Lec 3 | MIT 3.091 Introduction to Solid State Chemistry

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Lec 3 | MIT 3.091 Introduction to Solid State Chemistry

get started: tomorrow there will be a 10 minute quiz in recitation based upon the content of homework one Obviously, it’s not going to be a question identical to something you’ve done, but it’s going to cover that subject matter So, please don’t bring in your attorney if I didn’t ask a question that’s identical to one that you’ve worked Second thing, we started talking about the periodic table, and I believe that it’s a hallmark of any educated person in the 21st century who is technically literate to know the periodic table by heart And so, there will be another test It will be on the 23rd on a Thursday, ten minutes You will be asked to write down the periodic table But, you don’t have to do the whole table. We’re going to leave out the lanthanides and actinides So, this is what it’s going to look like. You’ll have S block, P block, and D block elements If I could just ask if the people can fix the video, it’s just a little bit set off to the left here So, this is what you’ll get You’ll get 10 minutes to fill it in, and people grouse about it They say, oh, this is rote learning This went out at the end of the 19th century, and so on And I say, no, I think any of you should know that potassium lies under sodium. I bet there are people in this room who know the lyrics to over 1, 00 songs, know the number of every individual in the National Basketball Association, so I think that learning some subset of elements is not unreasonable Everybody’s done it in the past They grouse about it when I assign it, and they all do it within a minute. And then, they’re proud of it and they insist that I, not inflict, but rather induce you, invite you to do the same thing But, I don’t want to leave out the lanthanides and actinides So, lanthanum, cerium, praseodymium, and so on. So, here’s an example of a mnemonic. So, there will be two of these contests, one for lanthanides, one for actinides. Submitted by e-mail by 5 p.m. eastern daylight time to my office to my e-mail address So, this is an example: lazy college professors never produced officially educated graduates to dramatically help executives trim yearly losses And if you remember this phrase, I don’t know why you would, but this You can see that this obviously came from industry There’s a reference to executives There is the slur against the academy here: lazy college professors. I mean, they have no idea how hard we work, and look at this gigantic split infinitive, to dramatically help We can do better. So, this is 3 91 winners from previous years This is one. [LAUGHTER] Clearly, There’s other ways to take chemistry at MIT. In fact, there’s a whole chemistry department full of loony chemistry professors Here’s another one. This one piqued my interest I like the engineering theory of it That’s what I liked But now, this is the piece de resistance. I’ve been doing this for many years, and all of a sudden comes a sonnet There are 14 f-block elements, and an Elizabethan sonnet contains 14 lines Well, OK, this looks good, and so there is the cerium, praseodymium, neodymium, you know, three stanzas, four lines apiece with the rhyming couplet at the end But what’s really shocking is when you compare this with this, it’s based upon sonnet 57 because lanthanum is element 57 This is really, really good And, I mean, I wouldn’t just give You see he mentioned smelting And, as an extractive metallurgist, that took the cake. When he said smelting, I said, OK, you got it. So, I think this is something to think about. We’ll wait before we go to that one, blank on that one So, the contest, the prizes are neckties, and ladies’ scarves They’re very hot They’re black with colored elements of the periodic table It’s very nice. Don’t laugh, I’ll bring samples next date. They really look sharp,

very sharp. There’s all kinds of gift giving coming down the road You never know when one of these could just do the trick So, don’t fail to enter And, I will have office hours today By all means, go to your own recitation instructor as well So, last date we were looking at some early taxonomy, and then on to a little bit more about the interior of the atom And, we looked at the representation of elements in the periodic table where we have the proton number, z, which is equal to the number of electrons in the neutral atom, and the atomic mass which is the sum of the proton number and the neutron number. We talked about isotopes, and whatnot Today, I want to continue So far, we’ve put looking at static elements. But most people think of chemistry as involving reactions So, let’s look at dynamics, reactions between chemicals So, how would we describe a chemical reaction? What are the rules? Well, the first thing you do is you write an equation And, the equation is subject to these constraints First of all, we invoke Dalton’s Law We invoke Dalton’s Law of molar proportions, and secondly we write it subject to conservation of mass We write it subject to conservation of mass. And, I mean literally, mass, not mole number And, let’s look at this This is probably best seen by This is the calcination of limestone Limestone is calcium carbonate, and at about 900íC, calcium carbonate decomposes to give lime or calcium oxide plus carbon dioxide **CaCO3 –>CaO + CO2** And, this is used as the first step for making cement concrete And so, when you think about how much cement concrete are consumed annually on the planet, this becomes a considerable point source of greenhouse gas emissions And as you know, carbon dioxide is implicated as a greenhouse gas And, there’s a huge amount of CO2 that comes from this process This is also used in steelmaking and so on. So, anything on the left side of the equation is called a reactant, and anything on the right side of the equation is called a product And, just to show some of the hidden balance here, here we have one mole I don’t put a one in front. We just take one for granted So, there’s 1 mole of calcium carbonate. That gives us 1 mole of calcium oxide and 1 mole of carbon dioxide. So, here we have 2 mole, and here we have 1 mole. So, what’s the conservation of mass if we divide by the atomic masses here? We will get 100 g of calcium carbonate and then discover that we have 56 g of calcium oxide, and 44 g of carbon dioxide So, clearly, mass is conserved, not mole numbers. And, if you have trouble balancing equations, you can look in section 2.11 in the text. And, they go through some mechanics. But now, I want to look at what happens when things are not in proper proportion So, in other words, what happens if we put a bunch of elements, And so, for that, I want to look at the production of titanium by the Kroll process And, this involves the reaction of titanium tetrachloride with magnesium to form magnesium chloride plus titanium **TiCl4 + 2 Mg — 2 MgCl2 + Ti**. And, this was invented in 1937 by W. J. Kroll While he was still in Luxembourg, just before World War II broke out, he emigrated to the United States make huge quantities of titanium And, this reaction is performed in a giant batch type reactor in which you feed titanium tetrachloride and magnesium and heat to about 900íC And, as the reaction goes, we’ll have some magnesium liquid sitting on top of magnesium chloride liquid, and then chunks of titanium solid forming at the bottom with

titanium chloride gas above And, this is a really clever reaction because titanium tetrachloride is a gas So, it’s obviously buoyant Magnesium is a liquid but it’s less dense than magnesium chloride So, as these products form, they So, the reaction can keep going And at the end of the reaction, you have the reactor consumed of titanium tetrachloride magnesium You have salt on top, and you have titanium on the bottom And, this is what the stuff looks like. Earlier this summer I was at a smelter in Japan, the largest titanium smelter on the planet. And this is coming out of one of these reactors This is both 3 m across, and about 6 m tall. This is titanium sponge that comes out of the bottom of this reactor, And, these are giant billets of solid titanium weighing tens of tons OK, so let’s say some young engineer is on the job the first day and says, OK, let’s put in 200 kg of tickle, and let’s put in about 25 kg of mag. I’m using the typical terms Nobody says titanium tetrachloride It’s tickle. This is mag. I had a graduate student She was a brilliant Ph student of mine and she had two dogs This is parenthetical And, she loved metallurgy as I do, and she named one of her dogs Maggie, and one of her dogs Molly, magnesium and molybdenum. Boy, you have no sense of humor whatsoever. Either that or you are dog lovers and you are offended by giving them metallic names I don’t know. All right, so what happens? What does this engineer OK, so what we have to do is get back underneath this reaction, and see what the molar quantities are. So, titanium tetrachloride, magnesium, I’ve got 200 kg here, 25 kg here, and if I divide by the appropriate quantities, I’ll discover I have a little over 1, 00 moles of tickle, and I’ve got about 1, 00 moles of mag But, the reaction says I need twice as much mag as tickle if this reaction is going to go to completion. Clearly, this isn’t twice that In fact, it’s even less than that So, we’ve got a problem here. This is much less that two times 1, 54, so therefore mag is the limiting reagent. Mag is the limiting reagent. And, that’s going to gate the yield It’s going to control the yield The yield is going to be throttled by magnesium. So, how much titanium can I make? I can only make as much titanium as So, if I look at the mole ratios on the reaction over there, I’m going to find that I’ll be able to consume, at most, 1,029 over two, right? Two moles of mag consume one mole of tickle, giving us one mole of Ti, and that’s 515 moles of tickle consumed And then, that produces 515 moles titanium. And then I convert that to mass, and that gives me 24 kg of titanium. If I charged the reactor in this manner, and of course I’m assuming 100% completion of the reaction which we know is overly optimistic There may be some inefficiencies, and at some point, if you catch me in the hallway, OK, so now the question is, how do we know the first place that this is a suitable reductant? How do we know that mag will reduce titanium tetrachloride? Well, for this, we have to look inside the atom And as I’m going to do many times in 3.091, I’m going to start a unit like this with a history lesson So, let’s go back to the thrilling days of the end of the 19th century, and just take stock. What did we know at the end of the 19th century about the structure of the atom? Well, first of all, we knew that the atom was electrically neutral We knew that the negative charge is carried by some particles called electrons. Furthermore, the electron has a very tiny mass in comparison to that of the overall atom. I mean, the atom has a tiny mass, too, but what we are saying is compared to the totaled atomic mass, the mass of the electron is tiny And, secondly, the bulk of the atom is positive If the atom is fixed mass, the It must be the positives have all the mass. So, inside the atom? Why do we want to know the answer

as to reactivity So, what do we know about spatial and the first model worth talking about is that of J He was a professor of physics at Cambridge University, and he was also the director of the Cavendish Laboratory Or I guess they would say laboratory. So, he was the director of the laboratory, and Cavendish made a fortune in the 1700s, and willed it to Cambridge And so, they established this laboratory in his name He said that the electrons were distributed throughout a uniformly charged positive sphere of atomic dimensions. So, electrons distributed throughout — — a uniformly charged positive sphere — — uniformly charged positive sphere, and let me finish it, of atomic dimension. So, essentially you’ve got a positive ball which is identical to the size of the atom This was termed the plum pudding model. This is cultural bias, of course. This is a British term I’ve never eaten the stuff. I don’t know if I’d eat it if it were put in front of me, but anyways, I’m told that it looks something like this, that you have the custard with little fragments of plum inside So, this is a positive sphere of custard, and inside are little, negative bits. This is the plum And, these bits are in motion. So, the bulk of the atom is positive That’s where the mass resides And, you get these tiny little negatives running around They are physically small They are very light, that is to say, low mass. They are mobile They’re moving around, and the worst thing is that J J., in 1897 did the pioneering work that got him the Nobel Prize He measured the charge to mass ratio of the electron But, he didn’t use the term of electron. He called this negative elemental particle the corpuscle And, he kept referring to them as corpuscles. And I’m really glad that along came Johnstone Stony, who was an electrochemist, the noblest form of chemistry, and as an electrochemist, he chose the term for the element of an electric charge, the electron, coming from the Greek word for amber because, So, thank goodness, Stony triumphed. Otherwise, we’d be talking about corpuscular mail. You’d have c-mail You wouldn’t have e-mail All right, so anyways, so all right we have a theory It’s 1904. What’s the method of science? You have a theory; what do you do? Put it to the test So, who puts it to the test? Ernest Rutherford. Ernest Rutherford: he was a professor of physics as well, but he was at Victoria University in Manchester just up the road from Cambridge Both of these were in the UK in the early part of the 20th century And, he conducted experiments to test the plum pudding model Basically what he did is he took a very thin metal foil, and he bombarded it with charged particles. And, here’s the Rutherford experiment It’s taken right out of your text But, before I go into details, a Rutherford was an interesting person He was born in New Zealand, and he came from a farming family He was the first generation to go to college, grew up in the farms, and as such, he was very skilled with machining He was very handy He was a brilliant experimentalist That’s not to say he wasn’t a brilliant thinker, but here the gift of a good minds and good hands, like the two parts of the MIT logo: two parts rolled into one He did his Ph He managed to get a fellowship, and he came to the UK all the way from New Zealand He got his Ph.D. under J J. Thompson at Cambridge. And there, he studied radiation coming from

radioactive elements, and he categorized to different types of radiation, which he termed alpha and beta, and what he found was that the alpha radiation as he studied it was very good at ionizing gases whereas beta radiation was not so good at ionizing gases On the other hand, when it came to penetrating solids, penetrating solids, the alpha radiation was poor at penetrating solids, whereas the beta radiation was very good at penetrating solids So, you see, this is formative information. He understood the interaction of particles of matter, and that’s important to set the stage for the Rutherford experiment went to another part of the British Empire and went to Canada, got a job at McGill. And, he worked for a little less than 10 years at McGill where he did more work on these particles that radiate from radioactive elements And there he was able to identify the alpha particle as the helium nucleus. It’s helium denuded of both of its electrons So, all that’s left is the helium nucleus, two protons, two neutrons. And, for this, he got the Nobel Prize in 1908 in physics Let me just check that, yes, no, excuse me. He got it in chemistry. And why I’m hesitating is, in the early days of the 20th century, the Nobels were first given in 1901. But, we’ll see as 3 91 progresses, people working almost on the same topic, making new discoveries out of the same lab, one of them might subsequently win the Nobel in physics One might win it in chemistry because the disciplines weren’t as diverse as they are today So, that’s why I hesitate So, he got the Nobel in chemistry, which made him a hot property academically. And so, he got hired to come to the UK, and got the job at Victoria University after bagging a Nobel in chemistry. By the way, he didn’t outdo his adviser, J. J. J. J. already got his Nobel So, let’s give him his credit, Nobel in physics. I rather suspect if J. J. hadn’t gotten his Nobel, it probably would have been tough for Rutherford to get one since some of these guys stood on the committees. But, it’s just a speculation All right, so now, let’s get on and talk about the experiment So, what we’ve got here is a source of alpha particles Alpha particles are these helium nuclei, and they are the result of sitting inside this leaded box with one opening. And so, we’ve got a beam. And, these particles are of extremely high energy, very, very high energy. And, they strike a thin foil of metal And, Rutherford tried various metals. But, the famous experiment is attributed to the use of gold We’ve known since antiquity that you could take gold, and you can hammer to very, very thin foil And, in this case, they had foil that was less than a micrometer thick This was 600 nanometers thick, very, very thin. And, so the experiment was to bombard the foil with these alpha particles, and that measure what happens to them. So, we have to be able to detect them. And so, And, Geiger invented a detector It’s called the scintillation screen. He ultimately invented the Geiger counter that bears his name But, he built a scintillation screen, which is essentially a cloth fiber that was covered with zinc sulfide. And, when zinc sulfide is hit by particles or by anything, by radiation or by particles of greater than a certain critical energy, there is a glow That’s from the Latin word scintilla, OK, spark So, you sit. You get graduate students or some other form of cheap labor and he had them sit in front of the scintillation screen, and they count. They count where these particles hit the screen And then, what they did is they made a map of where the particles scattered once they struck the screen. And, here’s what their findings were The important findings of note are the following First of all, the majority of the alpha particles were transmitted Majority of alphas transmitted, that means, when I use the term

transmitted that means passing through in the direction that they were originally traveling, transmitted and some deflected through small angles And, I’m going to abbreviate, just put theta. On what else do you use theta for, if not angles? So, deflected through small angles That’s the main thing that they observed, but there’s a second thing And this was really, really shocking. A tiny fraction of the incident alpha particles were deflected through large angles By large angles, I mean greater than 90í, essentially coming back in the direction from which they came OK, so tiny fraction, tiny fraction of alphas, tiny fraction of incident alphas, tiny fraction of incident And that, I mean, greater than 90í. So, this is called back scattering And, in fact, there’s a technique of analysis used today that’s called Rutherford back scattering where people actually saw that this is a means of identifying the substance, the sample. The scattering is an indication of the nature of the substance. And, this was a surprise because when you take a look at what that gold foil constitutes in the way of a resistance to a beam of charged particles of 7 8 million electron volts, when Rutherford learned of these results, he said, this is akin to having a 15 inch artillery shell deflect back from a piece of tissue paper, to give you a sense of the relative scales If you took a 15 inch artillery shell moving at the velocity it typically goes at, and take that amount of kinetic energy versus the resistive capacity of a sheet of tissue paper, that’s the scale that we’re looking at here. It was absolutely astonishing. So, they thought about this, and they said, you know, this cannot This can’t make sense because the plum pudding model says you’ve got uniformly distributed charge So, if I’ve got positive charge uniformly distributed, look at the choice. It’s a brilliant experiment He didn’t shoot neutrals He shot alpha particles which have a charge of plus two So, I’ve got plus twos, zooming in at high energy against a wall of positive charge And, most of the stuff goes flying through. So, you just say, well, this is like a bullet going through pumpkin So, what’s the big deal? But, how do you explain some of these going way, way back. And, that’s what Rutherford says, this can’t be right I’m going to come up with something else. I’m going to come up with this model. I’m going to say that the positive charge is not uniformly distributed. I’m going to say, quite to the contrary, the positive charge is concentrated at the center in a tiny, tiny, tiny volume So, I’ve got this tiny volume with, in the case of gold 79 plus of charge, and I’ve got some electrons out here somewhere, and the vast majority of the atom is nothing. Isn’t this a lot like Democritus? Being and void, being and void, so now I’ve got my plus two little projectile coming in, so the positives deflect. And so, there is a little bit of deflection because plus repels plus But once in awhile, one of these plus twos comes in almost on axis, and it gets whipped around by the Coulombic repulsive forces So, that’s Rutherford’s explanation of this set of data Oh, by the way, there is a third person There’s Rutherford, there’s Geiger, there’s Marsden. Marsden is an interesting character Marsden was not too different from you. Marsden was essentially a UROP He’d left school for a couple of years. He hadn’t gotten his undergrad yet He’d come back, and Rutherford accepted him in his lab. I think the man was something like 20 years of age So, he says to Marsden, take these data. I’m going to give you the data set of the scattering this. That’s the assignment Get busy. So, Marsden came up with

and electrodynamics, you’ll be able to do this analysis either side is nothing So, you’ve got a huge distance between center to center And, so all Marsden is doing is asking, what must be the, if I’ve got a wall of nothing with spots of high positive charge, and this is my scattering data, what must be the relative size of the spots versus the nothing? And, he solved the problem. And, he concluded, let’s get his name on the board. Heck, he deserves to have his name on the board, Marsden So, Marsden concluded by his analysis that the radius of the nucleus, and this is Rutherford, by the way, coining this term It’s a nuclear model The radius of the nucleus as compared to the radius of the entire atom is on the order of about one to 10,000. So, indeed, we are talking about a lot of void and a tiny little bit of extremely dense being. So, they published this And, what’s the result? You would think, well, they finally solved it, it’s terrific Hurray! No – it’s science They tear each other’s eyes out The reaction to a model was strongly negative Derision was the typical reaction They said, look, this is stupid First of all, this thing can’t sustain itself You’ve got a positive charge here with a negative charge around it Coulomb’s law says the negative will be attracted to the positive, and the atom will collapse. So, All the electrons fall into the nucleus. The data suggests that’s what it is. The problem is that the theory of the day can’t explain it So, of course, theoreticians bristle. It’s Huxley that said woe to the slaying of a beautiful theory by an ugly fact, nuclear collapse So, the Coulombic forces, You know what it means They’re Coulombic forces, end of story. All right, number two Second, even if it didn’t collapse, they said you’ve got a radiation problem. You’ve got negative charge in motion, and it’s in a circular orbit. And, you know acceleration means either change of speed or change of direction You will learn in 8 2 that if you have a charged body And, it will be accompanied by radiation. Radiation is the emission of energy And so, again, this thing will run out of gas. So, an energy deficit, accelerating charge, the accelerating negative charge, because it’s the negatives that are orbiting the positive center And that means radiation of energy, and that energy has to come from inside the atom itself So, on both counts, they say this is no good It’s no good. Well, time marches on. 1912: interesting A young Danish scientist by the name of Niels Bohr, he just finished his Ph in Copenhagen, and he had won himself a postdoctoral fellowship, courtesy of the Carlsberg Brewery foundation. Carlsberg Brewery for many years has sponsored scientific research through the Carlsberg Foundation So, Niels had a Ph and a Carlsberg Foundation Fellowship. And he decided, well, I’m interested in modern physics. There is some conflict in the air. One of the proponents is J J. Thompson. One of the proponents is Ernest Rutherford I know what I’ll do. I’ll spend six months with J J. in Cambridge, and I’ll spend six And that’s what he set out to do So, he goes to Cambridge, and he spends six months with Thompson And then, he heads up north. And then, he spends only three months in Manchester, not because he didn’t like Rutherford Actually, it was quite the contrary He far preferred Rutherford to Thompson. But, he got a teaching job, and so he zoomed back to Denmark to assume his teaching duties And, during the time of his interactions with Thompson and Rutherford, he got to thinking about

a way to explain the observations of Rutherford. And so, he finished the manuscript back in Copenhagen. In Copenhagen, he completes the manuscript and – I’m going to write MS for manuscript It’s a paper that describes a model to explain the results So, you see how we are oscillating back and forth? J. J. Thompson, model. Rutherford, experimental data. Now, Bohr comes with a new improved model So, obviously, what’s going to have to happen next is some more data to test Bohr’s model. So, first of all, let’s take a look at how we conduct science. I said Bohr came up with a model How do we find out about it? Did we read about it in the New York Times? Did we see it on the nightly news? No, people publish, and this is the publication of Bohr’s model It’s in a scientific journal that goes back to the 1600’s It’s called Philosophical Magazine and Journal of Science People just know it as Phil Mag It’s 1913. It’s London, Edinburgh, and Dublin. You see Ireland was part of the United Kingdom at that time. So, Dublin was a British city at the time this is published All right, July, 1913, blow this up, so On the Constitution of Atoms and Molecules by N Bohr, Doctor of Philosophy, Copenhagen, asterisk here, and I’ve blown up the bottom of the page, communicated by Professor Ernest Rutherford, F S., Fellow of the Royal Society So, only a member of the Royal Society could read the paper into the proceedings, into the session of the society for subsequent publication And, this was July 1913 So, we’re going to read We’re going to read this together I want you to see how science is conducted. So, introduction, “in order to explain the results of experiments on scattering of alpha rays by matter, Professor Rutherford,” and there is a footnote to the Rutherford model So, if you go and read Phil Mag 669-1911, you’ll see Rutherford’s model as it’s presented “Professor Rutherford has given a theory of the structure of atoms According to this theory, the atoms consist of a positively charged nucleus surrounded by a stream of The total negative charge of the electrons is equal to the positive charge of the nucleus Further, the nucleus is assumed to be the seat of the essential part of the mass of the atom, and to have linear dimensions exceedingly small compared with the linear dimensions of the whole atom This is beautiful writing. It’s crystal clear It was written by someone almost 100 years ago whose native language isn’t English I invite you to read If you go to the library, they have books. They have all of this. “The number of electrons in an atom is deduced to be approximately equal to half the atomic weight Great interest is to be attributed to this atom model That’s scientific talk When someone says great interest, that’s a euphemism for embroiled in controversy They don’t say that nobody believes this. They say great interest “For, as Rutherford has shown the assumption of the existence of nuclei, as those in question seems to be necessary in order to account for the results of the experiments on large angle scattering of the alpha rays. In an attempt to explain some of the properties of matter on the basis of this atom model, we meet, however, with the difficulties of a serious nature arising from the apparent instability of the system of electrons, difficulties purposely avoided in atom models previously considered, for instance, in the one proposed by Sir J J. Thompson.” That’s almost a slur That’s almost saying there are difficulties, and you didn’t treat them either. You just kind of swept them under the rug, but now, you are out there in full force with your knives sharpened If you’re so smart, why didn’t you explain it? All right, so they go on, and on, and on in talking about stability “The result of the discussion of these questions seems to be a general acknowledgment of the inadequacy of classical electrodynamics in describing the behavior of systems of atomic size So, he basically says, you know what? I can’t explain this because classical physics doesn’t work at atomic dimensions He says, I plead guilty, but your physics is useless at this length scale. So, we are even. Now, let’s start all over Size dependent behavior: that’s what nanotechnology is about, isn’t it? If everything is the same, you know, when you were a kid someone would say,

which has a higher boiling point, a quart of water or a gallon of water? And the answer is, well, water boils at 100íC, ha, ha, ha. Well, guess what? If I get you down to a cluster of about 30 water molecules, the boiling point is a function of the size of the water droplet Now, that’s new That’s new. But normally, no. So, Bohr came way ahead of the game. Now, let’s take a look at the Bohr model of the atom Let’s see what’s in there Here it is. These are the Bohr postulates. And, the stuff will be posted at the website so you don’t have to copy it all down. It’s just taken out of And, it involves a single electron orbiting a positively charged nucleus. OK, this is the Bohr model, Bohr model of the atom is planetary or nuclear. OK, and it’s got one electron only, one electron only. You’ve got to learn to crawl before you learn to run. But, it could be not just atomic hydrogen First of all, I want to point out that this is not to scale Marsden told us that this distance here is about 10, 00. So, we get a little speck here and an even tinier speck here So, this is not to scale. So, this distance here is R. This is the radius of the orbit in which the electron travels And, so we have the positive charge in the center I’m going to, just for convenience, call that Q1. And, that’s equal to the product of the proton number times e In other words, this could be any one electron what’s he talking about? OK, atomic hydrogen, one proton, You learned about ions last day If helium loses on electron, what So, helium plus is a one electron system. What about lithium 2+? That’s a one electron system OK, so all I do is I take into account that I’ve got all the positive charge, whatever it is, it’s a nucleus And the negative charge is always, Q2 is always equal to minus e because it’s a one electron system Who’s buried in Grant’s tomb? How many electrons in the one electron system, right? So, there it is So, this has got protons and neutrons. But the neutrons, it doesn’t matter about the neutrons And don’t ask me, well what about the relative dimension of this? At 10,000 to 1, who cares? It doesn’t matter how big it is So, what we’re going to do is we’re going to go through the derivation of that next day But I think at this point, it’s probably a good place to stop And, I will go through the actual line by line derivation not because I want to do derivations in class I will only do them on one condition, and that is I want to be able to teach you what the assumptions are that underlie the points in the derivation But I’m never going to ask you to derive things But, I’d ask you, since the class doesn’t end until 11:55, there’s no need to be gathering things up and snapping binders and so on I know you want to get on with life, and you’re onto the next thing, and you are tuning out, but you hear all the click, click, click, click, click? There’s actually one or two people down here that are feigning interest. I’d kind of like to let them hear. So, let’s be good neighbors Bohr and Einstein were considered the top two physicists in the world through the first part of the 20th century. If you go to Denmark and you break a $100 bill, you’re going to be given one of these, undoubtedly, the 500 kroner note, which is worth about $75-80, and it has Niels Bohr on it. And, if you look carefully, it tries to give the sense of a one electron system Here’s a young Niels Bohr Here’s Bohr with Heisenberg, and we’ll talk about Heisenberg’s uncertainty principle Heisenberg post-doced with Bohr These people all moved from one capital to another This one here, that’s Einstein This is the two giants of modern physics: Einstein and Bohr Check out the hats. There is a Homburg and there is a Borsalino, really cool. Here’s Bohr mixing it There’s Prince Philip, and this is some Danish royalty in the back. I never got invited to their place so I don’t know them Bohr liked music. He and Louis Armstrong are discussing

quantization [LAUGHTER] In the year 2000, the play by Michael Frain, Copenhagen, is set in Copenhagen in Nazi occupied Germany where Niels Bohr is in discussion with his And, you can see the stage set here There is Bohr at the center, and there is Heisenberg who is the one electron orbiting the center And then, there is Bohr’s wife who is the observer Heisenberg gave us the uncertainty principle, which we will visit later And so, it’s a very interesting play about the morality of developing nuclear weapons And, what does modern physics really have to give us? A couple of other things about hydrogen: hydrogen also, like other elements, has isotopes and we already saw that in 1766, Cavendish isolated atomic hydrogen and enunciated some of its properties. He was in London, and as I mentioned, he deeded his fortune to the Cambridge University And, Cavendish Lab is there to this day. In 1931, at Columbia University, Harold Yuri discovered this isotope, deuterium. And then, in 1934, it was Ernest Rutherford – by the mid-30s, J. J. Thompson had retired And, Rutherford was invited to occupy the chair and be the director of the Cavendish Laboratory So, he ended his career in Cambridge It is said of Rutherford, it is said of Rutherford that he is unique among Nobel Prize winners that when you look at what he did here with the experiment of the gold foil, and how it was able to engender the insights of Bohr, that, yeah, he got the Nobel Prize in 1908 for the decomposition or disintegration of matter, but people generally say Rutherford did his best work after he got the Nobel Prize. And, Last comments: hydrogen, now here, I’m using a little bit of license here. We’ve been talking about atomic hydrogen, H. Later on, we’ll learn that hydrogen as we typically encounter it is H2, the molecule And, you’ve undoubtedly heard a lot in the public press, and even in the political dialogue such as it is these days that hydrogen might be on environmentally friendly fuel And, even Cavendish, one of the things that he observed was that hydrogen could be combusted to produce water vapor So, you might say, well, gee, why don’t we just power our cars with hydrogen, use an internal combustion chamber But, in an internal combustion engine what happens is we don’t have an oxygen tank We, in fact, borrow oxygen or steal oxygen from the air free of charge But, as you know, air is only 20% oxygen, the balance being nitrogen And, although you think that nitrogen, I mean, it’s an inert gas Well, if you get the combustion chamber hot enough, in point of fact, there are some reactions between nitrogen and the oxygen. And so, you make not only water vapor, but you make some nitrous oxides, NOX, or nox as it is known, and this is the precursor to smog So, if you want to attack urban air quality, this is probably moving in the wrong direction, OK? So, people are talking about the use of hydrogen in fuel cells And, we’ll talk about fuel cells later in the semester when we do the unit on redox reactions Putting hydrogen onboard an automobile, it’s one thing to have hydrogen in the tank But, put it on a vehicle and keep that vehicle crash-worthy If the vehicle in the unfortunate circumstances of a collision, has to be able to maintain the security of the hydrogen, which means more mass, which means a lot of the efficiency is being squandered What’s the environmental impact of hydrogen production? Do you get hydrogen on the hydrogen tree? Where do you get it? Electrolysis of water, catalytic decomposition of hydrocarbons? Well, electrolysis of water consumes energy Where does the energy come from? It’s electrical energy. Burn coal to make it, catalytic decomposition of methane, you get the hydrogen, where does the carbon go? Goes up the stack as CO2 So, one of the things that you can do is to become technically literate so you can become part of the discussion and help formulate sensible policy Put something on the road that metaphorically we can all follow And last is cost, last is cost;

hydrogen is not cheap So, with that, I think I’ll leave it until Wednesday