WEBVTT 00:00:00.090 --> 00:00:02.430 The following content is provided under a Creative 00:00:02.430 --> 00:00:03.820 Commons license. 00:00:03.820 --> 00:00:06.030 Your support will help MIT OpenCourseWare 00:00:06.030 --> 00:00:10.120 continue to offer high-quality educational resources for free. 00:00:10.120 --> 00:00:12.660 To make a donation, or to view additional materials 00:00:12.660 --> 00:00:16.620 from hundreds of MIT courses, visit MIT OpenCourseWare 00:00:16.620 --> 00:00:17.850 at ocw.mit.edu. 00:00:22.350 --> 00:00:25.050 ROBERT FIELD: Last time, we talked 00:00:25.050 --> 00:00:26.685 about the photoelectric effect. 00:00:29.860 --> 00:00:30.795 What was that? 00:00:30.795 --> 00:00:32.275 And what were the important points? 00:00:36.980 --> 00:00:37.870 Yes? 00:00:37.870 --> 00:00:40.220 AUDIENCE: It's quantized and has energy 00:00:40.220 --> 00:00:41.630 associated with its frequency. 00:00:41.630 --> 00:00:42.460 ROBERT FIELD: Yes. 00:00:42.460 --> 00:00:48.500 OK, so, the idea of quantization of electromagnetic 00:00:48.500 --> 00:00:50.810 radiation and photons. 00:00:50.810 --> 00:00:55.010 And the photon has an energy h times nu. 00:00:55.010 --> 00:00:56.720 Nu is the frequency. 00:00:56.720 --> 00:01:10.070 And the evidence was mostly from a plot of what versus what. 00:01:10.070 --> 00:01:10.820 Somebody else? 00:01:14.790 --> 00:01:15.550 Yes? 00:01:15.550 --> 00:01:17.910 AUDIENCE: Frequency of the incoming photon versus-- 00:01:17.910 --> 00:01:19.390 or, that's the x-axis. 00:01:19.390 --> 00:01:21.650 So, kinetic energy of the ejected 00:01:21.650 --> 00:01:23.910 electron versus frequency. 00:01:23.910 --> 00:01:26.140 ROBERT FIELD: Exactly. 00:01:26.140 --> 00:01:32.210 And the slope of that plot, which was h, is universal. 00:01:32.210 --> 00:01:34.860 It doesn't matter where the electron came from. 00:01:34.860 --> 00:01:38.670 And this was really an amazing thing. 00:01:38.670 --> 00:01:41.730 And then, the other thing we talked about 00:01:41.730 --> 00:01:44.100 was Compton scattering. 00:01:44.100 --> 00:01:46.410 And what did Compton scattering tell us? 00:01:53.861 --> 00:01:54.360 Yes. 00:01:54.360 --> 00:01:55.670 AUDIENCE: Photon has a momentum-- 00:01:55.670 --> 00:01:56.230 ROBERT FIELD: Yes. 00:01:56.230 --> 00:01:57.270 AUDIENCE: --transfer. 00:02:02.589 --> 00:02:05.130 ROBERT FIELD: We're interested in the particle-like character 00:02:05.130 --> 00:02:08.039 of what we think of as waves. 00:02:08.039 --> 00:02:12.900 And we saw that the waves were particles. 00:02:12.900 --> 00:02:15.360 And particles-- or at least packets. 00:02:15.360 --> 00:02:19.620 And these packets had definite momentum. 00:02:19.620 --> 00:02:25.590 And that was a wonderful observation. 00:02:25.590 --> 00:02:28.900 So, today, this is the menu of what I'm going to talk about. 00:02:28.900 --> 00:02:33.420 And at the end, there's a magic word, "spectra." 00:02:33.420 --> 00:02:36.570 And I like that because what we're 00:02:36.570 --> 00:02:42.840 going to be discovering today is that the internal structure 00:02:42.840 --> 00:02:45.220 of atoms and molecules-- 00:02:45.220 --> 00:02:50.370 we are not allowed to observe it directly, but it's surprising. 00:02:50.370 --> 00:02:54.520 And it's encoded in something which we can observe, 00:02:54.520 --> 00:02:56.370 which is a spectrum. 00:02:56.370 --> 00:02:59.520 And the spectrum that I will show you at the end 00:02:59.520 --> 00:03:01.500 is one that is-- 00:03:01.500 --> 00:03:04.470 contains essentially no information, 00:03:04.470 --> 00:03:08.575 but acts as a template for what we really 00:03:08.575 --> 00:03:10.950 want to know about how things are different from hydrogen 00:03:10.950 --> 00:03:12.560 atom. 00:03:12.560 --> 00:03:18.590 And that's the beginning of our exploration of the structure 00:03:18.590 --> 00:03:20.880 of atoms and molecules. 00:03:20.880 --> 00:03:25.190 It's through the spectrum and it's how it's different from-- 00:03:25.190 --> 00:03:30.150 in subtle ways-- the spectrum of the hydrogen atom. 00:03:30.150 --> 00:03:40.170 OK, so, we're going to turn our focus today to the electron, 00:03:40.170 --> 00:03:42.240 as opposed to light. 00:03:42.240 --> 00:03:45.480 And we're going to play the same game. 00:03:45.480 --> 00:03:48.490 We know the electron is a particle. 00:03:48.490 --> 00:03:51.700 Does anyone want to tell me why we know that? 00:03:51.700 --> 00:03:54.590 Is there any-- anybody who's got a clue? 00:03:54.590 --> 00:03:55.880 You can-- oh, good. 00:03:55.880 --> 00:03:56.520 Yes. 00:03:56.520 --> 00:03:59.231 AUDIENCE: There's an experiment with the little oil drops, 00:03:59.231 --> 00:04:00.980 where they suspended them and found that-- 00:04:00.980 --> 00:04:01.240 ROBERT FIELD: Yes. 00:04:01.240 --> 00:04:02.290 AUDIENCE: --charge is quantized. 00:04:02.290 --> 00:04:03.831 ROBERT FIELD: I love that experiment. 00:04:03.831 --> 00:04:05.200 That's the Millikan experiment. 00:04:08.800 --> 00:04:13.270 One of the reasons I love it is because Millikan and Mulliken 00:04:13.270 --> 00:04:15.850 are two different people. 00:04:15.850 --> 00:04:19.269 So I find that it's really easy to come up with one of them. 00:04:19.269 --> 00:04:23.560 And I remember Mulliken is a spectroscopist 00:04:23.560 --> 00:04:29.110 and Millikan was a different kind of physicist. 00:04:29.110 --> 00:04:32.110 But they're both famous and they both have connections 00:04:32.110 --> 00:04:35.020 to important universities-- 00:04:35.020 --> 00:04:39.890 University of Chicago for Millikan and Mulliken, MIT 00:04:39.890 --> 00:04:40.390 and Caltech. 00:04:44.540 --> 00:04:49.580 So we're going to be looking at something 00:04:49.580 --> 00:04:53.020 that we know is a particle. 00:04:53.020 --> 00:04:55.510 And we're going to show that it has wave characteristics. 00:05:02.120 --> 00:05:11.430 We want to be able to show that the electron has a wavelength 00:05:11.430 --> 00:05:14.400 and it follows the same equation that we 00:05:14.400 --> 00:05:21.730 use to describe the behavior of electromagnetic radiation. 00:05:21.730 --> 00:05:28.350 So how would we control the momentum of an electron? 00:05:33.841 --> 00:05:34.340 Yes. 00:05:34.340 --> 00:05:36.298 AUDIENCE: So you can control the kinetic energy 00:05:36.298 --> 00:05:39.910 that it has by putting it through a certain potential. 00:05:39.910 --> 00:05:43.610 ROBERT FIELD: OK, so, we know we can easily measure 00:05:43.610 --> 00:05:45.110 the momentum of a particle. 00:05:45.110 --> 00:05:48.860 That's not a big challenge. 00:05:48.860 --> 00:05:53.155 But then how would we measure its wavelength? 00:05:55.911 --> 00:05:56.410 Yes. 00:05:56.410 --> 00:05:58.280 AUDIENCE: Some type of diffraction? 00:05:58.280 --> 00:05:59.900 ROBERT FIELD: Yes. 00:05:59.900 --> 00:06:06.100 We basically use some material, which acts a ruler. 00:06:06.100 --> 00:06:12.290 We have a thin metal foil and the distances between atoms 00:06:12.290 --> 00:06:16.820 in the foil are constant. 00:06:16.820 --> 00:06:20.570 So that's the ruler against which we measure 00:06:20.570 --> 00:06:22.530 the wavelength of light. 00:06:22.530 --> 00:06:29.630 And we'll talk about the Davisson-Germer experiment, 00:06:29.630 --> 00:06:33.900 where we measure the wavelength. 00:06:33.900 --> 00:06:38.060 And then we'll talk about the Geiger-Marsden experiment, 00:06:38.060 --> 00:06:43.070 where we say, well, atoms have electrons in them. 00:06:43.070 --> 00:06:48.580 And what is the structure of an atom? 00:06:48.580 --> 00:06:50.950 Remember, we can't look inside. 00:06:50.950 --> 00:06:53.490 So we have to use some kind of an experiment 00:06:53.490 --> 00:06:56.550 to be able to look inside the atom. 00:06:56.550 --> 00:07:04.890 Now, physicists have one trick they often use. 00:07:04.890 --> 00:07:07.980 To find out the internal structure of something, 00:07:07.980 --> 00:07:10.890 they shoot a particle, or a wave, 00:07:10.890 --> 00:07:16.080 at it that has a wavelength comparable to the distances 00:07:16.080 --> 00:07:18.330 you're hoping to measure. 00:07:18.330 --> 00:07:26.440 So if you have a very high energy probe particle, 00:07:26.440 --> 00:07:29.080 it will have a very short wavelength 00:07:29.080 --> 00:07:31.960 and it will look sort of like a bullet. 00:07:31.960 --> 00:07:35.830 And we know how bullets scatter off of targets or hit targets. 00:07:35.830 --> 00:07:38.650 We also, if we choose the wavelength 00:07:38.650 --> 00:07:40.930 to be comparable to the distances we're 00:07:40.930 --> 00:07:47.870 expecting to measure, then we're going to see diffraction. 00:07:47.870 --> 00:07:52.950 This is a kind of subject that lends itself to exam questions. 00:07:58.060 --> 00:08:02.110 So let's start out by talking about the Geiger-Marsden 00:08:02.110 --> 00:08:02.910 experiment-- 00:08:02.910 --> 00:08:06.140 I mean, the Davisson-Germer experiment. 00:08:06.140 --> 00:08:18.260 So we have a beam of X-rays or a beam of electrons-- 00:08:18.260 --> 00:08:19.610 either one. 00:08:19.610 --> 00:08:23.585 And we have an aluminum foil. 00:08:26.800 --> 00:08:30.700 And we have-- it's just an intense beam. 00:08:30.700 --> 00:08:34.330 We want to stop most of it before it hits a detector. 00:08:37.340 --> 00:08:39.520 And, so, this is some kind of a screen or-- 00:08:47.930 --> 00:08:51.590 So what we're looking for is, when 00:08:51.590 --> 00:08:59.930 the X-rays or the electrons scatter off of this ruler, 00:08:59.930 --> 00:09:09.910 we get something that appears on the screen as pairs of circles. 00:09:12.680 --> 00:09:15.980 This is the powder pattern because this 00:09:15.980 --> 00:09:20.580 is a multi-crystalline object. 00:09:20.580 --> 00:09:33.310 But in each object, we have a bunch of equally-spaced atoms, 00:09:33.310 --> 00:09:35.670 where this is the lattice constant 00:09:35.670 --> 00:09:40.080 and this is the square root of 2 times the lattice constant. 00:09:40.080 --> 00:09:43.440 So each atom has nearest neighbors 00:09:43.440 --> 00:09:46.470 and second-nearest neighbors. 00:09:46.470 --> 00:09:49.080 So we have two rulers going on. 00:09:49.080 --> 00:09:53.260 And one ruler will give one set of rings 00:09:53.260 --> 00:09:56.050 and the other ruler will give a different set of rings. 00:09:56.050 --> 00:09:59.790 And because these particles are randomly oriented, 00:09:59.790 --> 00:10:03.480 instead of having spots, you have circles. 00:10:03.480 --> 00:10:06.990 And there's all sorts of information in these powder 00:10:06.990 --> 00:10:07.560 patterns. 00:10:07.560 --> 00:10:10.900 But basically, they're saying, well, 00:10:10.900 --> 00:10:12.390 we're seeing a structure which is 00:10:12.390 --> 00:10:13.650 related to something we know. 00:10:13.650 --> 00:10:19.680 How would we know the distance between atoms in a foil? 00:10:19.680 --> 00:10:22.891 Using macroscopic measurements? 00:10:22.891 --> 00:10:23.390 Yes. 00:10:23.390 --> 00:10:24.210 You're hot today. 00:10:24.210 --> 00:10:25.710 AUDIENCE: You have access to density 00:10:25.710 --> 00:10:28.130 and you have access to the non-atomic weight. 00:10:28.130 --> 00:10:29.540 ROBERT FIELD: That's it, yes. 00:10:29.540 --> 00:10:34.310 So it's a simple matter to know at least what is 00:10:34.310 --> 00:10:36.660 the magnitude of the distance. 00:10:36.660 --> 00:10:42.104 There is an issue of what is the crystal structure. 00:10:42.104 --> 00:10:43.520 And there are different structures 00:10:43.520 --> 00:10:45.500 and that will give rise to different features 00:10:45.500 --> 00:10:47.030 in the powder pattern. 00:10:47.030 --> 00:10:50.540 But the important thing is we do this. 00:10:50.540 --> 00:10:59.420 We look at the pattern that emerges when we shoot X-rays 00:10:59.420 --> 00:11:01.405 at this screen. 00:11:01.405 --> 00:11:05.180 And we already know that X-rays have wavelengths. 00:11:07.740 --> 00:11:09.240 And we know that they have momentum. 00:11:14.306 --> 00:11:19.580 We know about the scattering of photons. 00:11:19.580 --> 00:11:23.960 And as a result, we know that we can 00:11:23.960 --> 00:11:30.410 predict exactly what the pattern associated with the X-ray 00:11:30.410 --> 00:11:31.790 scattering is going to be. 00:11:34.390 --> 00:11:39.440 And then we do the same thing with electrons. 00:11:39.440 --> 00:11:45.720 And now for the electrons, we can control the momentum. 00:11:45.720 --> 00:11:47.190 That's easy. 00:11:47.190 --> 00:11:51.560 And what we want to know is what is the wavelength. 00:11:51.560 --> 00:11:56.710 And we have the wavelength of the X-rays. 00:11:56.710 --> 00:12:05.230 And so what we do is we vary the momentum of the electrons until 00:12:05.230 --> 00:12:07.590 the powder pattern for the electron-- 00:12:07.590 --> 00:12:11.200 the diffraction pattern for the electron-- 00:12:11.200 --> 00:12:14.020 is exactly the same as the diffraction 00:12:14.020 --> 00:12:16.960 pattern for the X-ray. 00:12:16.960 --> 00:12:22.950 And we discover that, for the electron, 00:12:22.950 --> 00:12:30.320 we have the same result. 00:12:30.320 --> 00:12:34.400 OK, so, we have, now, photons. 00:12:34.400 --> 00:12:37.730 They have wavelengths. 00:12:37.730 --> 00:12:42.770 And the momentum was the surprise for the photons. 00:12:42.770 --> 00:12:47.770 And we have particles, which have wavelengths and momentum. 00:12:47.770 --> 00:12:50.870 And the wavelength was a surprise for the particle. 00:12:50.870 --> 00:12:53.790 So it doesn't matter. 00:12:53.790 --> 00:12:56.830 Everything follows this equation. 00:12:56.830 --> 00:13:05.380 And this equation was anticipated by de Broglie who, 00:13:05.380 --> 00:13:07.560 in his PhD thesis-- 00:13:07.560 --> 00:13:09.820 you know, he's a person about your age-- 00:13:09.820 --> 00:13:14.980 and he wrote his thesis in 1924. 00:13:14.980 --> 00:13:17.320 And, among other brilliant things, 00:13:17.320 --> 00:13:20.585 he said that everything should follow this simple equation. 00:13:23.690 --> 00:13:29.220 And that was a brave statement. 00:13:29.220 --> 00:13:36.570 And it predicted that de Broglie was 00:13:36.570 --> 00:13:40.180 going to make a lot of brilliant statements in his career. 00:13:40.180 --> 00:13:41.800 And this was just the first of-- 00:13:41.800 --> 00:13:43.140 and one of the nicest-- 00:13:43.140 --> 00:13:45.210 but we'll hear a little bit more about de Broglie 00:13:45.210 --> 00:13:47.580 by the time I'm finished with this lecture. 00:13:58.210 --> 00:14:04.580 So, we're now worried about atoms. 00:14:04.580 --> 00:14:09.725 And we already know that atoms have a diameter, roughly. 00:14:17.140 --> 00:14:19.870 We know that from the density, the typical size 00:14:19.870 --> 00:14:21.820 we like to have-- 00:14:21.820 --> 00:14:26.500 quantities that describe macroscopic objects. 00:14:26.500 --> 00:14:32.060 Which are not like 10 to the minus 20, but like 1 to 100. 00:14:32.060 --> 00:14:37.590 And so, the angstrom unit, which is 10 to the minus 10 meters, 00:14:37.590 --> 00:14:41.190 is a very useful thing for talking about sizes 00:14:41.190 --> 00:14:44.130 of atoms and molecules. 00:14:47.150 --> 00:14:54.520 So if we have an atom of a size about one angstrom, 00:14:54.520 --> 00:15:01.850 we can use this equation to say, well, 00:15:01.850 --> 00:15:06.670 what would it take for an electron to fit inside an atom? 00:15:09.880 --> 00:15:13.280 So we specify this-- 00:15:13.280 --> 00:15:14.740 we know this, we know that-- 00:15:14.740 --> 00:15:20.330 and that determines what the momentum would have to be. 00:15:20.330 --> 00:15:23.930 And these are all simple calculations. 00:15:23.930 --> 00:15:28.880 And since I don't like doing calculations on the board, 00:15:28.880 --> 00:15:31.520 and I don't really need to do this now-- 00:15:31.520 --> 00:15:34.880 you need to be able to do them, quickly, 00:15:34.880 --> 00:15:36.560 if I ask you on the exam. 00:15:36.560 --> 00:15:40.040 But basically, what we end up finding out 00:15:40.040 --> 00:15:45.620 is that the velocity of the electron 00:15:45.620 --> 00:15:54.150 would have to be 7.25 times 10 to the 6 meters per second. 00:15:54.150 --> 00:15:56.520 Which is OK, it's pretty fast. 00:15:56.520 --> 00:16:00.640 It's a few percent of the speed of light. 00:16:00.640 --> 00:16:04.790 But that would correspond to a kinetic energy, 00:16:04.790 --> 00:16:13.290 which is 2.4 times 10 to the minus 7 joules. 00:16:13.290 --> 00:16:17.840 Remember, I don't like these kinds of units. 00:16:17.840 --> 00:16:21.470 But it also corresponds to-- 00:16:21.470 --> 00:16:23.820 doing a unit conversion-- 00:16:23.820 --> 00:16:26.180 149 electron volts. 00:16:26.180 --> 00:16:31.750 Electron volts are a good unit for energy for atoms 00:16:31.750 --> 00:16:35.650 because the ionization energy-- 00:16:35.650 --> 00:16:39.160 the energy it takes to pull an electron off of an atom-- 00:16:39.160 --> 00:16:45.210 is always somewhere between five and 15 electron volts. 00:16:45.210 --> 00:16:48.650 So you always want to calibrate yourself, your insight, 00:16:48.650 --> 00:16:52.460 in terms of numbers which are in the small scale, 00:16:52.460 --> 00:16:54.870 rather than having to remember the exponent. 00:17:00.540 --> 00:17:03.870 All right, 149 electron volts. 00:17:03.870 --> 00:17:04.950 Should that bother you? 00:17:04.950 --> 00:17:06.930 Well, it can't bother you yet because you 00:17:06.930 --> 00:17:11.130 don't know about what the ionization energy is. 00:17:11.130 --> 00:17:13.420 But I just told you. 00:17:13.420 --> 00:17:15.579 It's between five and 15. 00:17:15.579 --> 00:17:19.089 This is a factor of 10-- too big. 00:17:19.089 --> 00:17:22.839 So this is going to be a problem. 00:17:22.839 --> 00:17:26.680 How is it possible for things so small 00:17:26.680 --> 00:17:32.920 to have an electron fitting in that small size without it just 00:17:32.920 --> 00:17:35.740 leaving because it's just way too high energy? 00:17:38.640 --> 00:17:42.560 And so that leads us to ask questions about, well, 00:17:42.560 --> 00:17:45.680 what is the internal structure of an atom? 00:17:45.680 --> 00:17:52.370 How can an atom somehow accommodate this electron which 00:17:52.370 --> 00:17:54.275 needs to somehow fit inside? 00:17:57.570 --> 00:18:03.630 So that was the basis for the Geiger-Marsden experiment. 00:18:03.630 --> 00:18:05.800 Now, the Geiger-Marsden experiment 00:18:05.800 --> 00:18:16.470 looks very similar to the previous experiment. 00:18:16.470 --> 00:18:18.750 And here we have-- 00:18:18.750 --> 00:18:22.430 whoops-- alpha particles. 00:18:22.430 --> 00:18:27.820 Alpha particles are helium-2 plus ions. 00:18:27.820 --> 00:18:30.850 And they're produced by radioactive decay. 00:18:30.850 --> 00:18:32.880 And they have a tremendous amount of energy. 00:18:35.680 --> 00:18:38.230 More energy than was possible in the days 00:18:38.230 --> 00:18:43.380 these experiments we're doing to create for a particle. 00:18:43.380 --> 00:18:49.590 In fact, one of the earliest experiments, 00:18:49.590 --> 00:18:53.400 or apparatuses, capable of producing very high 00:18:53.400 --> 00:18:57.780 energy electrons was built by Robert Van de Graaff, here 00:18:57.780 --> 00:18:59.160 at MIT. 00:18:59.160 --> 00:19:06.330 And this was in the form of cylindrical towers, 00:19:06.330 --> 00:19:08.430 right near the parking garage. 00:19:08.430 --> 00:19:11.910 And it was there for the first 10 years I was at MIT. 00:19:11.910 --> 00:19:14.750 I'm very old, but that's still fairly recent. 00:19:14.750 --> 00:19:19.110 But anyway, Van de Graaff could make high energy particles 00:19:19.110 --> 00:19:20.880 and it was really neat. 00:19:20.880 --> 00:19:24.420 And what he could do was dwarfed by what 00:19:24.420 --> 00:19:26.790 can be done in electron accelerators, now. 00:19:26.790 --> 00:19:34.410 But in the days when the Geiger-Marsden experiment was 00:19:34.410 --> 00:19:42.290 done, which was 1911, there was no way of making 00:19:42.290 --> 00:19:47.640 and controlling the energy of an electron-- 00:19:47.640 --> 00:19:49.650 or of any particle. 00:19:49.650 --> 00:19:52.380 And here we have some particles which 00:19:52.380 --> 00:19:54.780 are produced by radioactive decay, which 00:19:54.780 --> 00:19:57.010 have tremendous energy. 00:19:57.010 --> 00:20:00.140 So they're heavy and they have high energy. 00:20:00.140 --> 00:20:03.790 And so that means the wavelength is very small. 00:20:08.200 --> 00:20:12.550 We want to use these helium ions. 00:20:12.550 --> 00:20:13.902 Yes? 00:20:13.902 --> 00:20:15.886 AUDIENCE: Could you not also control 00:20:15.886 --> 00:20:19.370 the energy of each particle as they're passing through, right? 00:20:19.370 --> 00:20:20.490 ROBERT FIELD: Yes. 00:20:20.490 --> 00:20:26.560 But you would need a very high voltage. 00:20:26.560 --> 00:20:31.360 And though that is something we could imagine 00:20:31.360 --> 00:20:36.490 doing now, but in 1911, the ability 00:20:36.490 --> 00:20:43.060 to do that sort of thing with control was not there. 00:20:43.060 --> 00:20:46.150 There needed to be advances in vacuum technology. 00:20:46.150 --> 00:20:49.570 There needed to be advances in power supplies. 00:20:49.570 --> 00:20:55.560 I mean, we're talking about very high voltages. 00:20:55.560 --> 00:20:59.890 And you wouldn't want to do that in your laboratory, 00:20:59.890 --> 00:21:02.382 even now with the capability. 00:21:02.382 --> 00:21:04.090 I remember when I was a graduate student, 00:21:04.090 --> 00:21:07.510 we had these things called Spellman power supplies. 00:21:07.510 --> 00:21:10.090 And they could produce 40 kilovolts. 00:21:10.090 --> 00:21:11.050 They were really scary. 00:21:11.050 --> 00:21:14.290 But that's nothing compared to what you need. 00:21:14.290 --> 00:21:17.570 OK, so, we want bullets. 00:21:17.570 --> 00:21:24.200 We want to have these helium particles interacting 00:21:24.200 --> 00:21:30.015 with a thin metal foil. 00:21:38.870 --> 00:21:44.740 We have a whole array of atoms here. 00:21:44.740 --> 00:21:46.220 And we have a little hole here. 00:21:46.220 --> 00:21:49.460 And what's going to happen is this radiation 00:21:49.460 --> 00:21:50.990 is going to hit these atoms. 00:21:50.990 --> 00:21:53.120 And there's going to be backscatter 00:21:53.120 --> 00:21:55.250 and forward scattering. 00:21:55.250 --> 00:21:58.520 And the crucial experiment was to measure 00:21:58.520 --> 00:22:03.590 the ratio of backscattering to forward scattering. 00:22:03.590 --> 00:22:12.060 Now, if we have a target that looks sort of like a smear, 00:22:12.060 --> 00:22:16.990 then the forward and backward scattering would be similar. 00:22:16.990 --> 00:22:24.250 If we have a target that looked like a bunch of tiny points, 00:22:24.250 --> 00:22:27.840 there would very rarely be backscattering. 00:22:27.840 --> 00:22:30.870 All of the scattering would be forward 00:22:30.870 --> 00:22:33.390 because most of the particles don't hit anything. 00:22:36.420 --> 00:22:40.130 And so what was found, and what was the surprise, 00:22:40.130 --> 00:22:45.750 is that there was very little backscattering. 00:22:45.750 --> 00:22:50.470 And that implied that the ratio of the size 00:22:50.470 --> 00:22:55.800 of the target to the size of the particle was enormous. 00:22:55.800 --> 00:22:58.110 The particles that scattered-- 00:22:58.110 --> 00:23:04.350 the alpha particles-- were tiny. 00:23:04.350 --> 00:23:07.240 They had a size-- 00:23:07.240 --> 00:23:12.580 something like 10 to the minus 4 times the typical dimension 00:23:12.580 --> 00:23:15.720 of an atom. 00:23:15.720 --> 00:23:17.780 So this is jellium. 00:23:17.780 --> 00:23:21.450 And this is a perfectly reasonable approach. 00:23:21.450 --> 00:23:25.820 That the positive and negative charges that make up an atom 00:23:25.820 --> 00:23:28.234 are distributed uniformly. 00:23:28.234 --> 00:23:29.150 This was the surprise. 00:23:38.190 --> 00:23:42.540 How do we explain, now, if atoms that 00:23:42.540 --> 00:23:44.880 are scattering the alpha particles 00:23:44.880 --> 00:23:47.325 are really small, even compared to the one angstrom? 00:23:50.400 --> 00:23:52.830 Well, how do they stick together? 00:23:52.830 --> 00:23:58.220 Why is matter not compressable? 00:23:58.220 --> 00:23:59.630 So what is going on here? 00:24:05.933 --> 00:24:09.590 Now, I'm not exactly sure of the genealogy here, 00:24:09.590 --> 00:24:14.420 but Geiger and Marsden were workers, or students, 00:24:14.420 --> 00:24:17.150 in the Rutherford lab. 00:24:17.150 --> 00:24:22.780 And the old man wanted to save face or to say, oh, here's 00:24:22.780 --> 00:24:23.530 an experiment. 00:24:23.530 --> 00:24:25.430 We learned something from this. 00:24:25.430 --> 00:24:28.360 You know, this is what we do-- this is my job. 00:24:28.360 --> 00:24:32.980 But anyway, Rutherford said, well, maybe it's like this. 00:24:32.980 --> 00:24:40.000 We have a nucleus and we have the electrons. 00:24:40.000 --> 00:24:43.210 So we have a nucleus where all the positive charge 00:24:43.210 --> 00:24:47.330 of the atom, and most of the mass, resides. 00:24:47.330 --> 00:24:50.705 And we have electrons in circular orbits. 00:24:54.260 --> 00:24:56.590 So maybe these circular orbits explain 00:24:56.590 --> 00:25:02.830 why you can't compress atoms to something 00:25:02.830 --> 00:25:06.940 that would be commensurate with the size of the nuclei. 00:25:06.940 --> 00:25:12.490 That the electrons cause a repulsion and the structure 00:25:12.490 --> 00:25:14.990 is stable. 00:25:14.990 --> 00:25:17.570 So this is a pretty reasonable hypothesis 00:25:17.570 --> 00:25:18.860 until one analyzes it. 00:25:21.730 --> 00:25:24.340 So what we have is a positive charge here, 00:25:24.340 --> 00:25:26.410 negative charge here. 00:25:26.410 --> 00:25:30.740 And so, there is Coulomb attraction 00:25:30.740 --> 00:25:34.430 and there's centrifugal force, or centripetal acceleration. 00:25:34.430 --> 00:25:39.840 And we have to have these two things match. 00:25:39.840 --> 00:25:44.100 So the inward force is minus the charge 00:25:44.100 --> 00:25:49.320 on the electron squared over 4 by epsilon 0 00:25:49.320 --> 00:25:52.080 and 1 over r squared. 00:25:52.080 --> 00:25:57.435 And the centrifugal, it's-- 00:26:10.120 --> 00:26:12.760 OK, this is-- you know all this. 00:26:12.760 --> 00:26:14.640 You know to do this. 00:26:14.640 --> 00:26:17.520 Have known it since high school, probably. 00:26:17.520 --> 00:26:21.240 And so, you can combine all these things, say the inward 00:26:21.240 --> 00:26:24.000 and outward-- the inward force is exactly 00:26:24.000 --> 00:26:25.980 canceling the outward force. 00:26:25.980 --> 00:26:30.300 And you can solve for the velocity. 00:26:30.300 --> 00:26:38.950 And the velocity is q over the electron squared over 4 00:26:38.950 --> 00:26:43.910 by epsilon 0 mass of the electron 00:26:43.910 --> 00:26:48.260 and the radius of the orbit, square root. 00:26:48.260 --> 00:26:50.000 This is a trivial derivation. 00:26:50.000 --> 00:26:53.760 I won't insult you by attempting to do it and try 00:26:53.760 --> 00:26:57.320 to increase your understanding of the equation, 00:26:57.320 --> 00:26:59.070 because you already understand it. 00:26:59.070 --> 00:27:02.840 So this is the requirement for the radius 00:27:02.840 --> 00:27:05.060 of the circular orbit. 00:27:05.060 --> 00:27:08.000 And it has the mass-- 00:27:08.000 --> 00:27:11.180 I mean, this is the requirement for the velocity. 00:27:11.180 --> 00:27:12.830 And this is the radius, here. 00:27:12.830 --> 00:27:15.380 So we know all that. 00:27:15.380 --> 00:27:19.080 There is nothing about quantization, yet. 00:27:19.080 --> 00:27:23.430 We know that for any radius, the electron 00:27:23.430 --> 00:27:26.710 will have a certain velocity. 00:27:26.710 --> 00:27:28.620 And we can choose whatever radius, 00:27:28.620 --> 00:27:30.750 we want whatever velocity we want. 00:27:30.750 --> 00:27:33.410 And that corresponds to whatever energy we get. 00:27:43.630 --> 00:27:51.410 What we're interested in is the frequency of the orbit. 00:27:51.410 --> 00:27:53.890 And so that will be 1 over the time 00:27:53.890 --> 00:27:57.590 it takes for the electron to go around. 00:27:57.590 --> 00:28:01.160 And 1 over the time it takes for electron to go around 00:28:01.160 --> 00:28:05.520 is 2 pi r, the circumference, divided by the velocity. 00:28:05.520 --> 00:28:12.055 So we have the velocity is equal to-- 00:28:12.055 --> 00:28:15.760 I mean, the frequency is equal to 1 over 2 pi r. 00:28:15.760 --> 00:28:20.860 And we can write an equation for this. 00:28:20.860 --> 00:28:23.110 And that's in the notes. 00:28:23.110 --> 00:28:26.390 In fact, there was a typo in the notes. 00:28:26.390 --> 00:28:28.570 Which has been corrected and read. 00:28:28.570 --> 00:28:30.920 But I don't need to tell you what it is. 00:28:36.900 --> 00:28:40.170 We can calculate this frequency. 00:28:40.170 --> 00:28:41.790 The reason we calculate the frequency 00:28:41.790 --> 00:28:47.920 is because we know if we have electrons moving back and forth 00:28:47.920 --> 00:28:51.120 at some frequency, they're going to radiate 00:28:51.120 --> 00:28:55.590 electromagnetic radiation at that frequency. 00:28:55.590 --> 00:28:58.240 Well, where did that energy come from? 00:28:58.240 --> 00:29:00.550 It came from the motion of the electron. 00:29:00.550 --> 00:29:04.580 So it has to give up kinetic energy. 00:29:04.580 --> 00:29:10.300 Now, the energy is the kinetic energy 00:29:10.300 --> 00:29:11.830 plus the potential energy. 00:29:14.850 --> 00:29:23.590 So if it gives up energy, some of these two things 00:29:23.590 --> 00:29:26.700 has to decrease. 00:29:26.700 --> 00:29:28.370 And what happens is this decreases 00:29:28.370 --> 00:29:31.620 faster that this increases. 00:29:31.620 --> 00:29:42.140 And what ends up happening is that the electron 00:29:42.140 --> 00:29:44.370 has a death spiral. 00:29:44.370 --> 00:29:47.630 What happens will be that the electron will 00:29:47.630 --> 00:29:55.610 go in a spiral, going faster and faster as it 00:29:55.610 --> 00:30:02.450 goes to smaller and smaller radius, and annihilate itself. 00:30:02.450 --> 00:30:04.930 So this is garbage. 00:30:04.930 --> 00:30:07.550 This can't be true. 00:30:07.550 --> 00:30:12.230 It violates laws that everybody knows are right. 00:30:12.230 --> 00:30:16.970 So one needs to find a way to live with this. 00:30:19.930 --> 00:30:22.370 Now, one really doesn't need to find a way 00:30:22.370 --> 00:30:25.835 to live with it until you realize what happens. 00:30:28.970 --> 00:30:37.160 Because this picture, subject to a couple of hypotheses, 00:30:37.160 --> 00:30:40.580 predicts an infinite number of 10-digit numbers. 00:30:44.710 --> 00:30:45.700 It's not an accident. 00:30:45.700 --> 00:30:48.070 Maybe one prediction would be fine. 00:30:48.070 --> 00:30:53.500 But all of the lines in the spectra of hydrogen atom, 00:30:53.500 --> 00:30:57.070 helium ion, lithium doubly-charged ion, all 00:30:57.070 --> 00:31:02.050 of those are predicted with no adjustable parameters 00:31:02.050 --> 00:31:04.760 to measurement accuracy. 00:31:04.760 --> 00:31:06.310 Now, at the time this was being done, 00:31:06.310 --> 00:31:10.790 the measurement accuracy might have been only a part in 1,000, 00:31:10.790 --> 00:31:13.170 or maybe a part in a million. 00:31:13.170 --> 00:31:15.940 But a part in 10 to the 10th, beyond that we're 00:31:15.940 --> 00:31:18.700 starting to get into fundamental physics. 00:31:18.700 --> 00:31:21.280 But this is an astonishing thing. 00:31:21.280 --> 00:31:28.080 And so I have to explain what the additional assumptions were 00:31:28.080 --> 00:31:31.650 because we've got something that predicts things 00:31:31.650 --> 00:31:33.790 we have no business knowing. 00:31:33.790 --> 00:31:37.440 And there was no explanation for the spectrum 00:31:37.440 --> 00:31:43.920 before these experiments, or this picture, was developed. 00:31:43.920 --> 00:31:50.690 So we have to first find a way, whether it's believable or not, 00:31:50.690 --> 00:31:55.250 of getting rid of the radiative collapse. 00:31:55.250 --> 00:32:07.785 So Bohr proposed that angular momentum, l vector r 00:32:07.785 --> 00:32:12.590 cross p is conserved. 00:32:12.590 --> 00:32:16.700 Well, we know that angular momentum is conserved. 00:32:16.700 --> 00:32:20.450 But for a microscopic system, what it means to be conserved 00:32:20.450 --> 00:32:24.210 may be a little bit more subtle. 00:32:24.210 --> 00:32:26.920 He proposed that angular momentum is conserved 00:32:26.920 --> 00:32:31.840 and that the angular momentum, the magnitude of the angular 00:32:31.840 --> 00:32:34.510 momentum, had to have a particular value. 00:32:40.460 --> 00:32:46.640 And that value was integer times h bar. 00:32:46.640 --> 00:32:52.090 h bar is the Planck's constant divided by 2 pi. 00:32:52.090 --> 00:32:54.940 Now, this is complete nonsense. 00:32:54.940 --> 00:32:56.464 Why should it be conserved? 00:33:00.560 --> 00:33:04.395 Why should it be restricted to this set of values? 00:33:08.875 --> 00:33:14.650 Well, the reason we accept that it's restricted 00:33:14.650 --> 00:33:22.130 is because it gives the energy levels that are observed. 00:33:22.130 --> 00:33:25.270 Now, before I get to energy level-- well, I do. 00:33:25.270 --> 00:33:27.700 OK, we have energy levels. 00:33:27.700 --> 00:33:36.665 We find that the energy is equal to minus some constant over n 00:33:36.665 --> 00:33:37.165 squared. 00:33:39.990 --> 00:33:42.560 Same n as in here. 00:33:42.560 --> 00:33:44.870 This is the Rydberg constant. 00:33:44.870 --> 00:33:49.740 And it's something that you can measure. 00:33:49.740 --> 00:33:54.887 It's basically a whole bunch of fundamental constants combined. 00:33:54.887 --> 00:33:55.845 And so, it has a value. 00:34:07.640 --> 00:34:10.118 This is one of the numbers in my permanent memory. 00:34:13.610 --> 00:34:16.280 And that's the value of the Rydberg constant 00:34:16.280 --> 00:34:19.670 in reciprocal centimeter units. 00:34:19.670 --> 00:34:24.439 And to get it into energy units you multiply by h times c, 00:34:24.439 --> 00:34:26.480 or to get it into frequency, you just multiply it 00:34:26.480 --> 00:34:28.010 by the speed of light. 00:34:28.010 --> 00:34:30.080 So, anyway, this is a number that is 00:34:30.080 --> 00:34:32.960 known to many decimal places. 00:34:32.960 --> 00:34:42.790 And it is generated by this idea that the angular momentum 00:34:42.790 --> 00:34:45.400 has to be certain values. 00:34:45.400 --> 00:34:47.590 Conservation is good, that's easy. 00:34:47.590 --> 00:34:49.929 This is weird. 00:34:49.929 --> 00:34:54.159 And it's also wrong because we find out 00:34:54.159 --> 00:34:58.510 later that the possible values of n include 0. 00:35:01.340 --> 00:35:08.130 Which would completely mess up the Bohr model. 00:35:08.130 --> 00:35:13.140 But, anyway, this, then, in combination 00:35:13.140 --> 00:35:18.360 with this amazing statement that-- 00:35:18.360 --> 00:35:24.510 OK, we have the nth energy and the n prime-th energy. 00:35:24.510 --> 00:35:32.670 And the spectrum corresponds to the frequency, corresponds 00:35:32.670 --> 00:35:41.954 to e n minus e n prime, over h. 00:35:44.640 --> 00:35:50.390 So everything we see in the emission spectrum 00:35:50.390 --> 00:35:54.660 of the hydrogen atom, or in a gas-- 00:35:54.660 --> 00:35:56.610 which is mostly H2-- 00:35:56.610 --> 00:36:00.810 there are transitions associated with the free atoms. 00:36:00.810 --> 00:36:05.070 And they're always around this simple equation, 00:36:05.070 --> 00:36:08.550 based on the Rydberg equation. 00:36:08.550 --> 00:36:12.840 This says the spectra are telling us about the energy 00:36:12.840 --> 00:36:16.190 level differences. 00:36:16.190 --> 00:36:19.300 And it's a simple equation. 00:36:19.300 --> 00:36:21.190 And it's true. 00:36:21.190 --> 00:36:24.010 It's true at incredibly high accuracy. 00:36:24.010 --> 00:36:30.000 And it tells you nothing except the mass of the particle. 00:36:30.000 --> 00:36:32.150 Because the mass of the particle-- 00:36:32.150 --> 00:36:34.340 for this Rydberg equation-- we have 00:36:34.340 --> 00:36:37.140 it expressed in terms of the mass of the electron. 00:36:37.140 --> 00:36:41.610 But it really should be the reduced mass of the mass 00:36:41.610 --> 00:36:45.270 of the nucleus times the mass of the electron, 00:36:45.270 --> 00:36:50.250 or the mass of the nucleus plus the mass of the electron. 00:36:50.250 --> 00:36:53.280 And this is something we know for all two-body interactions. 00:36:53.280 --> 00:36:56.370 That was known well before the time of these experiments. 00:36:56.370 --> 00:37:00.870 If you have two things interacting, 00:37:00.870 --> 00:37:03.420 the reduced mass is what you want rather 00:37:03.420 --> 00:37:05.400 than the individual masses. 00:37:05.400 --> 00:37:10.350 And so, the only information in these one-electron spectra 00:37:10.350 --> 00:37:15.130 is the mass of the nucleus. 00:37:15.130 --> 00:37:23.290 And there's not much difference in this reduced mass effect. 00:37:23.290 --> 00:37:26.830 But it's enough to say this is a spectrum of hydrogen, 00:37:26.830 --> 00:37:30.180 as opposed to lithium 2 plus. 00:37:30.180 --> 00:37:33.990 OK, but we still have a problem-- 00:37:33.990 --> 00:37:35.420 a very serious problem. 00:37:43.000 --> 00:37:48.860 Why is the angular momentum conserved? 00:37:48.860 --> 00:37:52.910 Why is the angular momentum forced to have a certain value? 00:38:00.964 --> 00:38:03.130 Well, I've really finished this lecture pretty fast. 00:38:14.792 --> 00:38:18.560 Let me just get to the end and I will go back. 00:38:18.560 --> 00:38:28.050 All right, so, the problem is this electron 00:38:28.050 --> 00:38:30.930 is assumed to be a particle and it's assumed to be moving. 00:38:34.170 --> 00:38:38.100 So the equation-- 00:38:38.100 --> 00:38:40.260 Maxwell's equations-- all of the equations 00:38:40.260 --> 00:38:43.940 about motion of charged particles 00:38:43.940 --> 00:38:46.410 say if it's moving it's going to radiate, 00:38:46.410 --> 00:38:49.346 whereas if it's oscillating, it's going to radiate. 00:38:49.346 --> 00:38:51.220 So maybe the problem is that it's not moving. 00:38:55.390 --> 00:39:00.940 Remember, the particles are both particles and waves. 00:39:00.940 --> 00:39:10.420 So we could imagine that, around this circular orbit, 00:39:10.420 --> 00:39:12.850 we have standing waves-- 00:39:12.850 --> 00:39:13.450 no motion. 00:39:18.360 --> 00:39:21.860 And this led to this Schrodinger equation, 00:39:21.860 --> 00:39:28.105 which talks about the states of the electrons that are allowed. 00:39:31.700 --> 00:39:34.610 It's basically the classical wave equation, 00:39:34.610 --> 00:39:37.070 with a couple little twists. 00:39:37.070 --> 00:39:39.530 And the thing about waves, you remember, 00:39:39.530 --> 00:39:44.590 we can have constructive and destructive interference. 00:39:44.590 --> 00:39:45.760 We can have standing waves. 00:39:49.200 --> 00:39:52.320 So there doesn't need to be a motion of our particle. 00:39:52.320 --> 00:39:55.890 There could be some static description 00:39:55.890 --> 00:40:00.780 of the probability of finding the electron everywhere 00:40:00.780 --> 00:40:01.950 around this orbit. 00:40:05.351 --> 00:40:06.850 And that's the Schrodinger equation. 00:40:13.657 --> 00:40:15.240 In the next lecture, I'm going to talk 00:40:15.240 --> 00:40:19.160 about the classical wave equation, which 00:40:19.160 --> 00:40:22.220 will be the warm-up for the Schrodinger equation. 00:40:22.220 --> 00:40:26.710 And the Schrodinger equation explains everything. 00:40:26.710 --> 00:40:29.410 People have made some really fantastic 00:40:29.410 --> 00:40:31.960 philosophical statements about the Schrodinger. 00:40:31.960 --> 00:40:36.010 It contains everything that we need to know. 00:40:36.010 --> 00:40:39.460 The problem is we can't solve the equation exactly. 00:40:39.460 --> 00:40:40.900 But it's true. 00:40:40.900 --> 00:40:45.280 And it contains everything that we'd ever 00:40:45.280 --> 00:40:49.600 want to know about the microscopic structure of atoms 00:40:49.600 --> 00:40:51.880 and molecules. 00:40:51.880 --> 00:40:56.320 So we've been led by these very simple experiments, which, 00:40:56.320 --> 00:40:58.150 now, you could do-- 00:40:58.150 --> 00:40:58.960 really trivially. 00:40:58.960 --> 00:41:02.110 You wouldn't have to be a smart student of a smart advisor, 00:41:02.110 --> 00:41:03.520 or stupid advisor. 00:41:03.520 --> 00:41:06.160 You would be able to do these experiments. 00:41:06.160 --> 00:41:09.100 And you could say, yeah, this is all very weird, 00:41:09.100 --> 00:41:15.300 but know now we know that spectra are everything. 00:41:15.300 --> 00:41:16.380 And I'm a spectroscopist. 00:41:16.380 --> 00:41:19.680 I'm very proud of this because the idea 00:41:19.680 --> 00:41:23.250 that you can make a few measurements 00:41:23.250 --> 00:41:28.200 and say something about the internal structure of an atom 00:41:28.200 --> 00:41:29.910 or molecule-- 00:41:29.910 --> 00:41:32.520 that's a fantastic thing. 00:41:32.520 --> 00:41:35.690 And what we've seen-- 00:41:35.690 --> 00:41:38.310 the spectrum of one-electron atoms-- 00:41:38.310 --> 00:41:41.410 is something which is really simple. 00:41:41.410 --> 00:41:46.140 It's the template for understanding all complexity. 00:41:46.140 --> 00:41:50.160 Because everything is different from hydrogen. 00:41:50.160 --> 00:41:53.340 Hydrogen has a point charge at the center. 00:41:53.340 --> 00:41:57.240 It's not quite a point charge, and that's actually a subject 00:41:57.240 --> 00:42:01.470 of even modern physics. 00:42:01.470 --> 00:42:05.580 And other atoms are not a point charge 00:42:05.580 --> 00:42:08.070 because they have electrons. 00:42:08.070 --> 00:42:12.290 And so there is a concentration of charge-- 00:42:12.290 --> 00:42:17.970 the thing to which the electron is attached is space filling. 00:42:17.970 --> 00:42:22.650 So that results in a shift at the energy levels. 00:42:22.650 --> 00:42:24.900 And the shift at the energy levels, and how 00:42:24.900 --> 00:42:28.050 that shift depends on the orbital angular momentum, 00:42:28.050 --> 00:42:30.300 tells you something about the shape of this charge 00:42:30.300 --> 00:42:31.800 distribution-- 00:42:31.800 --> 00:42:33.840 the radial shape. 00:42:33.840 --> 00:42:38.280 So everything we do in spectroscopy 00:42:38.280 --> 00:42:40.560 is somehow referenced to something 00:42:40.560 --> 00:42:47.180 we understand perfectly, but which is not of much interest. 00:42:47.180 --> 00:42:49.940 But it's a template for building up our understanding 00:42:49.940 --> 00:42:52.380 of everything. 00:42:52.380 --> 00:42:54.900 And this is a kind of a radical statement. 00:42:54.900 --> 00:42:59.070 And I get to say this because I'm up here 00:42:59.070 --> 00:43:00.930 and I do this for a living. 00:43:00.930 --> 00:43:04.230 I mean-- not teaching, but research. 00:43:04.230 --> 00:43:09.000 And I really believe that the things 00:43:09.000 --> 00:43:14.310 that we are enabled to observe about the microscopic structure 00:43:14.310 --> 00:43:18.860 of things are encoded in something completely 00:43:18.860 --> 00:43:21.320 unlike looking at it. 00:43:21.320 --> 00:43:25.450 And our job is to figure out how to break that code. 00:43:25.450 --> 00:43:30.480 And that's what I've done for the last 50 years and it's fun. 00:43:30.480 --> 00:43:35.430 OK, so, what more could I say to amuse you 00:43:35.430 --> 00:43:37.200 for five-- six minutes? 00:43:37.200 --> 00:43:40.890 Not much, because I've skipped a lot of really great stuff. 00:43:40.890 --> 00:43:42.690 But go back to de Broglie. 00:43:45.640 --> 00:43:50.460 De Broglie had the hypothesis that there 00:43:50.460 --> 00:43:52.560 is an integer number of wavelengths 00:43:52.560 --> 00:43:55.260 around the circular orbit. 00:43:55.260 --> 00:44:00.220 And that was telling you that it's stable 00:44:00.220 --> 00:44:03.850 because if it weren't an integer number of wavelengths, 00:44:03.850 --> 00:44:07.530 the electron would self annihilate. 00:44:07.530 --> 00:44:14.110 But that takes a valid point and moves it 00:44:14.110 --> 00:44:17.320 into something which is a little bit wrong. 00:44:17.320 --> 00:44:22.480 Because we're not trying to have a particle moving, 00:44:22.480 --> 00:44:25.920 we're having a distribution of probabilities. 00:44:25.920 --> 00:44:31.370 And there are still wavelengths and nodal structures. 00:44:31.370 --> 00:44:36.140 And the stable solutions do involve the particle 00:44:36.140 --> 00:44:38.540 not self annihilating. 00:44:38.540 --> 00:44:45.690 And so, de Broglie scores another triple. 00:44:45.690 --> 00:44:48.170 I mean, he didn't come up with the Schrodinger equation. 00:44:48.170 --> 00:44:53.980 So that's the home run that says, OK, we have the material, 00:44:53.980 --> 00:44:56.380 now to explain everything. 00:44:59.510 --> 00:45:02.180 The next lecture will be just introducing 00:45:02.180 --> 00:45:06.950 the mathematics of the wave equation and the crucial ideas. 00:45:06.950 --> 00:45:10.190 And that will lead into the following lecture, where we all 00:45:10.190 --> 00:45:12.290 talk about the Schrodinger equation. 00:45:12.290 --> 00:45:14.210 So I can stop now. 00:45:14.210 --> 00:45:15.760 Thanks.