4.4: Electromagnetic Recording Methods
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The methods we have mentioned up to now examine the metabolic activity of the brain. But there are also other cases in which one wants to measure electrical activity of the brain or the magnetic fields produced by the electrical activity. The methods we discussed so far do a great job of identifying where activity is occurring in the brain. A disadvantage of these methods is that they do not measure brain activity on a millisecond-by-millisecond basis. This measuring can be done by electromagnetic recording methods, for example by single-cell recording or the Electroencephalography (EEG). These methods measure the brain activity really fast and over a longer period of time so that they can give a really good temporal resolution.
Single cell
When using the single-cell method an electrode is placed into a cell of the brain on which we want to focus our attention. Now, it is possible for the experimenter to record the electrical output of the cell that is contacted by the exposed electrode tip. That is useful for studying the underlying ion currents which are responsible for the cell’s resting potential . The researchers’ goal is then to determine for example, if the cell responds to sensory information from only specific details of the world or from many stimuli. So we could determine whether the cell is sensitive to input in only one sensory modality or is multimodal in sensitivity. One can also find out which properties of a stimulus make cells in those regions fire. Furthermore we can find out if the animal’s attention towards a certain stimulus influences in the cell’s respond.
Single cell studies are not very helpful for studying the human brain, since it is too invasive to be a common method. Hence, this method is most often used in animals. There are just a few cases in which the single-cell recording is also applied in humans. People with epilepsy sometimes get removed the epileptic tissue. A week before surgery electrodes are implanted into the brain or get placed on the surface of the brain during the surgery to better isolate the source of seizure activity. So using this method one can decrease the possibility that useful tissues will be removed. Due to the limitations of this method in humans there are other methods which measure electrical activity. Those we are going to discuss next.
EEG
One of the most famous techniques to study brain activity is probably the Electroencephalography (EEG). Most people might know it as a technique which is used clinically to detect aberrant activity such as epilepsy and disorders.
Electroencephalogram (Electroencephalography, EEG) is obtained by electro-electron electroencephalography, which collects weak creatures produced by the human brain from the scalp and enlarges notes. Measuring electroencephalogram, and EEG measures, voltage fluctuations generated by the flow of ionic neurons in the brain. EEG is a diagnosis of a brain-related disease, but because it is susceptible to interference, it is usually used in combination with other methods.
EEG is most commonly used to diagnose epilepsy because epilepsy can cause abnormal EEG readings. It is also used to diagnose sleep disorders, coma, cerebrovascular disease, etc., and brain death. Brain waves have been used in first-line methods to diagnose tumors, strokes, and other focal brain diseases, but this has been reduced with the advent of high-resolution anatomical imaging techniques, such as nuclear magnetic resonance (MRI). And computed tomography (CT). Unlike CT and MRI, EEGs have a higher temporal resolution. Therefore, although spatial resolution of EEG is limited, it is still a valuable tool for research and diagnostics, especially when determining studies that require time resolution in the millisecond range
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In an experimental way this technique is used to show the brain activity in certain psychological states, such as alertness or drowsiness. To measure the brain activity mental electrodes are placed on the scalp. Each electrode, also known as lead, makes a recording of its own. Next, a reference is needed which provides a baseline, to compare this value with each of the recording electrodes. This electrode must not cover muscles because its contractions are induced by electrical signals. Usually it is placed at the “mastoid bone” which is located behind the ear.
During the EEG electrodes are places like this. Over the right hemisphere electrodes are labelled with even numbers. Odd numbers are used for those on the left hemisphere. Those on the midline are labelled with a z. The capital letters stands for the location of the electrode(C=central, F=frontal, Fop= frontal pole, O= occipital, P= parietal and T= temporal).
After placing each electrode at the right position, the electrical potential can be measured. This electrical potential has a particular voltage and furthermore a particular frequency. Accordingly, to a person’s state the frequency and form of the EEG signal can differ. If a person is awake, beta activity can be recognized, which means that the frequency is relatively fast. Just before someone falls asleep one can observe alpha activity, which has a slower frequency. The slowest frequencies are called delta activity, which occur during sleep. Patients who suffer epilepsy show an increase of the amplitude of firing that can be observed on the EEG record. In addition EEG can also be used to help answering experimental questions. In the case of emotion for example, one can see that there is a greater alpha suppression over the right frontal areas than over the left ones, in the case of depression. One can conclude from this, that depression is accompanied by greater activation of right frontal regions than of left frontal regions.
The disadvantage of EEG is that the electric conductivity , and therefore the measured electrical potentials vary widely from person to person and, also during time. This is because all tissues (brain matter, blood, bones etc.) have other conductivities for electrical signals. That is why it is sometimes not clear from which exact brain-region the electrical signal comes from.
ERP
Whereas EEG recordings provide a continuous measure of brain activity, event-related potentials (ERPs) are recordings which are linked to the occurrence of an event. A presentation of a stimulus for example would be such an event. When a stimulus is presented, the electrodes, which are placed on a person’s scalp, record changes in the brain generated by the thousands of neurons under the electrodes. By measuring the brain's response to an event we can learn how different types of information are processed. Representing the word eats or bake for example causes a positive potential at about 200msec. From this one can conclude, that our brain processes these words 200 ms after presenting it. This positive potential is followed by a negative one at about 400ms. This one is also called N400 (whereas N stands for negative and 400 for the time). So in general one can say that there is a letter P or N to denote whether the deflection of the electrical signal is positive or negative. And a number, which represent, on average, how many hundreds of milliseconds after stimulus presentation the component appears. The event-related- potential shows special interest for researchers, because different components of the response indicate different aspects of cognitive processing. For example, presenting the sentences “The cats won’t eat” and “The cat won’t bake”, the N400 response for the word “eat” is smaller than for the word “bake”. From this one can draw the conclusion that our brain needs 400 ms to register information about a word’s meaning. Furthermore, one can figure out where this activity occurs in the brain, namely if one looks at the position on the scalp of the electrodes that pick up the largest response.
MEG
Magnetoencephalography (MEG) is related to electroencephalography (EEG). However, instead of recording electrical potentials on the scalp, it uses magnetic potentials near the scalp to index brain activity. To locate a dipole, the magnetic field can be used, because the dipole shows excellently the intensity of the magnetic field. By using devices called SQUIDs (superconducting quantum interference device) one can record these magnetic fields.
MEG is mainly used to localize the source of epileptic activity and to locate primary sensory cortices. This is helpful because by locating them they can be avoided during neurological intervention. Furthermore, MEG can be used to understand more about the neurophysiology underlying psychiatric disorders such as schizophrenia . In addition, MEG can also be used to examine a variety of cognitive processes, such as language, object recognition and spatial processing among others, in people who are neurologically intact.
MEG has some advantages over EEG. First, magnetic fields are less influenced than electrical currents by conduction through brain tissues, cerebral spinal fluid, the skull and scalp. Second, the strength of the magnetic field can tell us information about how deep within the brain the source is located. However, MEG also has some disadvantages. The magnetic field in the brain is about 100 million times smaller than that of the earth. Due to this, shielded rooms, made out of aluminum, are required. This makes MEG more expensive. Another disadvantage is that MEG cannot detect activity of cells with certain orientations within the brain. For example, magnetic fields created by cells with long axes radial to the surface will be invisible.


2.5.14: Summary
Proof systems provide purely syntactic methods for characterizing consequence and compatibility between sentences. Natural deduction is one such proof system. A derivation in it consists of a tree formulas. The topmost formulas in a derivation are assumptions . All other formulas, for the derivation to be correct, must be correctly justified by one of a number of inference rules . These come in pairs; an introduction and an elimination rule for each connective and quantifier. For instance, if a formula \(A\) is justified by a \(\Elim{\lif}\) rule, the preceding formulas (the premises ) must be \(B \lif A\) and \(B\) (for some \(B\) ). Some inference rules also allow assumptions to be discharged . For instance, if \(A \lif B\) is inferred from \(B\) using \(\Intro{\lif}\) , any occurrences of \(A\) as assumptions in the derivation leading to the premise \(B\) may be discharged, and is given a label that is also recorded at the inference.
If there is a derivation with end formula \(A\) and all assumptions are discharged, we say \(A\) is a theorem and write \(\Proves A\) . If all undischarged assumptions are in some set \(\Gamma\) , we say \(A\) is derivable from \(\Gamma\) and write \(\Gamma \Proves A\) . If \(\Gamma \Proves \lfalse\) we say \(\Gamma\) is inconsistent , otherwise consistent . These notions are interrelated, e.g., \(\Gamma \Proves A\) iff \(\Gamma \cup \{\lnot A\}\) is inconsistent. They are also related to the corresponding semantic notions, e.g., if \(\Gamma \Proves A\) then \(\Gamma \Entails A\) . This property of proof systems—what can be derived from \(\Gamma\) is guaranteed to be entailed by \(\Gamma\) —is called soundness . The soundness theorem is proved by induction on the length of derivations, showing that each individual inference preserves entailment of its conclusion from open assumptions provided its premises are entailed by their undischarged assumptions.


9.5: Strategic Objectives and Levels of Strategy
- What are strategic objectives, levels of strategy, and a grand strategy? How are they related?
Once a strategic analysis has been completed, the next step in the strategy process is to establish strategic objectives. At this point, the manager has decided why the company exists and how it will try to fulfill its mission. Strategic analysis has provided information about customer preferences, competitors, and the firm’s resources and capabilities. Now it is time to start planning for success.
Strategic objectives
Strategic objectives are the big-picture goals for the company: they describe what the company will do to try to fulfill its mission. Strategic objectives are usually some sort of performance goal—for example, to launch a new product, increase profitability, or grow market share for the company’s product.
Exhibit 9.6 shows what might be some strategic objectives for Disney. To make people happy (Disney’s vision), Disney focuses on entertainment (its mission). Top executives then decide each year what entertainment products the company will offer. Because Disney is a large corporation (more on that shortly), it has a variety of resources available to create entertainment products to offer. For example, they may decide to release three movies this year, as well as build a new theme park and create five new shows for their television network. In reality, the strategic objectives at Disney are much more complex than this, because some of these choices involve long-term efforts (they cannot build a theme park in one year).
Exhibit 9.6 A Possible Strategic Path from Vision to Objective for Disney (Attribution: Copyright Rice University, OpenStax, under CC-BY 4.0 license)
Exhibit 9.6 A Possible Strategic Path from Vision to Objective for Disney (Attribution: Copyright Rice University, OpenStax, under CC-BY 4.0 license)
Levels of Strategies
Once a firm has set its objectives, it then must turn to the question of how it will achieve them. A business level strategy is the framework a firm uses to organize its activities, and it is developed by the firm’s top managers. Examples of business-level strategies include cost leadership and differentiation. These strategies are pursued by businesses with a single product or a range of products.
For example, imagine that you own a coffee shop.  You have employees, but you are the manager, owner, and all-around decision maker. While developing your vision and mission statements, you have already made some basic decisions about how your shop will operate. For example, you have chosen to either offer quick, inexpensive coffee (cost leadership) or a full-service coffee experience (differentiation). That decision impacts whether or not you choose premium or discount suppliers, how your shop is decorated, and how many employees you have to offer attention (service) to your customers. A business-level strategy guides a company in how they approach the activities in the value chain. Operations, for example, would focus on efficiency for a cost leader and focus on adding value for a differentiator.
 If you decide that your objective is to grow, for example, you should set a specific target, say, to grow revenue by 10%. Once you set that specific objective, you can exhibit out exactly what business-level actions you will need to take to reach that target.
Even if a business is much larger than a local coffee shop, the strategic objectives pursued by these larger companies are not significantly different in concept. Large companies like Nike or Apple, which have many different business units, develop strategies at several levels. Each individual business unit (say Nike Basketball) will have a manager who decides the objectives for that unit, just as in the coffee shop example. However, the company as a whole will have a chief executive officer (the top manager for the company) who develops strategy for the entire corporation. Corporate strategy is the broadest level of strategy, and is concerned with decisions about growing, maintaining, or shrinking very large companies. At this level, business-level strategy activities, such as an advertising campaign to attract new customers for a single product line, are not going to be enough to significantly impact the company as a whole.
The corporate CEO essentially manages a group of businesses (unless the firm operates as one business unit) and develops strategies to create success for the overall group. Think of the group of businesses as an investment portfolio: investors try to have a diverse set of investments to spread risk and maximize the performance of the overall portfolio. On any given day, an investment that isn’t doing so well should be offset by one that is doing well. Corporate strategy tries to achieve the same thing, and CEOs have to weigh the pros and cons of each business unit and how it is contributing to the success of the overall corporation. For example, a company that has business units that do well in the winter (ski resorts) will try to also have business units that will perform in the summer (swimming pools) to reduce the risk of having periods of low revenue. One tool that corporate strategists use to understand how each of their businesses contributes to the corporation as a whole is the BCG Matrix , illustrated in Exhibit 9.7.
Exhibit 9.7 The BCG Matrix (Attribution: Copyright Rice University, OpenStax, under CC-BY 4.0 license)
The BCG Matrix gives managers a quick picture of which business units are doing well and which are not. The tool has recommendations for businesses in each quadrant—for example, a business in the dog quadrant should be sold or closed. Cash cows provide income to the corporation, and stars provide growth. A CEO is always trying to balance the group of business units throughout the quadrants to maximize overall corporate performance. Note that the BCG Matrix is not applicable for firm’s that operate in one business unit.
In order to achieve the scale of growth necessary to meet corporate strategic objectives, a CEO must find ways to develop entirely new business units or reach brand-new markets. For example, for Walmart to grow their 2017 revenue by 5%, they would need to add $25 billion in new revenue. That’s more revenue than opening some new stores could generate. CEOs have several ways of growing their corporations, as shown in Table 9.1.
| How Grand Strategies Are Translated into Objectives and Actions |
| Grand Strategy | Strategic Objective | Potential Action | |
| Business-Level Strategy | Growth | Increase business revenue by 25% |
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| Corporate-Level Strategy | Growth | Increase corporate revenue by 10% |
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| International Strategy | Growth | Attract 10% overall market share in a new country |
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Table 9.1 (Attribution: Copyright Rice University, OpenStax, under CC-BY 4.0 license)
In Walmart’s case, for example, growing has meant expanding their online capabilities to better compete with Amazon. They have acquired new companies to support this goal, including Shoebuy, Jet, ModCloth, and Flipkart to reach customers and increase their online product selection, as well as Parcel, to build delivery services. 6
International strategy is similar to corporate strategy because it is concerned with the large-scale actions involved in entering a brand-new geographic market. For companies operating internationally, strategic questions focus on how to successfully enter and compete in a foreign market. International strategy can combine with business-level or corporate-level strategies because a growth strategy at either scale can involve entering new markets in order to reach new customers.
The Grand Strategy
At all three levels, companies choose a grand strategy in response to the first question they should ask themselves: does the firm want to grow, strive for stability, or take a defensive position in the marketplace? Often, the choice of a grand strategy is based on conditions in the business environment because firms generally want to grow unless something (like a recession) makes that difficult. Note that a grand strategy and a corporate strategy can overlap significantly.
- A growth strategy involves developing plans to increase the size of the firm in terms of revenue, market share, or geographic reach (often a combination of these, as they can overlap significantly). Walmart is implementing a growth strategy with the acquisitions discussed in the corporate strategy section.
- A stability strategy is a strategy for a company to maintain its current income, market share, or geographic reach. A firm usually works to maintain a stable position when the alternative is to lose ground in one of those categories, for example because of competition or economic factors. In today’s business environment, publicly held firms rarely aim solely to maintain the status quo, because shareholders and the stock market reward firm growth.
- Firms pursue defensive strategies in the face of challenges. A company that is struggling may decide to shrink its operations to reduce costs in order to survive, for example. A company facing strong new competition may have to radically rethink its product offerings or pricing in order not to lose too much market share to the newcomer. A technological innovation may make a company’s products obsolete (or at least less attractive), forcing it to work to catch up to the new technology. Ford made a defensive decision when it recently decided to stop selling sedans in the United States because of slow sales compared to trucks and SUVs.
Operationalizing a Grand Strategy
A firm operationalizes its choice of a grand strategy differently at each level of strategy (business, corporate, international). At the business level, a growth strategy means that the manager will have to develop ways to grow the business by developing new products or expanding the customer base for existing products, either at home or abroad. Expanding a corporation can take a wider variety of forms. The CEO can develop new businesses, expand to new countries, acquire or merge with competitors, or perform previously outsourced activities. International expansion can be accomplished by exporting goods to another country or by acquiring a similar firm in another country to establish the company’s presence in that country. In all three of these cases, the grand strategy would be growth, and the strategic objectives could be expressed in terms of revenue growth, profit growth, market share growth, or even share price growth. Table 9.1 outlines how a grand strategy can be used to develop specific company actions.
- What is the difference between strategic objectives and a strategy?
- Describe the three levels of strategy and what a manager developing strategy at each level is concerned with.
- What is a grand strategy, and how does it relate to strategic objectives and the three levels of strategy?
- What are the three grand strategies, and why would firms pursue each of them?
References
6. CBInsights (2018). “Walmart’s Been On A Buying Spree. Which Company Could It Acquire Next?.” CBInsights.com. https://www.cbinsights.com/research/...ition-targets/ . Jan. 5, 2018.


10.3: Expected Labor Rate
Learning Outcomes
- Estimate expected labor costs
The chief financial officer is not happy. Labor is at an all time high, and something needs to give to be able to continue pricing your product competitively in a tight market. You go to your production manager to discuss options for reducing labor, but it seems as if she has the process down, and she can’t see a way to reduce the time per pair of shoes to anything lower than it is. Putting on your thinking caps, you work together to go through the process step-by-step, to see if there are ways to decrease the labor time, automate steps or have a lower wage employee complete certain steps. But then you get the news, that your best guy is leaving. Are you ready to take on this task of replacing him?
Take a look at this chart again and then watch this video for a review of variance analysis.
Hupana Running Company has a great direct labor budget prepared by their experienced production manager, Mary. She has production hours down like a well oiled machine. Once she got the sales and production numbers, she prepared her direct labor budget:
| Q1 | Q2 | Q3 | Q4 | Total | |
|---|---|---|---|---|---|
| Required Production in Pairs | 450 | 500 | 500 | 600 | 2050 |
| Direct labor hours-pair | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |
| Total direct labor hours needed | 225 | 250 | 250 | 300 | 1025 |
| Direct labor cost per hour | $20 | $20 | $20 | $20 | $20 |
| Total direct labor cost | $4,500 | $5,000 | $5,000 | $6,000 | $20,500 |
Mary has a great bunch of people working for her and is confident that they can stay on task from a labor perspective. But then she gets the fateful news. Her best machine operator is leaving for another opportunity. She is going to need to replace him, and that won’t be an easy task.
Mary interviews a few people, and settles on hiring Jake. He has some similar experience, but the labor market is tight, so she needs to pay him $22 per hour instead of $20. Bringing him on at that rate, requires raises all around, so now, the direct labor cost per hour is $22, an increase of $2 per hour.
How will that affect the direct labor budget? This could cause a couple of things to happen.
- Your hourly labor rate will go up since you are paying Jake more than you were paying the previous operator.
- You may see a production slow down as Jake learns his new job.
- You could see a lower employee engagement or satisfaction rate, with the departure of a long-term employee.
How do you handle all of these situations?
Practice Questions


17: Radical Expressions and Functions
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- 17.3: Simplify Radical Expressions
- We will simplify radical expressions in a way similar to how we simplified fractions. A fraction is simplified if there are no common factors in the numerator and denominator. To simplify a fraction, we look for any common factors in the numerator and denominator. A radical expression, ⁿ√ a , is considered simplified if it has no factors of mⁿ. So, to simplify a radical expression, we look for any factors in the radicand that are powers of the index.
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- 17.6: Divide Radical Expressions
- We have used the Quotient Property of Radical Expressions to simplify roots of fractions. We will need to use this property ‘in reverse’ to simplify a fraction with radicals. We give the Quotient Property of Radical Expressions again for easy reference. Remember, we assume all variables are greater than or equal to zero so that no absolute value bars re needed.
Thumbnail: The mathematical expression "The (principal) square root of x". Image used with permission (GPL, David Vignoni (original icon); Flamurai (SVG convertion); bayo (color)).


1.8: Percy Bysshe Shelley (1792-1822)
Percy Bysshe Shelley was probably the most intellectual of all the Romantic poets; he was certainly one of the most well-educated. He was a non-conformist thinker, a philosopher, and a rebel. All of these characteristics join in his theory of poetry and poetic output, with their commitment to radical politics and their visionary idealism influenced by Platonism. Like Byron, Shelley was born into an aristocratic family, was in line to inherit a large estate, and was secured of a seat in the House of Lords in Parliament. Instead, Shelley became the river that made its own banks.
This independence of both thought and action appeared when Shelley wrote a pamphlet On the Necessity of Atheism while at Oxford. Rather than leading to intellectual debate as he expected, this pamphlet led to his being expelled. At the age of nineteen, Shelley eloped with Harriet Westbrook, the daughter of a stable hand. He pursued his intellectual and political interests by befriending the socialist philosopher William Godwin (1756-1836) and publishing Queen Mab, a utopian poem. At the grave of Godwin’s deceased wife Mary Wollstonecraft, Shelley also wooed their daughter Mary Wollstonecraft Godwin. The two eloped to Europe, Shelley’s wife Harriet having refused to join them. In 1816, Harriet Shelley committed suicide by drowning herself in the shallow end of the Serpentine River; she was apparently pregnant with another man’s child. Mary Godwin and Percy Bysshe had lost two children of their own before they married upon Harriet’s death. Percy Bysshe lost custody of his and Harriet’s two children due to his reputation.
Percy Bysshe and Mary Shelley traveled throughout Italy where Percy Bysshe wrote the bulk of his most famous works. In 1822, he drowned while sailing his schooner Don Juan (named after a poem by Byron) from Livorno to Lerici. He may have desired this death, disappointed and disaffected with the “triumph of life” over vision. He certainly seems to have predicted this mode of death in Adonais , an elegy he wrote for John Keats: “My spirit’s bark is driven,/ Far from the shore, far from the trembling throng/ Whose sails were never to the tempest given” (489-91).
It is important to consider the breadth and height of Shelley’s demands on poetry. He had great expectations from poetry and from poets, whom he described as power figures; for poets channel the power of the source itself (rather than the dominion). He therefore presents poets as the channels of power for change, for freedom, for humanity. His The Defense of Poetry takes the challenge Plato made when ejecting poets from his Republic. In it, Shelley describes poets as the best men with the best thoughts who see the seeds of the future cast upon the present. As such, they are the “unacknowledged legislators of the world.”
1.11.1: “Mont Blanc”
Lines Written in the Vale of Chamouni
I
The everlasting universe of things
Flows through the mind, and rolls its rapid waves,
Now dark—now glittering—now reflecting gloom—
Now lending splendour, where from secret springs
The source of human thought its tribute brings
Of waters—with a sound but half its own,
Such as a feeble brook will oft assume,
In the wild woods, among the mountains lone,
Where waterfalls around it leap for ever,
Where woods and winds contend, and a vast river
Over its rocks ceaselessly bursts and raves.
II
Thus thou, Ravine of Arve—dark, deep Ravine—
Thou many-colour’d, many-voiced vale,
Over whose pines, and crags, and caverns sail
Fast cloud-shadows and sunbeams: awful scene,
Where Power in likeness of the Arve comes down
From the ice-gulfs that gird his secret throne,
Bursting through these dark mountains like the flame
Of lightning through the tempest;—thou dost lie,
Thy giant brood of pines around thee clinging,
Children of elder time, in whose devotion
The chainless winds still come and ever came
To drink their odours, and their mighty swinging
To hear—an old and solemn harmony;
Thine earthly rainbows stretch’d across the sweep
Of the aethereal waterfall, whose veil
Robes some unsculptur’d image; the strange sleep
Which when the voices of the desert fail
Wraps all in its own deep eternity;
Thy caverns echoing to the Arve’s commotion,
A loud, lone sound no other sound can tame;
Thou art pervaded with that ceaseless motion,
Thou art the path of that unresting sound—
Dizzy Ravine! and when I gaze on thee
I seem as in a trance sublime and strange
To muse on my own separate fantasy,
My own, my human mind, which passively
Now renders and receives fast influencings,
Holding an unremitting interchange
With the clear universe of things around;
One legion of wild thoughts, whose wandering wings
Now float above thy darkness, and now rest
Where that or thou art no unbidden guest,
In the still cave of the witch Poesy,
Seeking among the shadows that pass by
Ghosts of all things that are, some shade of thee,
Some phantom, some faint image; till the breast
From which they fled recalls them, thou art there!
III
Some say that gleams of a remoter world
Visit the soul in sleep, that death is slumber,
And that its shapes the busy thoughts outnumber
Of those who wake and live.—I look on high;
Has some unknown omnipotence unfurl’d
The veil of life and death? or do I lie
In dream, and does the mightier world of sleep
Spread far around and inaccessibly
Its circles? For the very spirit fails,
Driven like a homeless cloud from steep to steep
That vanishes among the viewless gales!
Far, far above, piercing the infinite sky,
Mont Blanc appears—still, snowy, and serene;
Its subject mountains their unearthly forms
Pile around it, ice and rock; broad vales between
Of frozen floods, unfathomable deeps,
Blue as the overhanging heaven, that spread
And wind among the accumulated steeps;
A desert peopled by the storms alone,
Save when the eagle brings some hunter’s bone,
And the wolf tracks her there—how hideously
Its shapes are heap’d around! rude, bare, and high,
Ghastly, and scarr’d, and riven.—Is this the scene
Where the old Earthquake-daemon taught her young
Ruin? Were these their toys? or did a sea
Of fire envelop once this silent snow?
None can reply—all seems eternal now.
The wilderness has a mysterious tongue
Which teaches awful doubt, or faith so mild,
So solemn, so serene, that man may be,
But for such faith, with Nature reconcil’d;
Thou hast a voice, great Mountain, to repeal
Large codes of fraud and woe; not understood
By all, but which the wise, and great, and good
Interpret, or make felt, or deeply feel.
IV
The fields, the lakes, the forests, and the streams,
Ocean, and all the living things that dwell
Within the daedal earth; lightning, and rain,
Earthquake, and fiery flood, and hurricane,
The torpor of the year when feeble dreams
Visit the hidden buds, or dreamless sleep
Holds every future leaf and flower; the bound
With which from that detested trance they leap;
The works and ways of man, their death and birth,
And that of him and all that his may be;
All things that move and breathe with toil and sound
Are born and die; revolve, subside, and swell.
Power dwells apart in its tranquillity,
Remote, serene, and inaccessible:
And this, the naked countenance of earth,
On which I gaze, even these primeval mountains
Teach the adverting mind. The glaciers creep
Like snakes that watch their prey, from their far fountains,
Slow rolling on; there, many a precipice
Frost and the Sun in scorn of mortal power
Have pil’d: dome, pyramid, and pinnacle,
A city of death, distinct with many a tower
And wall impregnable of beaming ice.
Yet not a city, but a flood of ruin
Is there, that from the boundaries of the sky
Rolls its perpetual stream; vast pines are strewing
Its destin’d path, or in the mangled soil
Branchless and shatter’d stand; the rocks, drawn down
From yon remotest waste, have overthrown
The limits of the dead and living world,
Never to be reclaim’d. The dwelling-place
Of insects, beasts, and birds, becomes its spoil;
Their food and their retreat for ever gone,
So much of life and joy is lost. The race
Of man flies far in dread; his work and dwelling
Vanish, like smoke before the tempest’s stream,
And their place is not known. Below, vast caves
Shine in the rushing torrents’ restless gleam,
Which from those secret chasms in tumult welling
Meet in the vale, and one majestic River,
The breath and blood of distant lands, for ever
Rolls its loud waters to the ocean-waves,
Breathes its swift vapours to the circling air.
V
Mont Blanc yet gleams on high:—the power is there,
The still and solemn power of many sights,
And many sounds, and much of life and death.
In the calm darkness of the moonless nights,
In the lone glare of day, the snows descend
Upon that Mountain; none beholds them there,
Nor when the flakes burn in the sinking sun,
Or the star-beams dart through them. Winds contend
Silently there, and heap the snow with breath
Rapid and strong, but silently! Its home
The voiceless lightning in these solitudes
Keeps innocently, and like vapour broods
Over the snow. The secret Strength of things
Which governs thought, and to the infinite dome
Of Heaven is as a law, inhabits thee!
And what were thou, and earth, and stars, and sea,
If to the human mind’s imaginings
Silence and solitude were vacancy?
1.11.2: “England in 1819”
An old, mad, blind, despised, and dying King;
Princes, the dregs of their dull race, who flow
Through public scorn,—mud from a muddy spring;
Rulers who neither see nor feel nor know,
But leechlike to their fainting country cling
Till they drop, blind in blood, without a blow.
A people starved and stabbed in th’ untilled field;
An army, whom liberticide and prey
Makes as a two-edged sword to all who wield;
Golden and sanguine laws which tempt and slay;
Religion Christless, Godless—a book sealed;
A senate, Time’s worst statute, unrepealed—
Are graves from which a glorious Phantom may
Burst, to illumine our tempestuous day.
1.11.3: “Ode to the West Wind”
I
O wild West Wind, thou breath of Autumn’s being,
Thou, from whose unseen presence the leaves dead
Are driven, like ghosts from an enchanter fleeing,
Yellow, and black, and pale, and hectic red,
Pestilence-stricken multitudes: O thou,
Who chariotest to their dark wintry bed
The winged seeds, where they lie cold and low,
Each like a corpse within its grave, until
Thine azure sister of the Spring shall blow
Her clarion o’er the dreaming earth, and fill
(Driving sweet buds like flocks to feed in air)
With living hues and odours plain and hill:
Wild Spirit, which art moving everywhere;
Destroyer and preserver; hear, oh hear!
II
Thou on whose stream, mid the steep sky’s commotion,
Loose clouds like earth’s decaying leaves are shed,
Shook from the tangled boughs of Heaven and Ocean,
Angels of rain and lightning: there are spread
On the blue surface of thine aëry surge,
Like the bright hair uplifted from the head
Of some fierce Maenad, even from the dim verge
Of the horizon to the zenith’s height,
The locks of the approaching storm. Thou dirge
Of the dying year, to which this closing night
Will be the dome of a vast sepulchre,
Vaulted with all thy congregated might
Of vapours, from whose solid atmosphere
Black rain, and fire, and hail will burst: oh hear!
III
Thou who didst waken from his summer dreams
The blue Mediterranean, where he lay,
Lull’d by the coil of his crystalline streams,
Beside a pumice isle in Baiae’s bay,
And saw in sleep old palaces and towers
Quivering within the wave’s intenser day,
All overgrown with azure moss and flowers
So sweet, the sense faints picturing them!
Thou For whose path the Atlantic’s level powers
Cleave themselves into chasms, while far below
The sea-blooms and the oozy woods which wear
The sapless foliage of the ocean, know
Thy voice, and suddenly grow gray with fear,
And tremble and despoil themselves: oh hear!
IV
If I were a dead leaf thou mightest bear;
If I were a swift cloud to fly with thee;
A wave to pant beneath thy power, and share
The impulse of thy strength, only less free
Than thou, O uncontrollable! If even
I were as in my boyhood, and could be
The comrade of thy wanderings over Heaven,
As then, when to outstrip thy skiey speed
Scarce seem’d a vision; I would ne’er have striven
As thus with thee in prayer in my sore need.
Oh, lift me as a wave, a leaf, a cloud!
I fall upon the thorns of life! I bleed!
A heavy weight of hours has chain’d and bow’d
One too like thee: tameless, and swift, and proud.
V
Make me thy lyre, even as the forest is:
What if my leaves are falling like its own!
The tumult of thy mighty harmonies
Will take from both a deep, autumnal tone,
Sweet though in sadness. Be thou, Spirit fierce,
My spirit! Be thou me, impetuous one!
Drive my dead thoughts over the universe
Like wither’d leaves to quicken a new birth!
And, by the incantation of this verse,
Scatter, as from an unextinguish’d hearth
Ashes and sparks, my words among mankind!
Be through my lips to unawaken’d earth
The trumpet of a prophecy! O Wind,
If Winter comes, can Spring be far behind?


17.5: Current Issues in IT
What you’ll learn to do: Identify security, privacy and ethical issues affected by information technology
Now that we have acknowledged the amount of data that business collects about people, what are the risks and challenges associated with keeping that information secure? Businesses stand to lose consumer confidence and respect if they allow unauthorized access to customer data. For this reason, businesses take information security and cyber-security seriously. Despite the importance of protecting customer data, breaches and hacks seem to be more and more common. Is this a result of inadequate security measures on the part of the businesses, or are hackers getting better at accessing so-called “secure networks”? The answer is probably both. In this section you’ll learn about some of the ongoing security issues businesses face in trying to safeguard their (and their customers’) electronic communications and data.
Learning Objectives
- Identify privacy issues associated with information technology
- Identify ethical issues associated with information technology
Security Issues in Information Technology
Now that we have acknowledged the amount of data that business collects about people, what are the risks and challenges associated with keeping that information secure? Businesses stand to lose consumer confidence and respect if they allow unauthorized access to customer data. For this reason, businesses take information security and cyber-security seriously. Despite the importance of protecting customer data, breaches and hacks seem to be more and more common. Is this a result of inadequate security measures on the part of the businesses, or are hackers getting better at accessing so-called “secure networks”? The answer is probably both. In this section you’ll learn about some of the ongoing security issues businesses face in trying to safeguard their (and their customers’) electronic communications and data.
Information technology has presented businesses with opportunities undreamt of only a couple of decades ago. But it also has introduced some unprecedented challenges.
It has been estimated that businesses expend more than 5% of their annual IT budgets protecting themselves against disrupted operations and theft due to information theft . A February 2018 report by McAfee estimates that cyber-crime costs the world over $800 billion or 0.08% of global GDP. Among the reasons given for the growing cost of cyber-crime are:
- Quick adoption of new technologies by cyber-criminals
- The increased number of new users online (these tend to be from low-income countries with weak cyber-security)
- The increased ease of committing cyber-crime, with the growth of Cyber-crime-as-a-Service
- An expanding number of cyber-crime “centers” that now include Brazil, India, North Korea, and Vietnam
- A growing financial sophistication among top-tier cyber criminals that, among other things, makes monetization easier
According to the McAfee report, “Monetization of stolen data, which has always been a problem for cyber-criminals, seems to have become
less difficult because of improvements in cyber-crime black markets and the use of digital currencies
[1]
.”
Cyber-crime can take on many faces from data breaches to malicious program that attack a company’s network and disrupt service or corrupt sensitive corporate data. We will examine just a few of the ways that criminals are using technology to wreak havoc on business operations.
Viruses and Malicious Programs
With the increased use of the Internet comes an increased risk of a business’s computer network being effected by malicious programs such as viruses.  This trigger can be as simple as opening a file attachment or downloading a file from the Internet. Viruses range from the playful, simply displaying an image on the users’ screen meant to be funny to extreme cases where data files are permanently erased. Most companies deploy anti-virus software across their network, but even the most sophisticated anti-virus software cannot keep up with the ever growing number of viruses and malicious programs out there. Motives for creating viruses can include seeking profit (e.g., with ransomware), desire to send a political message, personal amusement, to demonstrate that a vulnerability exists in software, for sabotage and denial of service, or simply because hackers wish to explore cyber-security issues. The consequences of such viruses and malicious programs can be catastrophic, effectively destroying a company’s entire network and electronic records.
Phishing
One of the most prevalent cyber-attacks is the phishing scam. Phishing is when a scammer uses fraudulent emails or texts, or copycat websites to get you to share valuable personal information – such as account numbers, Social Security numbers, or your login IDs and passwords. Scammers use your information to steal your money or your identity or both. Scammers also use phishing emails to get access to your computer or network then they install programs like ransomware that can lock you out of important files on your computer.
Phishing scammers lure their targets into a false sense of security by spoofing the familiar, trusted logos of established, legitimate companies. Or they pretend to be a friend or family member. Phishing scammers make it seem like they need your information or someone else’s, quickly – or something bad will happen. They might say your account will be frozen, you’ll fail to get a tax refund, your boss will get mad, even that a family member will be hurt or you could be arrested. They tell lies to get to you to give them information.
To protect yourself and your company’s information, the U.S. Federal Trade Commission recommends the following precautions:
- Be cautious about opening attachments or clicking on links in emails . Even your friend or family members’ accounts could be hacked. Files and links can contain malware that can weaken your computer’s security.
- Do your own typing . If a company or organization you know sends you a link or phone number, don’t click. Use your favorite search engine to look up the website or phone number yourself. Even though a link or phone number in an email may look like the real deal, scammers can hide the true destination.
- Make the call if you’re not sure. Do not respond to any emails that request personal or financial information. Phishers use pressure tactics and prey on fear. If you think a company, friend or family member really does need personal information from you, pick up the phone and call them yourself using the number on their website or in your address book, not the one in the email.
- Turn on two-factor authentication . For accounts that support it, two-factor authentication requires both your password and an additional piece of information to log in to your account. The second piece could be a code sent to your phone, or a random number generated by an app or a token. This protects your account even if your password is compromised.
- Back up your files to an external hard drive or cloud storage. Back up your files regularly to protect yourself against viruses or a ransomware attack.
- Keep your security up to date . Use security software you trust, and make sure you set it to update automatically.
Even with these precautions in place, highly sophisticated phishing scams are successful in achieving their goal. The following 2018 statistics from Dashlane (SOURCE: https://blog.dashlane.com/phishing-statistics/ ) illustrate just how prolific phishing attacks are:
- According to PhishMe’s Enterprise Phishing Resiliency and Defense Report , phishing attempts have grown 65% in the last year.
- According to Wombat Security State of the Phish, 76% of businesses reported being a victim of a phishing attack in the last year.
- According to the Verizon Data Breach Investigations Report , 30% of phishing messages get opened by targeted users and 12% of those users click on the malicious attachment or link.
- According to the SANS Institute , 95% of all attacks on enterprise networks are the result of successful spear phishing.
- According to Symantec , phishing rates have increased across most industries and organization sizes — no company or vertical is immune.
- According to the Webroot Threat Report, nearly 1.5 million new phishing sites are created each month.
Another way that cyber-criminals interrupt business operations is through DoS (Denial of Service attacks).
Denial of Service
A denial-of-service (DoS) attack occurs when legitimate users are unable to access information systems, devices, or other network resources due to the actions of a malicious cyber threat actor. Services affected may include email, websites, online accounts (e.g., banking), or other services that rely on the affected computer or network. A denial-of-service is accomplished by flooding the targeted host or network with traffic until the target cannot respond or simply crashes, preventing access for legitimate users. DoS attacks can cost an organization both time and money while their resources and services are inaccessible. In 2012, not one, not two, but a whopping six U.S. banks were targeted by a string of DoS attacks. The victims were no small-town banks either: They included Bank of America, JP Morgan Chase, U.S. Bancorp, Citigroup and PNC Bank.
These are just a few of the security issues associated with information technology. Such risks illustrate the need for increased cybersecurity to protect computer systems from theft or damage to their hardware, software or electronic data, as well as from disruption or misdirection of the services they provide. The field is of growing importance due to increasing reliance on computer systems, the Internet and wireless networks such as Bluetooth and Wi – Fi, and due to the growth of “smart” devices, including smartphones, televisions and the various devices that constitute the Internet of Things. Due to its complexity, both in terms of politics and technology, it is one of the major challenges of the contemporary world.
practice question \(\PageIndex{1}\)
The following are information security issues EXCEPT:
- Phishing
- Cyber currency
- Viruses and malicious programs
- Denial of Service
- Answer
-
b . Although there are issues associated with cyber currency, it is not itself an information security issue.
Ethical and Social Issues in Information Technology
As you’ll recall, the industrial revolution of the nineteenth century gave rise to a number of unforeseen ethical and social issues—for instance, concerns about workplace safety, wages, discrimination, and child labor—which led to real changes in worker protections, labor practices, and law. Similarly, the technology revolution of the twentieth century—starting with the widespread use of the Internet and home computers—has spawned a new set of ethical and social concerns that people a hundred years ago couldn’t have imagined: for example, how should personal information and online privacy be protected? Who gets to own the information about our habits and “likes”? Before the advent of the Internet, people thought about and controlled their personal information in very different ways. Today, many of us lead complex online lives, and we may not even realize how our personal information is being collected and used. Companies like Caesars can collect data on the purchasing patterns, personal preferences, and professional/social affiliations of their customers without their even knowing about it. In this section we’ll explore some of the ethical and social issues related to network security, privacy, and data collection that businesses must address.
Technoethics
Ethical and social issues arising from the use of technology in all areas of our lives—and in business, in particular—have lead to the creation of a new branch of ethics: technoethics.
Technoethics (TE) is an interdisciplinary research area concerned with all moral and ethical aspects of technology in society. It draws on theories and methods from multiple knowledge domains (such as communications, social sciences information studies, technology studies, applied ethics, and philosophy) to provide insights on ethical dimensions of technological systems and practices for advancing a technological society. [2]
Technoethics views technology and ethics as socially embedded enterprises and focuses on discovering the ethical use of technology, protecting against the misuse of technology, and devising common principles to guide new advances in technological development and application to benefit society. Typically, scholars in technoethics have a tendency to conceptualize technology and ethics as interconnected and embedded in life and society. Technoethics denotes a broad range of ethical issues revolving around technology- from specific areas of focus affecting professionals working with technology to broader social, ethical, and legal issues concerning the role of technology in society and everyday life. [3]
Recent advances in technology and their ability to transmit vast amounts of information in a short amount of time has changed the way information is being shared amongst co-workers and managers throughout organizations across the globe. Starting in the 1980s with information and communications technologies (ICTs), organizations have seen an increase in the amount of technology that they rely on to communicate within and outside of the workplace. However, these implementations of technology in the workplace create various ethical concerns and in turn a need for further analysis of technology in organizations. As a result of this growing trend, a subsection of technoethics known as organizational technoethics has emerged to address these issues.
Technoethical perspectives are constantly changing as technology advances into areas unseen by creators and users engage with technology in new ways.
Technology, Business, and Your Data
Technology makes businesses more efficient, makes tasks faster and easier to complete, and ultimately creates value from raw data. However, as much as technology impacts the way that companies do business, it also raises important new issues about the employer-employee relationship. If you send personal emails from your office computer, do you have the right to expect that they’re private? Does your employer have a legal and ethical right to “cyber-peek” at what you are doing with company assets? Twenty years ago this was not an issue; today it’s a case before the Supreme Court.
Social Media
Employers want to use technology to help them screen applicants and verify information about their workforce, which is understandable. In the module on Human Resource Management you learned about the cost of recruiting, hiring, and training employees. However, what if the company believes that one of the quickest ways to gather information about an employee is to access their social media accounts? A company would never ask for your login credentials for Facebook, Twitter, InstaGram, LinkdIn . . . or would they? And if they did, is it legally and ethically justified? What would you do if you found yourself in the situation presented in the following video?
Information As a Business
The fact is that technology has put our information at the fingertips of businesses—there for the taking and, in some cases, the selling. Is it ethical for a business to collect data about a person and then sell that information to another business? Many organizations collect data for their own purposes, but they also realize that your data has value to others. As a result, selling data has become an income stream for many organizations. If you didn’t realize that your data was collected by Company A, it’s even less likely you knew that it was sold to Company B.
We have discussed just a few of the emerging ethical issues surrounding business, technology, and personal data. We have yet to touch on security issues and the responsibility business has to protect your data once it has been collected.
practice question \(\PageIndex{2}\)
Name the area where information technology in the workplace can affect personal privacy:
- Food items left in the break room refrigerators
- Photos or personal effects left in company cubicles
- Emails or messages sent on company-owned devices
- Mileage accrued on company vehicles
- Answer
-
c . Emails or text messages using company owned devices are not the private property of the employee.
practice question \(\PageIndex{3}\)
Citing company’s “cyber-peeking” at employee communications, businesses accessing social media accounts to get information on an individual, or businesses buying and selling consumer personal data to each other, what conclusions can be drawn about the benefits and challenges in information technology today?
- Advances in IT have made companies more efficient but have raised consumer prices.
- Advances in IT have helped companies better satisfy consumer needs but at the cost of individual privacy
- Advances in IT have helped companies become more competitive and better able to meet regulatory constraints.
- Advances in IT have helped organizations become more productive but less attuned to the needs of their customers.
- Answer
-
b . We only need to look at how we live today to see the benefits of IT, but if we look a little deeper we see that there is a price to pay.
- csis-prod.s3.amazonaws.com/s3fs-public/publication/economic-impact-cybercrime.pdf?kab1HywrewRzH17N9wuE24soo1IdhuHdutm_source=Pressutm_campaign=bb9303ae70-EMAIL_CAMPAIGN_2018_02_21utm_medium=emailutm_term=0_7623d157be-bb9303ae70-194093869 ↵
- Luppicini, R. (2010). Technoethics and the evolving knowledge society. Hershey: Idea Group Publishing. ↵
- Luppicini, R. (2010). Technoethics and the evolving knowledge society. Hershey: Idea Group Publishing. ↵


2.2: Duration- Rest Length
- In standard music notation, rests of different lengths have different shapes.
A rest stands for a silence in music. For each kind of note, there is a written rest of the same length.
The Most Common Rests
For each note on the first line, write a rest of the same length on the second line. The first measure is done for you.
Solution
Rests don't necessarily mean that there is silence in the music at that point; only that that part is silent. Often, on a staff with multiple parts, a rest must be used as a placeholder for one of the parts, even if a single person is playing both parts. When the rhythms are complex, this is necessary to make the rhythm in each part clear.
The normal rule in common notation is that, for any line of music, the notes and rests in each measure must "add up" to exactly the amount in the time signature, no more and no less. For example, in 3/4 time, a measure can have any combination of notes and rests that is the same length as three quarter notes. There is only one common exception to this rule. As a simplifying shorthand, a completely silent measure can simply have a whole rest. In this case, "whole rest" does not necessarily mean "rest for the same length of time as a whole note"; it means "rest for the entire measure".


2.8: Astronomy
-
- Last updated
- Save as PDF
- Susan Rahman, Prateek Sunder, and Dahmitra Jackson
- CC ECHO
Astronomy is the study of everything in the universe beyond Earth's atmosphere. That includes objects we can see with our naked eyes, like the Sun, the Moon, the planets, and the stars. It also includes objects we can only see with telescopes or other instruments, like faraway galaxies and tiny particles (What is Astronomy?, n.d.). This discipline, like many others, has had a problem with inclusivity. Currently, astronomers are 90 percent white, about 1 percent black,about 1 percent Latino and 0 percent Native American. Students of color do not see themselves represented in Astronomy faculty and that is one reason for most students of color who enter as Astronomy majors to change their major. Like other fields of study, some of the issues creating this lack of diversity in faculty include representation in the field at large, and a long path to tenure. (McCrea, 2020)The Banneker Institute, named after Benjamin Banneker,creator of the Farmer’s Almanac,and the first Black Astronomer,was formed for undergraduate students of color to pursue graduate programs in astronomy, focusing on research, graduate coursework, and social science education. In their summer workshop they work to train astronomers of color in currently white dominated fields while simultaneously addressing social issues surrounding racism and social justice. Effective approaches to a focus on both Astronomy as a field and an emphasis on social issues involve asking questions as simple as, how are planets formed, and where are all the Black people in the field (Sokol, 2016)?The program was started by John Johnson who left a position at Caltech due to the institution's disinterest in diversifying the field.
There are countless unanswered questions in the field of Astronomy, and there are underrepresented groups such as women and minorities, who would be valuable additions in attempting to answer those questions.The institute seeks to help students find a sense of community in the field. In addition to a lack of inclusivity, sexual harassment has also plagued the field further marginalizing students. The governing body for the field, American Astronomical Society (AAS) failed to make a statement in support of Black Lives Matter which appeared disrespectful to its Black astronomers. It has also not as of yet, added a social justice focus to its charge which is something many see as a failing. There have been conversations to address these and other issues of discrimination. Advice from these discussions for white astronomers in the field who wish to ally in creating a more diverse field is to “calm down, it’s been bad for a long time, this isn’t new phenomenon even if it is new to you, [sic] listen to their colleagues of color, and learn about the discipline’s racist history”(McCrea, 2020). Actions to attract and retain more students of color are happening with a goal of diversifying the field.Both the Banneker Institute and a program at Vanderbilt University have taken the charge to do so. Vanderbilt has been identifying promising students in HBCUs and supporting them entering the doctoral program at Vanderbilt.


17.3: Ligand and Voltage Gated Channels in Neurotransmission
A. Measuring Ion Flow and Membrane Potential
When neurotransmitters bind to their receptors, ion channels in responding neuron or muscle cells open. The resulting influx of Na + ions disrupts the resting potential of the target cell. The effect is only transient if the membrane potential remains negative. However, if enough Na+ ions enter the cell, the membrane becomes depolarized. If the cell experiences hyperpolarization , a localized reversal of normal membrane polarity (say from –70 mV to +65mV or more) will generate an action potential . This action potential will travel like a current along the neural or muscle cell membrane, eventually triggering a physiological response, e.g., the excitation of the next nerve cell in a neuronal pathway or contraction of the muscle cell. The patch-clamp device detects specific ion flow and any the resulting change in potential difference across the membrane. Principles of patch-clamp measurement are illustrated below.
In the example above, closing the switch on the power supply sends an electrical charge to the cell, opening up voltage-gated ion channel . In this case, a potassium sensor in the device detects the flow of K+ ions through the channel and out of the cell. At the same time, a volt meter registers the resulting change in membrane potential.
297 A Patch Clamp Device Can Record Membrane Potential and Ion Flow
298 Patch Clamp Measures Resting Potential and Depolarization
In addition to voltage-gated ion channels, the patch clamp device can measure ion flow through ligand-gated ion channels and mechanically-gated ion channels .
The former channels are receptor-ion gates that open when they bind an effector molecule. Mechanically-gated ion channels detect physical pressure or stress that result in a local membrane deformation, opening the channel.
300 Types of Gated Ion Channels-Illustrated
Finally, cells maintain a high intracellular concentration of K + ions, causing K + ions to slowly leak from the cell, a phenomenon detectable by a patch-clamp. The presence of negative ions (Clions, organic ions) inside a cell limits the leakage. This creates the electronegative interior of a cell relative to outside the cell, i.e., the resting potential across its plasma membrane. The patch-clamp technique has been used to correlate the flow of ions and changes in membrane potential when a neuron fires, causing an action potential in a responding cell.
Such a correlation is described on the next page. In the illustration, follow the opening and closing of ion channels and the flow of ions. An action potential (in fact any shift from resting potential) results from facilitated diffusion of specific ions into or out of the cell through gated ion channels (green, above) that must open and close in sequence. The behavior of two different voltage-gated ion channels are illustrated in the graph. Electrical stimulation opens Na + channels. Na + ions rush into the cell, reducing the membrane potential from the resting state to zero, or even making the cytoplasm more positive than the extracellular fluid. If the reversal in polarity is high enough, a voltagegated K + opens and potassium ions rush into the cell, restoring the resting potential of the cell.
A cell can continue to respond to stimuli with action potentials for as long as there is sufficient Na+ outside the cell and K + inside the cell. While active transport of Na + and K + is not required to re-establish the resting potential, it will eventually be necessary to restore the balance of the two ions in the cell. If a nerve or muscle cell fires several times (or even if it just leaks ions), the [K + ] inside the cell and the [Na + ] outside the cell would drop to a point where the cell cannot generate an action potential when stimulated. Ultimately, it is the role of ATP-dependent Na + /K + pumps to restore the appropriate Na + :K + balance across the responding cell membrane. As we have seen, each cycle of pumping exchanges 3 Na + ions from the intracellular space for 2 K + ions from the extracellular space. The pump has two effects:
- It restores Na + concentrations in the extracellular space relative to the cytoplasm.
- It restores K + concentrations in the cytoplasm relative to the extracellular space.
301 Gated Ion Channels Open and Close in Order During an Action Potential
Together with the higher negative ion concentrations in the cytosol, the unequal exchange of Na+ for K+ ions maintains the resting potential of the cell over the long term and ensures that nerve and muscle cells remain excitable. Next, we will take a closer look at the role of both ligand-gated and voltage-gated ion channels in neurotransmission.
B. Ion Channels in Neurotransmission
Action potentials result in an orderly, sequential opening and closing of voltage- and ligand-gated channels along the neuronal axon. In the link below, you can see the sequential cycling of voltage-gated channels that propagates a localized action potential (membrane depolarization) along an axon towards a synapse.
302 Propogating an Action Potential Along an Axon
When a propagated depolarization reaches a synapse, gated ion channels either open or close in the neuron and the responding cell. The cooperation of voltage- and ligand-gated channels at a neuromuscular junction is illustrated below.
As you can see from the illustration, after a neuron fires, an electrical impulse (a moving region of hyperpolarization ) travels down the axon to the nerve ending. At the nerve ending, the traveling charge difference (electrical potential) across the cell membrane stimulates a Ca++ -specific voltage-gated channel to open. Ca++ ions then flow into the cell because they are at higher concentrations in the synaptic cleft than in the cytoplasm.
The Ca 2 + ions in the cell cause synaptic vesicles to fuse with the membrane at the nerve ending, releasing neurotransmitters into the synaptic cleft. Then, the neurotransmitters bind to a receptor on the responding cell plasma membrane. This receptor is a ligand-gated channel (also called a chemically-gated channel ). Upon binding of the neurotransmitter ligand, the channel opens. The rapid diffusion of Na+ ions into the cell creates an action potential that leads to the cellular response, in this case, muscle contraction. We have already seen that K+ channels participate in restoring membrane potential after an action potential, and the role of the sodium/potassium pump in restoring the cellular Na + /K + balance.
303 The Role of Gated Ion Channels at Neuromuscular Junction


4.3: Deriving Simple Energy Relationships
A. Energy in the Universe: the Universe is a Closed System
Consider an event, any even. I think we can agree that when stuff happens, participants in the happening go from an unstable state to a relatively more stable state.  The marbles would fall to the floor, roll and spread out, eventually coming to a stop. At that point, the marbles are in a more stable state than they were when you were holding the bag.
If asked, you would say that gravity made the marbles fall from the bag. That is certainly true. Could we then say that the drive to greater stability is what made the marbles fall? In fact, regardless of the force or impetus for the event, we can say that the drive to achieve greater stability that makes things/events happen! This is the essence of the Second Law of Thermodynamics : all universal energy transfer events occur with an increase in stability…, that is, an increase in entropy . We’ll consider the second law and entropy in detail shortly.
The tendency of things go from unstable to more stable is a natural, rational state of affairs…, like those marbles on the floor, or a messy bedroom with clothes strewn about. Intuitively, messy and disordered is more stable than ordered. Of course, marbles dropping or clothing going from folded and hung to wrinkled on the floor releases energy (potential energy) as they fall (kinetic energy). If you don’t believe that this release of energy is real, just think of how much energy you will need to pick up the marbles or re-fold your clothes (after laundering them of course!).
We can model the flow of energy in the universe in a way that is consistent with thermodynamic laws. Since the First law of Thermodynamics says that energy can be neither created nor destroyed , a simple statement of the First Law could be:
The equation sums up the different kinds of energy in the universe. Look at it this way:
Energy cannot get in or out of the universe. Energy can only be transferred from one place to another, or converted from one form to another. It follows then that E universal is the sum of all kinds of energy in the universe, and that this sum is a constant. The equation below is consistent with this idea.
This is a statement of the First Law of Thermodynamics .
139 First Law of Thermodynamics
If we go with the simpler binary notion or useful and useless energy, our equation shortens to the sum of just two kinds of energy in the universe:
In this equation, G is useful energy (“Gibbs” free energy ), S is useless energy (entropy), and T is absolute temperature (included because of the third law). This is also a statement of the First Law . Here is our revised circle diagram:
By the way, segregating things and concepts into circles is a way of logically viewing relationships between them. John Venn first formalized this approach in the late 19th century. The Venn diagrams used here to describe the universe are very simple. For examples of more complex overlapping components of the universe that share some but not all attributes, “Google” Venn Diagrams.
In this binary energy model, it follows that as universal entropy increases, free energy in the universe must decrease:
Free or ‘potentially useful’ energy is higher in more ordered, complex and therefore relatively unstable systems. Such unstable, ordered systems will release free energy spontaneously .
While the arithmetic statements about changes in energy are useful concepts, the parameters are of course, not measurable! But if we isolate a bit of the universe, we can measure energies and watch energy flow.
B. Energy is Exchanged Between Systems in the Universe
If we can measure the amount of energy put into or removed from a system within the universe , we can write a more useful equation to follow the transfer of energy between a system and its surroundings:
\[ΔH = ΔG + TΔS\]
In this formula, \(ΔH\) is the change (D) in enthalpy, i.e., as energy entering/leaving the system in units of heat energy); \(ΔG\) is change in free energy and \(ΔS\) is change in entropy; T = absolute temperature (oK).
Heat given off in a reaction (or other event) is often confused with entropy. It is true that much of the increase in entropy that occurs in living things is indeed in the form of random molecular motion, or heat. But remember that heat can have its uses; not all heat is entropic! Hence, it is more interesting (and accurate!) to think of energy in terms of changes in enthalpy, free energy and entropy during energy transfers.
According to the equation \(ΔH = ΔG + TΔS\), interacting systems in our universe would seem to be closed systems . Accordingly, energy put into or removed from the system (\(ΔH\)) will be exactly balanced by increases and/or decreases in the other two terms in the equation (\(ΔG + TΔS\) ) . Recall that we refer to these systems as closed systems not because they are really closed, but because we can isolate them well enough to account for energy flow into and out of the system. The value of this (or any) algebraic equation with three variables is that if you know two of the values, you can calculate the third! Here is a simple situation to illustrate the point: If I put a liter of water on a burner and light the flame, the water gets hot. If the temperature of the liter of water rises by 1oC, we know that it has absorbed 1000 calories (one Kcal, or one food Calorie) of the heat from the burner.
Since energy interactions depend on different physical conditions, such as temperature and air pressure, we need to standardize those conditions when conducting experiments that measure energy changes in experimentally isolated systems. For more on how standardizing these physical parameters enables measuring energy change in chemical reactions (in fact, any energy exchange), click the link below.
141 Deriving Closed System Thermodynamics
Turning to bioenergetics , let’s apply the equation \(ΔH = ΔG + TΔS\) to chemical reactions in cells. Because most life on earth lives at sea level where the air pressure is 1 atmosphere and the temperature is in the 20’s (Celsius), typical determinations of \(ΔH\), \(ΔG\), and \(ΔS\) are made under standard conditions where T=298oK (25oC), an atmospheric pressure of pressures of 1 atm, and a constant pH of 7.0. In addition, measured values are adjusted to calculate unimolar quantities of reactants (see below). Our equation for reactions under these standard conditions becomes: \(ΔH = ΔGo + TΔS\) , where \(ΔGo\) is the standard free energy change for the reaction conducted in a closed system under standard conditions, while \(ΔH\) and \(ΔS\) are still the enthalpy and entropy changes, but determined under standard conditions.
What are unimolar conditions in practice? It means that if you burn 180 mg of glucose in a calorimeter, multiply the calories released (\(ΔH\)) by 1000. This gives you the calories released by burning 180 gm (i.e., a whole mole) of the stuff. Now we are ready to consider examples of how we determine the energetics of reactions.
c. How is Enthalpy Change (\(ΔH\)) Determined?
\(ΔH\) for a chemical reaction can easily be determined by conducting the reaction under standard conditions in a bomb calorimeter (illustrated below).
Food manufacturers determine the Calorie content of food using a bomb calorimeter. As a reaction takes place in the beaker in the illustration, it will either release or absorb heat, either heating or cooling the water in the calorimeter jacket, as measured by the thermometer. A reaction that releases heat as it reaches equilibrium is defined as exothermic , and the \(ΔH\) for an exothermic reaction will be negative. For example, a package says that a chocolate bar has 90 Calories. This means that burning the bar will generate 90 kilocalories (Kcal) of heat as measured in the calorimeter. Recall that one Calorie (with a capital C) = 1000 calories, or one Kcal. One calorie (lower case) is the energy needed to raise a gram of water by 1oC).
You are probably most familiar with reactions that release heat, but some chemical reactions actually absorb heat. Take the common hospital cold pack for example. Squeeze it to get it going and toss it in the calorimeter. You can watch the temperature in the calorimeter drop as the pack absorbs heat from the surroundings! Such reactions are defined as endothermic , with a positive \(ΔH\). OK, so we can determine the value of one of the energy parameters… we need to know at least one other, either \(ΔGo\) or \(ΔS\) before the equation \(ΔH = ΔGo + TΔS\) becomes useful.
D. How is Standard Free Energy Change (\(ΔGo\)) Determined?
As it turns out, standard free energy change, \(ΔGo\) , is directly proportional to the concentrations of reactants and products of a reaction conducted to completion (i.e., equilibrium ) under standard conditions. Therefore, to determine \(ΔGo\), we need to be able to measure the concentration of reactants and reaction products before and after a chemical reaction (i.e., when the reaction reaches equilibrium ). Take the following generic chemical reaction:
\[2A + B <===> 2C + D\]
The following equation relates \(ΔGo\) the equilibrium concentrations of A, B, C and D:
\[ΔGo = -RTlnKeq = -RTln((C^2+D)/(A^2+B))\]
R = the gas constant (1.806 cal/mole-deg), T = 298oK and Keq is the equilibrium constant . This is the Boltzman equation . As you can see, the Keq for the reaction is the ratio of the product of the concentrations of the products (raised to their stoichiometric powers) to the product of the concentrations of the reactants (raised to their stoichiometric powers).
If you can determine equilibrium concentrations of reactants and products in a chemical reaction, you can use this equation to calculate \(ΔGo\) ( standard free energy change ) for a reaction. Consider the following generic chemical reaction:
\[A + B ⇔ C + D\]
If the \(ΔGo\) is a negative number, the reaction is defined as exergonic . We say that exergonic reactions release free energy. If the \(ΔGo\) is a positive number, the reaction absorbs free energy and is defined as endergonic .
E. Working an Example Using These Equations for Closed Systems
Consider the following reaction:
\[X ⇔ Y\]
If you are given [X] and [Y], you can also do the math. At equilibrium, the concentrations of the reactants and products for this reaction measured (assayed), with the following results:
[X] = 2.5 Kcal/Mole; [Y] = 500 cal/Mole
Use the Boltzmann equation (above) to calculate the standard free energy for this reaction. What is the Keq for this reaction? What is the \(ΔGo\) for the reaction? If you did not come up with a Keq of 0.2 and an absolute value for the standard free energy for | \(ΔGo\) | of 866.2 Kcal/mole, re-calculate or collaborate with a classmate. Hint: make sure that you convert the units in your equation so that they are all the same!). Based on the calculated value of \(ΔGo\), is this reaction endergonic or exergonic?
If you conduct the reaction in a bomb calorimeter, it proceeds to equilibrium with a \(ΔH\) = -750 Kcal/Mole. What kind of reaction is this? Together with the enthalpy change , it is now possible to calculate an absolute value for the entropy change to be | \(ΔS\) | = 116.2 cal/mol-deg for this reaction. At equilibrium, did the reaction proceed with an increase or decrease in entropy under standard conditions? Again, if you did not get the correct answer, re-calculate or collaborate with a classmate.
F. Summary: The Properties of Closed Systems
First, let’s reiterate that there is no such thing as a closed system, unless of course the universe is one! What we call a closed system is simply one in which we can measure the energy going into or coming out of the system, and within which we can measure energy transfers and transductions (changes from one kind of energy to another.
Features of systems can be defined by their properties:
Properties of Closed Systems
- Closed systems are experimentally defined by an investigator .
- Standard conditions apply.
- Energy entering or leaving the system is measurable .
- Reactions reach equilibrium regardless of reaction rate.
- Product and reactant concentrations at equilibrium are constant.
- Measured energy transfer/transduction values are constant .
G. Actual Free Energy Change in Open Systems
Later we will be discussing the flow of energy through living things, from sunlight to chemical energy in nutrient molecules into ATP, from chemical energy as ATP into the performance of all manner of cellular work. Cells are open systems that constantly exchange mass and energy with their environment and never reach equilibrium . In addition, diverse organisms live under very different atmospheric conditions and maintain different body temperatures (e.g., your cat has a higher body temperature than you do!). Clearly, the conditions under which cells conduct their biochemical reactions are decidedly non-standard . However, while open systems do not reach equilibrium, they do achieve a steady state in which the rate of input of energy and matter is equal to the rate of output of energy and matter. Think of a biochemical pathway like glycolysis. If a cell’s energy needs are constant, the pathway will reach a steady state . Of course, a cell’s need for energy (as ATP) can change as energy needs change. If it does, then the steady state of ATP production will change to meet the needs of the cell.
Since reaction rates can change (and are in fact regulated in cells), implying that the steady state of a reaction or biochemical pathway can change. We characterize open systems by their properties, as listed below.
Properties of Open Systems
- Open systems exchange energy and mass with their surroundings .
- Open systems never reach equilibrium
- They achieve steady state where the energy input rate = output rate.
- The steady state can change .
- In open systems, endergonic reactions can be energetically favorable (spontaneous).
Fortunately, there is an equation to determine free energy changes in open systems. For our chemical reaction \(2A + B <===> 2C + D\), this equation would be:
\[ΔG' = ΔGo + RT\ln(((Css)^2+Dss)/((Ass)^2+Bss))\]
Here, \(ΔG'\) is the actual free energy change for a reaction in an open system. \(ΔGo\) is the standard free energy change for the same reaction under standard conditions. In a closed system. R is again the gas constant (1.806 cal/mole-deg) and T is the absolute temperature in which the reaction is actually occurring. The subscript ‘ ss ’ designates reactant and product concentrations measured under steady state conditions. To determine the actual free energy of a biochemical reaction in a cell (in fact in any living tissue), all you need to know are the \(ΔGo\) for the reaction, the steady state concentrations of reaction components in the cells/tissues, and the absolute T under which the reactions are occurring.
144 The Energetics of Open Systems
Elsewhere, we will use the reactions of the glycolytic pathway to exemplify the energetics of open and closed systems. At that time, pay careful attention to the application of the terminology of energetics in describing energy flow in closed vs. open systems .


30.9: The Pauli Exclusion Principle
Learning Objectives
By the end of this section, you will be able to:
- Define the composition of an atom along with its electrons, neutrons, and protons.
- Explain the Pauli exclusion principle and its application to the atom.
- Specify the shell and subshell symbols and their positions.
- Define the position of electrons in different shells of an atom.
- State the position of each element in the periodic table according to shell filling.
Multiple-Electron Atoms
All atoms except hydrogen are multiple-electron atoms. The physical and chemical properties of elements are directly related to the number of electrons a neutral atom has. The periodic table of the elements groups elements with similar properties into columns. This systematic organization is related to the number of electrons in a neutral atom, called the atomic number , \(Z\). We shall see in this section that the exclusion principle is key to the underlying explanations, and that it applies far beyond the realm of atomic physics.
In 1925, the Austrian physicist Wolfgang Pauli (see Figure ) proposed the following rule: No two electrons can have the same set of quantum numbers. That is, no two electrons can be in the same state. This statement is known as the Pauli exclusion principle , because it excludes electrons from being in the same state. The Pauli exclusion principle is extremely powerful and very broadly applicable. It applies to any identical particles with half-integral intrinsic spin—that is, having \(s = 1/2, \, 3/2, . . .\) Thus no two electrons can have the same set of quantum numbers.
Pauli Exclusion Principle
No two electrons can have the same set of quantum numbers. That is, no two electrons can be in the same state.
Let us examine how the exclusion principle applies to electrons in atoms. The quantum numbers involved were defined in Quantum Numbers and Rules as \(n, \, l, \, m_l, \, s\) and \(m_s\). Since \(s\) is always \(1/2\) for electrons, it is redundant to list \(s\), and so we omit it and specify the state of an electron by a set of four numbers \((n, \, l, \, m_l, \, m_s)\). For example, the quantum numbers \((2, \, 1, \, 0, - 1/2)\) completely specify the state of an electron in an atom.
Since no two electrons can have the same set of quantum numbers, there are limits to how many of them can be in the same energy state. Note that \(n\) determines the energy state in the absence of a magnetic field. So we first choose \(n\), and then we see how many electrons can be in this energy state or energy level. Consider the \(n = 1\) level, for example. The only value \(l\) can have is 0 (see [link] for a list of possible values once \(n\) is known), and thus \(m_l\) can only be 0. The spin projection \(m_s\) can be either \(+1/2\) or \(-1/2\), and so there can be two electrons in the \(n = 1\) state. One has quantum numbers \((1,\space 0, \, 0, \, +1/2)\), and the other has \((1, \, 0, \, 0, \, -1/2)\). Figure illustrates that there can be one or two electrons having \(n = 1\), but not three.
Shells and Subshells
Because of the Pauli exclusion principle, only hydrogen and helium can have all of their electrons in the \(n = 1\) state. Lithium (see the periodic table) has three electrons, and so one must be in the \(n = 2\) level. This leads to the concept of shells and shell filling. As we progress up in the number of electrons, we go from hydrogen to helium, lithium, beryllium, boron, and so on, and we see that there are limits to the number of electrons for each value of \(n\). Higher values of the shell \(n\) correspond to higher energies, and they can allow more electrons because of the various combinations of \(l, \, m_l\), and \(m_s\) that are possible. Each value of the principal quantum number \(n\) thus corresponds to an atomic shell into which a limited number of electrons can go. Shells and the number of electrons in them determine the physical and chemical properties of atoms, since it is the outermost electrons that interact most with anything outside the atom.
The probability clouds of electrons with the lowest value of \(l\) are closest to the nucleus and, thus, more tightly bound. Thus when shells fill, they start with \(l = 0\), progress to \(l = 1\), and so on. Each value of \(l\) thus corresponds to a subshell .
The table given below lists symbols traditionally used to denote shells and subshells.
| Shell | Subshell | Symbol |
|---|---|---|
| \(n\) | \(l\) | |
| 1 | 0 | \(s\) |
| 2 | 1 | \(p\) |
| 3 | 2 | \(d\) |
| 4 | 3 | \(f\) |
| 5 | 4 | \(g\) |
| 6 | \(h\) | |
| \(6^i\) | \(i\) |
To denote shells and subshells, we write \(nl\) with a number for \(n\) and a letter for \(l\). For example, an electron in the \(n = 1\) state must have \(l = 0\) and it is denoted as a \(1s\) electron. Two electrons in the \(n = 1\) state is denoted as \(1s^2\). Another example is an electron in the \(n = 2\) state with \(l = 1\), written as \(2p\).The case of three electrons with these quantum numbers is written \(2p^3\). This notation, called spectroscopic notation, is generalized as shown in Figure .
Counting the number of possible combinations of quantum numbers allowed by the exclusion principle, we can determine how many electrons it takes to fill each subshell and shell.
Example \(\PageIndex{1}\): How Many Electrons Can Be in This Shell?
List all the possible sets of quantum numbers for the \(n = 2\) shell, and determine the number of electrons that can be in the shell and each of its subshells.
Strategy
Given \(n = 2\) for the shell, the rules for quantum numbers limit \(l\) to be 0 or 1. The shell therefore has two subshells, labeled \(2s\) and \(2p\). Since the lowest \(l\) subshell fills first, we start with the \(2s\) subshell possibilities and then proceed with the \(2p\) subshell.
Solution
It is convenient to list the possible quantum numbers in a table, as shown below.
Discussion
It is laborious to make a table like this every time we want to know how many electrons can be in a shell or subshell. There exist general rules that are easy to apply, as we shall now see.
The number of electrons that can be in a subshell depends entirely on the value of \(l\). Once \(l\) is known, there are a fixed number of values of \(m_l\), each of which can have two values for \(m_s\). First, since \(m_l\) goes from \(-l\) to \(l\) in steps of 1, there are \(2l + 1\) possibilities. This number is multiplied by 2, since each electron can be spin up or spin down. Thus the maximum number of electrons that can be in a subshell is \(2(2l + 1)\).
For example, the \(2s\) subshell in Example has a maximum of 2 electrons in it, since \(2(2l + 1) = 2(0 + 1) = 2\) for this subshell. Similarly, the \(2p\) subshell has a maximum of 6 electrons, since \(2(2l + 1) = 2(2 + 1) = 6\). For a shell, the maximum number is the sum of what can fit in the subshells. Some algebra shows that the maximum number of electrons that can be in a shell is \(2n^2\).
For example, for the first shell \(n = 1\), and so \(2n^2 = 2\). We have already seen that only two electrons can be in the \(n = 1\) shell. Similarly, for the second shell, \(n = 2\), and so \(2n^2 = 8\). As found in Example , the total number of electrons in the \(n = 2\) shell is 8.
Example \(\PageIndex{2}\): Subshells and Totals for \(n = 3\)
How many subshells are in the \(n = 3\) shell? Identify each subshell, calculate the maximum number of electrons that will fit into each, and verify that the total is \(2n^2\).
Strategy
Subshells are determined by the value of \(l\); thus, we first determine which values of \(l\) are allowed, and then we apply the equation “maximum number of electrons that can be in a subshell \(= 2(2l + 1)\)" to find the number of electrons in each subshell.
Solution
Since \(n = 3\), we know that \(l\) can be \(0,\space 1\) or \(2\), thus, there are three possible subshells. In standard notation, they are labeled the \(3s, \, 3p,\) and \(3d\) subshells. We have already seen that 2 electrons can be in an \(s\) state, and 6 in a \(p\) state, but let us use the equation “maximum number of electrons that can be in a subshell \(= 2(2l + 1)\)" to calculate the maximum number in each:
\[3s \, has \, l = 0; \, thus, \, 2(2l + 1) = 2(0 + 1) = 2\]
\[3p \, has \, l = 1; \, thus, \, 2(2l + 1) = 2(2 + 1) = 6\]
\[3d \, has \, l = 2; \, thus, \, 2(2l + 1) = 2(4 + 1) = 10\]
\[Total = 18\]
\[(in \, the \, n = 3 \, shell)\]
The equation “maximum number of electrons that can be in a shell \(= 2n^2\)" gives the maximum number in the \(n = 3\) shell to be
\[Maximum \, number \, of \, electrons = 2n^2 = 2(3)^2 = 2(9) = 18.\]
Discussion
The total number of electrons in the three possible subshells is thus the same as the formula \(2n^2\). In standard (spectroscopic) notation, a filled \(n = 3\) shell is denoted as \(3s^2 3p^6 3d^10\). Shells do not fill in a simple manner. Before the \(n = 3\) shell is completely filled, for example, we begin to find electrons in the \(n = 4\) shell.
Shell Filling and the Periodic Table
Table shows electron configurations for the first 20 elements in the periodic table, starting with hydrogen and its single electron and ending with calcium. The Pauli exclusion principle determines the maximum number of electrons allowed in each shell and subshell. But the order in which the shells and subshells are filled is complicated because of the large numbers of interactions between electrons.
| Element | Number of electrons (Z) | Ground state configuration |
|---|---|---|
| H | 1 | \(1s^1\) |
| He | 2 | \(1s^2\) |
| Li | 3 | \(1s^2 \, 2s^1\) |
| Be | 4 | \( " \, 2s^2\) |
| B | 5 | \( " \, 2s^2 \, 2p^1\) |
| C | 6 | \( " \, 2s^2 \, 2p^2\) |
| N | 7 | \( " \, 2s^2 \, 2p^3\) |
| O | 8 | \( " \, 2s^2 \, 2p^4\) |
| F | 9 | \( " \, 2s^2 \, 2p^5\) |
| Ne | 10 | \( " \, 2s^2 \, 2p^6\) |
| Na | 11 | \( " \, 2s^2 \, 2p^6 \, 3s^1\) |
| Mg | 12 | \( " \, " \, " \, 3s^2\) |
| Al | 13 | \( " \, " \, " \, 3s^2 \, 3p^1\) |
| Si | 14 | \( " \, " \space" \, 3s^2 \, 3p^2\) |
| P | 15 | \( " \space " \, " \, 3s^2 \, 3p^3\) |
| S | 16 | \( " \, " \, " \, 3s^2 \, 3p^4\) |
| Cl | 17 | \( " \, " \, " \, 3s^2 \, 3p^5\) |
| Ar | 18 | \( " \, " \, " \, 3s^2 \, 3p^6\) |
| K | 19 | \( " \, " \, " \, 3s^2 \, 3p^6 \, 4s^1\) |
| Ca | 20 | \( " \, " \, " \, " \, " \, 4s^2\) |
Examining the above table, you can see that as the number of electrons in an atom increases from 1 in hydrogen to 2 in helium and so on, the lowest-energy shell gets filled first—that is, the \(n = 1\) shell fills first, and then the \(n = 2\) shell begins to fill. Within a shell, the subshells fill starting with the lowest \(l\), or with the \(s\) subshell, then the \(p\), and so on, usually until all subshells are filled. The first exception to this occurs for potassium, where the \(4s\) subshell begins to fill before any electrons go into the \(3d\) subshell. The next exception is not shown in Table ; it occurs for rubidium, where the \(5s\) subshell starts to fill before the \(4d\) subshell. The reason for these exceptions is that \(l = 0\) electrons have probability clouds that penetrate closer to the nucleus and, thus, are more tightly bound (lower in energy).
Figure shows the periodic table of the elements, through element 118. Of special interest are elements in the main groups, namely, those in the columns numbered 1, 2, 13, 14, 15, 16, 17, and 18.
The number of electrons in the outermost subshell determines the atom’s chemical properties, since it is these electrons that are farthest from the nucleus and thus interact most with other atoms. If the outermost subshell can accept or give up an electron easily, then the atom will be highly reactive chemically. Each group in the periodic table is characterized by its outermost electron configuration. Perhaps the most familiar is Group 18 (Group VIII), the noble gases (helium, neon, argon, etc.). These gases are all characterized by a filled outer subshell that is particularly stable. This means that they have large ionization energies and do not readily give up an electron. Furthermore, if they were to accept an extra electron, it would be in a significantly higher level and thus loosely bound. Chemical reactions often involve sharing electrons. Noble gases can be forced into unstable chemical compounds only under high pressure and temperature.
Group 17 (Group VII) contains the halogens, such as fluorine, chlorine, iodine and bromine, each of which has one less electron than a neighboring noble gas. Each halogen has 5\(p\) electrons (a \(p^5\) configuration), while the \(p\) subshell can hold 6 electrons. This means the halogens have one vacancy in their outermost subshell. They thus readily accept an extra electron (it becomes tightly bound, closing the shell as in noble gases) and are highly reactive chemically. The halogens are also likely to form singly negative ions, such as \(Cl^-\) fitting an extra electron into the vacancy in the outer subshell. In contrast, alkali metals, such as sodium and potassium, all have a single \(s\) electron in their outermost subshell (an \(s^1\) configuration) and are members of Group 1 (Group I). These elements easily give up their extra electron and are thus highly reactive chemically. As you might expect, they also tend to form singly positive ions, such as \(Na^+\), by losing their loosely bound outermost electron. They are metals (conductors), because the loosely bound outer electron can move freely.
Of course, other groups are also of interest. Carbon, silicon, and germanium, for example, have similar chemistries and are in Group 4 (Group IV). Carbon, in particular, is extraordinary in its ability to form many types of bonds and to be part of long chains, such as inorganic molecules. The large group of what are called transitional elements is characterized by the filling of the \(d\) subshells and crossing of energy levels. Heavier groups, such as the lanthanide series, are more complex—their shells do not fill in simple order. But the groups recognized by chemists such as Mendeleev have an explanation in the substructure of atoms.
PHET EXPLORATIONS: BUILD AN ATOM
Build an atom out of protons, neutrons, and electrons, and see how the element, charge, and mass change. Then play a game to test your ideas!
Summary
- The state of a system is completely described by a complete set of quantum numbers. This set is written as \((n, \, l, \, m_i, \, m_s)\).
- The Pauli exclusion principle says that no two electrons can have the same set of quantum numbers; that is, no two electrons can be in the same state.
- This exclusion limits the number of electrons in atomic shells and subshells. Each value of \(n\) corresponds to a shell, and each value of \(l\) corresponds to a subshell.
- The maximum number of electrons that can be in a subshell is \(2(2l + 1)\).
- The maximum number of electrons that can be in a shell is \(2n^2\).
Footnotes
- 1 It is unusual to deal with subshells having \(l\) greater than 6, but when encountered, they continue to be labeled in alphabetical order.
Glossary
- atomic number
- the number of protons in the nucleus of an atom
- Pauli exclusion principle
- a principle that states that no two electrons can have the same set of quantum numbers; that is, no two electrons can be in the same state
- shell
- a probability cloud for electrons that has a single principal quantum number
- subshell
- the probability cloud for electrons that has a single angular momentum quantum number