1 00:00:00,030 --> 00:00:02,400 The following content is provided under a creative 2 00:00:02,400 --> 00:00:03,830 commons license. 3 00:00:03,830 --> 00:00:06,850 Your support will help MIT OpenCourseWare continue to 4 00:00:06,850 --> 00:00:10,510 offer high quality educational resources for free. 5 00:00:10,510 --> 00:00:13,390 To make a donation or view additional materials from 6 00:00:13,390 --> 00:00:17,490 hundreds of MIT courses, visit MIT OpenCourseWare at 7 00:00:17,490 --> 00:00:18,740 ocw.mit.edu. 8 00:00:20,800 --> 00:00:24,140 PROFESSOR: All right, a couple of announcements. 9 00:00:24,140 --> 00:00:27,930 Next week two minor celebrations, maybe receptions 10 00:00:27,930 --> 00:00:29,320 we would call them. 11 00:00:29,320 --> 00:00:32,720 Quiz 2 Tuesday based on homework 2, and periodic table 12 00:00:32,720 --> 00:00:35,090 quiz Thursday. 13 00:00:35,090 --> 00:00:37,220 I provide the numbers, you provide the letters. 14 00:00:37,220 --> 00:00:38,750 I guess that's how it works. 15 00:00:38,750 --> 00:00:41,860 And the contest ends Friday five PM. 16 00:00:44,400 --> 00:00:47,150 Last day we looked at the Bohr Model and we developed 17 00:00:47,150 --> 00:00:52,150 equations for the radius of the electronic and the orbit 18 00:00:52,150 --> 00:00:53,390 of the one electron atom. 19 00:00:53,390 --> 00:00:56,540 The energy of the electron and the velocity of the electron. 20 00:00:56,540 --> 00:01:00,000 And we found that for all of these they were 21 00:01:00,000 --> 00:01:01,610 a function of n. 22 00:01:01,610 --> 00:01:02,565 Quantum number. 23 00:01:02,565 --> 00:01:04,100 n takes on discrete values. 24 00:01:04,100 --> 00:01:06,140 One, two, three, and so on. 25 00:01:06,140 --> 00:01:09,660 We say that these energies radii 26 00:01:09,660 --> 00:01:11,480 velocities are quantized. 27 00:01:11,480 --> 00:01:14,800 They take discrete values. 28 00:01:14,800 --> 00:01:16,120 And then later in the lecture we 29 00:01:16,120 --> 00:01:19,510 started looking for evidence. 30 00:01:19,510 --> 00:01:23,570 And we found ourselves in an exercise of reconciliation 31 00:01:23,570 --> 00:01:29,670 with data taken by Angstrom about 50 years earlier and fit 32 00:01:29,670 --> 00:01:31,960 to an equation by J.J. 33 00:01:31,960 --> 00:01:33,930 Balmer. 34 00:01:33,930 --> 00:01:38,220 And we were part way through that and adjourned. 35 00:01:38,220 --> 00:01:43,570 So I'd like to pick up the discussion at that point. 36 00:01:43,570 --> 00:01:46,770 I've done a different drawing of what's going on inside the 37 00:01:46,770 --> 00:01:48,480 gas discharge tube. 38 00:01:48,480 --> 00:01:52,730 Last day I had the ballistic electronic here, and this is 39 00:01:52,730 --> 00:01:55,820 boiling off the cathodes. 40 00:01:55,820 --> 00:01:59,060 The cathode is inside the gas discharge tube and this 41 00:01:59,060 --> 00:02:02,200 electron, if the voltage is high enough, will leave the 42 00:02:02,200 --> 00:02:07,940 cathode and shoot across this low pressure gas, which 43 00:02:07,940 --> 00:02:11,240 contains, among other things, atomic hydrogen. 44 00:02:11,240 --> 00:02:14,140 And I'm trying to depict the atomic hydrogen atom here. 45 00:02:14,140 --> 00:02:16,820 Here's the proton, which is the nucleus-- 46 00:02:16,820 --> 00:02:19,700 that's the sum total of the contents of the nucleus-- 47 00:02:19,700 --> 00:02:25,190 and here's the lone electron that is orbiting the nucleus 48 00:02:25,190 --> 00:02:28,050 at some initial value. 49 00:02:28,050 --> 00:02:29,490 n sub i. 50 00:02:29,490 --> 00:02:30,640 Could be ground state. 51 00:02:30,640 --> 00:02:31,950 Doesn't necessarily have to be. 52 00:02:31,950 --> 00:02:36,680 With some thermal energy this could be n greater than one. 53 00:02:36,680 --> 00:02:40,820 Then we reason that if the electron, ballistic electron, 54 00:02:40,820 --> 00:02:45,520 and it's trajectory across the gas discharge tube over to the 55 00:02:45,520 --> 00:02:47,750 anode, which is charged positively. 56 00:02:47,750 --> 00:02:52,330 If it collided with this electron it could impart some 57 00:02:52,330 --> 00:02:56,290 of its energy, thereby promoting the electron from ni 58 00:02:56,290 --> 00:02:58,920 up to nf, the final level. 59 00:02:58,920 --> 00:03:01,200 And the electron would be up here. 60 00:03:01,200 --> 00:03:05,060 And for this transition there would be an energy cost. That 61 00:03:05,060 --> 00:03:06,700 energy cost is delta e. 62 00:03:06,700 --> 00:03:09,600 Delta e is the energy to go from ni to nf. 63 00:03:09,600 --> 00:03:11,240 And so the kinetic energy-- 64 00:03:11,240 --> 00:03:14,230 half mv squared of the incident electron-- 65 00:03:14,230 --> 00:03:16,440 is diminished by this amount. 66 00:03:16,440 --> 00:03:18,650 And the electronic continues on it's merry 67 00:03:18,650 --> 00:03:21,480 way at a slower speed. 68 00:03:21,480 --> 00:03:23,180 We assume it's mass doesn't change. 69 00:03:23,180 --> 00:03:26,260 The only way we can change its energy is to slow it down. 70 00:03:26,260 --> 00:03:29,020 And there's a conservation of energy, so the sum of the 71 00:03:29,020 --> 00:03:32,770 energy of the scattered electron and the transition 72 00:03:32,770 --> 00:03:36,510 energy of the electron within hydrogen must equal the 73 00:03:36,510 --> 00:03:39,970 incident kinetic energy of the ballistic electron. 74 00:03:39,970 --> 00:03:41,010 But there's more. 75 00:03:41,010 --> 00:03:42,190 This is a-- 76 00:03:42,190 --> 00:03:44,300 no pun intended-- a one shot deal. 77 00:03:44,300 --> 00:03:46,840 This is ballistics, and so the electron is 78 00:03:46,840 --> 00:03:48,720 not sustainably promoted. 79 00:03:48,720 --> 00:03:50,370 It falls back down. 80 00:03:50,370 --> 00:03:53,150 And when it falls back down we have the transition 81 00:03:53,150 --> 00:03:55,710 energy now given off. 82 00:03:55,710 --> 00:03:59,680 Here, to promote we had to call for energy. 83 00:03:59,680 --> 00:04:02,860 When the electron falls down it gives off that energy. 84 00:04:02,860 --> 00:04:05,600 And that energy is given off in the form 85 00:04:05,600 --> 00:04:08,050 of an emitted photon. 86 00:04:08,050 --> 00:04:11,570 And it's that emitted photon and it's that emitted photon 87 00:04:11,570 --> 00:04:15,850 that ultimately gives rise to the lines. 88 00:04:15,850 --> 00:04:19,390 The lines in the spectrum are generated by the emitted 89 00:04:19,390 --> 00:04:19,900 photon here. 90 00:04:19,900 --> 00:04:25,110 Everything else is preamble to this event, and this event 91 00:04:25,110 --> 00:04:27,300 gives rise to the emitted photons. 92 00:04:27,300 --> 00:04:30,020 And I think that's about where we got last day with the 93 00:04:30,020 --> 00:04:30,830 reconciliation. 94 00:04:30,830 --> 00:04:32,430 So let's look carefully here. 95 00:04:32,430 --> 00:04:33,950 We recognize that there needs to be 96 00:04:33,950 --> 00:04:36,060 conservation of energy again. 97 00:04:36,060 --> 00:04:40,300 In other words, the energy of the emitted photon, the energy 98 00:04:40,300 --> 00:04:46,000 of the photon, which we know from Planck is h times nu. 99 00:04:46,000 --> 00:04:47,150 I'm trying to distinguish. 100 00:04:47,150 --> 00:04:49,820 This, I'm making nu, the Greek symbol nu. 101 00:04:49,820 --> 00:04:51,500 And I put a little descender on it. 102 00:04:51,500 --> 00:04:55,180 It looks like a v, but I put a little ascender here to 103 00:04:55,180 --> 00:04:56,600 distinguish it. 104 00:04:56,600 --> 00:04:59,240 This is lowercase v, as in mv squared. 105 00:04:59,240 --> 00:05:02,040 This is nu. 106 00:05:02,040 --> 00:05:07,360 So h nu, or it could be hc over lambda. 107 00:05:07,360 --> 00:05:10,740 Or it could be hc nu bar. 108 00:05:10,740 --> 00:05:13,420 Three ways of writing the energy of the photon. 109 00:05:13,420 --> 00:05:18,240 And that must equal delta e of the transition. 110 00:05:18,240 --> 00:05:21,330 So let's keep going. 111 00:05:21,330 --> 00:05:26,010 We know that the delta e, the transition is given by the 112 00:05:26,010 --> 00:05:28,260 Bohr Model. 113 00:05:28,260 --> 00:05:34,340 Delta e transition will equal e final minus e initial, which 114 00:05:34,340 --> 00:05:37,850 will be minus kz squared-- 115 00:05:37,850 --> 00:05:40,190 I'm writing this generally, in this case with atomic 116 00:05:40,190 --> 00:05:41,940 hydrogen z as 1-- 117 00:05:41,940 --> 00:05:48,130 with minus k times 1 over n final squared minus one over n 118 00:05:48,130 --> 00:05:51,220 initial squared. 119 00:05:51,220 --> 00:05:55,650 What we can do then is equate these and roll them around to 120 00:05:55,650 --> 00:05:57,970 isolate nu bar. 121 00:05:57,970 --> 00:06:03,060 nu bar, then, equals minus kz squared over the product of 122 00:06:03,060 --> 00:06:07,990 the Planck constant, the speed of light, 1 over nf squared 123 00:06:07,990 --> 00:06:12,170 minus 1 over ni squared. 124 00:06:12,170 --> 00:06:19,190 Now for the Balmer series, that is to say the Balmer 125 00:06:19,190 --> 00:06:24,060 series of lines, that turns out to be a series where all 126 00:06:24,060 --> 00:06:27,530 of the transitions end up on n equals 2. 127 00:06:27,530 --> 00:06:31,130 We said nf equals 2. 128 00:06:31,130 --> 00:06:36,300 z equals 1 because we're talking about atomic hydrogen. 129 00:06:36,300 --> 00:06:41,880 Then what we have is a set of translations that go 1 over 2 130 00:06:41,880 --> 00:06:43,900 squared minus 1 over ni squared. 131 00:06:43,900 --> 00:06:49,460 ni must be greater than nf, so ni must come from the set 3, 132 00:06:49,460 --> 00:06:53,080 4, 5, et cetera. 133 00:06:53,080 --> 00:06:54,930 Furthermore, I'm going to put z equals 1. 134 00:06:54,930 --> 00:06:57,290 Let's evaluate k. 135 00:06:57,290 --> 00:07:03,990 We know that's 2.18 times 10 to the minus 18 joules, or 136 00:07:03,990 --> 00:07:06,570 13.6 electron volts. 137 00:07:06,570 --> 00:07:10,215 And we know the Planck constant, 6.6 times 10 138 00:07:10,215 --> 00:07:11,680 to the minus 36. 139 00:07:11,680 --> 00:07:14,960 And this is 3 times 18 of the 8th all in SI units. 140 00:07:14,960 --> 00:07:17,890 So this gives me 1.1 times 10 to the 7th 141 00:07:17,890 --> 00:07:19,870 in reciprocal meters. 142 00:07:19,870 --> 00:07:25,080 And if I put all this together I end up with exactly they 143 00:07:25,080 --> 00:07:29,240 equation that was published by Balmer. 144 00:07:29,240 --> 00:07:33,910 Exactly Balmer's equation in 1885, rewritten to express it 145 00:07:33,910 --> 00:07:35,300 in SI units. 146 00:07:35,300 --> 00:07:37,860 1 over 2 squared minus 1 over-- 147 00:07:37,860 --> 00:07:41,640 I'm just going to put ni squared-- 148 00:07:41,640 --> 00:07:47,250 or ni equals 3, 4, 5, 6. 149 00:07:47,250 --> 00:07:50,310 This is Balmer exactly. 150 00:07:50,310 --> 00:07:51,760 Balmer exactly. 151 00:07:51,760 --> 00:07:56,610 So the assumption of this planetary model, with all of 152 00:07:56,610 --> 00:08:00,380 the restrictions that Bohr placed on it in order to get 153 00:08:00,380 --> 00:08:02,940 this set of equations, reconciled 154 00:08:02,940 --> 00:08:06,750 with laboratory data. 155 00:08:06,750 --> 00:08:11,090 Very, very significant. 156 00:08:11,090 --> 00:08:12,420 So here we are. 157 00:08:12,420 --> 00:08:17,500 Those four lines all can be derived from the Bohr model. 158 00:08:17,500 --> 00:08:21,450 And here's another cartoon from your book and showing 159 00:08:21,450 --> 00:08:24,480 what I'm trying to depict here, namely it's the falling 160 00:08:24,480 --> 00:08:29,410 down, the return to the state from which the electron was 161 00:08:29,410 --> 00:08:31,650 promoted that generates the photon. 162 00:08:31,650 --> 00:08:34,500 And the set of those lines is what gives you this. 163 00:08:34,500 --> 00:08:41,030 There so there's the validation of the sixth piece. 164 00:08:41,030 --> 00:08:45,990 So Bohr Model agrees with Angstrom's data, but it also 165 00:08:45,990 --> 00:08:48,330 suggests other experiments. 166 00:08:48,330 --> 00:08:52,330 Let's think about this for a second. 167 00:08:52,330 --> 00:08:56,730 OK, here's another cartoons from your thing. 168 00:08:56,730 --> 00:08:58,910 You know, I told you that this thing is unstable. 169 00:08:58,910 --> 00:09:02,380 And in the Balmer series it goes from n equals 2 up. 170 00:09:02,380 --> 00:09:05,010 But there's a ground state, n equals 1. 171 00:09:05,010 --> 00:09:09,580 What was wrong with those electronics in Sweden in 1853 172 00:09:09,580 --> 00:09:12,520 than Angstrom could never find any electron that would fall 173 00:09:12,520 --> 00:09:15,060 all the way down to the ground state? 174 00:09:15,060 --> 00:09:16,480 What's wrong with it? 175 00:09:16,480 --> 00:09:19,900 Well, here's the answer. 176 00:09:19,900 --> 00:09:21,830 It has to do with instrumentation. 177 00:09:21,830 --> 00:09:26,260 So this is an example where science goes further thanks 178 00:09:26,260 --> 00:09:28,970 for the advent of new instrumentation that allows 179 00:09:28,970 --> 00:09:32,010 this to make measurements that previous people couldn't make, 180 00:09:32,010 --> 00:09:34,210 even though they were very competent experimentalists. 181 00:09:34,210 --> 00:09:38,270 Angstrom could have found n equals 1 series, but couldn't 182 00:09:38,270 --> 00:09:40,900 see them because he was using a photographic plate. 183 00:09:40,900 --> 00:09:46,720 This shows you the range of sensitivity for 184 00:09:46,720 --> 00:09:47,520 photographic plates. 185 00:09:47,520 --> 00:09:49,060 Here's the electromagnetic spectrum. 186 00:09:49,060 --> 00:09:52,010 Out here you have low energy radio waves and up here you 187 00:09:52,010 --> 00:09:54,470 have x-rays and gamma rays and so on. 188 00:09:54,470 --> 00:09:56,570 And the visible spectrum is parked right here in the 189 00:09:56,570 --> 00:09:58,670 middle, and here it is unpacked for you. 190 00:09:58,670 --> 00:10:02,360 And it roughly runs from 400 to 700 nanometers. 191 00:10:02,360 --> 00:10:03,540 That's the invisible spectrum. 192 00:10:03,540 --> 00:10:06,700 So wavelength increasing from left to right, which means 193 00:10:06,700 --> 00:10:09,510 energy frequency in wave number increase 194 00:10:09,510 --> 00:10:11,730 from right to left. 195 00:10:11,730 --> 00:10:14,050 They're complimentary, right? 196 00:10:14,050 --> 00:10:20,060 e nu, nu bar on the top, lambda is on the bottom. 197 00:10:20,060 --> 00:10:22,960 Some spectra are plotted in lambda, some are plotted in 198 00:10:22,960 --> 00:10:24,550 wave number, whatever. 199 00:10:24,550 --> 00:10:28,070 And by the way, I want to show you the power of 200 00:10:28,070 --> 00:10:28,810 knowing a few things. 201 00:10:28,810 --> 00:10:30,620 I don't expect you to know a lot of facts, but I expect you 202 00:10:30,620 --> 00:10:31,840 to know a few things. 203 00:10:31,840 --> 00:10:35,150 Every educated person ought to know that the visible spectrum 204 00:10:35,150 --> 00:10:38,240 runs round numbers 400 to 700 nanometers. 205 00:10:38,240 --> 00:10:41,370 But look, I can take 700 nanometers and use this 206 00:10:41,370 --> 00:10:43,220 formula and convert it to energy. 207 00:10:43,220 --> 00:10:47,710 And I'm going to get something like 3 times 10 to 208 00:10:47,710 --> 00:10:49,540 the minus 19 joules. 209 00:10:49,540 --> 00:10:50,250 Yuck. 210 00:10:50,250 --> 00:10:52,300 Instead, I go in electron volts. 211 00:10:52,300 --> 00:10:53,880 1.8 ev. 212 00:10:53,880 --> 00:10:57,790 Over here, 400 nanometers is 3.1 ev. 213 00:10:57,790 --> 00:11:01,780 So round numbers, the visible spectrum spans 2 214 00:11:01,780 --> 00:11:03,980 to 3 electron volts. 215 00:11:03,980 --> 00:11:08,260 Our eyes are photo detectors that operate on the band width 216 00:11:08,260 --> 00:11:11,740 2 to 3 electron volts. that's easy to remember. 217 00:11:11,740 --> 00:11:14,410 Those are good numbers. 218 00:11:14,410 --> 00:11:18,130 So where does that leave us? 219 00:11:18,130 --> 00:11:19,860 It leaves us here. 220 00:11:19,860 --> 00:11:24,770 We go back and we see these numbers, 656, 486, 434, 221 00:11:24,770 --> 00:11:26,120 they're all in the visible spectrum. 222 00:11:26,120 --> 00:11:28,700 So I went and I did a little calculation. 223 00:11:28,700 --> 00:11:32,240 I said, well what would I have if we'd gotten the wave length 224 00:11:32,240 --> 00:11:34,830 for the transition from 2 down to 1? 225 00:11:34,830 --> 00:11:36,900 This is n equals 2 down to ground state. 226 00:11:36,900 --> 00:11:40,040 If you plug in the numbers to the Bohr model, you'd find 227 00:11:40,040 --> 00:11:43,400 that that would give you 122 nanometers. 228 00:11:43,400 --> 00:11:44,460 122 nanometers? 229 00:11:44,460 --> 00:11:47,690 Well, 122 nanometers is going to put you way over. 230 00:11:47,690 --> 00:11:49,640 It's too high energy, right? 231 00:11:49,640 --> 00:11:54,000 122 nanometers is going to put you off to the left there into 232 00:11:54,000 --> 00:11:55,930 the ultraviolet, where the photographic 233 00:11:55,930 --> 00:11:58,560 film was not sensitive. 234 00:11:58,560 --> 00:12:02,170 So he couldn't measure those lines. 235 00:12:02,170 --> 00:12:05,420 So now I'm going to end by putting the master equation 236 00:12:05,420 --> 00:12:09,050 that captures all of this. 237 00:12:09,050 --> 00:12:10,660 And the master equation that captures of 238 00:12:10,660 --> 00:12:12,850 all of this is here. 239 00:12:12,850 --> 00:12:20,170 It's that nu bar goes as r times z squared, 1 over nf 240 00:12:20,170 --> 00:12:23,710 squared minus 1 over ni squared. 241 00:12:23,710 --> 00:12:31,150 So this is the most general form for all 1 electron atoms. 242 00:12:31,150 --> 00:12:34,200 That's why I've got z squared in there for all 1 electron 243 00:12:34,200 --> 00:12:35,230 atoms. 244 00:12:35,230 --> 00:12:40,480 And this is called the Rydberg equation. 245 00:12:40,480 --> 00:12:43,580 Named after another Swedish spectroscopist at the 246 00:12:43,580 --> 00:12:45,050 University of Lund. 247 00:12:45,050 --> 00:12:47,290 I think a Swede would probably pronounce this something 248 00:12:47,290 --> 00:12:49,810 Rydberg, but you don't have to say that. 249 00:12:49,810 --> 00:12:52,560 You can just say Rydberg and it'll be fine. 250 00:12:52,560 --> 00:12:56,150 And in honor of Rydberg, the constant here is given the 251 00:12:56,150 --> 00:12:57,390 symbol, capital R. 252 00:12:57,390 --> 00:13:02,380 The capital R as the Rydberg constant and it has a value of 253 00:13:02,380 --> 00:13:05,860 1.1 times 10 to the 7th reciprocal 254 00:13:05,860 --> 00:13:09,460 meters in good ST units. 255 00:13:09,460 --> 00:13:12,030 Well, there was more evidence for the 256 00:13:12,030 --> 00:13:14,270 support of Bohr's Model. 257 00:13:14,270 --> 00:13:16,390 More evidence for the support of Bohr's Model. 258 00:13:16,390 --> 00:13:19,190 By the way, as the detectors got better and better we could 259 00:13:19,190 --> 00:13:20,290 get more and more lines. 260 00:13:20,290 --> 00:13:23,820 You see these, as you get higher and higher series 261 00:13:23,820 --> 00:13:27,530 ending on higher and higher end numbers, you move off into 262 00:13:27,530 --> 00:13:29,020 the infrared. 263 00:13:29,020 --> 00:13:31,090 Because this is not to scale. 264 00:13:31,090 --> 00:13:34,210 These n equal 4, n equal 5 are closer and closer to closer 265 00:13:34,210 --> 00:13:36,800 together in terms of energy. 266 00:13:36,800 --> 00:13:40,360 They're farther and farther apart in terms of spacing, but 267 00:13:40,360 --> 00:13:42,510 they're closer and closer together in terms of energy. 268 00:13:42,510 --> 00:13:43,930 Because they're farther from the nucleus. 269 00:13:43,930 --> 00:13:45,710 You say, gee, shouldn't it cost more 270 00:13:45,710 --> 00:13:47,010 energy to go farther? 271 00:13:47,010 --> 00:13:47,500 Uh-uh. 272 00:13:47,500 --> 00:13:50,350 Because you're farther from the positive nucleus. 273 00:13:50,350 --> 00:13:51,040 Be careful. 274 00:13:51,040 --> 00:13:53,980 Don't let your intuition send you in the wrong direction. 275 00:13:53,980 --> 00:13:55,830 It's all about Coulombics. 276 00:13:55,830 --> 00:13:59,160 Anyway, so the Lyman series ends at n equals 1. 277 00:13:59,160 --> 00:14:00,370 And these are different scientists. 278 00:14:00,370 --> 00:14:03,020 Paschen, Bracket, Pfund, Humphreys, and so on. 279 00:14:03,020 --> 00:14:05,870 So maybe, I don't know, if somebody hasn't claimed n 280 00:14:05,870 --> 00:14:08,870 equals 214, all the lines that end there, you know, maybe 281 00:14:08,870 --> 00:14:11,760 that could be your name on the series. 282 00:14:11,760 --> 00:14:13,485 As if anybody cares. 283 00:14:19,620 --> 00:14:22,100 Looks like this quantum condition is validated. 284 00:14:22,100 --> 00:14:25,220 See this is really important because this was the big break 285 00:14:25,220 --> 00:14:27,380 away from classical theory. 286 00:14:27,380 --> 00:14:33,000 That the motion of a body, something with mass, could be 287 00:14:33,000 --> 00:14:37,720 quantized in its behavior shook this physics community. 288 00:14:37,720 --> 00:14:41,080 But this reconciliation of the data says that 289 00:14:41,080 --> 00:14:42,330 assumption is valid. 290 00:14:46,810 --> 00:14:48,730 There's more that happens. 291 00:14:48,730 --> 00:14:55,210 So in 1913 in Berlin-- 292 00:14:55,210 --> 00:14:57,960 remember 1913 is when Bohr published the paper-- 293 00:14:57,960 --> 00:15:03,860 1913 in Berlin there was James Franck and Gustav Hertz. 294 00:15:03,860 --> 00:15:08,490 James Franck and Gustav Hertz. 295 00:15:08,490 --> 00:15:10,110 And they were conducting experiments on 296 00:15:10,110 --> 00:15:11,270 gas discharge tubes. 297 00:15:11,270 --> 00:15:14,080 Only they filled a gas discharge tube, instead of 298 00:15:14,080 --> 00:15:16,640 with hydrogen, they filled it with mercury vapor. 299 00:15:16,640 --> 00:15:19,430 So gas discharge tube-- 300 00:15:19,430 --> 00:15:20,250 GDT-- 301 00:15:20,250 --> 00:15:26,010 gas discharge tube containing mercury vapor. 302 00:15:26,010 --> 00:15:27,260 The same thing. 303 00:15:29,740 --> 00:15:33,200 Put the electrodes, connect on a power supply, and started 304 00:15:33,200 --> 00:15:35,230 varying the potential. 305 00:15:35,230 --> 00:15:38,610 So I'm going to show you what they found. 306 00:15:38,610 --> 00:15:42,550 This is the Planck voltage, and this is the current 307 00:15:42,550 --> 00:15:48,180 between electrodes, or if you like, across the tube. 308 00:15:48,180 --> 00:15:51,000 Between the electrodes, or through the tube. 309 00:15:51,000 --> 00:15:53,630 Or if you like, tube current. 310 00:15:53,630 --> 00:15:56,100 Meaning from one electrode to the other. 311 00:15:56,100 --> 00:15:57,110 The tube current. 312 00:15:57,110 --> 00:15:59,500 Well, low voltage, low current. 313 00:15:59,500 --> 00:16:00,950 High voltage, high currently. 314 00:16:00,950 --> 00:16:03,610 They get up to a certain value of voltage, all of sudden the 315 00:16:03,610 --> 00:16:07,210 tube starts glowing blindly and the current falls to 0. 316 00:16:10,600 --> 00:16:13,200 Then they continued to raise the voltage. 317 00:16:13,200 --> 00:16:15,800 More voltage, more current, up, up, up, up, up. 318 00:16:15,800 --> 00:16:19,160 And then they get to another critical value of voltage, 319 00:16:19,160 --> 00:16:21,180 even more intensity. 320 00:16:21,180 --> 00:16:24,960 And then the current falls to 0. 321 00:16:24,960 --> 00:16:27,560 So you look at those data and say, well, what's that got to 322 00:16:27,560 --> 00:16:28,650 do with the Bohr Model? 323 00:16:28,650 --> 00:16:31,250 Because mercury is not a 1 electron atom. 324 00:16:31,250 --> 00:16:33,020 It's got a boat load of electrons. 325 00:16:33,020 --> 00:16:35,370 This is not a 1 electron atom. 326 00:16:35,370 --> 00:16:36,530 So you say, I know what it is. 327 00:16:36,530 --> 00:16:37,540 It's ionization energy. 328 00:16:37,540 --> 00:16:38,990 Must be ionizing the mercury. 329 00:16:38,990 --> 00:16:41,740 So you go to the periodic table and you look up the 330 00:16:41,740 --> 00:16:46,430 ionization energy of mercury and you discover that that's 331 00:16:46,430 --> 00:16:48,230 10.4 volts. 332 00:16:48,230 --> 00:16:51,370 10.4 electron volts is the ionization energy. 333 00:16:51,370 --> 00:16:56,470 And this first null is at 4.9 volts. 334 00:16:56,470 --> 00:16:59,390 Well, 4.9 is a long way from 10.4. 335 00:16:59,390 --> 00:17:04,250 And this second null occurs at 6.7 volts. 336 00:17:04,250 --> 00:17:06,730 6.7 volts. 337 00:17:06,730 --> 00:17:08,490 So what's this telling us? 338 00:17:08,490 --> 00:17:11,320 What this is telling us is that when you get to a value 339 00:17:11,320 --> 00:17:16,290 of 4.9 volts, you've hit a certain value that allows you 340 00:17:16,290 --> 00:17:21,290 to promote electrons within mercury between one level and 341 00:17:21,290 --> 00:17:22,370 the next level. 342 00:17:22,370 --> 00:17:24,980 And those electrons are being promoted and 343 00:17:24,980 --> 00:17:26,330 then cascading down. 344 00:17:26,330 --> 00:17:28,510 And they're cascading down and they're emitting in the 345 00:17:28,510 --> 00:17:31,600 visible and it's blinding you. 346 00:17:31,600 --> 00:17:33,400 Say, OK, so what does that mean? 347 00:17:33,400 --> 00:17:37,350 Well, it means that the Bohr Model, which is for a 1 348 00:17:37,350 --> 00:17:40,330 electron atom, assumes that energy levels 349 00:17:40,330 --> 00:17:42,130 within it are quantized. 350 00:17:42,130 --> 00:17:46,760 These data indicate that on the basis the behavior of this 351 00:17:46,760 --> 00:17:50,260 gas discharge tube, there must be quantized energy levels 352 00:17:50,260 --> 00:17:54,820 inside of mercury, which means all atoms have quantized 353 00:17:54,820 --> 00:17:56,342 energy levels. 354 00:17:56,342 --> 00:17:57,670 You understand? 355 00:17:57,670 --> 00:17:59,840 Everything is quantized. 356 00:17:59,840 --> 00:18:01,050 That's really powerful. 357 00:18:01,050 --> 00:18:04,350 It starts off with this nerdy little 1 electron atom, and 358 00:18:04,350 --> 00:18:06,900 now he's applying it across matter. 359 00:18:06,900 --> 00:18:10,550 And this is gas, this is more elaborate gas. 360 00:18:10,550 --> 00:18:13,750 Heaven forbid, it might exist in liquids and solids. 361 00:18:16,850 --> 00:18:19,110 So that's the Franck, Hertz experiment. 362 00:18:19,110 --> 00:18:23,590 So his stock goes way, way up as a result of that. 363 00:18:23,590 --> 00:18:26,700 And they win a Nobel Prize. 364 00:18:26,700 --> 00:18:28,220 Here's James Franck. 365 00:18:28,220 --> 00:18:29,000 Here's Gustav Hertz. 366 00:18:29,000 --> 00:18:30,570 You know what the Hertz is. 367 00:18:30,570 --> 00:18:32,120 200 kilohertz, so on. 368 00:18:32,120 --> 00:18:32,690 That's Hertz. 369 00:18:32,690 --> 00:18:38,060 James Franck was at Gottingen when he won this, but he 370 00:18:38,060 --> 00:18:41,210 ultimately came to the United States when the political 371 00:18:41,210 --> 00:18:44,780 changes started occurring in the thirties in Germany. 372 00:18:44,780 --> 00:18:49,100 Franck decided to seek safer surroundings and ended up at 373 00:18:49,100 --> 00:18:52,090 the University of Chicago, where there is to this day the 374 00:18:52,090 --> 00:18:54,400 James Franck Institute of Physics. 375 00:18:54,400 --> 00:18:57,310 Very, very high-end physics institution. 376 00:19:00,240 --> 00:19:02,350 So this is good. 377 00:19:02,350 --> 00:19:05,320 But all good things come to an end. 378 00:19:05,320 --> 00:19:09,000 So 1913 was a bittersweet year for Bohr. 379 00:19:09,000 --> 00:19:13,180 Because he got some good news, but he also got some bad news. 380 00:19:13,180 --> 00:19:17,670 So now I want to move over to limitations of the Bohr Model. 381 00:19:17,670 --> 00:19:19,370 Limitations of the Bohr Model. 382 00:19:22,810 --> 00:19:24,460 So I know what you're going to say-- well, it only talks 383 00:19:24,460 --> 00:19:26,430 about 1 electron atoms, so that's a limitation. 384 00:19:26,430 --> 00:19:28,120 No, there's more to it than that. 385 00:19:28,120 --> 00:19:33,340 Even the 1 electron atom model doesn't capture everything. 386 00:19:33,340 --> 00:19:37,350 I'm going to summarize the limitations. 387 00:19:37,350 --> 00:19:42,160 I'm going to show you three, and they all fall under the 388 00:19:42,160 --> 00:19:45,520 general umbrella of fine structure. 389 00:19:45,520 --> 00:19:46,320 Fine structure. 390 00:19:46,320 --> 00:19:49,100 In other words, the Bohr Model is good, give us the big 391 00:19:49,100 --> 00:19:52,530 lines, but when you start looking more carefully it 392 00:19:52,530 --> 00:19:54,090 fails to capture some of the physics. 393 00:19:54,090 --> 00:19:57,450 So first of all, let's go back to some earlier data. 394 00:19:57,450 --> 00:19:59,460 1887. 395 00:19:59,460 --> 00:20:01,940 1887, there were already data out there that were going to 396 00:20:01,940 --> 00:20:04,020 give heartburn to the Bohr Model. 397 00:20:04,020 --> 00:20:07,650 And those data were taken by Michelson and Morley. 398 00:20:07,650 --> 00:20:08,900 Michelson and Morley. 399 00:20:11,830 --> 00:20:14,820 Everything I've taught you so far, with one exception, has 400 00:20:14,820 --> 00:20:16,680 been European science. 401 00:20:16,680 --> 00:20:18,870 Americans were not active in science because this was a 402 00:20:18,870 --> 00:20:19,560 young country. 403 00:20:19,560 --> 00:20:22,800 We were really good engineers because we were blockaded by 404 00:20:22,800 --> 00:20:23,670 the rest of the world. 405 00:20:23,670 --> 00:20:25,550 We had to live by our wits-- that's where you get the term 406 00:20:25,550 --> 00:20:28,420 "yankee ingenuity." Science was hifalutin stuff. 407 00:20:28,420 --> 00:20:29,560 We didn't have time for it. 408 00:20:29,560 --> 00:20:33,200 But towards the latter half of the 19th century, we started 409 00:20:33,200 --> 00:20:35,012 moving into fundamental science. 410 00:20:35,012 --> 00:20:38,770 The first American to win the Nobel Prize was Michelson. 411 00:20:38,770 --> 00:20:43,040 Michelson was doing work at Case in Cleveland, which 412 00:20:43,040 --> 00:20:47,130 eventually became Case Western Reserve University. 413 00:20:47,130 --> 00:20:51,740 So he was at Case in Cleveland and he was studying optics. 414 00:20:51,740 --> 00:20:56,720 And he was a brilliant experimentalist. In fact, he 415 00:20:56,720 --> 00:21:00,270 made the first reliable measure of the speed of light. 416 00:21:00,270 --> 00:21:04,470 Back before 1900. 417 00:21:04,470 --> 00:21:06,720 What they were doing is they were looking at Angstrom's 418 00:21:06,720 --> 00:21:09,230 lines and they noticed something peculiar. 419 00:21:09,230 --> 00:21:11,990 If you take a look at even this drawing, you notice the 420 00:21:11,990 --> 00:21:14,830 red line is a little bit fatter than the others. 421 00:21:14,830 --> 00:21:17,230 Now you might just say, well, that's just the artist taking 422 00:21:17,230 --> 00:21:20,480 liberties and somebody didn't catch it in proof reading. 423 00:21:20,480 --> 00:21:26,670 But in point of fact, what he found was that if you look at 424 00:21:26,670 --> 00:21:31,440 that line, which is really the line for the 3-2 transition-- 425 00:21:31,440 --> 00:21:36,890 the 3-2 transition in the Balmer series-- 426 00:21:36,890 --> 00:21:41,480 what you find is that if you look at the photographic plate 427 00:21:41,480 --> 00:21:45,980 more carefully, you find that this thing in fact is a pair 428 00:21:45,980 --> 00:21:49,010 of lines, but very, very closely spaced. 429 00:21:49,010 --> 00:21:51,890 This is known as a doublet. 430 00:21:51,890 --> 00:21:57,200 Two lines very closely spaced, centered at 656 nanometers. 431 00:21:57,200 --> 00:22:02,500 And with his interferometer he gets super, super good data. 432 00:22:02,500 --> 00:22:03,970 And he could split the doublet. 433 00:22:03,970 --> 00:22:06,130 Well, what's that mean for Bohr? 434 00:22:06,130 --> 00:22:08,180 Bohr has no way of explaining this. 435 00:22:08,180 --> 00:22:12,000 If you look at the Bohr Model, you've got n equals 2, you've 436 00:22:12,000 --> 00:22:14,230 got n equals 3, alright? 437 00:22:14,230 --> 00:22:19,230 So this is energy 2, energy 3, right? 438 00:22:19,230 --> 00:22:23,380 And so when the electron falls from 3 to 2, we get a photon 439 00:22:23,380 --> 00:22:24,920 of a certain value. 440 00:22:24,920 --> 00:22:27,750 It's going to be nu 3 to 2. 441 00:22:27,750 --> 00:22:31,800 That's the frequency or wave number, what have you. 442 00:22:31,800 --> 00:22:34,530 Now, the fact that you've got a doublet here means that 443 00:22:34,530 --> 00:22:38,600 there must be two transitions, but darn close. 444 00:22:38,600 --> 00:22:43,410 There's either a 3 and a 3 primed, or there's a 2 and a 2 445 00:22:43,410 --> 00:22:47,790 primed, but it's not simply 3 and 2. 446 00:22:47,790 --> 00:22:50,260 So that piece of information runs 447 00:22:50,260 --> 00:22:51,670 counter to the Bohr Model. 448 00:22:51,670 --> 00:22:53,250 Bohr Model is silent about it. 449 00:22:53,250 --> 00:22:56,040 It gets the big picture, but if you look more carefully it 450 00:22:56,040 --> 00:22:58,300 can't capture the doublet. 451 00:22:58,300 --> 00:23:01,950 And Michelson ultimately gets the Nobel Price. 452 00:23:01,950 --> 00:23:04,940 And I think I've got him here. 453 00:23:04,940 --> 00:23:05,960 There he is. 454 00:23:05,960 --> 00:23:08,430 The Nobel Prize. 455 00:23:08,430 --> 00:23:11,240 By the time he got the Nobel Prize he was at the University 456 00:23:11,240 --> 00:23:14,620 of Chicago, but he did the work that won the Nobel Prize 457 00:23:14,620 --> 00:23:16,000 for him at Case. 458 00:23:16,000 --> 00:23:18,430 So sometimes when you see even Millikan, Millikan did his 459 00:23:18,430 --> 00:23:21,250 work at University of Chicago, but eventually took a position 460 00:23:21,250 --> 00:23:22,320 at Caltech. 461 00:23:22,320 --> 00:23:25,460 So the Nobel Prize says, Robert Millikan, Caltech. 462 00:23:25,460 --> 00:23:27,035 But he didn't do that work at Caltech. 463 00:23:27,035 --> 00:23:28,750 He did it at Chicago. 464 00:23:28,750 --> 00:23:31,320 Anyways, you can go to the Nobel website. 465 00:23:31,320 --> 00:23:32,920 You can read about these people. 466 00:23:32,920 --> 00:23:36,540 And what's really cool is when you win the Nobel Prize-- you 467 00:23:36,540 --> 00:23:37,700 notice I didn't say if-- 468 00:23:37,700 --> 00:23:42,020 I say, when you win the Nobel Prize, what you do is you get 469 00:23:42,020 --> 00:23:45,330 on an airplane, you go to Stockholm, and then you go and 470 00:23:45,330 --> 00:23:47,310 you have dinner in this beautiful hall. 471 00:23:47,310 --> 00:23:51,070 I've been there and it's gorgeous, gilded and so on. 472 00:23:51,070 --> 00:23:54,370 Very nice kitchen, excellent wine list. And-- 473 00:23:54,370 --> 00:23:57,540 yes-- and you can go there and they serve meals. 474 00:23:57,540 --> 00:24:02,620 the menu is taken from previous Nobel Prize dinners. 475 00:24:02,620 --> 00:24:04,480 So you can sit and-- 476 00:24:04,480 --> 00:24:07,830 whatever it is, it could be the Nobel Prizes of 1927 and 477 00:24:07,830 --> 00:24:10,560 that's what's going to be on the menu today-- 478 00:24:10,560 --> 00:24:15,660 and after the dinner they have a presentation ceremony with 479 00:24:15,660 --> 00:24:16,870 the King of Sweden. 480 00:24:16,870 --> 00:24:18,730 You get your Nobel Prize, and then people 481 00:24:18,730 --> 00:24:20,750 listen to your lecture. 482 00:24:20,750 --> 00:24:24,750 And those Nobel lectures are really, really expository. 483 00:24:24,750 --> 00:24:27,750 So if you want to go and read the Nobel lecture that 484 00:24:27,750 --> 00:24:31,320 Michelson gave on the occasion of winning the Nobel Prize, 485 00:24:31,320 --> 00:24:34,570 you'll probably learn all of about this and more. 486 00:24:34,570 --> 00:24:37,680 It's really, really good, so go there and read. 487 00:24:37,680 --> 00:24:40,010 Now back to the story. 488 00:24:40,010 --> 00:24:42,800 Second problem with the Bohr Model. 489 00:24:42,800 --> 00:24:44,520 1896-- 490 00:24:44,520 --> 00:24:46,850 see, all this data had been accumulating-- 491 00:24:46,850 --> 00:24:51,330 1896, there was a postdoc by the name of Zeeman. 492 00:24:51,330 --> 00:24:52,430 Piet Zeeman. 493 00:24:52,430 --> 00:24:55,530 He was a postdoc at Leiden. 494 00:24:55,530 --> 00:24:58,400 Leiden in Holland under Lorentz. 495 00:25:01,970 --> 00:25:07,400 You'll learn about the Lorentz force when you study 802. 496 00:25:07,400 --> 00:25:10,010 What he was doing-- 497 00:25:10,010 --> 00:25:11,940 again, gas discharge tube. 498 00:25:11,940 --> 00:25:17,080 So this was gas discharge tube, and what Zeeman was 499 00:25:17,080 --> 00:25:20,195 doing on his postdoc was in a magnetic field. 500 00:25:23,730 --> 00:25:26,420 These people were doing all sorts of experiments. 501 00:25:26,420 --> 00:25:29,400 They were trying to block out the whole experimental space. 502 00:25:29,400 --> 00:25:32,470 So one guy, his specialty is high energy. 503 00:25:32,470 --> 00:25:33,990 One guy's specialty is low pressure. 504 00:25:33,990 --> 00:25:36,620 These people are taking a gas discharge tube and putting in 505 00:25:36,620 --> 00:25:38,920 the jaws of a powerful, permanent magnet and then 506 00:25:38,920 --> 00:25:40,390 measuring the spectrum. 507 00:25:40,390 --> 00:25:44,690 And what he found was that for certain lines, 508 00:25:44,690 --> 00:25:47,130 this was the rest-- 509 00:25:47,130 --> 00:25:49,460 b, I'm going to use as magnetic field-- 510 00:25:49,460 --> 00:25:51,650 in the absence of applied magnetic 511 00:25:51,650 --> 00:25:54,330 field you have a line. 512 00:25:54,330 --> 00:25:56,050 And this is not a doublet, triplet-- 513 00:25:56,050 --> 00:25:58,270 it's just a plain old line. 514 00:25:58,270 --> 00:25:59,770 Well behaved line. 515 00:25:59,770 --> 00:26:03,040 But when they take that gas discharge tube and put it into 516 00:26:03,040 --> 00:26:09,660 a magnetic field, they see a plurality of lines. 517 00:26:09,660 --> 00:26:14,940 And furthermore, the spacing-- 518 00:26:14,940 --> 00:26:16,500 I'm going to use c here-- 519 00:26:16,500 --> 00:26:20,990 the spacing in the lines is proportional to the intensity 520 00:26:20,990 --> 00:26:22,550 of the magnetic field. 521 00:26:22,550 --> 00:26:25,100 No magnetic field, single line. 522 00:26:25,100 --> 00:26:28,250 Modest magnetic field, modest amount of what 523 00:26:28,250 --> 00:26:29,960 is called line splitting. 524 00:26:32,720 --> 00:26:35,770 So a modest amount of applied magnetic 525 00:26:35,770 --> 00:26:37,220 field, modest splitting. 526 00:26:37,220 --> 00:26:41,270 Intense magnetic field, intense splitting. 527 00:26:41,270 --> 00:26:43,160 Bohr Model is silent about that. 528 00:26:43,160 --> 00:26:45,340 Because you know, if you've got different lines, it means 529 00:26:45,340 --> 00:26:46,910 you must have different energy levels. 530 00:26:46,910 --> 00:26:51,180 It's as though the energy level diagrams opens up in a 531 00:26:51,180 --> 00:26:52,780 magnetic field. 532 00:26:52,780 --> 00:26:56,420 The Bohr Model can't account for that. 533 00:26:56,420 --> 00:27:02,190 And parenthetically, they got the Nobel Prize, too. 534 00:27:02,190 --> 00:27:03,560 So there's Piet Zeeman. 535 00:27:03,560 --> 00:27:06,810 Got his PhD in 1896. 536 00:27:06,810 --> 00:27:08,330 He's got his Noble Prize, 1902. 537 00:27:08,330 --> 00:27:10,010 He's off to a good start, I'd say. 538 00:27:10,010 --> 00:27:11,580 And there's Lorentz. 539 00:27:11,580 --> 00:27:14,040 Two of them. 540 00:27:14,040 --> 00:27:15,700 We'll get to him in a second. 541 00:27:15,700 --> 00:27:20,070 So third piece of bad news for the Bohr Model. 542 00:27:20,070 --> 00:27:23,560 And that comes, again, in 1913 in November. 543 00:27:23,560 --> 00:27:27,050 In November of 1913 there was a man by the 544 00:27:27,050 --> 00:27:32,340 name of Stark in Germany. 545 00:27:32,340 --> 00:27:35,300 And Stark was doing analogous experiments. 546 00:27:35,300 --> 00:27:39,710 He was studying gas discharge tube in electric fields. 547 00:27:44,620 --> 00:27:46,450 Obviously, you've got an electric field across the 548 00:27:46,450 --> 00:27:50,370 electrodes to excite the electrons. 549 00:27:50,370 --> 00:27:52,720 But he's taking a whole gas discharge tube and putting it 550 00:27:52,720 --> 00:27:56,050 between flights and then applying an electric field. 551 00:27:56,050 --> 00:27:57,150 And what did he find? 552 00:27:57,150 --> 00:27:58,680 He found the same sort of thing. 553 00:27:58,680 --> 00:28:07,940 He got line splitting in an E field, and furthermore that 554 00:28:07,940 --> 00:28:12,443 extent of splitting, extent dependent upon the intensity. 555 00:28:16,220 --> 00:28:17,360 E intensity. 556 00:28:17,360 --> 00:28:19,150 So no field, no splitting. 557 00:28:19,150 --> 00:28:21,200 Modest field, modest splitting. 558 00:28:21,200 --> 00:28:22,990 Intense field, intense splitting. 559 00:28:22,990 --> 00:28:26,230 Well, again, that's a headache for the Bohr Model. 560 00:28:26,230 --> 00:28:31,120 So this is all three problems, and it's all under aegis of 561 00:28:31,120 --> 00:28:33,820 fine structure. 562 00:28:33,820 --> 00:28:35,630 So we know the Bohr Model has its limitations. 563 00:28:35,630 --> 00:28:36,460 OK, Stark. 564 00:28:36,460 --> 00:28:38,580 I know he's got his Nobel Prize. 565 00:28:38,580 --> 00:28:39,830 There he is. 566 00:28:42,120 --> 00:28:47,060 So 1913 ends on a sour note. 567 00:28:47,060 --> 00:28:48,640 But people don't give up. 568 00:28:48,640 --> 00:28:56,440 1916, Arnold Sommerfeld in Munich. 569 00:28:56,440 --> 00:29:00,270 He was a professor of physics and he proposed modifications. 570 00:29:00,270 --> 00:29:02,110 Modifications to Bohr Model. 571 00:29:05,780 --> 00:29:08,450 It's a patch, we would call it a patch. 572 00:29:08,450 --> 00:29:08,570 going? 573 00:29:08,570 --> 00:29:10,790 To put a patch on the Bohr Model. 574 00:29:10,790 --> 00:29:11,520 And what's he going to do? 575 00:29:11,520 --> 00:29:13,590 What's the gist of his idea? 576 00:29:13,590 --> 00:29:18,990 Well, he retains the planetary structure. 577 00:29:18,990 --> 00:29:20,910 He liked that idea-- 578 00:29:20,910 --> 00:29:23,570 nice orbits, so on. 579 00:29:23,570 --> 00:29:27,370 But he took a page out of Kepler's book. 580 00:29:27,370 --> 00:29:31,050 The planets in the Kepler model, when they revolve 581 00:29:31,050 --> 00:29:33,475 around the sun their orbit is not circular. 582 00:29:33,475 --> 00:29:35,300 It's elliptical. 583 00:29:35,300 --> 00:29:39,150 So Sommerfeld said, why don't we give that a try? 584 00:29:39,150 --> 00:29:45,710 What if we said the electronic orbit can be 585 00:29:45,710 --> 00:29:49,835 elliptical or circular? 586 00:29:53,700 --> 00:29:54,850 And he was quite specific. 587 00:29:54,850 --> 00:29:56,660 He said, suppose-- 588 00:29:56,660 --> 00:30:03,980 and this, again, is not to scale, but to emphasize this 589 00:30:03,980 --> 00:30:09,090 is going to be elliptical or circular, but very, very mild 590 00:30:09,090 --> 00:30:10,550 eccentricity. 591 00:30:10,550 --> 00:30:14,380 What I'm going to draw for you is extreme eccentricity to 592 00:30:14,380 --> 00:30:15,060 make a point. 593 00:30:15,060 --> 00:30:18,990 But suppose we had the circular orbit as I'm drawing 594 00:30:18,990 --> 00:30:24,680 it now, and then we had an elliptical orbit that is 595 00:30:24,680 --> 00:30:27,640 centered on that circle. 596 00:30:27,640 --> 00:30:29,960 So it's mild eccentricity. 597 00:30:29,960 --> 00:30:33,130 We might have another one-- let's do one more. 598 00:30:33,130 --> 00:30:34,790 This is good enough. 599 00:30:34,790 --> 00:30:37,740 The gist here is that we have a circular orbit and an 600 00:30:37,740 --> 00:30:41,690 elliptical orbit, but the bandwidth here 601 00:30:41,690 --> 00:30:43,780 is very, very narrow. 602 00:30:43,780 --> 00:30:48,240 So this is very, very thin. 603 00:30:48,240 --> 00:30:50,570 And it's sort of like an egg shell. 604 00:30:50,570 --> 00:30:53,550 So if I asked you, what's the dimension of an egg? 605 00:30:53,550 --> 00:30:55,770 You'd say, well, it's dimension of the 606 00:30:55,770 --> 00:30:56,390 surface of the egg. 607 00:30:56,390 --> 00:30:57,900 Then I'd say, but the egg shell has 608 00:30:57,900 --> 00:30:58,970 some thickness, right? 609 00:30:58,970 --> 00:31:01,580 But that thickness is relatively small in comparison 610 00:31:01,580 --> 00:31:03,550 to the total dimension of the egg. 611 00:31:03,550 --> 00:31:04,750 So an analogy. 612 00:31:04,750 --> 00:31:09,040 He said that the range of distance from the nucleus, 613 00:31:09,040 --> 00:31:11,440 whether it's circular or elliptical, 614 00:31:11,440 --> 00:31:12,580 is very, very narrow. 615 00:31:12,580 --> 00:31:17,200 So we can say the set of circular and elliptical orbits 616 00:31:17,200 --> 00:31:20,690 lie within a shell, as in egg shell. 617 00:31:20,690 --> 00:31:22,890 So this is a shell model. 618 00:31:22,890 --> 00:31:26,170 It's a shell model. 619 00:31:26,170 --> 00:31:31,070 So now how do you designate the different orbits? 620 00:31:31,070 --> 00:31:32,740 You've got some that are circular, some that are 621 00:31:32,740 --> 00:31:33,530 elliptical. 622 00:31:33,530 --> 00:31:35,560 He needs to distinguish them and he needs to be able to 623 00:31:35,560 --> 00:31:36,270 label them. 624 00:31:36,270 --> 00:31:40,600 So he introduces new quantum numbers to 625 00:31:40,600 --> 00:31:42,050 allow us to name them. 626 00:31:42,050 --> 00:31:46,320 So let's go and take a look at the quantum numbers that 627 00:31:46,320 --> 00:31:47,670 Sommerfeld gave us. 628 00:31:47,670 --> 00:31:49,140 So he starts off with n. 629 00:31:49,140 --> 00:31:52,410 He retains that from the Bohr Model and he calls that the 630 00:31:52,410 --> 00:31:54,280 principal quantum number. 631 00:31:54,280 --> 00:31:58,740 And it's primary attribute is size. 632 00:31:58,740 --> 00:32:03,900 It captures the distance, the principal r from the nucleus. 633 00:32:03,900 --> 00:32:08,910 And it takes values 1, 2, 3, all the way up to infinity. 634 00:32:08,910 --> 00:32:12,650 So n equals 1, small radius. 635 00:32:12,650 --> 00:32:15,560 n equals 10, large radius. 636 00:32:15,560 --> 00:32:19,050 Oh, by the way, there's another numbering system. 637 00:32:19,050 --> 00:32:23,880 This is what we use, but the spectroscopists use letters. 638 00:32:23,880 --> 00:32:25,910 The spectroscopists use letters-- why? 639 00:32:25,910 --> 00:32:28,220 Because remember the Balmer series? 640 00:32:28,220 --> 00:32:30,480 Everybody was hooked on the Balmer series and it ended up 641 00:32:30,480 --> 00:32:31,330 being n equals 2. 642 00:32:31,330 --> 00:32:33,050 And then later with better detectors we find 643 00:32:33,050 --> 00:32:34,320 there's an n equals 1. 644 00:32:34,320 --> 00:32:36,060 So the spectroscopists said, we're going 645 00:32:36,060 --> 00:32:37,150 to get fooled again. 646 00:32:37,150 --> 00:32:38,730 So we're going use letters. 647 00:32:38,730 --> 00:32:41,420 And we're going to start with the letter k. 648 00:32:41,420 --> 00:32:43,680 It's in the middle of the alphabet. 649 00:32:43,680 --> 00:32:47,210 That way if we discover even lower energies, we've got some 650 00:32:47,210 --> 00:32:49,220 head room here, we can label those. 651 00:32:49,220 --> 00:32:51,090 But we never found any. 652 00:32:51,090 --> 00:32:53,960 So if you go over to Building Thirteen and you do some x-ray 653 00:32:53,960 --> 00:32:57,220 refraction and you use the line that emanates from a 654 00:32:57,220 --> 00:33:00,150 copper target, n equals 1-- it's called the k 655 00:33:00,150 --> 00:33:01,420 alpha line of copper. 656 00:33:01,420 --> 00:33:02,270 To this day. 657 00:33:02,270 --> 00:33:05,030 So k, l, m, and so on. 658 00:33:05,030 --> 00:33:07,620 You can't get to infinity, obviously. 659 00:33:07,620 --> 00:33:10,720 You know, I didn't think this thing through. 660 00:33:10,720 --> 00:33:11,830 Now the l. 661 00:33:11,830 --> 00:33:13,210 l is, what's his name? 662 00:33:13,210 --> 00:33:14,060 Sommerfeld. 663 00:33:14,060 --> 00:33:17,830 And it's called the orbital quantum number. 664 00:33:17,830 --> 00:33:18,170 Why? 665 00:33:18,170 --> 00:33:21,480 Because he said that the electron is in an orbital 666 00:33:21,480 --> 00:33:22,520 instead of an orbit. 667 00:33:22,520 --> 00:33:26,400 Orbit is Bohr, orbital is Bohr-Sommerfeld. 668 00:33:26,400 --> 00:33:29,950 And it speaks to the shape. 669 00:33:29,950 --> 00:33:32,300 Somehow, I've got to distinguish between elliptical 670 00:33:32,300 --> 00:33:34,470 and circular. 671 00:33:34,470 --> 00:33:39,260 And it takes values 0, 1, up to n minus 1. 672 00:33:39,260 --> 00:33:43,480 So the n number controls the range of l. 673 00:33:43,480 --> 00:33:47,100 And again, the spectroscopists, they're real 674 00:33:47,100 --> 00:33:48,280 number weenies, they're afraid, 675 00:33:48,280 --> 00:33:50,580 so they use s, lowercase. 676 00:33:50,580 --> 00:33:52,360 See this is uppercase, this is lowercase. 677 00:33:52,360 --> 00:33:56,070 s, p, d, f. 678 00:33:56,070 --> 00:33:59,480 For sharp, this is the sharpest line from the l 679 00:33:59,480 --> 00:34:03,860 equals 0-- then the principal because as you go to z they 680 00:34:03,860 --> 00:34:07,050 all seem to converge and look like hydrogen-- 681 00:34:07,050 --> 00:34:10,260 d is diffuse, f is fine, and then after that they ran out 682 00:34:10,260 --> 00:34:13,460 of ideas so g and h. 683 00:34:13,460 --> 00:34:17,820 So you'll talk about the one s-orbital, meaning n equals 1, 684 00:34:17,820 --> 00:34:20,680 l equals 0. 685 00:34:20,680 --> 00:34:24,100 And there are some values here for shapes. 686 00:34:24,100 --> 00:34:25,730 I'm going to put that right above it. 687 00:34:25,730 --> 00:34:29,420 When l equals 0, l equals 0 means you 688 00:34:29,420 --> 00:34:31,610 have a circular orbit. 689 00:34:31,610 --> 00:34:36,010 And when l equals 1 it's elliptical. 690 00:34:36,010 --> 00:34:43,820 And when l equals 2 it's much more complex, and we'll just 691 00:34:43,820 --> 00:34:44,700 leave it at that. 692 00:34:44,700 --> 00:34:46,710 1, 2, and 3. 693 00:34:46,710 --> 00:34:48,440 So there's l values. 694 00:34:48,440 --> 00:34:51,390 And then m is the magnetic quantum number. 695 00:34:55,060 --> 00:34:56,386 And it talks about orientation. 696 00:35:00,770 --> 00:35:02,870 I'll show you what I mean by that in a second. 697 00:35:02,870 --> 00:35:06,090 The values are governed by l, which is governed by n. 698 00:35:06,090 --> 00:35:10,330 Starts at l, l minus 1, goes down through 0, goes to minus 699 00:35:10,330 --> 00:35:13,300 values and ends at minus l. 700 00:35:13,300 --> 00:35:17,155 So for example, we could do something like this-- 701 00:35:20,570 --> 00:35:25,010 when n equals 1, then l most equal 0, so therefore 702 00:35:25,010 --> 00:35:26,830 m must equals 0. 703 00:35:26,830 --> 00:35:30,330 So this means for n equals 1, it's only a circular orbit and 704 00:35:30,330 --> 00:35:32,760 this thing is going to be immune to line splitting in a 705 00:35:32,760 --> 00:35:35,140 magnetic field. 706 00:35:35,140 --> 00:35:41,480 When n equals 2, l can equals 0 or l can equal 1. 707 00:35:41,480 --> 00:35:44,050 When l equals 0, m equals 0. 708 00:35:44,050 --> 00:35:45,480 That's boring, that's circular. 709 00:35:45,480 --> 00:35:47,600 But here's another possibility. 710 00:35:47,600 --> 00:35:52,580 And that is, when l equals 1 then m can equal 1, 711 00:35:52,580 --> 00:35:55,020 0, and minus 1. 712 00:35:55,020 --> 00:35:57,160 Now I said it has something to do with orientation. 713 00:35:57,160 --> 00:36:00,960 Most of quantum mechanics doesn't translate into the 714 00:36:00,960 --> 00:36:03,970 Cartesian world, but this one does, mercifully, and I think 715 00:36:03,970 --> 00:36:05,320 it's a cute analogy. 716 00:36:05,320 --> 00:36:09,060 If I were to tell you that I've got three different 717 00:36:09,060 --> 00:36:12,160 quantum numbers and I've got an elliptical thing-- and one 718 00:36:12,160 --> 00:36:16,400 way to think, see, the number 0 looks like a circle and the 719 00:36:16,400 --> 00:36:19,910 number 1 has some asperity associated with it, so you can 720 00:36:19,910 --> 00:36:21,330 think of that as the ellipse-- 721 00:36:21,330 --> 00:36:27,020 so I know that I can, with no prior knowledge of where the 722 00:36:27,020 --> 00:36:31,100 true origin of the universe it is, I can arbitrarily define a 723 00:36:31,100 --> 00:36:33,800 set of rectangular coordinates, orthogonal 724 00:36:33,800 --> 00:36:35,270 coordinates, x, y, and z. 725 00:36:35,270 --> 00:36:40,260 And that means I could put one orbital here, one orbital 726 00:36:40,260 --> 00:36:41,640 here, and one orbital here. 727 00:36:41,640 --> 00:36:47,010 So those are three orthogonal orientations, which I think is 728 00:36:47,010 --> 00:36:50,620 consistent with the fact that m takes on three values. 729 00:36:50,620 --> 00:36:52,230 OK, that's cute. 730 00:36:52,230 --> 00:36:57,720 So that's as far as Sommerfeld went. 731 00:36:57,720 --> 00:36:59,960 I'm going to go and do something as a retronym. 732 00:36:59,960 --> 00:37:02,530 I want to get the fourth quantum number up here now, 733 00:37:02,530 --> 00:37:04,670 but we're going to pause the story. 734 00:37:04,670 --> 00:37:08,690 We're going to fast forward to 1925 so I can get the last 735 00:37:08,690 --> 00:37:10,020 quantum number up here. 736 00:37:10,020 --> 00:37:12,120 And that's called the spin quantum number. 737 00:37:14,810 --> 00:37:18,680 And it takes values plus or minus a half. 738 00:37:18,680 --> 00:37:20,990 Where did that come from? 739 00:37:20,990 --> 00:37:25,950 Well, in 1922-- 740 00:37:25,950 --> 00:37:28,250 oh, you know everybody's getting Nobel Prizes and I 741 00:37:28,250 --> 00:37:35,060 didn't give Niels Bohr his proper recognition. 742 00:37:35,060 --> 00:37:36,450 He gets the Noble Prize, as well. 743 00:37:39,240 --> 00:37:42,200 Oh, when Sommerfeld turned 80, they had a symposium in his 744 00:37:42,200 --> 00:37:44,480 honor and they published a book. 745 00:37:44,480 --> 00:37:47,490 And the book had papers and well-wishes, papers that were 746 00:37:47,490 --> 00:37:49,140 given at the symposium. 747 00:37:49,140 --> 00:37:53,720 And in the front they had Sommerfeld's picture and they 748 00:37:53,720 --> 00:37:58,450 also had this twin picture, this diptych. 749 00:37:58,450 --> 00:38:01,490 So on the right is Sommerfeld, and on the left is the same 750 00:38:01,490 --> 00:38:03,630 picture but they've morphed it. 751 00:38:03,630 --> 00:38:05,870 Now remember, there's no Photoshop. 752 00:38:05,870 --> 00:38:08,290 Horrors, there's no Photoshop. 753 00:38:08,290 --> 00:38:09,190 Can you imagine? 754 00:38:09,190 --> 00:38:10,240 So how could they do this? 755 00:38:10,240 --> 00:38:13,120 They had to take the negative, which was a photographic 756 00:38:13,120 --> 00:38:16,690 plate, and when they were printing the negative using a 757 00:38:16,690 --> 00:38:19,740 light box they had to hold the negative on an angle to get 758 00:38:19,740 --> 00:38:21,340 the distortion. 759 00:38:21,340 --> 00:38:24,340 And in holding it on an angle to get the distortion, they 760 00:38:24,340 --> 00:38:27,720 turned this image into something that was a little 761 00:38:27,720 --> 00:38:28,610 more spread out. 762 00:38:28,610 --> 00:38:33,470 And the caption that went with this, "To Arnold Sommerfeld, 763 00:38:33,470 --> 00:38:37,400 who taught us that the circle is the degenerate form of the 764 00:38:37,400 --> 00:38:41,520 ellipse." Now that's geek humor. 765 00:38:41,520 --> 00:38:42,720 I mean, they laughed. 766 00:38:42,720 --> 00:38:44,200 They thought that was so funny, hahaha. 767 00:38:44,200 --> 00:38:46,210 You know. 768 00:38:46,210 --> 00:38:47,320 They were having a great time. 769 00:38:47,320 --> 00:38:49,970 It was Germany, and nineteen twenties. 770 00:38:49,970 --> 00:38:52,640 And there he is. 771 00:38:52,640 --> 00:38:54,550 OK, so now let's go to 1922. 772 00:38:54,550 --> 00:38:56,250 This is the Stern-Gerlach experiment. 773 00:38:56,250 --> 00:38:57,990 Very interesting experiment. 774 00:38:57,990 --> 00:39:00,110 This is really physical vapor deposition. 775 00:39:00,110 --> 00:39:02,500 Over here I've got a crucible and it's 776 00:39:02,500 --> 00:39:04,240 full of molten silver. 777 00:39:04,240 --> 00:39:08,280 So Stern and Gerlach were studying the magnetic behavior 778 00:39:08,280 --> 00:39:11,090 of liquid metals. 779 00:39:11,090 --> 00:39:13,690 So what they were doing is they had this-- 780 00:39:13,690 --> 00:39:15,720 over here you see it's red even though it's silver, 781 00:39:15,720 --> 00:39:18,290 because this is that about 1,000 centigrade. 782 00:39:18,290 --> 00:39:20,200 Silver melts at about 960. 783 00:39:20,200 --> 00:39:22,000 Everything, I don't care what it's color is at room 784 00:39:22,000 --> 00:39:24,340 temperature, at 1,000 degrees it's red. 785 00:39:24,340 --> 00:39:26,200 It's called red hot. 786 00:39:26,200 --> 00:39:26,590 All right. 787 00:39:26,590 --> 00:39:29,370 So this is red hot silver and there's a vapor here and 788 00:39:29,370 --> 00:39:32,010 there's a slit and the silver atoms come out of the slit. 789 00:39:32,010 --> 00:39:35,290 And they go across over here to a substrate and then they 790 00:39:35,290 --> 00:39:36,970 pause it on the substrate. 791 00:39:36,970 --> 00:39:40,040 So making little band of silver on the substrate. 792 00:39:40,040 --> 00:39:43,150 And furthermore, he sometimes put them 793 00:39:43,150 --> 00:39:44,700 through a magnetic field. 794 00:39:44,700 --> 00:39:49,190 So he's got a slit here that narrows the beam, and then he 795 00:39:49,190 --> 00:39:53,730 sends it through a magnetic field that is asymmetric. 796 00:39:53,730 --> 00:39:54,570 It's divergent. 797 00:39:54,570 --> 00:39:55,330 Can you see here? 798 00:39:55,330 --> 00:39:56,280 Look at the end. 799 00:39:56,280 --> 00:39:59,030 The south pole as a tip and the north pole is 800 00:39:59,030 --> 00:40:00,670 this arc, this cup. 801 00:40:00,670 --> 00:40:03,920 So the field lines don't go just directly from tip to tip, 802 00:40:03,920 --> 00:40:05,910 they go from tip off to the side. 803 00:40:05,910 --> 00:40:08,210 So you can see the divergence of the magnetic field. 804 00:40:08,210 --> 00:40:11,910 And so he looked at what kind of deposits he got as a 805 00:40:11,910 --> 00:40:17,460 function of the magnetic field. 806 00:40:17,460 --> 00:40:20,470 Here's what the observed. 807 00:40:20,470 --> 00:40:22,250 Very puzzling. 808 00:40:22,250 --> 00:40:24,020 The whole thing was about Maxwell's equation. 809 00:40:24,020 --> 00:40:26,183 So he's got a silver beam. 810 00:40:29,070 --> 00:40:35,330 And when it went directly from the furnace to the substrate 811 00:40:35,330 --> 00:40:37,200 he just got the shadow of the slit. 812 00:40:40,780 --> 00:40:44,490 And they have the split crosswise with respect to the 813 00:40:44,490 --> 00:40:45,910 divergent magnetic field. 814 00:40:45,910 --> 00:40:50,750 So if you look at the substrate you just see a band. 815 00:40:50,750 --> 00:40:53,590 So this is a band of silver and you can imagine there was 816 00:40:53,590 --> 00:40:56,260 a slit out here and it just cast a shadow and that's the 817 00:40:56,260 --> 00:40:57,650 band of silver. 818 00:40:57,650 --> 00:41:01,340 This is PVD, physical vapor deposition of silver. 819 00:41:01,340 --> 00:41:05,580 Now when b is not equal 0, what would you expect? 820 00:41:05,580 --> 00:41:08,160 You'd think the beam would bend, right? 821 00:41:08,160 --> 00:41:09,610 So what do you think happens? 822 00:41:09,610 --> 00:41:11,100 The beam bends up? 823 00:41:11,100 --> 00:41:12,910 The beam bends down? 824 00:41:12,910 --> 00:41:16,790 Or beam bends to the right or to the left? 825 00:41:16,790 --> 00:41:17,560 Think about it. 826 00:41:17,560 --> 00:41:18,870 I don't want to hear your answer. 827 00:41:18,870 --> 00:41:20,710 Think about it. 828 00:41:20,710 --> 00:41:22,070 What do they observe? 829 00:41:22,070 --> 00:41:27,050 What they observe is, if this is where the original one is. 830 00:41:27,050 --> 00:41:28,970 Two. 831 00:41:28,970 --> 00:41:31,100 The beam splits in two. 832 00:41:31,100 --> 00:41:33,670 And it gets two deposits, one above, one 833 00:41:33,670 --> 00:41:36,520 below, of equal intensity. 834 00:41:36,520 --> 00:41:38,700 That's a problem. 835 00:41:38,700 --> 00:41:39,940 Beam splitting. 836 00:41:39,940 --> 00:41:42,605 But now it's a beam of matter. 837 00:41:47,040 --> 00:41:48,670 Beam splitting. 838 00:41:48,670 --> 00:41:52,230 Boy, they had them scratching their heads on that one. 839 00:41:52,230 --> 00:41:55,570 No way to explain that. 840 00:41:55,570 --> 00:41:57,830 So along come a couple of graduate students. 841 00:41:57,830 --> 00:42:00,270 1925, couple of graduates. 842 00:42:00,270 --> 00:42:03,230 So this is 1992 in Frankfurt. 843 00:42:03,230 --> 00:42:08,070 1925, two graduate students in Leiden, again. 844 00:42:08,070 --> 00:42:11,000 Gaudsmit and Uhlenbeck. 845 00:42:15,420 --> 00:42:16,960 They're just like my TA's. 846 00:42:16,960 --> 00:42:18,740 Grad students. 847 00:42:18,740 --> 00:42:22,000 And they looked at this thing, I don't know, maybe sitting 848 00:42:22,000 --> 00:42:24,180 around over a beer one night, and they said, you know, so 849 00:42:24,180 --> 00:42:28,700 far what we've been saying is the electron revolves around 850 00:42:28,700 --> 00:42:30,230 the nucleus. 851 00:42:30,230 --> 00:42:33,400 And sometimes it revolves in a circular orbit, and sometimes 852 00:42:33,400 --> 00:42:35,920 it revolves in an elliptical orbit, but here's 853 00:42:35,920 --> 00:42:37,280 the electron revolving. 854 00:42:37,280 --> 00:42:41,590 And they said, what if in addition to revolve, the 855 00:42:41,590 --> 00:42:45,320 electron rotated so that it's going like this? 856 00:42:45,320 --> 00:42:46,570 [GESTURES] 857 00:42:48,690 --> 00:42:50,580 But there's two choices. 858 00:42:50,580 --> 00:42:53,310 It can be going like this, or can be going like this. 859 00:42:53,310 --> 00:42:55,730 [GESTURES] 860 00:42:55,730 --> 00:43:00,880 Now, it's a charged species and it's rotating, which means 861 00:43:00,880 --> 00:43:03,670 that it's going to have a magnetic moment 862 00:43:03,670 --> 00:43:05,580 depending on rotation. 863 00:43:05,580 --> 00:43:07,120 And now I'm going to send it through a 864 00:43:07,120 --> 00:43:08,550 divergent magnetic field. 865 00:43:08,550 --> 00:43:12,170 Doesn't it follow to reason that if I put it through a 866 00:43:12,170 --> 00:43:15,320 magnetic field and I've got some of them doing this and 867 00:43:15,320 --> 00:43:17,460 some of them doing that, they're going to go in 868 00:43:17,460 --> 00:43:18,550 different directions? 869 00:43:18,550 --> 00:43:20,380 Opposite directions? 870 00:43:20,380 --> 00:43:22,150 And what do you think the numbers are? 871 00:43:22,150 --> 00:43:25,420 If I give you Avogadro's number of silvers, you think 872 00:43:25,420 --> 00:43:28,630 I'm going to get a dominant clockwise and a minority 873 00:43:28,630 --> 00:43:29,980 anti-clockwise? 874 00:43:29,980 --> 00:43:30,560 No. 875 00:43:30,560 --> 00:43:32,180 We're going to get equal numbers. 876 00:43:32,180 --> 00:43:33,520 Some are going to spin like this, some are going 877 00:43:33,520 --> 00:43:34,340 to spin like that. 878 00:43:34,340 --> 00:43:36,320 And you're going say, but electrons don't spin, they're 879 00:43:36,320 --> 00:43:37,150 not doing this. 880 00:43:37,150 --> 00:43:42,050 But if you model them as though they are doing this, 881 00:43:42,050 --> 00:43:44,690 you get those results. 882 00:43:44,690 --> 00:43:46,930 Those results make sense. 883 00:43:46,930 --> 00:43:51,530 And so they introduced the spin quantum numbers. 884 00:43:51,530 --> 00:43:54,675 And I think these are the ones that have been erased. 885 00:43:57,230 --> 00:43:58,270 Such is education. 886 00:43:58,270 --> 00:43:58,550 OK. 887 00:43:58,550 --> 00:43:59,080 So you know it. 888 00:43:59,080 --> 00:44:00,750 S plus or minus a half. 889 00:44:00,750 --> 00:44:03,060 By the way, Gaudsmit and Uhlenbeck were here during 890 00:44:03,060 --> 00:44:04,260 World War Two. 891 00:44:04,260 --> 00:44:05,900 They worked in Building Four. 892 00:44:05,900 --> 00:44:08,270 You go down the corridor, Building Four just off the 893 00:44:08,270 --> 00:44:11,140 Infinite Corridor, there's a plaque there for the Radiation 894 00:44:11,140 --> 00:44:11,780 Laboratory. 895 00:44:11,780 --> 00:44:13,180 That's where they worked, in the Rad Lab. 896 00:44:13,180 --> 00:44:16,150 That's where radar was first engineered. 897 00:44:16,150 --> 00:44:17,630 There was work in the UK, there was 898 00:44:17,630 --> 00:44:18,570 work in other places. 899 00:44:18,570 --> 00:44:22,050 But this is the Radiation Laboratory, started here and 900 00:44:22,050 --> 00:44:24,300 they were both here at the time. 901 00:44:24,300 --> 00:44:27,440 OK, well, I think that's a-- 902 00:44:27,440 --> 00:44:30,090 So this is a plate from the paper. 903 00:44:30,090 --> 00:44:32,692 No magnetic field with the magnetic field. 904 00:44:32,692 --> 00:44:35,870 And by the way, why did they choose silver? 905 00:44:35,870 --> 00:44:39,670 They chose silver because it's atomic number is 47-- 906 00:44:39,670 --> 00:44:41,240 it has an odd number of electrons. 907 00:44:41,240 --> 00:44:43,270 You're going to learn later that you get two electrons in 908 00:44:43,270 --> 00:44:45,780 an orbital, and if you have two electrons, one will be 909 00:44:45,780 --> 00:44:47,660 spin up, one will be spin down. 910 00:44:47,660 --> 00:44:49,020 There's no magnetic moment. 911 00:44:49,020 --> 00:44:51,720 So they were clever about choosing an element that had 912 00:44:51,720 --> 00:44:56,360 an odd number of electrons so that there would, at the end, 913 00:44:56,360 --> 00:44:58,260 be an unpaired electron. 914 00:44:58,260 --> 00:45:00,920 And there's Otto Stern with his Nobel Prize. 915 00:45:00,920 --> 00:45:03,310 And he came to the United States, as well. 916 00:45:03,310 --> 00:45:05,530 And you're going to see the ascendancy of American Science 917 00:45:05,530 --> 00:45:07,940 as people flee Europe up in the nineteen thirties. 918 00:45:07,940 --> 00:45:10,630 And America is the beneficiary, and then you see 919 00:45:10,630 --> 00:45:12,340 American science rise. 920 00:45:12,340 --> 00:45:15,570 But for now it's European science. 921 00:45:15,570 --> 00:45:17,370 OK, so I'm going to talk a little bit about hydrogen and 922 00:45:17,370 --> 00:45:18,760 transportation. 923 00:45:18,760 --> 00:45:20,780 And we're going to talk about the Hindenburg because it was 924 00:45:20,780 --> 00:45:21,940 full of hydrogen. 925 00:45:21,940 --> 00:45:24,470 And to give you a sense of scale, this is what a 747 926 00:45:24,470 --> 00:45:26,960 would look like and is what the Titanic would look like. 927 00:45:26,960 --> 00:45:29,880 It was almost as long as the Titanic. 928 00:45:29,880 --> 00:45:32,920 It was built in Germany by the Zeppelin company. 929 00:45:32,920 --> 00:45:37,490 And the Titanic, the Hindenburg rather, was LZ129 930 00:45:37,490 --> 00:45:38,080 serial number. 931 00:45:38,080 --> 00:45:42,120 That's Luftschiff Zeppelin. 932 00:45:42,120 --> 00:45:43,090 Airship Zeppelin. 933 00:45:43,090 --> 00:45:44,810 135 feet in diameter. 934 00:45:44,810 --> 00:45:47,860 804 feet long. 935 00:45:47,860 --> 00:45:49,170 How long is a football field? 936 00:45:52,320 --> 00:45:55,510 So that's a big boat. 937 00:45:55,510 --> 00:46:00,590 Seven million cubic feet of gas, giving you 112 tons of 938 00:46:00,590 --> 00:46:01,480 useful lift. 939 00:46:01,480 --> 00:46:03,950 You ever have to lift something very heavy, there's 940 00:46:03,950 --> 00:46:05,200 your sky crane. 941 00:46:07,770 --> 00:46:10,010 So why are they using hydrogen? 942 00:46:10,010 --> 00:46:12,620 Well, when the Nazis came to power in Germany, Congress 943 00:46:12,620 --> 00:46:14,200 passed the Helium Control Act. 944 00:46:14,200 --> 00:46:16,480 The dominant supplier of helium to the world was the 945 00:46:16,480 --> 00:46:17,520 United States. 946 00:46:17,520 --> 00:46:21,190 Helium comes from helium wells in the earth. 947 00:46:21,190 --> 00:46:25,410 And so as of 1933 the United States refused to sell Helium 948 00:46:25,410 --> 00:46:29,850 to Germany, so the engineers were forced to use hydrogen. 949 00:46:29,850 --> 00:46:32,690 Next best thing. 950 00:46:32,690 --> 00:46:33,640 Here are some posters. 951 00:46:33,640 --> 00:46:36,550 "Only 2 1/2 half days to Europe." And here one, a 952 00:46:36,550 --> 00:46:37,490 German one. 953 00:46:37,490 --> 00:46:39,960 "And now over the North Atlantic." That's Manhattan. 954 00:46:39,960 --> 00:46:41,280 That's the lower tip of Manhattan. 955 00:46:41,280 --> 00:46:45,710 There's the Chrysler Building, look at that. 956 00:46:45,710 --> 00:46:46,960 Now look at that picture, isn't that magnificent? 957 00:46:49,400 --> 00:46:52,170 10 transatlantic flights, 1936. 958 00:46:52,170 --> 00:46:55,080 1002 passengers. 959 00:46:55,080 --> 00:46:57,220 Cruising speed, 78 miles an hour. 960 00:46:57,220 --> 00:46:59,650 Took two and a half days. 961 00:46:59,650 --> 00:47:02,940 By the way, 100 feet in diameter-- 962 00:47:02,940 --> 00:47:05,440 when people traveled, they traveled in style. 963 00:47:05,440 --> 00:47:08,390 They had a ballroom there and a grand piano. 964 00:47:08,390 --> 00:47:09,550 People didn't sit like this. 965 00:47:09,550 --> 00:47:09,950 [CROUCHES] 966 00:47:09,950 --> 00:47:13,230 With a plastic knife and fork. 967 00:47:13,230 --> 00:47:16,480 That's progress, right? 968 00:47:16,480 --> 00:47:21,040 Two and a half dancing, tux, tails, champagne. 969 00:47:21,040 --> 00:47:22,150 Now, like this. 970 00:47:22,150 --> 00:47:24,920 [CROUCHES] 971 00:47:24,920 --> 00:47:27,020 May sixth, 1937. 972 00:47:27,020 --> 00:47:30,520 Arrival of first flight to the U.S. while docking in 973 00:47:30,520 --> 00:47:31,340 Lakehurst, New Jersey. 974 00:47:31,340 --> 00:47:33,370 Why were they docking in Lakehurst, New Jersey? 975 00:47:33,370 --> 00:47:36,370 If you go to the top of the Empire State Building, look 976 00:47:36,370 --> 00:47:39,980 and you will see at the corners moorings. 977 00:47:39,980 --> 00:47:41,770 Moorings sticking out. 978 00:47:41,770 --> 00:47:46,400 The plan was to dock airships at the Empire State Building. 979 00:47:46,400 --> 00:47:50,150 So you'd come in from Europe, you'd dock at Fifth Avenue, 980 00:47:50,150 --> 00:47:53,010 get on the elevator, and there you were. 981 00:47:53,010 --> 00:47:55,990 When they tried to dock the air currents were so violent 982 00:47:55,990 --> 00:47:57,690 that they couldn't safely dock the ship. 983 00:47:57,690 --> 00:48:00,780 So then they moved across to the fair grounds at Lakehurst, 984 00:48:00,780 --> 00:48:03,960 New Jersey, where obviously this mooring is much closer to 985 00:48:03,960 --> 00:48:05,980 the ground than the top of the Empire State Building. 986 00:48:05,980 --> 00:48:07,810 The wild currents, they're bad, but 987 00:48:07,810 --> 00:48:08,970 they're manageably bad. 988 00:48:08,970 --> 00:48:12,680 At the top of the Empire State Building, impossible. 989 00:48:12,680 --> 00:48:14,720 There's another image. 990 00:48:14,720 --> 00:48:17,410 So what happened? 991 00:48:17,410 --> 00:48:19,270 It did not explode. 992 00:48:19,270 --> 00:48:21,430 It did not explode. 993 00:48:21,430 --> 00:48:22,650 It couldn't explode. 994 00:48:22,650 --> 00:48:25,580 Seven million cubic feet of hydrogen to explode requires 995 00:48:25,580 --> 00:48:29,040 seven million cubic feet of oxygen instantaneously. 996 00:48:29,040 --> 00:48:32,170 And air is 20% oxygen. 997 00:48:32,170 --> 00:48:36,910 So it was a very violent fire, roman candle from the point of 998 00:48:36,910 --> 00:48:38,490 egress of the hydrogen. 999 00:48:38,490 --> 00:48:43,050 Most of the people on board walked off the Hindenburg. 1000 00:48:43,050 --> 00:48:45,770 Most of the people walked off the Hindenburg uninjured. 1001 00:48:48,630 --> 00:48:51,110 They think it was electrical discharge in the vicinity of a 1002 00:48:51,110 --> 00:48:52,400 hydrogen leak. 1003 00:48:52,400 --> 00:48:56,000 Recent research has indicated the skin was made of resin 1004 00:48:56,000 --> 00:48:57,700 finished with a lacquer dope. 1005 00:48:57,700 --> 00:49:00,380 And then to make it shiny they put aluminum powder. 1006 00:49:00,380 --> 00:49:03,680 And why they put iron oxide on the inside I don't know, but 1007 00:49:03,680 --> 00:49:07,610 this is what NASA uses for solid rocket motor grains. 1008 00:49:07,610 --> 00:49:10,620 So when this thing catches fire, this is a thermite 1009 00:49:10,620 --> 00:49:12,495 reaction and could be very violent. 1010 00:49:15,330 --> 00:49:17,280 And this spelled the end of rigid error ships in 1011 00:49:17,280 --> 00:49:20,290 commercial air transportation. 1012 00:49:20,290 --> 00:49:22,840 Now this a U.S. Navy airship filled with helium. 1013 00:49:22,840 --> 00:49:25,420 And there was a small gasoline fire, look what happened. 1014 00:49:25,420 --> 00:49:26,735 Again, it was the skin. 1015 00:49:31,890 --> 00:49:33,580 That's a blow up of that one. 1016 00:49:33,580 --> 00:49:35,280 So I looked at that and I thought, geez, that looks 1017 00:49:35,280 --> 00:49:37,540 Lichtenstein, doesn't it? 1018 00:49:37,540 --> 00:49:38,940 You know this one? 1019 00:49:38,940 --> 00:49:39,520 This one. 1020 00:49:39,520 --> 00:49:40,470 Look at that. 1021 00:49:40,470 --> 00:49:42,560 Look at that. 1022 00:49:42,560 --> 00:49:45,430 So you know, I can be an artist, too, right? 1023 00:49:45,430 --> 00:49:47,450 OK, I'm going to tell you one more story. 1024 00:49:47,450 --> 00:49:49,140 Another Niels Bohr story. 1025 00:49:49,140 --> 00:49:53,660 So in 1896 there was a guy, and astronomer at Harvard 1026 00:49:53,660 --> 00:49:55,530 called Pickering. 1027 00:49:55,530 --> 00:50:00,190 Pickering at Harvard, 1896, and he was studying the lines 1028 00:50:00,190 --> 00:50:01,360 in star light. 1029 00:50:01,360 --> 00:50:05,910 And he attributed to some of the spectra that he was 1030 00:50:05,910 --> 00:50:11,480 getting, he said he was seeing atomic hydrogen in star light. 1031 00:50:11,480 --> 00:50:15,300 And then there was a fellow in London called Fowler. 1032 00:50:15,300 --> 00:50:19,750 And Fowler, in 1912, reproduced the experiments in 1033 00:50:19,750 --> 00:50:20,235 the laboratory. 1034 00:50:20,235 --> 00:50:25,640 He put gas in a tube and got the same thing in the lab. 1035 00:50:25,640 --> 00:50:31,680 So this guy's at Harvard and the other guy is at London. 1036 00:50:31,680 --> 00:50:33,220 Well, Bohr looks at this stuff and he says, 1037 00:50:33,220 --> 00:50:34,820 you guys are wrong. 1038 00:50:34,820 --> 00:50:36,435 You guys are wrong-- your lines are off 1039 00:50:36,435 --> 00:50:38,540 by a factor of 4x. 1040 00:50:38,540 --> 00:50:41,280 You've got the right series, but you got the wrong element. 1041 00:50:41,280 --> 00:50:43,860 What you guys are looking at is helium plus. 1042 00:50:43,860 --> 00:50:46,455 You're not looking at hydrogen, and you know, from-- 1043 00:50:46,455 --> 00:50:48,100 it goes to z squared. 1044 00:50:48,100 --> 00:50:50,370 So the lines are going to be shifted by factor of four 1045 00:50:50,370 --> 00:50:52,670 because this z is equal to 2. 1046 00:50:52,670 --> 00:50:55,120 So Fowler was a pompous ass and he didn't like being 1047 00:50:55,120 --> 00:50:57,190 called on his bad science. 1048 00:50:57,190 --> 00:51:00,360 So he does a calculation and he looks more carefully and he 1049 00:51:00,360 --> 00:51:01,760 says, Bohr, you're wrong. 1050 00:51:01,760 --> 00:51:06,260 In fact, our lines are off by 4.0016. 1051 00:51:06,260 --> 00:51:08,440 Now don't laugh. 1052 00:51:08,440 --> 00:51:12,130 The reason is the spectroscopy was so precise that they could 1053 00:51:12,130 --> 00:51:14,530 go to five significant figures. 1054 00:51:14,530 --> 00:51:16,730 So Bohr says, hmm. 1055 00:51:16,730 --> 00:51:18,670 And he goes back and he says, you know, we've been doing all 1056 00:51:18,670 --> 00:51:22,040 these calculations with a one electron atom just neglecting 1057 00:51:22,040 --> 00:51:22,980 the center. 1058 00:51:22,980 --> 00:51:25,990 So he redoes the calculations for the entire Bohr model, 1059 00:51:25,990 --> 00:51:29,430 including considerations of the mass of the nucleus and 1060 00:51:29,430 --> 00:51:32,260 the mass of the electron in the form of the reduced mass. 1061 00:51:32,260 --> 00:51:37,740 The reduced mass is-- you're learning this in-- 1062 00:51:37,740 --> 00:51:40,020 the reciprocal of the sum of the reciprocals. 1063 00:51:40,020 --> 00:51:43,890 And when he does that, he gets that the value of the line 1064 00:51:43,890 --> 00:51:49,730 shift should be 4.00163. 1065 00:51:49,730 --> 00:51:52,190 So he says, you guys are wrong. 1066 00:51:52,190 --> 00:51:55,050 It should be 4.0016. 1067 00:51:55,050 --> 00:51:57,500 You got 4.0016, you idiots. 1068 00:51:57,500 --> 00:52:00,750 You're looking at helium plus. 1069 00:52:00,750 --> 00:52:02,300 That was Bohr. 1070 00:52:02,300 --> 00:52:04,840 Did not want to get into an argument with Bohr. 1071 00:52:04,840 --> 00:52:05,850 All right. 1072 00:52:05,850 --> 00:52:07,530 Have a nice weekend.