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Hi, I'm John Green, this is Crash Course U.S. History, and today, we're going to talk about slavery, which is not funny. 0:06 Yeah, so we put a lei on the eagle to try and cheer you up, but let's face it, this is going to be depressing. 0:10 With slavery, every time you think, like, "Aw, it couldn't have been that bad," it turns out to have been much worse. 0:14 Mr. Green, Mr. Green! But what about – 0:15 Yeah, Me from the Past, I'm going to stop you right there, because you're going to embarrass yourself. Slavery was hugely important to America. 0:20 I mean, it led to a civil war and it also lasted what, at least in U.S. history, counts as a long-ass time, from 1619 to 1865. 0:29 And yes, I know there's a 1200-year-old church in your neighborhood in Denmark, but we're not talking about Denmark! 0:35 But slavery is most important because we still struggle with its legacy. 0:38 So, yes, today's episode will probably not be funny, but it will be important. 0:42 [Theme Music] North & South economic ties 0:51 So the slave-based economy in the South is sometimes characterized as having been separate from the Market Revolution, but that's not really the case. 0:57 Without southern cotton, the North wouldn't have been able to industrialize, at least not as quickly, because cotton textiles were one of the first industrially products. 1:04 And the most important commodity in world trade by the nineteenth century, and 3/4 of the world's cotton came from the American South. 1:11 And speaking of cotton, why has no one mentioned to me that my collar has been half popped this entire episode, like I'm trying to recreate the Flying Nun's hat. 1:18 And although there were increasingly fewer slaves in the North as northern states outlawed slavery, cotton shipments overseas made northern merchants rich. 1:26 Northern bankers financed the purchase of land for plantations. 1:29 Northern insurance companies insured slaves who were, after all, considered property, and very valuable property. 1:35 And in addition to turning cotton into cloth for sale overseas, northern manufacturers sold cloth back to the South, where it was used to clothe the very slaves who had cultivated it. 1:45 But certainly the most prominent effects of the slave-based economy were seen in the South. Slave-based agriculture in the South 1:49 The profitability of slaved-based agriculture, especially King Cotton, meant that the South would remain largely agricultural and rural. 1:56 Slave states were home to a few cities, like St. Louis and Baltimore, but with the exception of New Orleans, 2:00 almost all southern urbanization took place in the upper South, further away from the large cotton plantations. 2:06 And slave-based agriculture was so profitable that it siphoned money away from other economic endeavors. 2:11 Like, there was very little industry in the South. 2:13 It produced only 10% of the nation's manufactured goods. 2:16 And, as most of the capital was being plowed into the purchase of slaves, there was very little room for technological innovation, like, for instance, railroads. 2:23 This lack of industry and railroads would eventually make the South suck at the Civil War, thankfully. 2:27 In short, slavery dominated the South, shaping it both economically and culturally, and slavery wasn't a minor aspect of American society. Popular attitudes concerning slavery 2:35 By 1860, there were four million slaves in the U.S., and in the South, they made up one third of the total population. 2:42 Although in the popular imagination, most plantations were these sprawling affairs with hundreds of slaves, 2:47 in reality, the majority of slaveholders owned five or fewer slaves. 2:51 And, of course, most white people in the South owned no slaves at all, though, if they could afford to, they would sometimes rent slaves to help with their work. 2:57 These were the so-called yeoman farmers who lived self-sufficiently, raised their own food, and purchased very little in the Market Economy. 3:04 They worked the poorest land and, as a result, were mostly pretty poor themselves. 3:08 But even they largely supported slavery, partly, perhaps, for aspirational reasons, and partly because the racism inherent to the system gave even the poorest whites legal and social status. 3:18 And southern intellectuals worked hard to encourage these ideas of white solidarity and to make the case for slavery. 3:23 Many of the founders, a bunch of whom you'll remember, held slaves, saw slavery as a necessary evil. 3:29 Jefferson once wrote, quote, "As it is, we have the wolf by the ear, and we can neither hold him, nor safely let him go. 3:37 Justice is on one scale, and self-preservation in the other." 3:41 The belief that justice and self-preservation couldn't sit on the same side of the scale was really opposed to the American idea, 3:47 and, in the end, it would make the Civil War inevitable. 3:50 But as slavery became more entrenched in these ideas of liberty and political equality were embraced by more people, 3:55 some southerners began to make the case that slavery wasn't just a necessary evil. 3:59 They argued, for instance, that slaves benefited from slavery. 4:03 Because, you know, because their masters fed them and clothed them and took care of them in their old age. 4:07 You still hear this argument today, astonishingly. 4:09 In fact, you'll probably see asshats in the comments saying that in the comments. 4:12 I will remind you, it's not cursing if you are referring to an actual ass. 4:15 This paternalism allowed masters to see themselves as benevolent and to contrast their family-oriented slavery with the cold, mercenary Capitalism of the free-labor North. 4:26 So yeah, in the face of rising criticism of slavery, some southerners began to argue that the institution was actually good for the social order. 4:33 One of the best-known proponents of this view was John C. Calhoun, who, in 1837, said this in a speech on the Senate floor: 4:40 "I hold that, in the present state of civilization, 4:43 where two races of different origin and distinguished by color and other physical differences as well as intellectual, are brought together, 4:51 the relation now existing in the slave-holding states between the two is, instead of an evil, a good. A positive good." 4:59 Now, of course, John C. Calhoun was a fringe politician, and nobody took his views particularly seriously. 5:04 Stan: Well, he was Secretary of State from 1844 to 1845. 5:07 John: Well, I mean, who really cares about the Secretary of State, Stan? 5:10 Danica: Eh, he was also Secretary of War from 1817 to 1825. 5:13 John: All right, but we don't even have a Secretary of War anymore, so... 5:16 Meredith: And he was Vice President from 1825 to 1832. 5:19 John: Oh my god, were we insane?! 5:21 We were, of course, but we justified the insanity with Biblical passages and with the examples of the Greeks and Romans, 5:28 and with outright racism, arguing that black people were inherently inferior to whites. 5:33 And that not to keep them in slavery would upset the natural order of things. 5:37 A worldview popularized millennia ago by my nemesis, Aristotle. God, I hate Aristotle. 5:42 You know what defenders of Aristotle always say? 5:44 "He was the first person to identify dolphins." 5:47 Well, ok, dolphin identifier. 5:50 Yes, that is what he should be remembered for, but he's a terrible philosopher! Lives & experiences of enslaved people 5:53 Here's the truth about slavery: 5:55 It was coerced labor that relied upon intimidation and brutality and dehumanization. 6:00 And this wasn't just a cultural system, it was a legal one. 6:03 I mean, Louisiana law proclaimed that a slave "owes his master... a respect without bounds, and an absolute obedience." 6:09 The signal feature of slaves' lives was work. 6:12 I mean, conditions and tasks varied, but all slaves labored, usually from sunup to sundown, and almost always without any pay. 6:20 Most slaves worked in agriculture on plantations, and conditions were different, depending on which crops are grown. 6:25 Like, slaves on the rice plantations of South Carolina had terrible working conditions, 6:29 but they labored under the task system, which meant that once they had completed their allotted daily work, they would have time to do other things. 6:36 But lest you imagine this is like how we have work and leisure time, bear in mind that they were owned and treated as property. 6:42 On cotton plantations, most slaves worked in gangs, usually under the control of an overseer, or another slave who was called a "driver." 6:49 This was back-breaking work done in the southern sun and humidity, and so it's not surprising that whippings – or the threat of them – were often necessary to get slaves to work. 6:58 It's easy enough to talk about the brutality of slave discipline, but it can be difficult to internalize it. 7:03 Like, you look at these pictures, but because you've seen them over and over again, they don't have the power they once might have. 7:09 The pictures can tell a story about cruelty, but they don't necessarily communicate how arbitrary it all was. 7:14 As, for example, in this story, told by a woman who was a slave as a young girl: 7:18 "[The] overseer... went to my father one morning and said, "Bob, I'm gonna whip you this morning." 7:22 Daddy said, "I ain't done nothing," and he said, "I know it, I'm going to whip you to keep you from doing nothing," 7:28 and he hit him with that cowhide – you know it would cut the blood out of you with every lick if they hit you hard." 7:33 That brutality – the whippings, the brandings, the rape – was real, and it was intentional, because, in order for slavery to function, slaves had to be dehumanized. 7:43 This enabled slaveholders to rationalize what they were doing, and it was hoped to reduce slaves to the animal property that is implied by the term "chattel slavery." 7:51 So the idea was that slaveholders wouldn't think of their slaves as human, and slaves wouldn't think of themselves as human. 7:57 But it didn't work. Let's go to the Thought Bubble. 7:59 Slaves' resistance to their dehumanization took many forms, but the primary way was by forming families. Family, love, & religion of enslaved people 8:05 Family was a refuge for slaves and a source of dignity that masters recognized and sought to stifle. 8:10 A paternalistic slave owner named Bennet H. Barrow wrote in his rules for the Highland Plantation: 8:15 "No rule that I have stated is of more importance than that relating to Negroes marrying outside of the plantation... It creates a feeling of independence." 8:23 Most slaves did marry, usually for life, and, when possible, slaves grew up in two-parent households. 8:28 Single-parent households were common, though, as a result of one parent being sold. 8:32 In the upper South, where the economy was shifting from tobacco to different, less labor-intensive cash crops, the sale of slaves was common. 8:40 Perhaps one-third of slave marriages in states like Virginia were broken up by sale. 8:45 Religion was also an important part of life in slavery. 8:47 While masters wanted their slaves to learn the parts of the Bible that talked about being happy in bondage, 8:52 slave worship tended to focus on the stories of Exodus, where Moses brought the slaves out of bondage, 8:57 or Biblical heroes, who overcame great odds, like Daniel and David. 9:01 And, although most slaves were forbidden to learn to read and write, many did anyway. And some became preachers. 9:07 Slave preachers were often very charismatic leaders, and they roused the suspicion of slave owners, and not without reason. 9:13 Two of the most important slave uprisings in the South were led by preachers. 9:16 Thanks, Thought Bubble. 9:17 Oh, it's time for the Mystery Document? Mystery Document 9:19 We're doing two set pieces in a row? All right. [buzzing noise] [music] 9:24 The rules here are simple. 9:26 I wanted to re-shoot that, but Stan said no. 9:29 I guess the author of the Mystery Document. 9:30 If I am wrong, I get shocked with the shock pen. 9:33 "Since I have been in the Queen's dominions I have been well contented, yes well contented for sure, man is as God intended he should be. 9:40 That is, all are born free and equal. 9:43 This is a wholesome law, not like the southern laws which puts man made in the image of God on level with brutes. 9:49 O, what will become of the people, and where will they stand in the day of judgment. 9:53 Would that the 5th verse of the 3rd chapter of Malachi were written as with a bar of iron, 9:59 and the point of a diamond upon every oppressor's heart that they might repent of this evil, and let the oppressed go free..." 10:06 All right, it's definitely a preacher, because only preachers have read Malachi. 10:10 Probably African American, probably not someone from the South. 10:13 I'm going to guess that it is Richard Allen, the founder of the African Methodist Episcopal Church? 10:18 [buzzing noise] DAAAH, DANG IT! 10:19 It's Joseph Taper, and Stan just pointed out to me that I should have known it was Joseph Taper because it starts out, 10:24 "Since I have been in the Queen's dominions..." 10:27 He was in Canada. He escaped slavery to Canada. The Queen's dominions! 10:31 All right, Canadians, I blame you for this, although, thank you for abolishing slavery decades before we did. 10:36 [electric sounds] AHHH! How people resisted & escaped slavery 10:37 So, the Mystery Document shows one of the primary ways that slaves resisted their oppression: by running away. 10:42 Although some slaves like Joseph Taper escaped for good by running away to northern free states, 10:47 or even to Canada, where they wouldn't have to worry about fugitive slave laws, even more slaves ran away temporarily, hiding out in the woods or the swamps, and eventually returning. 10:55 No one knows exactly how many slaves escaped to freedom, but the best estimate is that a thousand or so a year made the journey northward. 11:01 Most fugitive slaves were young men, but the most famous runaway has been hanging out behind me all day long: Harriet Tubman. 11:07 Harriet Tubman escaped to Philadelphia at the age of 29, and over the course of her life, she made about 20 trips back to Maryland to help friends and relatives make the journey north on the Underground Railroad. 11:17 But a more dramatic form of resistance to slavery was actual, armed rebellion, which was attempted. 11:22 Now, individuals sometimes took matters into their own hands and beat or even killed their white overseers or masters. 11:27 Like Bob, the guy who received the arbitrary beating, responded to it by killing his overseer with a hoe. 11:33 But that said, large-scale slave uprisings were relatively rare. 11:36 The four most famous ones all took place in a 35-year period at the beginning of the 19th century. Slave rebellions 11:41 Gabriel's Rebellion in 1800 – which we've talked about before – was discovered before he was able to carry out his plot. 11:45 Then, in 1811, a group of slaves upriver from New Orleans seized cane, knives, and guns, and marched on the city before militia stopped them. 11:52 And in 1822, Denmark Vesey, a former slave who had purchased his freedom, may have organized a plot to destroy Charleston, South Carolina. 11:59 I say "may have" because the evidence against him is disputed and comes from a trial that was not fair. 12:05 But regardless, the end result of that trial was that he was executed, as were 34 slaves. Nat Turner's Rebellion 12:09 But the most successful slave rebellion, at least in the sense that they actually killed some people, was Nat Turner's in August 1831. 12:15 Turner was a preacher, and with a group of about 80 slaves, he marched from farm to farm in South Hampton County, Virginia, 12:21 killing the inhabitants, most of whom were women and children, because the men were attending a religious revival meeting in North Carolina. 12:27 Turner and 17 other rebels were captured and executed, but not before they struck terror into the hearts of whites all across the American South. 12:34 Virginia's response was to make slavery worse, passing even harsher laws that forbade slaves from preaching, and prohibited teaching them to read. 12:42 Other slave states followed Virginia's lead and, by the 1830s, slavery had grown, if anything, more harsh. 12:47 So, this shows that large-scaled armed resistance was – Django Unchained aside – not just suicidal, but also a threat to loved ones and, really, to all slaves. How enslaved people resisted their oppression & why it matters 12:55 But, it is hugely important to emphasize that slaves did resist their oppression. 12:59 Sometimes this meant taking up arms, but usually it meant more subtle forms of resistance, 13:03 like intentional work slowdowns or sabotaging equipment, or pretending not to understand instructions. 13:08 And, most importantly, in the face of systematic legal and cultural degradation, they re-affirmed their humanity through family and through faith. 13:16 Why is this so important? 13:17 Because too often in America, we still talk about slaves as if they failed to rise up, 13:21 when, in fact, rising up would not have made life better for them or for their families. 13:26 The truth is, sometimes carving out an identity as a human being in a social order that is constantly seeking to dehumanize you, is the most powerful form of resistance. 13:34 Refusing to become the chattel that their masters believed them to be is what made slavery untenable and the Civil War inevitable, so make no mistake, slaves fought back. 13:45 And in the end, they won. I'll see you next week. Credits 13:48 Crash Course is produced and directed by Stan Muller. 13:50 The script supervisor is Meredith Danko. 13:52 Our associate producer is Danica Johnson. 13:54 The show is written by my high school history teacher Raoul Meyer and myself. 13:57 And our graphics team is Thought Cafe. 13:58 Every week, there's a new caption to the Libertage, but today's episode was so sad that we couldn't fit a Libertage in... 14:04 UNTIL NOW! [Libertage Rock Music] 14:08 Suggest Libertage caption in comments, where you can also ask questions about today's video that will be answered by our team of historians. 14:13 Thanks for watching Crash Course, and as we say in my home town, don't forget to be abolitionist.

As long as the birth rate of a population exceeds the death rate, the population size will continue to increase. At a steady, positive per capita growth rate, the population will add a larger number of indi- viduals with each generation. So, a population can increase rapidly with even a small growth rate. A pattern of increase in number due to a steady growth rate is called exponential growth. The observa- tion that populations can grow in this pattern is called the exponential (EKS-poh-NEN-shuhl) model of population growth. One way to understand the exponential model is to study a graph of population size over time. A graph of exponential growth makes the characteristic J-shaped curve shown in Figure 19-6. With expo- nential growth, population size grows slowly when it is small, but growth speeds up as individuals join the population. The exponen- tial model leads us to predict that the population size will increase indefinitely and by a greater number with each time period. Applying the Exponential Model A scientific model is useful if it helps to predict or explain pat- terns that can be observed in reality. Indeed, the exponential model matches observed patterns of growth of real populations, but only under certain conditions and for limited periods of time. For example, a population of microorganisms can grow exponen- tially if provided with an abundance of food and space and if waste is removed. Figure 19-7 shows the growth of bacteria in a laboratory. However, the exponential model does not apply to most popu- lations. In natural environments, populations cannot grow indefi- nitely because the resources they depend on become scarce and harmful wastes accumulate. Any factor, such as space, that restrains the growth of a population is called a limiting factor. All populations are ultimately limited by their environment.SPECIES INTERACTIONS Just as populations contain interacting members of a single species, communities contain interacting populations of many species. Many species have specific types of interactions with other species. This chapter introduces the five major types of interactions among species: predation, competition, parasitism, mutualism, and commensalism. These categories are based on whether each species causes any benefit or harm to the other species in a given relationship. PREDATION In predation (pree-DAY-shuhn), an individual of one species, called the predator, eats all or part of an individual of another species, called the prey. Predation is a powerful force in a community. The relationship between predator and prey influences the size of each population and affects where and how each species lives. Examples of predators include carnivores—predators that eat ani- mals—and herbivores—predators that eat plants. Many types of organisms can act as predators or prey. All heterotrophs are either predators or parasites or both. Predator Adaptations Natural selection favors the evolution of predator adaptations for finding, capturing, and consuming prey. For example, rattlesnakes have an acute sense of smell and have heat-sensitive pits located below each nostril. These pits enable a rattlesnake to detect warm- bodied prey, even in the dark. Many snakes use venom to disable or kill their prey. A venomous rat- tlesnake is shown in Figure 20-1. Other predator adaptations include the sticky webs of spiders, the flesh-cutting teeth of wolves and coyotes, the speed of cheetahs, and the striped pat- tern of a tiger’s coat, which provides camouflage in a grassland habitat. Many herbivores have mouthparts suited to cutting and chewing tough vegetation. A predator’s survival depends on its ability to capture food, but a prey’s survival depends on its ability to avoid being captured. Therefore, natural selection also favors adaptations in prey that allow the prey to escape, avoid, or otherwise ward off

The word “paragraph” is associated with two Greeks words: “para” which means “beyond” or ‘beside” and “graphein” which means “to write.” A paragraph is a collection of related sentences with one central idea. Each sentence shows connection to other sentences in the paragraph. It is independent unit or related unit. As an independent unit, it is a part of a composition that is combined with other paragraph to make a larger composition. Whether paragraph is an independent or related unit, it has its beginning, middle and ending.

Understanding Quantum Theory of Electrons in Atoms The goal of this section is to understand the electron orbitals (location of electrons in atoms), their different energies, and other properties. The use of quantum theory provides the best understanding to these topics. This knowledge is a precursor to chemical bonding. As was described previously, electrons in atoms can exist only on discrete energy levels but not between them. It is said that the energy of an electron in an atom is quantized, that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels. The energy levels are labeled with an n value, where n = 1, 2, 3, …. Generally speaking, the energy of an electron in an atom is greater for greater values of n. This number, n, is referred to as the principal quantum number. The principal quantum number defines the location of the energy level. It is essentially the same concept as the n in the Bohr atom description. Another name for the principal quantum number is the shell number. The shells of an atom can be thought of concentric circles radiating out from the nucleus. The electrons that belong to a specific shell are most likely to be found within the corresponding circular area. The further we proceed from the nucleus, the higher the shell number, and so the higher the energy level (Figure 9.4.1). The positively charged protons in the nucleus stabilize the electronic orbitals by electrostatic attraction between the positive charges of the protons and the negative charges of the electrons. So the further away the electron is from the nucleus, the greater the energy it has. This quantum mechanical model for where electrons reside in an atom can be used to look at electronic transitions, the events when an electron moves from one energy level to another. If the transition is to a higher energy level, energy is absorbed, and the energy change has a positive value. To obtain the amount of energy necessary for the transition to a higher energy level, a photon is absorbed by the atom. A transition to a lower energy level involves a release of energy, and the energy change is negative. This process is accompanied by emission of a photon by the atom. The following equation summarizes these relationships and is based on the hydrogen atom: The values nf and ni are the final and initial energy states of the electron. The principal quantum number is one of three quantum numbers used to characterize an orbital. An atomic orbital, which is distinct from an orbit, is a general region in an atom within which an electron is most probable to reside. The quantum mechanical model specifies the probability of finding an electron in the three-dimensional space around the nucleus and is based on solutions of the Schrödinger equation. In addition, the principal quantum number defines the energy of an electron in a hydrogen or hydrogen-like atom or an ion (an atom or an ion with only one electron) and the general region in which discrete energy levels of electrons in a multi-electron atoms and ions are located. Another quantum number is l, the angular momentum quantum number. It is an integer that defines the shape of the orbital, and takes on the values, l = 0, 1, 2, …, n – 1. This means that an orbital with n = 1 can have only one value of l, l = 0, whereas n = 2 permits l = 0 and l = 1, and so on. The principal quantum number defines the general size and energy of the orbital. The l value specifies the shape of the orbital. Orbitals with the same value of l form a subshell. In addition, the greater the angular momentum quantum number, the greater is the angular momentum of an electron at this orbital. Orbitals with l = 0 are called s orbitals (or the s subshells). The value l = 1 corresponds to the p orbitals. For a given n, p orbitals constitute a p subshell (e.g., 3p if n = 3). The orbitals with l = 2 are called the d orbitals, followed by the f-, g-, and h-orbitals for l = 3, 4, 5, and there are higher values we will not consider. There are certain distances from the nucleus at which the probability density of finding an electron located at a particular orbital is zero. In other words, the value of the wavefunction ψ is zero at this distance for this orbital. Such a value of radius r is called a radial node. The number of radial nodes in an orbital is n – l – 1. Consider the examples in Figure 9.4.2. The orbitals depicted are of the s type, thus l = 0 for all of them. It can be seen from the graphs of the probability densities that there are 1 – 0 – 1 = 0 places where the density is zero (nodes) for 1s (n = 1), 2 – 0 – 1 = 1 node for 2s, and 3 – 0 – 1 = 2 nodes for the 3s orbitals. The s subshell electron density distribution is spherical and the p subshell has a dumbbell shape. The d and f orbitals are more complex. These shapes represent the three-dimensional regions within which the electron is likely to be found. Principal quantum number (n) & Orbital angular momentum (l): The Orbital Subshell: https://youtu.be/ms7WR149fAY If an electron has an angular momentum (l ≠ 0), then this vector can point in different directions. In addition, the z component of the angular momentum can have more than one value. This means that if a magnetic field is applied in the z direction, orbitals with different values of the z component of the angular momentum will have different energies resulting from interacting with the field. The magnetic quantum number, called ml, specifies the z component of the angular momentum for a particular orbital. For example, for an s orbital, l = 0, and the only value of ml is zero. For p orbitals, l = 1, and ml can be equal to –1, 0, or +1. Generally speaking, ml can be equal to –l, –(l – 1), …, –1, 0, +1, …, (l – 1), l. The total number of possible orbitals with the same value of l (a subshell) is 2l + 1. Thus, there is one s-orbital for ml = 0, there are three p-orbitals for ml = 1, five d-orbitals for ml = 2, seven f-orbitals for ml = 3, and so forth. The principal quantum number defines the general value of the electronic energy. The angular momentum quantum number determines the shape of the orbital. And the magnetic quantum number specifies orientation of the orbital in space, as can be seen in Figure 9.4.3. Figure 9.4.4 illustrates the energy levels for various orbitals. The number before the orbital name (such as 2s, 3p, and so forth) stands for the principal quantum number, n. The letter in the orbital name defines the subshell with a specific angular momentum quantum number l = 0 for s orbitals, 1 for p orbitals, 2 for d orbitals. Finally, there are more than one possible orbitals for l ≥ 1, each corresponding to a specific value of ml. In the case of a hydrogen atom or a one-electron ion (such as He+, Li2+, and so on), energies of all the orbitals with the same n are the same. This is called a degeneracy, and the energy levels for the same principal quantum number, n, are called degenerate energy levels. However, in atoms with more than one electron, this degeneracy is eliminated by the electron–electron interactions, and orbitals that belong to different subshells have different energies. Orbitals within the same subshell (for example ns, np, nd, nf, such as 2p, 3s) are still degenerate and have the same energy. While the three quantum numbers discussed in the previous paragraphs work well for describing electron orbitals, some experiments showed that they were not sufficient to explain all observed results. It was demonstrated in the 1920s that when hydrogen-line spectra are examined at extremely high resolution, some lines are actually not single peaks but, rather, pairs of closely spaced lines. This is the so-called fine structure of the spectrum, and it implies that there are additional small differences in energies of electrons even when they are located in the same orbital. These observations led Samuel Goudsmit and George Uhlenbeck to propose that electrons have a fourth quantum number. They called this the spin quantum number, or ms. The other three quantum numbers, n, l, and ml, are properties of specific atomic orbitals that also define in what part of the space an electron is most likely to be located. Orbitals are a result of solving the Schrödinger equation for electrons in atoms. The electron spin is a different kind of property. It is a completely quantum phenomenon with no analogues in the classical realm. In addition, it cannot be derived from solving the Schrödinger equation and is not related to the normal spatial coordinates (such as the Cartesian x, y, and z). Electron spin describes an intrinsic electron “rotation” or “spinning.” Each electron acts as a tiny magnet or a tiny rotating object with an angular momentum, even though this rotation cannot be observed in terms of the spatial coordinates. The magnitude of the overall electron spin can only have one value, and an electron can only “spin” in one of two quantized states. One is termed the α state, with the z component of the spin being in the positive direction of the z axis. This corresponds to the spin quantum number ms=12. The other is called the β state, with the z component of the spin being negative and ms=−12. Any electron, regardless of the atomic orbital it is located in, can only have one of those two values of the spin quantum number. The energies of electrons having ms=−12 and ms=12 are different if an external magnetic field is applied. Figure 9.4.5 illustrates this phenomenon. An electron acts like a tiny magnet. Its moment is directed up (in the positive direction of the z axis) for the 12 spin quantum number and down (in the negative z direction) for the spin quantum number of −12. A magnet has a lower energy if its magnetic moment is aligned with the external magnetic field (the left electron) and a higher energy for the magnetic moment being opposite to the applied field. This is why an electron with ms=12 has a slightly lower energy in an external field in the positive z direction, and an electron with ms=−12 has a slightly higher energy in the same field. This is true even for an electron occupying the same orbital in an atom. A spectral line corresponding to a transition for electrons from the same orbital but with different spin quantum numbers has two possible values of energy; thus, the line in the spectrum will show a fine structure splitting. The Pauli Exclusion Principle An electron in an atom is completely described by four quantum numbers: n, l, ml, and ms. The first three quantum numbers define the orbital and the fourth quantum number describes the intrinsic electron property called spin. An Austrian physicist Wolfgang Pauli formulated a general principle that gives the last piece of information that we need to understand the general behavior of electrons in atoms. The Pauli exclusion principle can be formulated as follows: No two electrons in the same atom can have exactly the same set of all the four quantum numbers. What this means is that electrons can share the same orbital (the same set of the quantum numbers n, l, and ml), but only if their spin quantum numbers ms have different values. Since the spin quantum number can only have two values (±12), no more than two electrons can occupy the same orbital (and if two electrons are located in the same orbital, they must have opposite spins). Therefore, any atomic orbital can be populated by only zero, one, or two electrons. The properties and meaning of the quantum numbers of electrons in atoms are briefly

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