1 00:00:00,090 --> 00:00:02,430 The following content is provided under a Creative 2 00:00:02,430 --> 00:00:03,820 Commons license. 3 00:00:03,820 --> 00:00:06,030 Your support will help MIT OpenCourseWare 4 00:00:06,030 --> 00:00:10,120 continue to offer high-quality educational resources for free. 5 00:00:10,120 --> 00:00:12,660 To make a donation, or to view additional materials 6 00:00:12,660 --> 00:00:16,620 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:16,620 --> 00:00:17,850 at ocw.mit.edu. 8 00:00:22,350 --> 00:00:25,050 ROBERT FIELD: Last time, we talked 9 00:00:25,050 --> 00:00:26,685 about the photoelectric effect. 10 00:00:29,860 --> 00:00:30,795 What was that? 11 00:00:30,795 --> 00:00:32,275 And what were the important points? 12 00:00:36,980 --> 00:00:37,870 Yes? 13 00:00:37,870 --> 00:00:40,220 AUDIENCE: It's quantized and has energy 14 00:00:40,220 --> 00:00:41,630 associated with its frequency. 15 00:00:41,630 --> 00:00:42,460 ROBERT FIELD: Yes. 16 00:00:42,460 --> 00:00:48,500 OK, so, the idea of quantization of electromagnetic 17 00:00:48,500 --> 00:00:50,810 radiation and photons. 18 00:00:50,810 --> 00:00:55,010 And the photon has an energy h times nu. 19 00:00:55,010 --> 00:00:56,720 Nu is the frequency. 20 00:00:56,720 --> 00:01:10,070 And the evidence was mostly from a plot of what versus what. 21 00:01:10,070 --> 00:01:10,820 Somebody else? 22 00:01:14,790 --> 00:01:15,550 Yes? 23 00:01:15,550 --> 00:01:17,910 AUDIENCE: Frequency of the incoming photon versus-- 24 00:01:17,910 --> 00:01:19,390 or, that's the x-axis. 25 00:01:19,390 --> 00:01:21,650 So, kinetic energy of the ejected 26 00:01:21,650 --> 00:01:23,910 electron versus frequency. 27 00:01:23,910 --> 00:01:26,140 ROBERT FIELD: Exactly. 28 00:01:26,140 --> 00:01:32,210 And the slope of that plot, which was h, is universal. 29 00:01:32,210 --> 00:01:34,860 It doesn't matter where the electron came from. 30 00:01:34,860 --> 00:01:38,670 And this was really an amazing thing. 31 00:01:38,670 --> 00:01:41,730 And then, the other thing we talked about 32 00:01:41,730 --> 00:01:44,100 was Compton scattering. 33 00:01:44,100 --> 00:01:46,410 And what did Compton scattering tell us? 34 00:01:53,861 --> 00:01:54,360 Yes. 35 00:01:54,360 --> 00:01:55,670 AUDIENCE: Photon has a momentum-- 36 00:01:55,670 --> 00:01:56,230 ROBERT FIELD: Yes. 37 00:01:56,230 --> 00:01:57,270 AUDIENCE: --transfer. 38 00:02:02,589 --> 00:02:05,130 ROBERT FIELD: We're interested in the particle-like character 39 00:02:05,130 --> 00:02:08,039 of what we think of as waves. 40 00:02:08,039 --> 00:02:12,900 And we saw that the waves were particles. 41 00:02:12,900 --> 00:02:15,360 And particles-- or at least packets. 42 00:02:15,360 --> 00:02:19,620 And these packets had definite momentum. 43 00:02:19,620 --> 00:02:25,590 And that was a wonderful observation. 44 00:02:25,590 --> 00:02:28,900 So, today, this is the menu of what I'm going to talk about. 45 00:02:28,900 --> 00:02:33,420 And at the end, there's a magic word, "spectra." 46 00:02:33,420 --> 00:02:36,570 And I like that because what we're 47 00:02:36,570 --> 00:02:42,840 going to be discovering today is that the internal structure 48 00:02:42,840 --> 00:02:45,220 of atoms and molecules-- 49 00:02:45,220 --> 00:02:50,370 we are not allowed to observe it directly, but it's surprising. 50 00:02:50,370 --> 00:02:54,520 And it's encoded in something which we can observe, 51 00:02:54,520 --> 00:02:56,370 which is a spectrum. 52 00:02:56,370 --> 00:02:59,520 And the spectrum that I will show you at the end 53 00:02:59,520 --> 00:03:01,500 is one that is-- 54 00:03:01,500 --> 00:03:04,470 contains essentially no information, 55 00:03:04,470 --> 00:03:08,575 but acts as a template for what we really 56 00:03:08,575 --> 00:03:10,950 want to know about how things are different from hydrogen 57 00:03:10,950 --> 00:03:12,560 atom. 58 00:03:12,560 --> 00:03:18,590 And that's the beginning of our exploration of the structure 59 00:03:18,590 --> 00:03:20,880 of atoms and molecules. 60 00:03:20,880 --> 00:03:25,190 It's through the spectrum and it's how it's different from-- 61 00:03:25,190 --> 00:03:30,150 in subtle ways-- the spectrum of the hydrogen atom. 62 00:03:30,150 --> 00:03:40,170 OK, so, we're going to turn our focus today to the electron, 63 00:03:40,170 --> 00:03:42,240 as opposed to light. 64 00:03:42,240 --> 00:03:45,480 And we're going to play the same game. 65 00:03:45,480 --> 00:03:48,490 We know the electron is a particle. 66 00:03:48,490 --> 00:03:51,700 Does anyone want to tell me why we know that? 67 00:03:51,700 --> 00:03:54,590 Is there any-- anybody who's got a clue? 68 00:03:54,590 --> 00:03:55,880 You can-- oh, good. 69 00:03:55,880 --> 00:03:56,520 Yes. 70 00:03:56,520 --> 00:03:59,231 AUDIENCE: There's an experiment with the little oil drops, 71 00:03:59,231 --> 00:04:00,980 where they suspended them and found that-- 72 00:04:00,980 --> 00:04:01,240 ROBERT FIELD: Yes. 73 00:04:01,240 --> 00:04:02,290 AUDIENCE: --charge is quantized. 74 00:04:02,290 --> 00:04:03,831 ROBERT FIELD: I love that experiment. 75 00:04:03,831 --> 00:04:05,200 That's the Millikan experiment. 76 00:04:08,800 --> 00:04:13,270 One of the reasons I love it is because Millikan and Mulliken 77 00:04:13,270 --> 00:04:15,850 are two different people. 78 00:04:15,850 --> 00:04:19,269 So I find that it's really easy to come up with one of them. 79 00:04:19,269 --> 00:04:23,560 And I remember Mulliken is a spectroscopist 80 00:04:23,560 --> 00:04:29,110 and Millikan was a different kind of physicist. 81 00:04:29,110 --> 00:04:32,110 But they're both famous and they both have connections 82 00:04:32,110 --> 00:04:35,020 to important universities-- 83 00:04:35,020 --> 00:04:39,890 University of Chicago for Millikan and Mulliken, MIT 84 00:04:39,890 --> 00:04:40,390 and Caltech. 85 00:04:44,540 --> 00:04:49,580 So we're going to be looking at something 86 00:04:49,580 --> 00:04:53,020 that we know is a particle. 87 00:04:53,020 --> 00:04:55,510 And we're going to show that it has wave characteristics. 88 00:05:02,120 --> 00:05:11,430 We want to be able to show that the electron has a wavelength 89 00:05:11,430 --> 00:05:14,400 and it follows the same equation that we 90 00:05:14,400 --> 00:05:21,730 use to describe the behavior of electromagnetic radiation. 91 00:05:21,730 --> 00:05:28,350 So how would we control the momentum of an electron? 92 00:05:33,841 --> 00:05:34,340 Yes. 93 00:05:34,340 --> 00:05:36,298 AUDIENCE: So you can control the kinetic energy 94 00:05:36,298 --> 00:05:39,910 that it has by putting it through a certain potential. 95 00:05:39,910 --> 00:05:43,610 ROBERT FIELD: OK, so, we know we can easily measure 96 00:05:43,610 --> 00:05:45,110 the momentum of a particle. 97 00:05:45,110 --> 00:05:48,860 That's not a big challenge. 98 00:05:48,860 --> 00:05:53,155 But then how would we measure its wavelength? 99 00:05:55,911 --> 00:05:56,410 Yes. 100 00:05:56,410 --> 00:05:58,280 AUDIENCE: Some type of diffraction? 101 00:05:58,280 --> 00:05:59,900 ROBERT FIELD: Yes. 102 00:05:59,900 --> 00:06:06,100 We basically use some material, which acts a ruler. 103 00:06:06,100 --> 00:06:12,290 We have a thin metal foil and the distances between atoms 104 00:06:12,290 --> 00:06:16,820 in the foil are constant. 105 00:06:16,820 --> 00:06:20,570 So that's the ruler against which we measure 106 00:06:20,570 --> 00:06:22,530 the wavelength of light. 107 00:06:22,530 --> 00:06:29,630 And we'll talk about the Davisson-Germer experiment, 108 00:06:29,630 --> 00:06:33,900 where we measure the wavelength. 109 00:06:33,900 --> 00:06:38,060 And then we'll talk about the Geiger-Marsden experiment, 110 00:06:38,060 --> 00:06:43,070 where we say, well, atoms have electrons in them. 111 00:06:43,070 --> 00:06:48,580 And what is the structure of an atom? 112 00:06:48,580 --> 00:06:50,950 Remember, we can't look inside. 113 00:06:50,950 --> 00:06:53,490 So we have to use some kind of an experiment 114 00:06:53,490 --> 00:06:56,550 to be able to look inside the atom. 115 00:06:56,550 --> 00:07:04,890 Now, physicists have one trick they often use. 116 00:07:04,890 --> 00:07:07,980 To find out the internal structure of something, 117 00:07:07,980 --> 00:07:10,890 they shoot a particle, or a wave, 118 00:07:10,890 --> 00:07:16,080 at it that has a wavelength comparable to the distances 119 00:07:16,080 --> 00:07:18,330 you're hoping to measure. 120 00:07:18,330 --> 00:07:26,440 So if you have a very high energy probe particle, 121 00:07:26,440 --> 00:07:29,080 it will have a very short wavelength 122 00:07:29,080 --> 00:07:31,960 and it will look sort of like a bullet. 123 00:07:31,960 --> 00:07:35,830 And we know how bullets scatter off of targets or hit targets. 124 00:07:35,830 --> 00:07:38,650 We also, if we choose the wavelength 125 00:07:38,650 --> 00:07:40,930 to be comparable to the distances we're 126 00:07:40,930 --> 00:07:47,870 expecting to measure, then we're going to see diffraction. 127 00:07:47,870 --> 00:07:52,950 This is a kind of subject that lends itself to exam questions. 128 00:07:58,060 --> 00:08:02,110 So let's start out by talking about the Geiger-Marsden 129 00:08:02,110 --> 00:08:02,910 experiment-- 130 00:08:02,910 --> 00:08:06,140 I mean, the Davisson-Germer experiment. 131 00:08:06,140 --> 00:08:18,260 So we have a beam of X-rays or a beam of electrons-- 132 00:08:18,260 --> 00:08:19,610 either one. 133 00:08:19,610 --> 00:08:23,585 And we have an aluminum foil. 134 00:08:26,800 --> 00:08:30,700 And we have-- it's just an intense beam. 135 00:08:30,700 --> 00:08:34,330 We want to stop most of it before it hits a detector. 136 00:08:37,340 --> 00:08:39,520 And, so, this is some kind of a screen or-- 137 00:08:47,930 --> 00:08:51,590 So what we're looking for is, when 138 00:08:51,590 --> 00:08:59,930 the X-rays or the electrons scatter off of this ruler, 139 00:08:59,930 --> 00:09:09,910 we get something that appears on the screen as pairs of circles. 140 00:09:12,680 --> 00:09:15,980 This is the powder pattern because this 141 00:09:15,980 --> 00:09:20,580 is a multi-crystalline object. 142 00:09:20,580 --> 00:09:33,310 But in each object, we have a bunch of equally-spaced atoms, 143 00:09:33,310 --> 00:09:35,670 where this is the lattice constant 144 00:09:35,670 --> 00:09:40,080 and this is the square root of 2 times the lattice constant. 145 00:09:40,080 --> 00:09:43,440 So each atom has nearest neighbors 146 00:09:43,440 --> 00:09:46,470 and second-nearest neighbors. 147 00:09:46,470 --> 00:09:49,080 So we have two rulers going on. 148 00:09:49,080 --> 00:09:53,260 And one ruler will give one set of rings 149 00:09:53,260 --> 00:09:56,050 and the other ruler will give a different set of rings. 150 00:09:56,050 --> 00:09:59,790 And because these particles are randomly oriented, 151 00:09:59,790 --> 00:10:03,480 instead of having spots, you have circles. 152 00:10:03,480 --> 00:10:06,990 And there's all sorts of information in these powder 153 00:10:06,990 --> 00:10:07,560 patterns. 154 00:10:07,560 --> 00:10:10,900 But basically, they're saying, well, 155 00:10:10,900 --> 00:10:12,390 we're seeing a structure which is 156 00:10:12,390 --> 00:10:13,650 related to something we know. 157 00:10:13,650 --> 00:10:19,680 How would we know the distance between atoms in a foil? 158 00:10:19,680 --> 00:10:22,891 Using macroscopic measurements? 159 00:10:22,891 --> 00:10:23,390 Yes. 160 00:10:23,390 --> 00:10:24,210 You're hot today. 161 00:10:24,210 --> 00:10:25,710 AUDIENCE: You have access to density 162 00:10:25,710 --> 00:10:28,130 and you have access to the non-atomic weight. 163 00:10:28,130 --> 00:10:29,540 ROBERT FIELD: That's it, yes. 164 00:10:29,540 --> 00:10:34,310 So it's a simple matter to know at least what is 165 00:10:34,310 --> 00:10:36,660 the magnitude of the distance. 166 00:10:36,660 --> 00:10:42,104 There is an issue of what is the crystal structure. 167 00:10:42,104 --> 00:10:43,520 And there are different structures 168 00:10:43,520 --> 00:10:45,500 and that will give rise to different features 169 00:10:45,500 --> 00:10:47,030 in the powder pattern. 170 00:10:47,030 --> 00:10:50,540 But the important thing is we do this. 171 00:10:50,540 --> 00:10:59,420 We look at the pattern that emerges when we shoot X-rays 172 00:10:59,420 --> 00:11:01,405 at this screen. 173 00:11:01,405 --> 00:11:05,180 And we already know that X-rays have wavelengths. 174 00:11:07,740 --> 00:11:09,240 And we know that they have momentum. 175 00:11:14,306 --> 00:11:19,580 We know about the scattering of photons. 176 00:11:19,580 --> 00:11:23,960 And as a result, we know that we can 177 00:11:23,960 --> 00:11:30,410 predict exactly what the pattern associated with the X-ray 178 00:11:30,410 --> 00:11:31,790 scattering is going to be. 179 00:11:34,390 --> 00:11:39,440 And then we do the same thing with electrons. 180 00:11:39,440 --> 00:11:45,720 And now for the electrons, we can control the momentum. 181 00:11:45,720 --> 00:11:47,190 That's easy. 182 00:11:47,190 --> 00:11:51,560 And what we want to know is what is the wavelength. 183 00:11:51,560 --> 00:11:56,710 And we have the wavelength of the X-rays. 184 00:11:56,710 --> 00:12:05,230 And so what we do is we vary the momentum of the electrons until 185 00:12:05,230 --> 00:12:07,590 the powder pattern for the electron-- 186 00:12:07,590 --> 00:12:11,200 the diffraction pattern for the electron-- 187 00:12:11,200 --> 00:12:14,020 is exactly the same as the diffraction 188 00:12:14,020 --> 00:12:16,960 pattern for the X-ray. 189 00:12:16,960 --> 00:12:22,950 And we discover that, for the electron, 190 00:12:22,950 --> 00:12:30,320 we have the same result. 191 00:12:30,320 --> 00:12:34,400 OK, so, we have, now, photons. 192 00:12:34,400 --> 00:12:37,730 They have wavelengths. 193 00:12:37,730 --> 00:12:42,770 And the momentum was the surprise for the photons. 194 00:12:42,770 --> 00:12:47,770 And we have particles, which have wavelengths and momentum. 195 00:12:47,770 --> 00:12:50,870 And the wavelength was a surprise for the particle. 196 00:12:50,870 --> 00:12:53,790 So it doesn't matter. 197 00:12:53,790 --> 00:12:56,830 Everything follows this equation. 198 00:12:56,830 --> 00:13:05,380 And this equation was anticipated by de Broglie who, 199 00:13:05,380 --> 00:13:07,560 in his PhD thesis-- 200 00:13:07,560 --> 00:13:09,820 you know, he's a person about your age-- 201 00:13:09,820 --> 00:13:14,980 and he wrote his thesis in 1924. 202 00:13:14,980 --> 00:13:17,320 And, among other brilliant things, 203 00:13:17,320 --> 00:13:20,585 he said that everything should follow this simple equation. 204 00:13:23,690 --> 00:13:29,220 And that was a brave statement. 205 00:13:29,220 --> 00:13:36,570 And it predicted that de Broglie was 206 00:13:36,570 --> 00:13:40,180 going to make a lot of brilliant statements in his career. 207 00:13:40,180 --> 00:13:41,800 And this was just the first of-- 208 00:13:41,800 --> 00:13:43,140 and one of the nicest-- 209 00:13:43,140 --> 00:13:45,210 but we'll hear a little bit more about de Broglie 210 00:13:45,210 --> 00:13:47,580 by the time I'm finished with this lecture. 211 00:13:58,210 --> 00:14:04,580 So, we're now worried about atoms. 212 00:14:04,580 --> 00:14:09,725 And we already know that atoms have a diameter, roughly. 213 00:14:17,140 --> 00:14:19,870 We know that from the density, the typical size 214 00:14:19,870 --> 00:14:21,820 we like to have-- 215 00:14:21,820 --> 00:14:26,500 quantities that describe macroscopic objects. 216 00:14:26,500 --> 00:14:32,060 Which are not like 10 to the minus 20, but like 1 to 100. 217 00:14:32,060 --> 00:14:37,590 And so, the angstrom unit, which is 10 to the minus 10 meters, 218 00:14:37,590 --> 00:14:41,190 is a very useful thing for talking about sizes 219 00:14:41,190 --> 00:14:44,130 of atoms and molecules. 220 00:14:47,150 --> 00:14:54,520 So if we have an atom of a size about one angstrom, 221 00:14:54,520 --> 00:15:01,850 we can use this equation to say, well, 222 00:15:01,850 --> 00:15:06,670 what would it take for an electron to fit inside an atom? 223 00:15:09,880 --> 00:15:13,280 So we specify this-- 224 00:15:13,280 --> 00:15:14,740 we know this, we know that-- 225 00:15:14,740 --> 00:15:20,330 and that determines what the momentum would have to be. 226 00:15:20,330 --> 00:15:23,930 And these are all simple calculations. 227 00:15:23,930 --> 00:15:28,880 And since I don't like doing calculations on the board, 228 00:15:28,880 --> 00:15:31,520 and I don't really need to do this now-- 229 00:15:31,520 --> 00:15:34,880 you need to be able to do them, quickly, 230 00:15:34,880 --> 00:15:36,560 if I ask you on the exam. 231 00:15:36,560 --> 00:15:40,040 But basically, what we end up finding out 232 00:15:40,040 --> 00:15:45,620 is that the velocity of the electron 233 00:15:45,620 --> 00:15:54,150 would have to be 7.25 times 10 to the 6 meters per second. 234 00:15:54,150 --> 00:15:56,520 Which is OK, it's pretty fast. 235 00:15:56,520 --> 00:16:00,640 It's a few percent of the speed of light. 236 00:16:00,640 --> 00:16:04,790 But that would correspond to a kinetic energy, 237 00:16:04,790 --> 00:16:13,290 which is 2.4 times 10 to the minus 7 joules. 238 00:16:13,290 --> 00:16:17,840 Remember, I don't like these kinds of units. 239 00:16:17,840 --> 00:16:21,470 But it also corresponds to-- 240 00:16:21,470 --> 00:16:23,820 doing a unit conversion-- 241 00:16:23,820 --> 00:16:26,180 149 electron volts. 242 00:16:26,180 --> 00:16:31,750 Electron volts are a good unit for energy for atoms 243 00:16:31,750 --> 00:16:35,650 because the ionization energy-- 244 00:16:35,650 --> 00:16:39,160 the energy it takes to pull an electron off of an atom-- 245 00:16:39,160 --> 00:16:45,210 is always somewhere between five and 15 electron volts. 246 00:16:45,210 --> 00:16:48,650 So you always want to calibrate yourself, your insight, 247 00:16:48,650 --> 00:16:52,460 in terms of numbers which are in the small scale, 248 00:16:52,460 --> 00:16:54,870 rather than having to remember the exponent. 249 00:17:00,540 --> 00:17:03,870 All right, 149 electron volts. 250 00:17:03,870 --> 00:17:04,950 Should that bother you? 251 00:17:04,950 --> 00:17:06,930 Well, it can't bother you yet because you 252 00:17:06,930 --> 00:17:11,130 don't know about what the ionization energy is. 253 00:17:11,130 --> 00:17:13,420 But I just told you. 254 00:17:13,420 --> 00:17:15,579 It's between five and 15. 255 00:17:15,579 --> 00:17:19,089 This is a factor of 10-- too big. 256 00:17:19,089 --> 00:17:22,839 So this is going to be a problem. 257 00:17:22,839 --> 00:17:26,680 How is it possible for things so small 258 00:17:26,680 --> 00:17:32,920 to have an electron fitting in that small size without it just 259 00:17:32,920 --> 00:17:35,740 leaving because it's just way too high energy? 260 00:17:38,640 --> 00:17:42,560 And so that leads us to ask questions about, well, 261 00:17:42,560 --> 00:17:45,680 what is the internal structure of an atom? 262 00:17:45,680 --> 00:17:52,370 How can an atom somehow accommodate this electron which 263 00:17:52,370 --> 00:17:54,275 needs to somehow fit inside? 264 00:17:57,570 --> 00:18:03,630 So that was the basis for the Geiger-Marsden experiment. 265 00:18:03,630 --> 00:18:05,800 Now, the Geiger-Marsden experiment 266 00:18:05,800 --> 00:18:16,470 looks very similar to the previous experiment. 267 00:18:16,470 --> 00:18:18,750 And here we have-- 268 00:18:18,750 --> 00:18:22,430 whoops-- alpha particles. 269 00:18:22,430 --> 00:18:27,820 Alpha particles are helium-2 plus ions. 270 00:18:27,820 --> 00:18:30,850 And they're produced by radioactive decay. 271 00:18:30,850 --> 00:18:32,880 And they have a tremendous amount of energy. 272 00:18:35,680 --> 00:18:38,230 More energy than was possible in the days 273 00:18:38,230 --> 00:18:43,380 these experiments we're doing to create for a particle. 274 00:18:43,380 --> 00:18:49,590 In fact, one of the earliest experiments, 275 00:18:49,590 --> 00:18:53,400 or apparatuses, capable of producing very high 276 00:18:53,400 --> 00:18:57,780 energy electrons was built by Robert Van de Graaff, here 277 00:18:57,780 --> 00:18:59,160 at MIT. 278 00:18:59,160 --> 00:19:06,330 And this was in the form of cylindrical towers, 279 00:19:06,330 --> 00:19:08,430 right near the parking garage. 280 00:19:08,430 --> 00:19:11,910 And it was there for the first 10 years I was at MIT. 281 00:19:11,910 --> 00:19:14,750 I'm very old, but that's still fairly recent. 282 00:19:14,750 --> 00:19:19,110 But anyway, Van de Graaff could make high energy particles 283 00:19:19,110 --> 00:19:20,880 and it was really neat. 284 00:19:20,880 --> 00:19:24,420 And what he could do was dwarfed by what 285 00:19:24,420 --> 00:19:26,790 can be done in electron accelerators, now. 286 00:19:26,790 --> 00:19:34,410 But in the days when the Geiger-Marsden experiment was 287 00:19:34,410 --> 00:19:42,290 done, which was 1911, there was no way of making 288 00:19:42,290 --> 00:19:47,640 and controlling the energy of an electron-- 289 00:19:47,640 --> 00:19:49,650 or of any particle. 290 00:19:49,650 --> 00:19:52,380 And here we have some particles which 291 00:19:52,380 --> 00:19:54,780 are produced by radioactive decay, which 292 00:19:54,780 --> 00:19:57,010 have tremendous energy. 293 00:19:57,010 --> 00:20:00,140 So they're heavy and they have high energy. 294 00:20:00,140 --> 00:20:03,790 And so that means the wavelength is very small. 295 00:20:08,200 --> 00:20:12,550 We want to use these helium ions. 296 00:20:12,550 --> 00:20:13,902 Yes? 297 00:20:13,902 --> 00:20:15,886 AUDIENCE: Could you not also control 298 00:20:15,886 --> 00:20:19,370 the energy of each particle as they're passing through, right? 299 00:20:19,370 --> 00:20:20,490 ROBERT FIELD: Yes. 300 00:20:20,490 --> 00:20:26,560 But you would need a very high voltage. 301 00:20:26,560 --> 00:20:31,360 And though that is something we could imagine 302 00:20:31,360 --> 00:20:36,490 doing now, but in 1911, the ability 303 00:20:36,490 --> 00:20:43,060 to do that sort of thing with control was not there. 304 00:20:43,060 --> 00:20:46,150 There needed to be advances in vacuum technology. 305 00:20:46,150 --> 00:20:49,570 There needed to be advances in power supplies. 306 00:20:49,570 --> 00:20:55,560 I mean, we're talking about very high voltages. 307 00:20:55,560 --> 00:20:59,890 And you wouldn't want to do that in your laboratory, 308 00:20:59,890 --> 00:21:02,382 even now with the capability. 309 00:21:02,382 --> 00:21:04,090 I remember when I was a graduate student, 310 00:21:04,090 --> 00:21:07,510 we had these things called Spellman power supplies. 311 00:21:07,510 --> 00:21:10,090 And they could produce 40 kilovolts. 312 00:21:10,090 --> 00:21:11,050 They were really scary. 313 00:21:11,050 --> 00:21:14,290 But that's nothing compared to what you need. 314 00:21:14,290 --> 00:21:17,570 OK, so, we want bullets. 315 00:21:17,570 --> 00:21:24,200 We want to have these helium particles interacting 316 00:21:24,200 --> 00:21:30,015 with a thin metal foil. 317 00:21:38,870 --> 00:21:44,740 We have a whole array of atoms here. 318 00:21:44,740 --> 00:21:46,220 And we have a little hole here. 319 00:21:46,220 --> 00:21:49,460 And what's going to happen is this radiation 320 00:21:49,460 --> 00:21:50,990 is going to hit these atoms. 321 00:21:50,990 --> 00:21:53,120 And there's going to be backscatter 322 00:21:53,120 --> 00:21:55,250 and forward scattering. 323 00:21:55,250 --> 00:21:58,520 And the crucial experiment was to measure 324 00:21:58,520 --> 00:22:03,590 the ratio of backscattering to forward scattering. 325 00:22:03,590 --> 00:22:12,060 Now, if we have a target that looks sort of like a smear, 326 00:22:12,060 --> 00:22:16,990 then the forward and backward scattering would be similar. 327 00:22:16,990 --> 00:22:24,250 If we have a target that looked like a bunch of tiny points, 328 00:22:24,250 --> 00:22:27,840 there would very rarely be backscattering. 329 00:22:27,840 --> 00:22:30,870 All of the scattering would be forward 330 00:22:30,870 --> 00:22:33,390 because most of the particles don't hit anything. 331 00:22:36,420 --> 00:22:40,130 And so what was found, and what was the surprise, 332 00:22:40,130 --> 00:22:45,750 is that there was very little backscattering. 333 00:22:45,750 --> 00:22:50,470 And that implied that the ratio of the size 334 00:22:50,470 --> 00:22:55,800 of the target to the size of the particle was enormous. 335 00:22:55,800 --> 00:22:58,110 The particles that scattered-- 336 00:22:58,110 --> 00:23:04,350 the alpha particles-- were tiny. 337 00:23:04,350 --> 00:23:07,240 They had a size-- 338 00:23:07,240 --> 00:23:12,580 something like 10 to the minus 4 times the typical dimension 339 00:23:12,580 --> 00:23:15,720 of an atom. 340 00:23:15,720 --> 00:23:17,780 So this is jellium. 341 00:23:17,780 --> 00:23:21,450 And this is a perfectly reasonable approach. 342 00:23:21,450 --> 00:23:25,820 That the positive and negative charges that make up an atom 343 00:23:25,820 --> 00:23:28,234 are distributed uniformly. 344 00:23:28,234 --> 00:23:29,150 This was the surprise. 345 00:23:38,190 --> 00:23:42,540 How do we explain, now, if atoms that 346 00:23:42,540 --> 00:23:44,880 are scattering the alpha particles 347 00:23:44,880 --> 00:23:47,325 are really small, even compared to the one angstrom? 348 00:23:50,400 --> 00:23:52,830 Well, how do they stick together? 349 00:23:52,830 --> 00:23:58,220 Why is matter not compressable? 350 00:23:58,220 --> 00:23:59,630 So what is going on here? 351 00:24:05,933 --> 00:24:09,590 Now, I'm not exactly sure of the genealogy here, 352 00:24:09,590 --> 00:24:14,420 but Geiger and Marsden were workers, or students, 353 00:24:14,420 --> 00:24:17,150 in the Rutherford lab. 354 00:24:17,150 --> 00:24:22,780 And the old man wanted to save face or to say, oh, here's 355 00:24:22,780 --> 00:24:23,530 an experiment. 356 00:24:23,530 --> 00:24:25,430 We learned something from this. 357 00:24:25,430 --> 00:24:28,360 You know, this is what we do-- this is my job. 358 00:24:28,360 --> 00:24:32,980 But anyway, Rutherford said, well, maybe it's like this. 359 00:24:32,980 --> 00:24:40,000 We have a nucleus and we have the electrons. 360 00:24:40,000 --> 00:24:43,210 So we have a nucleus where all the positive charge 361 00:24:43,210 --> 00:24:47,330 of the atom, and most of the mass, resides. 362 00:24:47,330 --> 00:24:50,705 And we have electrons in circular orbits. 363 00:24:54,260 --> 00:24:56,590 So maybe these circular orbits explain 364 00:24:56,590 --> 00:25:02,830 why you can't compress atoms to something 365 00:25:02,830 --> 00:25:06,940 that would be commensurate with the size of the nuclei. 366 00:25:06,940 --> 00:25:12,490 That the electrons cause a repulsion and the structure 367 00:25:12,490 --> 00:25:14,990 is stable. 368 00:25:14,990 --> 00:25:17,570 So this is a pretty reasonable hypothesis 369 00:25:17,570 --> 00:25:18,860 until one analyzes it. 370 00:25:21,730 --> 00:25:24,340 So what we have is a positive charge here, 371 00:25:24,340 --> 00:25:26,410 negative charge here. 372 00:25:26,410 --> 00:25:30,740 And so, there is Coulomb attraction 373 00:25:30,740 --> 00:25:34,430 and there's centrifugal force, or centripetal acceleration. 374 00:25:34,430 --> 00:25:39,840 And we have to have these two things match. 375 00:25:39,840 --> 00:25:44,100 So the inward force is minus the charge 376 00:25:44,100 --> 00:25:49,320 on the electron squared over 4 by epsilon 0 377 00:25:49,320 --> 00:25:52,080 and 1 over r squared. 378 00:25:52,080 --> 00:25:57,435 And the centrifugal, it's-- 379 00:26:10,120 --> 00:26:12,760 OK, this is-- you know all this. 380 00:26:12,760 --> 00:26:14,640 You know to do this. 381 00:26:14,640 --> 00:26:17,520 Have known it since high school, probably. 382 00:26:17,520 --> 00:26:21,240 And so, you can combine all these things, say the inward 383 00:26:21,240 --> 00:26:24,000 and outward-- the inward force is exactly 384 00:26:24,000 --> 00:26:25,980 canceling the outward force. 385 00:26:25,980 --> 00:26:30,300 And you can solve for the velocity. 386 00:26:30,300 --> 00:26:38,950 And the velocity is q over the electron squared over 4 387 00:26:38,950 --> 00:26:43,910 by epsilon 0 mass of the electron 388 00:26:43,910 --> 00:26:48,260 and the radius of the orbit, square root. 389 00:26:48,260 --> 00:26:50,000 This is a trivial derivation. 390 00:26:50,000 --> 00:26:53,760 I won't insult you by attempting to do it and try 391 00:26:53,760 --> 00:26:57,320 to increase your understanding of the equation, 392 00:26:57,320 --> 00:26:59,070 because you already understand it. 393 00:26:59,070 --> 00:27:02,840 So this is the requirement for the radius 394 00:27:02,840 --> 00:27:05,060 of the circular orbit. 395 00:27:05,060 --> 00:27:08,000 And it has the mass-- 396 00:27:08,000 --> 00:27:11,180 I mean, this is the requirement for the velocity. 397 00:27:11,180 --> 00:27:12,830 And this is the radius, here. 398 00:27:12,830 --> 00:27:15,380 So we know all that. 399 00:27:15,380 --> 00:27:19,080 There is nothing about quantization, yet. 400 00:27:19,080 --> 00:27:23,430 We know that for any radius, the electron 401 00:27:23,430 --> 00:27:26,710 will have a certain velocity. 402 00:27:26,710 --> 00:27:28,620 And we can choose whatever radius, 403 00:27:28,620 --> 00:27:30,750 we want whatever velocity we want. 404 00:27:30,750 --> 00:27:33,410 And that corresponds to whatever energy we get. 405 00:27:43,630 --> 00:27:51,410 What we're interested in is the frequency of the orbit. 406 00:27:51,410 --> 00:27:53,890 And so that will be 1 over the time 407 00:27:53,890 --> 00:27:57,590 it takes for the electron to go around. 408 00:27:57,590 --> 00:28:01,160 And 1 over the time it takes for electron to go around 409 00:28:01,160 --> 00:28:05,520 is 2 pi r, the circumference, divided by the velocity. 410 00:28:05,520 --> 00:28:12,055 So we have the velocity is equal to-- 411 00:28:12,055 --> 00:28:15,760 I mean, the frequency is equal to 1 over 2 pi r. 412 00:28:15,760 --> 00:28:20,860 And we can write an equation for this. 413 00:28:20,860 --> 00:28:23,110 And that's in the notes. 414 00:28:23,110 --> 00:28:26,390 In fact, there was a typo in the notes. 415 00:28:26,390 --> 00:28:28,570 Which has been corrected and read. 416 00:28:28,570 --> 00:28:30,920 But I don't need to tell you what it is. 417 00:28:36,900 --> 00:28:40,170 We can calculate this frequency. 418 00:28:40,170 --> 00:28:41,790 The reason we calculate the frequency 419 00:28:41,790 --> 00:28:47,920 is because we know if we have electrons moving back and forth 420 00:28:47,920 --> 00:28:51,120 at some frequency, they're going to radiate 421 00:28:51,120 --> 00:28:55,590 electromagnetic radiation at that frequency. 422 00:28:55,590 --> 00:28:58,240 Well, where did that energy come from? 423 00:28:58,240 --> 00:29:00,550 It came from the motion of the electron. 424 00:29:00,550 --> 00:29:04,580 So it has to give up kinetic energy. 425 00:29:04,580 --> 00:29:10,300 Now, the energy is the kinetic energy 426 00:29:10,300 --> 00:29:11,830 plus the potential energy. 427 00:29:14,850 --> 00:29:23,590 So if it gives up energy, some of these two things 428 00:29:23,590 --> 00:29:26,700 has to decrease. 429 00:29:26,700 --> 00:29:28,370 And what happens is this decreases 430 00:29:28,370 --> 00:29:31,620 faster that this increases. 431 00:29:31,620 --> 00:29:42,140 And what ends up happening is that the electron 432 00:29:42,140 --> 00:29:44,370 has a death spiral. 433 00:29:44,370 --> 00:29:47,630 What happens will be that the electron will 434 00:29:47,630 --> 00:29:55,610 go in a spiral, going faster and faster as it 435 00:29:55,610 --> 00:30:02,450 goes to smaller and smaller radius, and annihilate itself. 436 00:30:02,450 --> 00:30:04,930 So this is garbage. 437 00:30:04,930 --> 00:30:07,550 This can't be true. 438 00:30:07,550 --> 00:30:12,230 It violates laws that everybody knows are right. 439 00:30:12,230 --> 00:30:16,970 So one needs to find a way to live with this. 440 00:30:19,930 --> 00:30:22,370 Now, one really doesn't need to find a way 441 00:30:22,370 --> 00:30:25,835 to live with it until you realize what happens. 442 00:30:28,970 --> 00:30:37,160 Because this picture, subject to a couple of hypotheses, 443 00:30:37,160 --> 00:30:40,580 predicts an infinite number of 10-digit numbers. 444 00:30:44,710 --> 00:30:45,700 It's not an accident. 445 00:30:45,700 --> 00:30:48,070 Maybe one prediction would be fine. 446 00:30:48,070 --> 00:30:53,500 But all of the lines in the spectra of hydrogen atom, 447 00:30:53,500 --> 00:30:57,070 helium ion, lithium doubly-charged ion, all 448 00:30:57,070 --> 00:31:02,050 of those are predicted with no adjustable parameters 449 00:31:02,050 --> 00:31:04,760 to measurement accuracy. 450 00:31:04,760 --> 00:31:06,310 Now, at the time this was being done, 451 00:31:06,310 --> 00:31:10,790 the measurement accuracy might have been only a part in 1,000, 452 00:31:10,790 --> 00:31:13,170 or maybe a part in a million. 453 00:31:13,170 --> 00:31:15,940 But a part in 10 to the 10th, beyond that we're 454 00:31:15,940 --> 00:31:18,700 starting to get into fundamental physics. 455 00:31:18,700 --> 00:31:21,280 But this is an astonishing thing. 456 00:31:21,280 --> 00:31:28,080 And so I have to explain what the additional assumptions were 457 00:31:28,080 --> 00:31:31,650 because we've got something that predicts things 458 00:31:31,650 --> 00:31:33,790 we have no business knowing. 459 00:31:33,790 --> 00:31:37,440 And there was no explanation for the spectrum 460 00:31:37,440 --> 00:31:43,920 before these experiments, or this picture, was developed. 461 00:31:43,920 --> 00:31:50,690 So we have to first find a way, whether it's believable or not, 462 00:31:50,690 --> 00:31:55,250 of getting rid of the radiative collapse. 463 00:31:55,250 --> 00:32:07,785 So Bohr proposed that angular momentum, l vector r 464 00:32:07,785 --> 00:32:12,590 cross p is conserved. 465 00:32:12,590 --> 00:32:16,700 Well, we know that angular momentum is conserved. 466 00:32:16,700 --> 00:32:20,450 But for a microscopic system, what it means to be conserved 467 00:32:20,450 --> 00:32:24,210 may be a little bit more subtle. 468 00:32:24,210 --> 00:32:26,920 He proposed that angular momentum is conserved 469 00:32:26,920 --> 00:32:31,840 and that the angular momentum, the magnitude of the angular 470 00:32:31,840 --> 00:32:34,510 momentum, had to have a particular value. 471 00:32:40,460 --> 00:32:46,640 And that value was integer times h bar. 472 00:32:46,640 --> 00:32:52,090 h bar is the Planck's constant divided by 2 pi. 473 00:32:52,090 --> 00:32:54,940 Now, this is complete nonsense. 474 00:32:54,940 --> 00:32:56,464 Why should it be conserved? 475 00:33:00,560 --> 00:33:04,395 Why should it be restricted to this set of values? 476 00:33:08,875 --> 00:33:14,650 Well, the reason we accept that it's restricted 477 00:33:14,650 --> 00:33:22,130 is because it gives the energy levels that are observed. 478 00:33:22,130 --> 00:33:25,270 Now, before I get to energy level-- well, I do. 479 00:33:25,270 --> 00:33:27,700 OK, we have energy levels. 480 00:33:27,700 --> 00:33:36,665 We find that the energy is equal to minus some constant over n 481 00:33:36,665 --> 00:33:37,165 squared. 482 00:33:39,990 --> 00:33:42,560 Same n as in here. 483 00:33:42,560 --> 00:33:44,870 This is the Rydberg constant. 484 00:33:44,870 --> 00:33:49,740 And it's something that you can measure. 485 00:33:49,740 --> 00:33:54,887 It's basically a whole bunch of fundamental constants combined. 486 00:33:54,887 --> 00:33:55,845 And so, it has a value. 487 00:34:07,640 --> 00:34:10,118 This is one of the numbers in my permanent memory. 488 00:34:13,610 --> 00:34:16,280 And that's the value of the Rydberg constant 489 00:34:16,280 --> 00:34:19,670 in reciprocal centimeter units. 490 00:34:19,670 --> 00:34:24,439 And to get it into energy units you multiply by h times c, 491 00:34:24,439 --> 00:34:26,480 or to get it into frequency, you just multiply it 492 00:34:26,480 --> 00:34:28,010 by the speed of light. 493 00:34:28,010 --> 00:34:30,080 So, anyway, this is a number that is 494 00:34:30,080 --> 00:34:32,960 known to many decimal places. 495 00:34:32,960 --> 00:34:42,790 And it is generated by this idea that the angular momentum 496 00:34:42,790 --> 00:34:45,400 has to be certain values. 497 00:34:45,400 --> 00:34:47,590 Conservation is good, that's easy. 498 00:34:47,590 --> 00:34:49,929 This is weird. 499 00:34:49,929 --> 00:34:54,159 And it's also wrong because we find out 500 00:34:54,159 --> 00:34:58,510 later that the possible values of n include 0. 501 00:35:01,340 --> 00:35:08,130 Which would completely mess up the Bohr model. 502 00:35:08,130 --> 00:35:13,140 But, anyway, this, then, in combination 503 00:35:13,140 --> 00:35:18,360 with this amazing statement that-- 504 00:35:18,360 --> 00:35:24,510 OK, we have the nth energy and the n prime-th energy. 505 00:35:24,510 --> 00:35:32,670 And the spectrum corresponds to the frequency, corresponds 506 00:35:32,670 --> 00:35:41,954 to e n minus e n prime, over h. 507 00:35:44,640 --> 00:35:50,390 So everything we see in the emission spectrum 508 00:35:50,390 --> 00:35:54,660 of the hydrogen atom, or in a gas-- 509 00:35:54,660 --> 00:35:56,610 which is mostly H2-- 510 00:35:56,610 --> 00:36:00,810 there are transitions associated with the free atoms. 511 00:36:00,810 --> 00:36:05,070 And they're always around this simple equation, 512 00:36:05,070 --> 00:36:08,550 based on the Rydberg equation. 513 00:36:08,550 --> 00:36:12,840 This says the spectra are telling us about the energy 514 00:36:12,840 --> 00:36:16,190 level differences. 515 00:36:16,190 --> 00:36:19,300 And it's a simple equation. 516 00:36:19,300 --> 00:36:21,190 And it's true. 517 00:36:21,190 --> 00:36:24,010 It's true at incredibly high accuracy. 518 00:36:24,010 --> 00:36:30,000 And it tells you nothing except the mass of the particle. 519 00:36:30,000 --> 00:36:32,150 Because the mass of the particle-- 520 00:36:32,150 --> 00:36:34,340 for this Rydberg equation-- we have 521 00:36:34,340 --> 00:36:37,140 it expressed in terms of the mass of the electron. 522 00:36:37,140 --> 00:36:41,610 But it really should be the reduced mass of the mass 523 00:36:41,610 --> 00:36:45,270 of the nucleus times the mass of the electron, 524 00:36:45,270 --> 00:36:50,250 or the mass of the nucleus plus the mass of the electron. 525 00:36:50,250 --> 00:36:53,280 And this is something we know for all two-body interactions. 526 00:36:53,280 --> 00:36:56,370 That was known well before the time of these experiments. 527 00:36:56,370 --> 00:37:00,870 If you have two things interacting, 528 00:37:00,870 --> 00:37:03,420 the reduced mass is what you want rather 529 00:37:03,420 --> 00:37:05,400 than the individual masses. 530 00:37:05,400 --> 00:37:10,350 And so, the only information in these one-electron spectra 531 00:37:10,350 --> 00:37:15,130 is the mass of the nucleus. 532 00:37:15,130 --> 00:37:23,290 And there's not much difference in this reduced mass effect. 533 00:37:23,290 --> 00:37:26,830 But it's enough to say this is a spectrum of hydrogen, 534 00:37:26,830 --> 00:37:30,180 as opposed to lithium 2 plus. 535 00:37:30,180 --> 00:37:33,990 OK, but we still have a problem-- 536 00:37:33,990 --> 00:37:35,420 a very serious problem. 537 00:37:43,000 --> 00:37:48,860 Why is the angular momentum conserved? 538 00:37:48,860 --> 00:37:52,910 Why is the angular momentum forced to have a certain value? 539 00:38:00,964 --> 00:38:03,130 Well, I've really finished this lecture pretty fast. 540 00:38:14,792 --> 00:38:18,560 Let me just get to the end and I will go back. 541 00:38:18,560 --> 00:38:28,050 All right, so, the problem is this electron 542 00:38:28,050 --> 00:38:30,930 is assumed to be a particle and it's assumed to be moving. 543 00:38:34,170 --> 00:38:38,100 So the equation-- 544 00:38:38,100 --> 00:38:40,260 Maxwell's equations-- all of the equations 545 00:38:40,260 --> 00:38:43,940 about motion of charged particles 546 00:38:43,940 --> 00:38:46,410 say if it's moving it's going to radiate, 547 00:38:46,410 --> 00:38:49,346 whereas if it's oscillating, it's going to radiate. 548 00:38:49,346 --> 00:38:51,220 So maybe the problem is that it's not moving. 549 00:38:55,390 --> 00:39:00,940 Remember, the particles are both particles and waves. 550 00:39:00,940 --> 00:39:10,420 So we could imagine that, around this circular orbit, 551 00:39:10,420 --> 00:39:12,850 we have standing waves-- 552 00:39:12,850 --> 00:39:13,450 no motion. 553 00:39:18,360 --> 00:39:21,860 And this led to this Schrodinger equation, 554 00:39:21,860 --> 00:39:28,105 which talks about the states of the electrons that are allowed. 555 00:39:31,700 --> 00:39:34,610 It's basically the classical wave equation, 556 00:39:34,610 --> 00:39:37,070 with a couple little twists. 557 00:39:37,070 --> 00:39:39,530 And the thing about waves, you remember, 558 00:39:39,530 --> 00:39:44,590 we can have constructive and destructive interference. 559 00:39:44,590 --> 00:39:45,760 We can have standing waves. 560 00:39:49,200 --> 00:39:52,320 So there doesn't need to be a motion of our particle. 561 00:39:52,320 --> 00:39:55,890 There could be some static description 562 00:39:55,890 --> 00:40:00,780 of the probability of finding the electron everywhere 563 00:40:00,780 --> 00:40:01,950 around this orbit. 564 00:40:05,351 --> 00:40:06,850 And that's the Schrodinger equation. 565 00:40:13,657 --> 00:40:15,240 In the next lecture, I'm going to talk 566 00:40:15,240 --> 00:40:19,160 about the classical wave equation, which 567 00:40:19,160 --> 00:40:22,220 will be the warm-up for the Schrodinger equation. 568 00:40:22,220 --> 00:40:26,710 And the Schrodinger equation explains everything. 569 00:40:26,710 --> 00:40:29,410 People have made some really fantastic 570 00:40:29,410 --> 00:40:31,960 philosophical statements about the Schrodinger. 571 00:40:31,960 --> 00:40:36,010 It contains everything that we need to know. 572 00:40:36,010 --> 00:40:39,460 The problem is we can't solve the equation exactly. 573 00:40:39,460 --> 00:40:40,900 But it's true. 574 00:40:40,900 --> 00:40:45,280 And it contains everything that we'd ever 575 00:40:45,280 --> 00:40:49,600 want to know about the microscopic structure of atoms 576 00:40:49,600 --> 00:40:51,880 and molecules. 577 00:40:51,880 --> 00:40:56,320 So we've been led by these very simple experiments, which, 578 00:40:56,320 --> 00:40:58,150 now, you could do-- 579 00:40:58,150 --> 00:40:58,960 really trivially. 580 00:40:58,960 --> 00:41:02,110 You wouldn't have to be a smart student of a smart advisor, 581 00:41:02,110 --> 00:41:03,520 or stupid advisor. 582 00:41:03,520 --> 00:41:06,160 You would be able to do these experiments. 583 00:41:06,160 --> 00:41:09,100 And you could say, yeah, this is all very weird, 584 00:41:09,100 --> 00:41:15,300 but know now we know that spectra are everything. 585 00:41:15,300 --> 00:41:16,380 And I'm a spectroscopist. 586 00:41:16,380 --> 00:41:19,680 I'm very proud of this because the idea 587 00:41:19,680 --> 00:41:23,250 that you can make a few measurements 588 00:41:23,250 --> 00:41:28,200 and say something about the internal structure of an atom 589 00:41:28,200 --> 00:41:29,910 or molecule-- 590 00:41:29,910 --> 00:41:32,520 that's a fantastic thing. 591 00:41:32,520 --> 00:41:35,690 And what we've seen-- 592 00:41:35,690 --> 00:41:38,310 the spectrum of one-electron atoms-- 593 00:41:38,310 --> 00:41:41,410 is something which is really simple. 594 00:41:41,410 --> 00:41:46,140 It's the template for understanding all complexity. 595 00:41:46,140 --> 00:41:50,160 Because everything is different from hydrogen. 596 00:41:50,160 --> 00:41:53,340 Hydrogen has a point charge at the center. 597 00:41:53,340 --> 00:41:57,240 It's not quite a point charge, and that's actually a subject 598 00:41:57,240 --> 00:42:01,470 of even modern physics. 599 00:42:01,470 --> 00:42:05,580 And other atoms are not a point charge 600 00:42:05,580 --> 00:42:08,070 because they have electrons. 601 00:42:08,070 --> 00:42:12,290 And so there is a concentration of charge-- 602 00:42:12,290 --> 00:42:17,970 the thing to which the electron is attached is space filling. 603 00:42:17,970 --> 00:42:22,650 So that results in a shift at the energy levels. 604 00:42:22,650 --> 00:42:24,900 And the shift at the energy levels, and how 605 00:42:24,900 --> 00:42:28,050 that shift depends on the orbital angular momentum, 606 00:42:28,050 --> 00:42:30,300 tells you something about the shape of this charge 607 00:42:30,300 --> 00:42:31,800 distribution-- 608 00:42:31,800 --> 00:42:33,840 the radial shape. 609 00:42:33,840 --> 00:42:38,280 So everything we do in spectroscopy 610 00:42:38,280 --> 00:42:40,560 is somehow referenced to something 611 00:42:40,560 --> 00:42:47,180 we understand perfectly, but which is not of much interest. 612 00:42:47,180 --> 00:42:49,940 But it's a template for building up our understanding 613 00:42:49,940 --> 00:42:52,380 of everything. 614 00:42:52,380 --> 00:42:54,900 And this is a kind of a radical statement. 615 00:42:54,900 --> 00:42:59,070 And I get to say this because I'm up here 616 00:42:59,070 --> 00:43:00,930 and I do this for a living. 617 00:43:00,930 --> 00:43:04,230 I mean-- not teaching, but research. 618 00:43:04,230 --> 00:43:09,000 And I really believe that the things 619 00:43:09,000 --> 00:43:14,310 that we are enabled to observe about the microscopic structure 620 00:43:14,310 --> 00:43:18,860 of things are encoded in something completely 621 00:43:18,860 --> 00:43:21,320 unlike looking at it. 622 00:43:21,320 --> 00:43:25,450 And our job is to figure out how to break that code. 623 00:43:25,450 --> 00:43:30,480 And that's what I've done for the last 50 years and it's fun. 624 00:43:30,480 --> 00:43:35,430 OK, so, what more could I say to amuse you 625 00:43:35,430 --> 00:43:37,200 for five-- six minutes? 626 00:43:37,200 --> 00:43:40,890 Not much, because I've skipped a lot of really great stuff. 627 00:43:40,890 --> 00:43:42,690 But go back to de Broglie. 628 00:43:45,640 --> 00:43:50,460 De Broglie had the hypothesis that there 629 00:43:50,460 --> 00:43:52,560 is an integer number of wavelengths 630 00:43:52,560 --> 00:43:55,260 around the circular orbit. 631 00:43:55,260 --> 00:44:00,220 And that was telling you that it's stable 632 00:44:00,220 --> 00:44:03,850 because if it weren't an integer number of wavelengths, 633 00:44:03,850 --> 00:44:07,530 the electron would self annihilate. 634 00:44:07,530 --> 00:44:14,110 But that takes a valid point and moves it 635 00:44:14,110 --> 00:44:17,320 into something which is a little bit wrong. 636 00:44:17,320 --> 00:44:22,480 Because we're not trying to have a particle moving, 637 00:44:22,480 --> 00:44:25,920 we're having a distribution of probabilities. 638 00:44:25,920 --> 00:44:31,370 And there are still wavelengths and nodal structures. 639 00:44:31,370 --> 00:44:36,140 And the stable solutions do involve the particle 640 00:44:36,140 --> 00:44:38,540 not self annihilating. 641 00:44:38,540 --> 00:44:45,690 And so, de Broglie scores another triple. 642 00:44:45,690 --> 00:44:48,170 I mean, he didn't come up with the Schrodinger equation. 643 00:44:48,170 --> 00:44:53,980 So that's the home run that says, OK, we have the material, 644 00:44:53,980 --> 00:44:56,380 now to explain everything. 645 00:44:59,510 --> 00:45:02,180 The next lecture will be just introducing 646 00:45:02,180 --> 00:45:06,950 the mathematics of the wave equation and the crucial ideas. 647 00:45:06,950 --> 00:45:10,190 And that will lead into the following lecture, where we all 648 00:45:10,190 --> 00:45:12,290 talk about the Schrodinger equation. 649 00:45:12,290 --> 00:45:14,210 So I can stop now. 650 00:45:14,210 --> 00:45:15,760 Thanks.