices. The ability to control the electronic and opto-electronic properties of these materials is based on an understanding of their structure. In addition, the metals and many of the insulators employed within a microelectronic device are also crystalline.
-
-
7.3: X-ray Crystallography
-
The significance of this for chemistry is that given this fact, crystalline solids will be easily identifiable once a database has been established. Much like solving a puzzle, crystal structures of heterogeneous compounds could be solved very methodically by comparison of chemical composition and their interactions.
-
-
7.4: Low Energy Electron Diffraction
-
Low energy electron diffraction (LEED) is a very powerful technique that allows for the characterization of the surface of materials. Its high surface sensitivity is due to the use of electrons with energies between 20-200 eV, which have wavelengths equal to 2.7 – 0.87 Å (comparable to the atomic spacing). Therefore, the electrons can be elastically scattered easily by the atoms in the first few layers of the sample. Its features, such as little penetration of low–energy electrons have positione
-
-
7.5: Neutron Diffraction
-
The first neutron diffraction experiment was in 1945 by Ernest O. Wollan using the Graphite Reactor at Oak Ridge. Along with Clifford Shull they outlined the principles of the technique. However, the concept that neutrons would diffract like X-rays was first proposed by Dana Mitchell and Philip Powers. They proposed that neutrons have a wave like structure, which is explained by the de Broglie equation.
-
-
7.6: XAFS
-
X-ray absorption fine structure (XAFS) spectroscopy includes both X-ray absorption near edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) spectroscopies. The difference between both techniques is the area to analyze and the information each technique provides.
-
-
7.7: Circular Dichroism Spectroscopy and its Application for Determination of Secondary Structure of Optically Active Species
-
Circular dichroism (CD) spectroscopy is one of few structure assessmet methods that can be utilized as an alternative and amplification to many conventional analysis techniques with advatages such as rapid data collection and ease of use. Since most of the efforts and time spent in advancement of chemical sciences are devoted to elucidation and analysis of structure and composition of synthesized molecules or isolated natural products rather than their preparation, one should be aware of all the
-
-
7.8: Protein Analysis using Electrospray Ionization Mass Spectroscopy
-
Electrospray ionization-mass spectrometry (ESI-MS) is an analytical method that focuses on macromolecular structural determination. The unique component of ESI-MS is the electrospray ionization. The development of electrospraying, the process of charging a liquid into a fine aerosol, was completed in the 1960’s when Malcolm Dole.
-
-
7.9: The Analysis of Liquid Crystal Phases using Polarized Optical Microscopy
-
Liquid crystals are a state of matter that has the properties between solid crystal and common liquid.
Template:HideTOC


14.14: Introduction to Analyzing Data
What you’ll learn to do: Analyze data
In this section we will explore a variety of topics that support data analysis. First, data must be “cleaned” in order to be useful. This process is known as data transformation and Access has several features that aid in preparing data for analysis purposes. Next, we will explore the rich set of calculations built-in to Access to be used for data analysis. Finally, we will touch on some more complex topics: conditional analysis and subqueries—very powerful tools of relational databases to get the most of data analysis.
Contributors and Attributions
CC licensed content, Original
- Introduction to Analyzing Data. Authored by : Robert Danielson. Provided by : Lumen Learning. License : CC BY: Attribution


10.2: Digestive System Infections
Gastrointestinal (GI) diseases are so common that, unfortunately, most people have had first-hand experience with the unpleasant symptoms, such as diarrhea, vomiting, and abdominal discomfort. The causes of gastrointestinal illness can vary widely, but such diseases can be grouped into two categories: those caused by infection (the growth of a pathogen in the GI tract) or intoxication (the presence of a microbial toxin in the GI tract).
Foodborne pathogens like Escherichia coli O157:H7 are among the most common sources of gastrointestinal disease. Contaminated food and water have always posed a health risk for humans, but in today’s global economy, outbreaks can occur on a much larger scale. E. coli O157:H7 is a potentially deadly strain of E. coli with a history of contaminating meat and produce that are not properly processed. The source of an E. coli O157:H7 outbreak can be difficult to trace, especially if the contaminated food is processed in a foreign country. Once the source is identified, authorities may issue recalls of the contaminated food products, but by then there are typically numerous cases of food poisoning, some of them fatal.
-
- 10.2.1: Anatomy and Normal Microbiota of the Digestive System
- The human digestive system, or the gastrointestinal (GI) tract, begins with the mouth and ends with the anus. The parts of the mouth include the teeth, the gums, the tongue, the oral vestibule (the space between the gums, lips, and teeth), and the oral cavity proper (the space behind the teeth and gums). Other parts of the GI tract are the pharynx, esophagus, stomach, small intestine, large intestine, rectum, and anus.
-
- 10.2.2: Microbial Diseases of the Mouth and Oral Cavity
- Despite the presence of saliva and the mechanical forces of chewing and eating, some microbes thrive in the mouth. These microbes can cause damage to the teeth and can cause infections that have the potential to spread beyond the mouth and sometimes throughout the body.
-
- 10.2.3: Bacterial Infections of the Gastrointestinal Tract
- Major causes of gastrointestinal illness include Salmonella spp., Staphylococcus spp., Helicobacter pylori, Clostridium perfringens, Clostridium difficile, Bacillus cereus, and Yersinia bacteria. C. difficile is an important cause of hospital acquired infection. Vibrio cholerae causes cholera, which can be a severe diarrheal illness. Different strains of E. coli, including ETEC, EPEC, EIEC, and EHEC, cause different illnesses with varying degrees of severity.
-
- 10.2.4: Viral Infections of the Gastrointestinal Tract
- Common viral causes of gastroenteritis include rotaviruses, noroviruses, and astroviruses. Hepatitis may be caused by several unrelated viruses: hepatitis viruses A, B, C, D, and E. The hepatitis viruses differ in their modes of transmission, treatment, and potential for chronic infection.
-
- 10.2.5: Protozoan Infections of the Gastrointestinal Tract
- Like other microbes, protozoa are abundant in natural microbiota but can also be associated with significant illness. Gastrointestinal diseases caused by protozoa are generally associated with exposure to contaminated food and water, meaning that those without access to good sanitation are at greatest risk. Even in developed countries, infections can occur and these microbes have sometimes caused significant outbreaks from contamination of public water supplies.
-
- 10.2.6: Helminthic Infections of the Gastrointestinal Tract
- Helminths are widespread intestinal parasites. These parasites can be divided into three common groups: round-bodied worms also described as nematodes, flat-bodied worms that are segmented (also described as cestodes), and flat-bodied worms that are non-segmented (also described as trematodes). The nematodes include roundworms, pinworms, hookworms, and whipworms. Many of these parasites are so well adapted to the human host that there is little obvious disease.
Thumbnail: This is an adult Taenia saginata tapeworm. Humans become infected by ingesting raw or undercooked infected meat. In the human intestine, the cysticercus develops over 2 mo. into an adult tapeworm, which can survive for years, attaching to, and residing in the small intestine. (Public Domain; UC CDC)


20.5: Chapter 5 (Safety)
Answer Key to Chapter 5 Learning Activities
1. Risk factors: hip fracture, morphine pain medication, diminished eyesight and hearing, ambulates with walker, weakness, experience of recent fall.
2. Morse Fall Risk Assessment Scoring:
- History of fall – 25
- Walker – 15
- Weak Gait -10
- Total: 50 – High Risk
3. Interventions to address risk factors:
- Provide adequate lighting and night-light
- Use of half rails
- Encourage rest
- Place articles within reach at bedside
- Use elevated toilet seat in bathroom
- Use assistive devices, glasses and hearing aids
- Obtain orthostatic blood pressures
- Wear shoes or slippers with non-skid soles
4. Potential response: “Mr. Moore, your safety is most important and we need to ensure you do not fall. If you have a bowel movement, we will clean it up. Moving forward, it may be helpful for us to have a commode chair closer to your bedside so we do not need to travel so far if urgency arises.”
Answers to interactive elements are given within the interactive element.


15.E: The Sun- A Garden-Variety Star (Exercises)
For Further Exploration
Articles
Berman, B.  Astronomy (September 2013): 22. Up-to-date review of how events on the Sun can hurt our civilization.
Frank, A. “Blowin’ in the Solar Wind.” Astronomy (October 1998): 60. On results from the SOHO spacecraft.
Holman, G. “The Mysterious Origins of Solar Flares.” Scientific American (April 2006): 38. New ideas involving magnetic reconnection and new observations of flares.
James, C. “Solar Forecast: Storm Ahead.” Sky & Telescope (July 2007): 24. Nice review on the effects of the Sun’s outbursts and on Earth and how we monitor “space weather.”
Schaefer, B. “Sunspots That Changed the World.” Sky & Telescope (April 1997): 34. Historical events connected with sunspots and solar activity.
Schrijver, C. and Title, A. “Today’s Science of the Sun.” Sky & Telescope (February 2001): 34; (March 2001): 34. Excellent reviews of recent results about the solar atmosphere.
Wadhwa, M. “Order from Chaos: Genesis Samples the Solar Wind.” Astronomy (October 2013): 54. On a satellite that returned samples of the Sun’s wind.
Websites
Dr. Sten Odenwald’s “Solar Storms” site: http://www.solarstorms.org/ .
ESA/NASA’s Solar & Heliospheric Observatory: http://sohowww.nascom.nasa.gov . A satellite mission with a rich website to explore.
High Altitude Observatory Introduction to the Sun: www.hao.ucar.edu/education/basic.php. For beginners.
NASA’s Solar Missions: https://www.nasa.gov/mission_pages/s...ons/index.html . Good summary of the many satellites and missions NASA has.
NOAA Profile of Space Weather: www.swpc.noaa.gov/sites/defau...r_2010_new.pdf. A primer.
NOAA Space Weather Prediction Center Information Pages: www.swpc.noaa.gov/content/edu...n-and-outreach. Includes primers, videos, a curriculum and training modules.
Nova Sun Lab: http://www.pbs.org/wgbh/nova/labs/lab/sun/ . Videos, scientist profiles, a research challenge related to the active Sun from the PBS science program.
Space Weather: Storms on the Sun: www.swpc.noaa.gov/sites/defau...wx_booklet.pdf. An illustrated booklet from NOAA.
Stanford Solar Center: http://solar-center.stanford.edu/ . An excellent site with information for students and teachers.
Apps
These can tell you and your students more about what’s happening on the Sun in real time.
NASA’s 3-D Sun: http://3dsun.org/ .
NASA Space Weather: itunes.apple.com/us/app/nasa...422621403?mt=8.
Solaris Alpha: play.google.com/store/apps/d...y.solarisalpha.
Solar Monitor Pro: www.solarmonitor.eu/.
Videos
Journey into the Sun: https://www.youtube.com/watch?v=fqKFQ7z0Nuk . 2010 KQED Quest TV Program mostly about the Solar Dynamics Observatory spacecraft, its launch and capabilities, but with good general information on how the Sun works (12:24).
NASA | SDO: Three Years in Three Minutes--With Expert Commentary: https://www.youtube.com/watch?v=QaCG0wAjJSY&src . Video of 3 years of observations of the Sun by the Solar Dynamics Observatory made into a speeded up movie, with commentary by solar physicist Alex Young (5:03).
Our Explosive Sun: http://www.youtube.com/watch?v=kI6YGSIJqrE . Video of a 2011 public lecture in the Silicon Valley Astronomy Lecture Series by Dr. Thomas Berger about solar activity and recent satellite missions to observe and understand it (1:20:22).
Out There Raining Fire: www.nytimes.com/video/science....html?emc=eta1. Nice overview and introduction to the Sun by science reporter Dennis Overbye of the NY Times (2:28)
Space Weather Impacts: www.swpc.noaa.gov/content/edu...n-and-outreach. Video from NOAA (2:47); https://www.youtube.com/playlist?lis...bIUzBO6JI0Pvx0 . Videos from the National Weather Service (four short videos) (14:41).
Space Weather: Storms on the Sun: http://www.youtube.com/watch?v=vWsmp4o-qVg . Science bulletin from the American Museum of Natural History, giving the background to what happens on the Sun to cause space weather (6:10).
Sun Storms: www.livescience.com/11754-sun...nic-world.html. From the Starry Night company about storms from the Sun now and in the past (4:49).
Sunspot Group AR 2339 Crosses the Sun: http://apod.nasa.gov/apod/ap150629.html .
What Happens on the Sun Doesn’t Stay on the Sun: https://www.youtube.com/watch?v=bg_gD2-ujCk . From the National Oceanic and Atmospheric Administration: introduction to the Sun, space weather, its effects, and how we monitor it (4:56).
Collaborative Group Activities
- Have your group make a list of all the ways the Sun personally affects your life on Earth. (Consider the everyday effects as well as the unusual effects due to high solar activity.)
- Long before the nature of the Sun was fully understood, astronomer (and planet discoverer) William Herschel (1738–1822) proposed that the hot Sun may have a cool interior and may be inhabited. Have your group discuss this proposal and come up with modern arguments against it.
- We discussed how the migration of Europeans to North America was apparently affected by short-term climate change. If Earth were to become significantly hotter, either because of changes in the Sun or because of greenhouse warming, one effect would be an increase in the rate of melting of the polar ice caps. How would this affect modern civilization?
- Suppose we experience another Maunder Minimum on Earth, and it is accompanied by a drop in the average temperature like the Little Ice Age in Europe. Have your group discuss how this would affect civilization and international politics. Make a list of the most serious effects that you can think of.
- Watching sunspots move across the disk of the Sun is one way to show that our star rotates on its axis. Can your group come up with other ways to show the Sun’s rotation?
- Suppose in the future, we are able to forecast space weather as well as we forecast weather on Earth. And suppose we have a few days of warning that a big solar storm is coming that will overload Earth’s magnetosphere with charged particles and send more ultraviolet and X-rays toward our planet. Have your group discuss what steps we might take to protect our civilization?
- Have your group members research online to find out what satellites are in space to help astronomers study the Sun. In addition to searching for NASA satellites, you might also check for satellites launched by the European Space Agency and the Japanese Space Agency.
- Some scientists and engineers are thinking about building a “solar sail”—something that can use the Sun’s wind or energy to propel a spacecraft away from the Sun. The Planetary Society is a nonprofit organization that is trying to get solar sails launched, for example. Have your group do a report on the current state of solar-sail projects and what people are dreaming about for the future.
Review Questions
- Describe the main differences between the composition of Earth and that of the Sun.
- Describe how energy makes its way from the nuclear core of the Sun to the atmosphere. Include the name of each layer and how energy moves through the layer.
- Make a sketch of the Sun’s atmosphere showing the locations of the photosphere, chromosphere, and corona. What is the approximate temperature of each of these regions?
- Why do sunspots look dark?
- Which aspects of the Sun’s activity cycle have a period of about 11 years? Which vary during intervals of about 22 years?
- Summarize the evidence indicating that over several hundreds of years or more there have been variations in the level of the solar activity.
- What it the Zeeman effect and what does it tell us about the Sun?
- Explain how the theory of the Sun’s dynamo results in an average 22-year solar activity cycle. Include the location and mechanism for the dynamo.
- Compare and contrast the four different types of solar activity above the photosphere.
- What are the two sources of particles coming from the Sun that cause space weather? How are they different?
- How does activity on the Sun affect human technology on Earth and in the rest of the solar system?
- How does activity on the Sun affect natural phenomena on Earth?
Thought Questions
- Table \(15.1.1\) indicates that the density of the Sun is 1.41 g/cm 3 . Since other materials, such as ice, have similar densities, how do you know that the Sun is not made of ice?
- Starting from the core of the Sun and going outward, the temperature decreases. Yet, above the photosphere, the temperature increases. How can this be?
- Since the rotation period of the Sun can be determined by observing the apparent motions of sunspots, a correction must be made for the orbital motion of Earth. Explain what the correction is and how it arises. Making some sketches may help answer this question.
- Suppose an (extremely hypothetical) elongated sunspot forms that extends from a latitude of 30° to a latitude of 40° along a fixed of longitude on the Sun. How will the appearance of that sunspot change as the Sun rotates? (Figure \(15.2.5\) should help you figure this out.)
- The text explains that plages are found near sunspots, but Figure \(15.2.6\) shows that they appear even in areas without sunspots. What might be the explanation for this?
- Why would a flare be observed in visible light, when they are so much brighter in X-ray and ultraviolet light?
- How can the prominences, which are so big and ‘float’ in the corona, stay gravitationally attached to the Sun while flares can escape?
- If you were concerned about space weather and wanted to avoid it, where would be the safest place on Earth for you to live?
- Suppose you live in northern Canada and an extremely strong flare is reported on the Sun. What precautions might you take? What might be a positive result?
Figuring for Yourself
- The edge of the Sun doesn’t have to be absolutely sharp in order to look that way to us. It just has to go from being transparent to being completely opaque in a distance that is smaller than your eye can resolve. Remember from Astronomical Instruments that the ability to resolve detail depends on the size of the telescope’s aperture. The pupil of your eye is very small relative to the size of a telescope and therefore is very limited in the amount of detail you can see. In fact, your eye cannot see details that are smaller than 1/30 of the diameter of the Sun (about 1 arcminute). Nearly all the light from the Sun emerges from a layer that is only about 400 km thick. What fraction is this of the diameter of the Sun? How does this compare with the ability of the human eye to resolve detail? Suppose we could see light emerging directly from a layer that was 300,000 km thick. Would the Sun appear to have a sharp edge?
- Show that the statement that 92% of the Sun’s atoms are hydrogen is consistent with the statement that 73% of the Sun’s mass is made up of hydrogen, as found in Table \(15.1.2\). (Hint: Make the simplifying assumption, which is nearly correct, that the Sun is made up entirely of hydrogen and helium.)
- From Doppler shifts of the spectral lines in the light coming from the east and west edges of the Sun, astronomers find that the radial velocities of the two edges differ by about 4 km/s, meaning that the Sun’s rotation rate is 2 km/s. Find the approximate period of rotation of the Sun in days. The circumference of a sphere is given by 2π R , where R is the radius of the sphere.
- Assuming an average sunspot cycle of 11 years, how many revolutions does the equator of the Sun make during that one cycle? Do higher latitudes make more or fewer revolutions compared to the equator?
- This chapter gives the average sunspot cycle as 11 years. Verify this using Figure \(15.4.3\).
- The escape velocity from any astronomical object can be calculated as \(v_{\text{escape}} = \sqrt{2GM/R}\). Using the data in Appendix E, calculate the escape velocity from the photosphere of the Sun. Since coronal mass ejections escape from the corona, would the escape velocity from there be more or less than from the photosphere?
- Suppose you observe a major solar flare while astronauts are orbiting Earth. Use the data in the text to calculate how long it will before the charged particles ejected from the Sun during the flare reach them.
- Suppose an eruptive prominence rises at a speed of 150 km/s. If it does not change speed, how far from the photosphere will it extend after 3 hours? How does this distance compare with the diameter of Earth?
- From the information in Figure \(15.3.4\), estimate the speed with which the particles in the CME in parts (c) and (d) are moving away from the Sun.


6.2: Separation and confirmation of individual ions in group IV precipitates and group V mixture
Separating and confirming barium ion
The precipitates of Group IV cations, i.e., \(\ce{CaCO3}\) and \(\ce{BaCO3}\) are soluble in acidic medium. In these experiments acetic acid \(\ce{CH3COOH}\) is used to make the solution acidic that results in the dissolution of \(\ce{CaCO3}\) and \(\ce{BaCO3}\):
\[\ce{4CH3COOH(aq) + 4H2O(l) <=> 4CH3COO^{-}(aq) + 4H3O^{+}(aq)}\nonumber\]
\[\ce{CaCO3(s, white) <=> Ca^{2+}(aq) + CO3^{2-}(aq)}\nonumber\]
\[\ce{BaCO3(s, white) <=> Ba^{2+}(aq) + CO3^{2-}(aq)}\nonumber\]
\[\ce{2CO3^{2-}(aq) + 4H3O^{+}(aq) <=> 2H2CO3(aq) +4H2O(l)}\nonumber\]
\[\ce{2H2CO3(aq) <=> 2H2O(l) + 2CO2(g)(^)}\nonumber\]
\[\text{Overall reaction: }\ce{~4CH3COOH(aq) + CaCO3(s, white) + BaCO3(s, white) <=> 4CH3COO^{-}(aq) + Ca^{2+} + Ba^{2+} + 2H2O(l) + 4CO2(g)(^)}\nonumber\]
\(\ce{CO3^{2-}}\) ion is a weak base that reacts with \(\ce{H3O^{+}}\) and forms carbonic acid (\(\ce{H2CO3}\). Carbonic acid is unstable in water and decomposes into carbon dioxide and water. Carbon dioxide leaves the solution that drives the reactions forward, as shown in Figure \(\PageIndex{1}\).
The Acetate ion (\(\ce{CH3COO^{-}}\)) produced in the above reactions is a conjugate base of a weak acid acetic acid (\(\ce{CH3COOH}\)). More acetic acid is added to the solution to make a \(\ce{CH3COOH}\)/\(\ce{CH3COO^{-}}\) buffer that can maintain \(pH\) at ~5.
Potassium chromate (\(\ce{K2CrO4}\)) solution is added at this stage that introduces chromate ion \(\ce{CrO4^{2-}}\):
\[\ce{K2CrO4(s) <=> 2K^{+}(aq) + CrO4^{2-}(aq)}\nonumber\]
Although both calcium and barium ions form insoluble salt with chromate ion (\(\ce{CaCrO4}\) \(K_{sp}\) = 7.1 x 10 -4 and \(\ce{BaCrO4}\) \(K_{sp}\) = 1.8 x 10 -10 ), \(\ce{BaCrO4}\) is less soluble and can be selectively precipitated by controlling \(\ce{CrO4^{2-}}\) concentration. The chromate ion is involved in the following \(pH\) dependent equilibrium:
\[\ce{2CrO4^{2-}(aq) + 2H3O^{+}(aq) <=> Cr2O7^{2-}(aq) + 3H2O(l)}\quad K = 4.0\times10^{14}\nonumber\]
At \(pH\) ~5 in a \(\ce{CH3COOH}\)/\(\ce{CH3COO^{-}}\) buffer, the concentration of \(\ce{CrO4^{2-}}\) is enough to selectively precipitate barium ions leaving calcium ions in the solution:
\[\ce{Ba^{2+}(aq) + CrO4^{2-}(aq) <=> BaCrO4(s, light~yellow)(v)}\nonumber\]
The mixture is centrifuged and decanted to separate \(\ce{BaCrO4}\) precipitate from the supernatant containing \(\ce{Ca^{2+}}\) ions as shown in Figure \(\PageIndex{2}\). Although the formation of a light yellow precipitate (\(\ce{BaCrO4}\) ) at this stage is a strong indication that \(\ce{Ba^{2+}}\) is present in the test sample, \(\ce{Ca^{2+}}\) may also form a light yellow precipitate (\(\ce{CaCrO4}\) ), particularly if pH is higher than the recommended value of 5.
Group IV and V cations are most often confirmed by the flame test. Figure \(\PageIndex{3}\) shows the flame test results of group IV cations. The presence of barium is further confirmed by a flame test. For this purpose, \(\ce{BaCrO4}\) precipitate is treated with 12M \(\ce{HCl}\). The concentrated \(\ce{HCl}\) removes \(\ce{CrO4^{2-}}\) by converting it to dichromate (\(\ce{Cr2O7^{2-}}\)) that resulting in the dissolution of \(\ce{BaCrO4}\):
\[\ce{2BaCrO4(s, light~yellow) <=> 2Ba^{2+}(aq) + 2CrO4^{2-}(aq)}\nonumber\]
\[\ce{2CrO4^{2-}(aq) + 2H3O^{+}(aq) <=> Cr2O7^{2-}(aq) + 3H2O(l)}\nonumber\]
A flame test is applied to the solution. \(\ce{Ba^{2+}}\) imparts characteristic yellow-green color to the flame. If the yellow-green color is observed in the flame test, it confirms \(\ce{Ba^{2+}}\) is present in the test sample.
Confirming calcium ion
The \(\ce{Ca^{2+}}\) present in the supernatant is precipitated by adding oxalate ion (\(\ce{C2O4^{2-}}\)):
\[\ce{Ca^{2+}(aq) + C2O4^{2-}(aq) <=> CaC2O4(s, white)(v)}\nonumber\]
The formation of white precipitate, i.e., \(\ce{CaC2O4}\) shown in Figure \(\PageIndex{4}\), is a strong indication that \(\ce{Ca^{2+}}\) is present in the test sample. However, if \(\ce{Ba^{2+}}\) is not fully separated earlier, it also forms a white precipitate \(\ce{BaC2O4}\). The presence of \(\ce{Ca^{2+}}\) is further verified by flame test. For this purpose, the precipitate is dissolved in 6M \(\ce{HCl}\):
\[\ce{CaC2O4(s, white) <=> Ca^{2+}(aq) + C2O4^{2-}(aq)}\nonumber\]
\[\ce{C2O4^{2-}(aq) + 2H3O^{+}(aq) <=> H2C2O4(aq)}\nonumber\]
Strong acid like \(\ce{HCl}\) increases \(\ce{H3O^{+}}\) ion concentration that drives the above reaction forward based on Le Chatelier's principle. The flame test is applied to the solution. If \(\ce{Ca^{2+}}\) is present in the solution, it imparts characteristic brick-red color to the flame, as shown in Fig. 6.2.3. Observation of the brick-red color in the flame test confirms the presence of \(\ce{Ca^{2+}}\) in the test sample. The flame color changes to light green when seen through cobalt blue glass.
Confirming group V cations by the flame test
Group V cations, i.e., alkali metal, \(\ce{Na^{+}}\), \(\ce{K^{+}}\), etc. form soluble ionic compounds. Separation of alkali metals cations by selective precipitation is not possible using commonly available reagents. So, group V cations are not separated in these analyses. However, alkali metal cations impart characteristic color to the flame that helps in their confirmation as shown in Figure \(\PageIndex{5}\). The supernatant after separating group IV precipitate is concentrated by heating the solution to evaporate the solvent. A flame test is applied to the concentrated solution.
Lithium imparts carmine red, sodium imparts intense yellow, and potassium imparts lilac color to the flame.


7.4: Healthy Aging
Implications of an Aging Society
By 2030, the number of U.S. adults aged 65 or older will more than double to about 71 million. The rapidly increasing number of older Americans has far-reaching implications for our nation’s public health system and will place unprecedented demands on the provision of health care and aging-related services. Public health efforts to promote health and functional independence are critical strategies in helping older adults stay healthy. Research has shown that poor health does not have to be an inevitable consequence of aging. Older adults who practice healthy behaviors, take advantage of clinical preventive services, and continue to engage with family and friends are more likely to remain healthy, live independently, and incur fewer health-related costs.
An essential component to keeping older adults healthy is preventing chronic diseases and reducing associated complications. About 80% of older adults have one chronic condition, and 50% have at least two. Infectious diseases (such as influenza and pneumococcal disease) and injuries also take a disproportionate toll on older adults. Efforts to identify strategies to prevent or reduce the risk of disease and injury and to widely apply effective interventions must be pursued.
Tips on how to stay healthy, get good health care, and manage lifestyle changes as you age are available at Healthy Aging at NIH Senior Health.
Sources
Source: Helping People To Live Long and Productive Lives and Enjoy a Good Quality Of Life: At a Glance 2011, www.cdc.gov/chronicdisease/resources/publications/AAG/aging.htm


1.3: Intersectionality
-
- Last updated
- Save as PDF
- Miliann Kang, Donovan Lessard, Laura Heston, and Sonny Nordmarken
- University of Massachusetts Amherst via UMass Amherst Libraries
- Miliann Kang, Donovan Lessard, Laura Heston, and Sonny Nordmarken
- University of Massachusett Amherst
Articulated by legal scholar Kimberlé Crenshaw (1991), the concept of intersectionality identifies a mode of analysis integral to women, gender, sexuality studies. Within intersectional frameworks, race, class, gender, sexuality, age, ability, and other aspects of identity are considered mutually constitutive; that is, people experience these multiple aspects of identity simultaneously and the meanings of different aspects of identity are shaped by one another. In other words, notions of gender and the way a person’s gender is interpreted by others are always impacted by notions of race and the way that person’s race is interpreted. For example, a person is never received as just a woman, but how that person is racialized impacts how the person is received as a woman. So, notions of blackness, brownness, and whiteness always influence gendered experience, and there is no experience of gender that is outside of an experience of race. In addition to race, gendered experience is also shaped by age, sexuality, class, and ability; likewise, the experience of race is impacted by gender, age, class, sexuality, and ability.
This work is in the Public Domain, CC0
Understanding intersectionality requires a particular way of thinking. It is different than how many people imagine identities operate. An intersectional analysis of identity is distinct from single-determinant identity models and additive models of identity. A single determinant model of identity presumes that one aspect of identity, say, gender, dictates one’s access to or disenfranchisement from power. An example of this idea is the concept of “global sisterhood,” or the idea that all women across the globe share some basic common political interests, concerns, and needs (Morgan 1996). If women in different locations did share common interests, it would make sense for them to unite on the basis of gender to fight for social changes on a global scale. Unfortunately, if the analysis of social problems stops at gender, what is missed is an attention to how various cultural contexts shaped by race, religion, and access to resources may actually place some women’s needs at cross-purposes to other women’s needs. Therefore, this approach obscures the fact that women in different social and geographic locations face different problems. Although many white, middle-class women activists of the mid-20th century US fought for freedom to work and legal parity with men, this was not the major problem for women of color or working-class white women who had already been actively participating in the US labor market as domestic workers, factory workers, and slave laborers since early US colonial settlement. Campaigns for women’s equal legal rights and access to the labor market at the international level are shaped by the experience and concerns of white American women, while women of the global south, in particular, may have more pressing concerns: access to clean water, access to adequate health care, and safety from the physical and psychological harms of living in tyrannical, war-torn, or economically impoverished nations.
This work is in the Public Domain, CC0
In contrast to the single-determinant identity model, the additive model of identity simply adds together privileged and disadvantaged identities for a slightly more complex picture. For instance, a Black man may experience some advantages based on his gender, but has limited access to power based on his race. This kind of analysis is exemplified in how race and gender wage gaps are portrayed in statistical studies and popular news reports. Below, you can see a median wage gap table from the Institute for Women’s Policy Research compiled in 2009. In reading the table, it can be seen that the gender wage gap is such that in 2009, overall, women earned 77% of what men did in the US. The table breaks down the information further to show that earnings varied not only by gender but by race as well. Thus, Hispanic or Latino women earned only 52.9% of what white men did while white women made 75%. This is certainly more descriptive than a single gender wage gap figure or a single race wage gap figure. The table is useful at pointing to potential structural explanations that may make earnings differ between groups. For instance, looking at the chart, you may immediately wonder why these gaps exist; is it a general difference of education levels, occupations, regions of residence or skill levels between groups, or is it something else, such as discrimination in hiring and promotion? What it is not useful for is predicting people’s incomes by plugging in their gender plus their race, even though it may be our instinct to do so. Individual experiences differ vastly and for a variety of reasons; there are outliers in every group. Most importantly, even if this chart helps in understanding structural reasons why incomes differ, it doesn’t provide all the answers.
Table 1: Average Annual Earnings for Year-Round Full-Time Workers age 15 Years and Older by Race and Ethnicity, 2015
| Racial/Ethnic Background* | Men ($) | Women ($) | Women’s Earnings as % of White Male Earnings |
| All Racial/Ethnic Groups | 51,212 | 40,742 | – |
| White | 57,204 | 43,063 | 75.3% |
| Black | 41,094 | 36,212 | 63.3% |
| Asian American | 61,672 | 48,313 | 84.5% |
| Hispanic or Latino | 35,673 | 31,109 | 54.4% |
|
*White alone, not Hispanic; Black alone or in combination (may include Hispanic); Asian American alone or in combination (may include Hispanic); and Hispanic/Latina/o (may be of any race).
Source: Institute for Women’s Policy Research. Compilation of U.S. Census Bureau, Current Population Survey. 2016. “Historical Income Tables: Table P-38. Full-Time, Year Round Workers by Median Earnings and Sex: 1987 to 2015. <www.census.gov/data/tables/t...me-people.html> |
The additive model does not take into account how our shared cultural ideas of gender are racialized and our ideas of race are gendered and that these ideas structure access to resources and power—material, political, interpersonal. Sociologist Patricia Hill Collins (2005) has developed a strong intersectional framework through her discussion of race, gender, and sexuality in her historical analysis of representations of Black sexuality in the US. Hill Collins shows how contemporary white American culture exoticizes Black men and women and she points to a history of enslavement and treatment as chattel as the origin and motivator for the use of these images. In order to justify slavery, African-Americans were thought of and treated as less than human. Sexual reproduction was often forced among slaves for the financial benefit of plantation owners, but owners reframed this coercion and rape as evidence of the “natural” and uncontrollable sexuality of people from the African continent. Images of Black men and women were not completely the same, as Black men were constructed as hypersexual “bucks” with little interest in continued relationships whereas Black women were framed as hypersexual “Jezebels” that became the “matriarchs” of their families. Again, it is important to note how the context, where enslaved families were often forcefully dismantled, is often left unacknowledged and contemporary racialized constructions are assumed and framed as individual choices or traits. It is shockingly easy to see how these images are still present in contemporary media, culture, and politics, for instance, in discussions of American welfare programs. This analysis reveals how race, gender, and sexuality intersect. We cannot simply pull these identities apart because they are interconnected and mutually enforcing.
Although the framework of intersectional has contributed important insights to feminist analyses, there are problems. Intersectionality refers to the mutually co-constitutive nature of multiple aspects of identity, yet in practice this term is typically used to signify the specific difference of “women of color,” which effectively produces women of color (and in particular, Black women) as Other and again centers white women (Puar 2012). In addition, the framework of intersectionality was created in the context of the United States; therefore, the use of the framework reproduces the United States as the dominant site of feminist inquiry and women’s studies’ Euro-American bias (Puar 2012). Another failing of intersectionality is its premise of fixed categories of identity, where descriptors like race, gender, class, and sexuality are assumed to be stable. In contrast, the notion of assemblage considers categories events, actions, and encounters between bodies, rather than simply attributes (Puar 2012). Assemblage refers to a collage or collection of things, or the act of assembling. An assemblage perspective emphasizes how relations, patterns, and connections between concepts give concepts meaning (Puar 2012). Although assemblage has been framed against intersectionality, identity categories’ mutual co-constitution is accounted for in both intersectionality and assemblage.
“Gender” is too often used simply and erroneously to mean “white women,” while “race” too often connotes “Black men.” An intersectional perspective examines how identities are related to each other in our own experiences and how the social structures of race, class, gender, sexuality, age, and ability intersect for everyone. As opposed to single-determinant and additive models of identity, an intersectional approach develops a more sophisticated understanding of the world and how individuals in differently situated social groups experience differential access to both material and symbolic resources.


1.1: Why It Matters
DEFINE GEOLOGY AS A SCIENCE AND UNDERSTAND THE BASIC METHODS OF SCIENCE USED IN GEOLOGY AND RELATED SCIENTIFIC DISCIPLINES
Introduction
When you ask the question “What is geology?” most people will initially respond that it is the study of rocks. This is true, but geology is also so much more than that. What if I told you geology is an intricate part of your everyday life? You may have to stop and think for a minute about that statement, but let’s consider the following questions:
- Where do your energy resources come from—not just the gas in car, but the components in your cell phones and tablets as well?
- Why does Japan have so many active volcanoes and earthquakes?
- Do you enjoy eating or cooking or gardening?
- Do you enjoy bottled, spring, or tap water?
While some of those questions are obviously geology related, it may take so exploring to find the answers to all of them. Throughout the course, you will learn the information necessary to answer these questions and others like them. We will see that geology is not just rocks but is far more encompassing than that. However, I can’t let this introduction go by without saying GEOLOGY ROCKS!
Learning Outcomes
- Define the science of geology
- Identify and use scientific processes and the scientific methods as used by geologists and with other related scientific disciplines.
Ok, let's get started!
Contributors and Attributions
-
Original content from Kimberly Schulte (Columbia Basin College) and supplemented by Lumen Learning . The content on this page is copyrighted under a Creative Commons Attribution 4.0 International license.


5.8: Endnotes
- Engel, Matthew. That’s The Way It Crumbles: The American Conquest of the English Language . London: Profile Books, 2017)
- https://www.theguardian.com/us-news/...language-study
- https://www.nytimes.com/2012/10/11/f...itishisms.html
- Data adapted from https://www.kaggle.com/rtatman/world...age-family-map and http://jonathansoma.com/open-source-language-map/
- Ethnologue. 2013. https://www.ethnologue.com/world
-
Noack, Rick. 2015. “The World’s Languages, in 7 Maps and Charts.” Washington Post.
www.washingtonpost.com/news/...23/the-worlds-languages-in-7-maps-and-charts/
- Nisen, Max. 2013. “Map Shows How American Speak 24 Different English Dialects.” Business Insider. https://www.businessinsider.com/dial...nglish-2013-12
- “Languages.” 2016. Accredited Language Services (blog). www.accreditedlanguage.com/category/languages/
- United States Census Bureau. https://www.census.gov/programs-surveys/acs/news/ data-releases/2015.html
- Hallock, Jie Zong, Jeanne Batalova Jie Zong, Jeanne Batalova, and Jeffrey. 2018. “Frequently Requested Statistics on Immigrants and Immigration in the United States.” Migrationpolicy.Org. February 2, 2018. https://www.migrationpolicy.org/ article/frequently-requested-statistics-immigrants-and-immigration-united-states .
- United States Census Bureau. www.census.gov/programs-surveys/acs/news/ data-releases/2015.html
- “What Is Social Media? - Definition from WhatIs.Com.” 2018. https://whatis.techtarget.com/definition/social-media .
- “Social Media.” 2018. Wikipedia. en.Wikipedia.org/w/index.php?title=Social_ media&oldid=855175226 .