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MIT OpenCourseWare http://ocw.mit.edu 5.111 Principles of Chemical Science, Fall 2005 Transcript Lecture 2 So let's get going today. And what we were talking about last time is the discovery that the atom was not the most basic constituent of matter, that there was a particle that was even less massive than an atom. And that is the electron. But today we're going to discover the nucleus. And so this is 1911. And this is Ernest Rutherford in England. And what he was interested in doing was studying the emission from these newly radioactive elements that were being discovered. So the emission from radium, for example. What he did was he got a sample of radium bromide from his friend Marie Curie. And what was known was that this radium bromide emitted something called alpha particles. And the exact nature of these alpha particles was not known. However, what was known was that they were heavy particles, that they were charged and that they were energetic. And, of course, today we know what these alpha particles are. They are helium double plus, a helium with two electrons removed. All right. So he got this radium bromide. And alpha particles are being emitted from the radium bromide. And he had some kind of detector way out here which detected these alpha particles. And what he found was that at the detector there were about 132,000 alpha particles per minute. That was the count rate that he was able to measure. And then, because he was just trying to figure out what is the nature of these particles, he did this experiment. He took a gold foil, a really thin gold foil here, really thin meaning 2 times 10 to the negative 5 inches. That's two orders of magnitude thinner than the diameter of your hair. I've always wondered how he handled that. That is pretty thin. But he put that in there. And, low and behold, the count rate that he measured, once this gold foil was in place, the count rate was still 132,000 alpha particles per minute. It appears that all of the alpha particles that were being emitted just went through the foil right to the detector. It didn't even seem like those alpha particles knew the foil was there. The same count rate. It doesn't sound like a very interesting experiment, but at that time he was working with a person named Geiger, a post-doc named Geiger. The same Geiger as the Geiger counter. And Geiger wasn't too happy about the results of these experiments. And, in addition, Geiger had this undergraduate student hanging around the lab. This undergraduate named Marsden.

And Marsden was really excited about doing science. He just hung around there. He really wanted to do something. And Geiger was, jeez, what am I going to do with this guy? Geiger goes to Rutherford and says I've got Marsden here, he really wants to do something, what should I do with him? And Rutherford said well, OK, let's have him build a detector that can swing around that gold sample. Let's have him build a detector that will rotate around such that the detector can be positioned this way so that we can look for any alpha particles that might be backscattered, backscattered meaning scattered back in the direction from which they came. And Geiger said ah-ha, this will keep this guy busy and not in my hair. No problem. So he goes down to Marsden, Marsden is all excited to build this detector. He builds the detector and gets Geiger, OK, we're ready to go. Let's try this. And so they put the radium bromide there in this arrangement. They're sitting there at the detector and they hear tick, tick, tick, etc. Hey, particles at the detector. And they go oh, well, that must just be a general background. So what they do then is they take this gold foil away so that presumably all the particles are going in that direction and they listen and they hear nothing. And they put the gold foil back. And they listen and they hear tick, tick, tick, etc., 20 alpha particles per minute. And they then pick another foil, platinum foil, basically the same result. They go up to Rutherford, they get him down in the laboratory, and Rutherford is looking over their shoulder, tick, tick, tick, etc. Hey, there are some alpha particles coming off. Not many. Look at what the probability here is of the backscatter. Hey, that probability, we can calculate that. The probability is simply the number of backscattered particles, 20, the count rate of the backscattered particles, 20, over the count rate of the incident number of particles, 132,000. That probability is 2 times 10 to the negative 4. Not large but not zero. There is something coming off. And Rutherford was amazed. And what he wrote later on was that this experiment was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15 inch shell at a piece of tissue paper and it came back and bit you. So how does he interpret that experiment? Well, what he said is that since most of these alpha particles went right through this foil to the detector that must mean that those gold atoms that make up that gold foil must be mostly empty. So the picture is that you've got this gold atom here. And he knew, roughly speaking, how large that gold atom was. He knew it to be about 10 to the negative 10 meters. But what he was proposing is that these helium ions going through, these alpha particles are just going right through that volume because most of the atom -- And he knew that there were electrons in this atom because he knew about the electrons already, most of that atom is empty.

However, occasionally, once in a while, not very often but occasionally these helium ions, these alpha particles, what happened? Well, occasionally they hit something very massive in that atom. And when it hit that massive part of the atom it reflected, it scattered back into the direction from which it came. And from knowing what these scattering probabilities are and from knowing roughly the size of this atom and the thickness of the gold foil, he could calculate what the diameter of this nucleus was. And that number came out to be about 10 to the negative 14 meters, the diameter of this heavy massive part of the atom. Now, he called that massive part, he called it the nucleus. He called it a nucleus in analogy to the massive center of a living cell. That's where that name comes from. And this number of 10 to the negative 14 diameter, that's a good number to know, the relative size of the nucleus. All MIT students should know that. He also knew that that nucleus really had to be positively charged. Why did it have to be positively charged? Well, because he knew that these atoms were neutral, he knew already that an electron was part of an atom. And so this nucleus had to be positively charged. And, in addition, he made some very sophisticated measurements of the angular distribution of the backscattered alpha particles. And from those measurements of the angular distribution, he was able to back out the fact that this nucleus had a charge of +Z, where Z is the atomic number, times unit charge e. So his model is the Z electrons filled this volume, this sphere effectively of 10 to the negative 10 meters in diameter. The electrons filled that up, but somewhere in the center there is something that is very small and very massive that has a diameter of 10 to the negative 14 meters. Because occasionally that alpha particle hit that massive part so most of the mass of the atom is in this nucleus. Now, isn't this a great UROP project for Mr. Marsden? What did he do? He discovered the nucleus. Fantastic. I also want to tell you that this kind of Rutherford backscattering experiment here is also the basis of the experiment that was done to discover the quark, the quark that is the elementary particles that make up the proton, the neutron. Same idea. There is a high energetic particle that comes into the proton and backscatters from the quark essentially. That is an experiment carried out by one of my colleagues in the Physics Department, Jerry Friedman and Henry Kendall. Henry Kendall has since passed away. But the same idea. It's really the Rutherford backscattering experiment that was done. All right. Well, now it is time for us to do our own Rutherford backscattering experiment. And the way we are going to do that is we're going to be scattering off of this lattice here, this lattice of these Styrofoam balls. These Styrofoam balls are gold atoms, gold nuclei, and then the space around them is where the electrons are.

So this is one monolayer of gold atoms. Now, this scale is a little wrong. The real scale would be if we had a pinhead in the center of this room and then the rest of the room was the atom and then there would be another room 1051 with a pinhead in the center of that. That's the real scale, but the fact that the scale isn't right that's OK. We are going to be able to understand the principle here. And what we want to do is we want to be able to measure the diameter of these Styrofoam balls or the diameter of those gold nuclei. And we're going to measure it by measuring the probability of backscattering. And the way we're going to measure the probability of backscattering is we're going to take these ping-pong balls, and they are going to be our alpha particles. And we are going to aim them at the lattice. And we are going to have a total of 287 pin pong balls, or 287 alpha particles. And so the probability of backscattering will be simply the number backscattered over the total number incident, which will be 287. So this is what we are going to measure. Now, the next thing we have to do is that we've got to relate this probability of backscattering. We are going to have to relate it to the diameter of those nuclei. How do we do that? Well, the probability of a particle backscattering is simply going to be the total area of this crystal, there's our crystal, the total areas of this. Now, you've got to ignore these aluminum blocks here because this piece of equipment comes from my laboratory. And I pressed it into service for this demonstration. This has nothing to do with the demo that we're going to put here. It's just structural because this is my manipulator puller-outer from our machine. So you've got to ignore those, but that whole area there is equal to 2,148 square inches. And now the probability of that backscattering is this total area of the nuclei to the total area of the crystal. And the total area of the nuclei then is just the sum over all nuclei, and there are 119 of them here. So i=1 to 119 of the area of each one of the nuclei. And so that is just 119 times the crossectional area of these nuclei actually, which is p d2/4 and this is all over 2,148. That's the probability. This is the diameter of the nuclei. And now I am going to rearrange that and solve for the diameter. And when I do that I get 4.79 times PΩ. If I measure the probability of backscattering by this, measuring the number of backscattered balls over the total number we throw at it then I can calculate the diameter of the nuclei, the diameter of those Styrofoam balls. That is the idea. Now, you're going to do this experiment. And so now the TAs are going to give you all a pin pong ball or two. Come on. We need to distribute the pin pong balls. Here's the deal. What you have to do is you have to aim to hit this lattice. That's all you've got to do. Then you have to watch your ball, and you have to see if it scatters back to you. Now, what doesn't count is if you hit these steel bars and it scatters back.

That doesn't count, OK? It also doesn't count if the ball hits the Styrofoam but it continues going in that direction. Your pin pong ball has to actually scatter back at you to count. And then, when we get all done, I am going to ask whose ball backscattered. That's what we've got to do. Now, some of you aren't in the optimal position to hit the lattice. I invite you to come down and get a little closer. That is OK. Now, are you roughly ready? Yeah. All right. But there is one other piece of information that is very important that I have got to tell you. And that is that only fools aim for their chemistry professor. [LAUGHTER] OK, go to it. Watch your ball. OK. Have all the alpha particles been launched? Yes. Fantastic. All right. Now comes the moment of truth. How many of you had an alpha particle that backscattered? OK, so now I've got to count. Keep your hands up because there are some lights that make it a little hard for me to see. Anybody in this section here? Yes. One, two, three, four, five. Six. Anymore? Did I get everybody? That's it? Six alpha particles that backscattered. OK, so now we have to calculate some probabilities here. The probability of backscattering is the number that backscattered. Six divided by 287 and that gives me 0.021, carrying one extra significant figure. And if I now take that probability and I plug this into here, I've already done a calculation. I got a table here. I find that that diameter to the correct number of significant figures is 0.7. And the actual diameter of these balls is 0.8. So you guys did a very great job. [APPLAUSE] All right. This works. That's how they calculated the diameter of the nucleus. That's it. Nothing else involved in this. That is the principle behind how it was done. Very simple. That is the principle behind how the quark was discovered and the size of the quark was revealed. That is terrific. Now, we've got the problem that the scientific community had in 1911, 1912, right after the discovery of the nucleus. And the problem is now we know the atom has got a nucleus, we know it has got an electron, what is the structure of the atom? How does the electron and the nucleus hang together? In particular, what we have to do is we have to ask what is the force of attraction that keeps the nucleus and the electron together? We are going to talk here about this classical description of the atom. And we've got to talk about the force of the interaction first. Well, there are four known fundamental forces. What is the force that is the weakest force? Gravity. Absolutely. What is the force that is the next stronger force? Electromagnetic. Absolutely. What is the next stronger force? Weak force. And the next force? Strong force. All right. The weak and the strong forces here, these are intranuclear forces within the nucleus. That's what keeps the protons and neutrons and the quarks together.

For the most part, the weak and the strong force don't have an effect in chemistry, with the exception for beta decay, for some radioactive elements. That's where you need to think about, in particular, the weak force. Gravity also -- Well, gravity actually has no known consequence for chemistry. It doesn't mean that there isn't one, but it has no known consequence for chemistry. All of chemistry is tied up in this force, the electromagnetic force. Now, what I am going to do is I am going to simplify it just a little bit and just call this the Coulomb force. And why I am going to do that is going to be a little more obvious when you get to 8.02. But I am going to call it the Coulomb interaction. And we know what the Coulomb force law looks like. The Coulomb force law is the following. Say I have a positive charge, which is my nucleus. I am going to call that force plus e. And at some distance R, R is the distance now, between that nucleus and the negatively charged particle which is my electron. I can describe the force of attraction between this electron in the nucleus by the following expression. That force, which is a function of the distance between the two charges, is just the magnitude of the charge on the negatively charged particle times the magnitude on the positively charged particle over 4p epsilon knot r2. Now, I am going to treat this force, just for simplicity purposes right now, as a scaler. I am not going to talk about the direction, but because this is a force between a positive and negative charge this is an attractive force. This epsilon down here is the permittivity of the vacuum. It is in there for doing our unit conversion correctly. That is all I will say about it. Maybe you will talk a little bit more about it in 8.02. And then, finally, here is the r2 that is the important part. That is the distance between the electron and the nucleus. And what I want you to notice here, I don't need the screen down yet. Hello. She just switched it? Oh, all right. Sorry. It looks like I'm not going to get to it, actually. Thank you. What I want you to notice here is that when R goes to infinity, what is the force going to do? Zero. When those two particles are infinitely far apart, you've got an infinity in the denominator, this force is zero, there is no attraction between them. But when R goes to zero, what does that force do? Infinity. When R is zero there is an infinity large force. And in between what is happening is that the closer the particles get to each other the larger the force. The more attraction there is. The more they want to be even closer to each other. All right. Now, what this equation is telling me is simply what is the force of attraction between the nucleus in an electron for a fixed distance r? In other words, if I were holding the electron and the nucleus in my hands at some distance R that equation would tell me what the force was.

And you can bet that in order to keep them apart, I would really have to be pulling like this. You'd feel it. But you also know that if you let them go what would happen is that they would move toward each other. What this equation does not tell us is how they move toward each other. It does not tell us how R changes with time. It doesn't tell us anything about R as a function of time. Although we know the force law, we don't know anything from that force law about how those two particles move under influence of that force. And so what we need is we need an equation of motion. And the equation of motion that was known at that time is, of course, Newton's equations of motion, Newtonian mechanics, classical mechanics, the mechanics that governs the motion of all bodies around us that we see easily and astronomical bodies. In particular, Newton's second law, F = ma, this force equal the mass of the particles times the acceleration. And, of course, in this acceleration term, well, I think you know what's in there. In that acceleration term, let me just write it out, the acceleration then is the change in velocity with respect to time and the velocity is the change in the position R with respect to time. So we have a second derivative here. What is in this force law is a way to get R as a function of time under influence of this force. So we take this force and we substitute it in here and we would be able to solve a differential equation for how those two bodies move under influence of that force. And when we solve this equation we would know exactly where the two bodies would be at all times. As long as we know where the bodies were when they started out, using that force law and this equation of motion we could tell you what R would be for all future times. That's called deterministic. That's classical mechanics. Well, we're not going to do it but we could actually set up a differential equation and solve for what R of T is using that force law. We could do that. And if I did that and if I started out the electron and the nucleus at one angstrom from each other like they are, roughly speaking, in an atom, what would happen is that that electron would plummet into the nucleus in 10-10 seconds. If I solved these equations, I would find that R would be equal to zero and T equal to 10-10 seconds. We've got a problem here. The problem is that this classical physics, Newton's second law and the force law, it is predicting that after 10-10 seconds the electron and the nucleus are on top of each other, they've neutralized each other. We no longer have an atom that has a diameter of 10-10 meters. That's contrary to our observations. This is saying the atom collapses in 10-10 seconds. But what we see is that the atom seemingly lives forever. So we've got a big problem here. Yes they did in 1911, 1912. And the problem is that this kind of classical way of thinking does not predict our observations. It does not predict the fact that the atom lives together, it lives forever.

It says the atom falls apart. So it could be that the Coulomb force law is wrong or it could be that this equation of motion is incorrect. And of course what's going to turn out is that this equation of motion does not work for electrons in atoms. You cannot use classical mechanics to describe the electron within the atom. We need a new kind of mechanics, and that new kind of mechanics is going to be quantum mechanics. That is where we will pick up on Monday. Have a nice weekend.