WEBVTT 00:00:00.030 --> 00:00:02.400 The following content is provided under a creative 00:00:02.400 --> 00:00:03.830 commons license. 00:00:03.830 --> 00:00:06.850 Your support will help MIT OpenCourseWare continue to 00:00:06.850 --> 00:00:10.510 offer high quality educational resources for free. 00:00:10.510 --> 00:00:13.390 To make a donation or view additional materials from 00:00:13.390 --> 00:00:17.490 hundreds of MIT courses, visit MIT OpenCourseWare at 00:00:17.490 --> 00:00:18.740 ocw.mit.edu. 00:00:20.800 --> 00:00:24.140 PROFESSOR: All right, a couple of announcements. 00:00:24.140 --> 00:00:27.930 Next week two minor celebrations, maybe receptions 00:00:27.930 --> 00:00:29.320 we would call them. 00:00:29.320 --> 00:00:32.720 Quiz 2 Tuesday based on homework 2, and periodic table 00:00:32.720 --> 00:00:35.090 quiz Thursday. 00:00:35.090 --> 00:00:37.220 I provide the numbers, you provide the letters. 00:00:37.220 --> 00:00:38.750 I guess that's how it works. 00:00:38.750 --> 00:00:41.860 And the contest ends Friday five PM. 00:00:44.400 --> 00:00:47.150 Last day we looked at the Bohr Model and we developed 00:00:47.150 --> 00:00:52.150 equations for the radius of the electronic and the orbit 00:00:52.150 --> 00:00:53.390 of the one electron atom. 00:00:53.390 --> 00:00:56.540 The energy of the electron and the velocity of the electron. 00:00:56.540 --> 00:01:00.000 And we found that for all of these they were 00:01:00.000 --> 00:01:01.610 a function of n. 00:01:01.610 --> 00:01:02.565 Quantum number. 00:01:02.565 --> 00:01:04.100 n takes on discrete values. 00:01:04.100 --> 00:01:06.140 One, two, three, and so on. 00:01:06.140 --> 00:01:09.660 We say that these energies radii 00:01:09.660 --> 00:01:11.480 velocities are quantized. 00:01:11.480 --> 00:01:14.800 They take discrete values. 00:01:14.800 --> 00:01:16.120 And then later in the lecture we 00:01:16.120 --> 00:01:19.510 started looking for evidence. 00:01:19.510 --> 00:01:23.570 And we found ourselves in an exercise of reconciliation 00:01:23.570 --> 00:01:29.670 with data taken by Angstrom about 50 years earlier and fit 00:01:29.670 --> 00:01:31.960 to an equation by J.J. 00:01:31.960 --> 00:01:33.930 Balmer. 00:01:33.930 --> 00:01:38.220 And we were part way through that and adjourned. 00:01:38.220 --> 00:01:43.570 So I'd like to pick up the discussion at that point. 00:01:43.570 --> 00:01:46.770 I've done a different drawing of what's going on inside the 00:01:46.770 --> 00:01:48.480 gas discharge tube. 00:01:48.480 --> 00:01:52.730 Last day I had the ballistic electronic here, and this is 00:01:52.730 --> 00:01:55.820 boiling off the cathodes. 00:01:55.820 --> 00:01:59.060 The cathode is inside the gas discharge tube and this 00:01:59.060 --> 00:02:02.200 electron, if the voltage is high enough, will leave the 00:02:02.200 --> 00:02:07.940 cathode and shoot across this low pressure gas, which 00:02:07.940 --> 00:02:11.240 contains, among other things, atomic hydrogen. 00:02:11.240 --> 00:02:14.140 And I'm trying to depict the atomic hydrogen atom here. 00:02:14.140 --> 00:02:16.820 Here's the proton, which is the nucleus-- 00:02:16.820 --> 00:02:19.700 that's the sum total of the contents of the nucleus-- 00:02:19.700 --> 00:02:25.190 and here's the lone electron that is orbiting the nucleus 00:02:25.190 --> 00:02:28.050 at some initial value. 00:02:28.050 --> 00:02:29.490 n sub i. 00:02:29.490 --> 00:02:30.640 Could be ground state. 00:02:30.640 --> 00:02:31.950 Doesn't necessarily have to be. 00:02:31.950 --> 00:02:36.680 With some thermal energy this could be n greater than one. 00:02:36.680 --> 00:02:40.820 Then we reason that if the electron, ballistic electron, 00:02:40.820 --> 00:02:45.520 and it's trajectory across the gas discharge tube over to the 00:02:45.520 --> 00:02:47.750 anode, which is charged positively. 00:02:47.750 --> 00:02:52.330 If it collided with this electron it could impart some 00:02:52.330 --> 00:02:56.290 of its energy, thereby promoting the electron from ni 00:02:56.290 --> 00:02:58.920 up to nf, the final level. 00:02:58.920 --> 00:03:01.200 And the electron would be up here. 00:03:01.200 --> 00:03:05.060 And for this transition there would be an energy cost. That 00:03:05.060 --> 00:03:06.700 energy cost is delta e. 00:03:06.700 --> 00:03:09.600 Delta e is the energy to go from ni to nf. 00:03:09.600 --> 00:03:11.240 And so the kinetic energy-- 00:03:11.240 --> 00:03:14.230 half mv squared of the incident electron-- 00:03:14.230 --> 00:03:16.440 is diminished by this amount. 00:03:16.440 --> 00:03:18.650 And the electronic continues on it's merry 00:03:18.650 --> 00:03:21.480 way at a slower speed. 00:03:21.480 --> 00:03:23.180 We assume it's mass doesn't change. 00:03:23.180 --> 00:03:26.260 The only way we can change its energy is to slow it down. 00:03:26.260 --> 00:03:29.020 And there's a conservation of energy, so the sum of the 00:03:29.020 --> 00:03:32.770 energy of the scattered electron and the transition 00:03:32.770 --> 00:03:36.510 energy of the electron within hydrogen must equal the 00:03:36.510 --> 00:03:39.970 incident kinetic energy of the ballistic electron. 00:03:39.970 --> 00:03:41.010 But there's more. 00:03:41.010 --> 00:03:42.190 This is a-- 00:03:42.190 --> 00:03:44.300 no pun intended-- a one shot deal. 00:03:44.300 --> 00:03:46.840 This is ballistics, and so the electron is 00:03:46.840 --> 00:03:48.720 not sustainably promoted. 00:03:48.720 --> 00:03:50.370 It falls back down. 00:03:50.370 --> 00:03:53.150 And when it falls back down we have the transition 00:03:53.150 --> 00:03:55.710 energy now given off. 00:03:55.710 --> 00:03:59.680 Here, to promote we had to call for energy. 00:03:59.680 --> 00:04:02.860 When the electron falls down it gives off that energy. 00:04:02.860 --> 00:04:05.600 And that energy is given off in the form 00:04:05.600 --> 00:04:08.050 of an emitted photon. 00:04:08.050 --> 00:04:11.570 And it's that emitted photon and it's that emitted photon 00:04:11.570 --> 00:04:15.850 that ultimately gives rise to the lines. 00:04:15.850 --> 00:04:19.390 The lines in the spectrum are generated by the emitted 00:04:19.390 --> 00:04:19.900 photon here. 00:04:19.900 --> 00:04:25.110 Everything else is preamble to this event, and this event 00:04:25.110 --> 00:04:27.300 gives rise to the emitted photons. 00:04:27.300 --> 00:04:30.020 And I think that's about where we got last day with the 00:04:30.020 --> 00:04:30.830 reconciliation. 00:04:30.830 --> 00:04:32.430 So let's look carefully here. 00:04:32.430 --> 00:04:33.950 We recognize that there needs to be 00:04:33.950 --> 00:04:36.060 conservation of energy again. 00:04:36.060 --> 00:04:40.300 In other words, the energy of the emitted photon, the energy 00:04:40.300 --> 00:04:46.000 of the photon, which we know from Planck is h times nu. 00:04:46.000 --> 00:04:47.150 I'm trying to distinguish. 00:04:47.150 --> 00:04:49.820 This, I'm making nu, the Greek symbol nu. 00:04:49.820 --> 00:04:51.500 And I put a little descender on it. 00:04:51.500 --> 00:04:55.180 It looks like a v, but I put a little ascender here to 00:04:55.180 --> 00:04:56.600 distinguish it. 00:04:56.600 --> 00:04:59.240 This is lowercase v, as in mv squared. 00:04:59.240 --> 00:05:02.040 This is nu. 00:05:02.040 --> 00:05:07.360 So h nu, or it could be hc over lambda. 00:05:07.360 --> 00:05:10.740 Or it could be hc nu bar. 00:05:10.740 --> 00:05:13.420 Three ways of writing the energy of the photon. 00:05:13.420 --> 00:05:18.240 And that must equal delta e of the transition. 00:05:18.240 --> 00:05:21.330 So let's keep going. 00:05:21.330 --> 00:05:26.010 We know that the delta e, the transition is given by the 00:05:26.010 --> 00:05:28.260 Bohr Model. 00:05:28.260 --> 00:05:34.340 Delta e transition will equal e final minus e initial, which 00:05:34.340 --> 00:05:37.850 will be minus kz squared-- 00:05:37.850 --> 00:05:40.190 I'm writing this generally, in this case with atomic 00:05:40.190 --> 00:05:41.940 hydrogen z as 1-- 00:05:41.940 --> 00:05:48.130 with minus k times 1 over n final squared minus one over n 00:05:48.130 --> 00:05:51.220 initial squared. 00:05:51.220 --> 00:05:55.650 What we can do then is equate these and roll them around to 00:05:55.650 --> 00:05:57.970 isolate nu bar. 00:05:57.970 --> 00:06:03.060 nu bar, then, equals minus kz squared over the product of 00:06:03.060 --> 00:06:07.990 the Planck constant, the speed of light, 1 over nf squared 00:06:07.990 --> 00:06:12.170 minus 1 over ni squared. 00:06:12.170 --> 00:06:19.190 Now for the Balmer series, that is to say the Balmer 00:06:19.190 --> 00:06:24.060 series of lines, that turns out to be a series where all 00:06:24.060 --> 00:06:27.530 of the transitions end up on n equals 2. 00:06:27.530 --> 00:06:31.130 We said nf equals 2. 00:06:31.130 --> 00:06:36.300 z equals 1 because we're talking about atomic hydrogen. 00:06:36.300 --> 00:06:41.880 Then what we have is a set of translations that go 1 over 2 00:06:41.880 --> 00:06:43.900 squared minus 1 over ni squared. 00:06:43.900 --> 00:06:49.460 ni must be greater than nf, so ni must come from the set 3, 00:06:49.460 --> 00:06:53.080 4, 5, et cetera. 00:06:53.080 --> 00:06:54.930 Furthermore, I'm going to put z equals 1. 00:06:54.930 --> 00:06:57.290 Let's evaluate k. 00:06:57.290 --> 00:07:03.990 We know that's 2.18 times 10 to the minus 18 joules, or 00:07:03.990 --> 00:07:06.570 13.6 electron volts. 00:07:06.570 --> 00:07:10.215 And we know the Planck constant, 6.6 times 10 00:07:10.215 --> 00:07:11.680 to the minus 36. 00:07:11.680 --> 00:07:14.960 And this is 3 times 18 of the 8th all in SI units. 00:07:14.960 --> 00:07:17.890 So this gives me 1.1 times 10 to the 7th 00:07:17.890 --> 00:07:19.870 in reciprocal meters. 00:07:19.870 --> 00:07:25.080 And if I put all this together I end up with exactly they 00:07:25.080 --> 00:07:29.240 equation that was published by Balmer. 00:07:29.240 --> 00:07:33.910 Exactly Balmer's equation in 1885, rewritten to express it 00:07:33.910 --> 00:07:35.300 in SI units. 00:07:35.300 --> 00:07:37.860 1 over 2 squared minus 1 over-- 00:07:37.860 --> 00:07:41.640 I'm just going to put ni squared-- 00:07:41.640 --> 00:07:47.250 or ni equals 3, 4, 5, 6. 00:07:47.250 --> 00:07:50.310 This is Balmer exactly. 00:07:50.310 --> 00:07:51.760 Balmer exactly. 00:07:51.760 --> 00:07:56.610 So the assumption of this planetary model, with all of 00:07:56.610 --> 00:08:00.380 the restrictions that Bohr placed on it in order to get 00:08:00.380 --> 00:08:02.940 this set of equations, reconciled 00:08:02.940 --> 00:08:06.750 with laboratory data. 00:08:06.750 --> 00:08:11.090 Very, very significant. 00:08:11.090 --> 00:08:12.420 So here we are. 00:08:12.420 --> 00:08:17.500 Those four lines all can be derived from the Bohr model. 00:08:17.500 --> 00:08:21.450 And here's another cartoon from your book and showing 00:08:21.450 --> 00:08:24.480 what I'm trying to depict here, namely it's the falling 00:08:24.480 --> 00:08:29.410 down, the return to the state from which the electron was 00:08:29.410 --> 00:08:31.650 promoted that generates the photon. 00:08:31.650 --> 00:08:34.500 And the set of those lines is what gives you this. 00:08:34.500 --> 00:08:41.030 There so there's the validation of the sixth piece. 00:08:41.030 --> 00:08:45.990 So Bohr Model agrees with Angstrom's data, but it also 00:08:45.990 --> 00:08:48.330 suggests other experiments. 00:08:48.330 --> 00:08:52.330 Let's think about this for a second. 00:08:52.330 --> 00:08:56.730 OK, here's another cartoons from your thing. 00:08:56.730 --> 00:08:58.910 You know, I told you that this thing is unstable. 00:08:58.910 --> 00:09:02.380 And in the Balmer series it goes from n equals 2 up. 00:09:02.380 --> 00:09:05.010 But there's a ground state, n equals 1. 00:09:05.010 --> 00:09:09.580 What was wrong with those electronics in Sweden in 1853 00:09:09.580 --> 00:09:12.520 than Angstrom could never find any electron that would fall 00:09:12.520 --> 00:09:15.060 all the way down to the ground state? 00:09:15.060 --> 00:09:16.480 What's wrong with it? 00:09:16.480 --> 00:09:19.900 Well, here's the answer. 00:09:19.900 --> 00:09:21.830 It has to do with instrumentation. 00:09:21.830 --> 00:09:26.260 So this is an example where science goes further thanks 00:09:26.260 --> 00:09:28.970 for the advent of new instrumentation that allows 00:09:28.970 --> 00:09:32.010 this to make measurements that previous people couldn't make, 00:09:32.010 --> 00:09:34.210 even though they were very competent experimentalists. 00:09:34.210 --> 00:09:38.270 Angstrom could have found n equals 1 series, but couldn't 00:09:38.270 --> 00:09:40.900 see them because he was using a photographic plate. 00:09:40.900 --> 00:09:46.720 This shows you the range of sensitivity for 00:09:46.720 --> 00:09:47.520 photographic plates. 00:09:47.520 --> 00:09:49.060 Here's the electromagnetic spectrum. 00:09:49.060 --> 00:09:52.010 Out here you have low energy radio waves and up here you 00:09:52.010 --> 00:09:54.470 have x-rays and gamma rays and so on. 00:09:54.470 --> 00:09:56.570 And the visible spectrum is parked right here in the 00:09:56.570 --> 00:09:58.670 middle, and here it is unpacked for you. 00:09:58.670 --> 00:10:02.360 And it roughly runs from 400 to 700 nanometers. 00:10:02.360 --> 00:10:03.540 That's the invisible spectrum. 00:10:03.540 --> 00:10:06.700 So wavelength increasing from left to right, which means 00:10:06.700 --> 00:10:09.510 energy frequency in wave number increase 00:10:09.510 --> 00:10:11.730 from right to left. 00:10:11.730 --> 00:10:14.050 They're complimentary, right? 00:10:14.050 --> 00:10:20.060 e nu, nu bar on the top, lambda is on the bottom. 00:10:20.060 --> 00:10:22.960 Some spectra are plotted in lambda, some are plotted in 00:10:22.960 --> 00:10:24.550 wave number, whatever. 00:10:24.550 --> 00:10:28.070 And by the way, I want to show you the power of 00:10:28.070 --> 00:10:28.810 knowing a few things. 00:10:28.810 --> 00:10:30.620 I don't expect you to know a lot of facts, but I expect you 00:10:30.620 --> 00:10:31.840 to know a few things. 00:10:31.840 --> 00:10:35.150 Every educated person ought to know that the visible spectrum 00:10:35.150 --> 00:10:38.240 runs round numbers 400 to 700 nanometers. 00:10:38.240 --> 00:10:41.370 But look, I can take 700 nanometers and use this 00:10:41.370 --> 00:10:43.220 formula and convert it to energy. 00:10:43.220 --> 00:10:47.710 And I'm going to get something like 3 times 10 to 00:10:47.710 --> 00:10:49.540 the minus 19 joules. 00:10:49.540 --> 00:10:50.250 Yuck. 00:10:50.250 --> 00:10:52.300 Instead, I go in electron volts. 00:10:52.300 --> 00:10:53.880 1.8 ev. 00:10:53.880 --> 00:10:57.790 Over here, 400 nanometers is 3.1 ev. 00:10:57.790 --> 00:11:01.780 So round numbers, the visible spectrum spans 2 00:11:01.780 --> 00:11:03.980 to 3 electron volts. 00:11:03.980 --> 00:11:08.260 Our eyes are photo detectors that operate on the band width 00:11:08.260 --> 00:11:11.740 2 to 3 electron volts. that's easy to remember. 00:11:11.740 --> 00:11:14.410 Those are good numbers. 00:11:14.410 --> 00:11:18.130 So where does that leave us? 00:11:18.130 --> 00:11:19.860 It leaves us here. 00:11:19.860 --> 00:11:24.770 We go back and we see these numbers, 656, 486, 434, 00:11:24.770 --> 00:11:26.120 they're all in the visible spectrum. 00:11:26.120 --> 00:11:28.700 So I went and I did a little calculation. 00:11:28.700 --> 00:11:32.240 I said, well what would I have if we'd gotten the wave length 00:11:32.240 --> 00:11:34.830 for the transition from 2 down to 1? 00:11:34.830 --> 00:11:36.900 This is n equals 2 down to ground state. 00:11:36.900 --> 00:11:40.040 If you plug in the numbers to the Bohr model, you'd find 00:11:40.040 --> 00:11:43.400 that that would give you 122 nanometers. 00:11:43.400 --> 00:11:44.460 122 nanometers? 00:11:44.460 --> 00:11:47.690 Well, 122 nanometers is going to put you way over. 00:11:47.690 --> 00:11:49.640 It's too high energy, right? 00:11:49.640 --> 00:11:54.000 122 nanometers is going to put you off to the left there into 00:11:54.000 --> 00:11:55.930 the ultraviolet, where the photographic 00:11:55.930 --> 00:11:58.560 film was not sensitive. 00:11:58.560 --> 00:12:02.170 So he couldn't measure those lines. 00:12:02.170 --> 00:12:05.420 So now I'm going to end by putting the master equation 00:12:05.420 --> 00:12:09.050 that captures all of this. 00:12:09.050 --> 00:12:10.660 And the master equation that captures of 00:12:10.660 --> 00:12:12.850 all of this is here. 00:12:12.850 --> 00:12:20.170 It's that nu bar goes as r times z squared, 1 over nf 00:12:20.170 --> 00:12:23.710 squared minus 1 over ni squared. 00:12:23.710 --> 00:12:31.150 So this is the most general form for all 1 electron atoms. 00:12:31.150 --> 00:12:34.200 That's why I've got z squared in there for all 1 electron 00:12:34.200 --> 00:12:35.230 atoms. 00:12:35.230 --> 00:12:40.480 And this is called the Rydberg equation. 00:12:40.480 --> 00:12:43.580 Named after another Swedish spectroscopist at the 00:12:43.580 --> 00:12:45.050 University of Lund. 00:12:45.050 --> 00:12:47.290 I think a Swede would probably pronounce this something 00:12:47.290 --> 00:12:49.810 Rydberg, but you don't have to say that. 00:12:49.810 --> 00:12:52.560 You can just say Rydberg and it'll be fine. 00:12:52.560 --> 00:12:56.150 And in honor of Rydberg, the constant here is given the 00:12:56.150 --> 00:12:57.390 symbol, capital R. 00:12:57.390 --> 00:13:02.380 The capital R as the Rydberg constant and it has a value of 00:13:02.380 --> 00:13:05.860 1.1 times 10 to the 7th reciprocal 00:13:05.860 --> 00:13:09.460 meters in good ST units. 00:13:09.460 --> 00:13:12.030 Well, there was more evidence for the 00:13:12.030 --> 00:13:14.270 support of Bohr's Model. 00:13:14.270 --> 00:13:16.390 More evidence for the support of Bohr's Model. 00:13:16.390 --> 00:13:19.190 By the way, as the detectors got better and better we could 00:13:19.190 --> 00:13:20.290 get more and more lines. 00:13:20.290 --> 00:13:23.820 You see these, as you get higher and higher series 00:13:23.820 --> 00:13:27.530 ending on higher and higher end numbers, you move off into 00:13:27.530 --> 00:13:29.020 the infrared. 00:13:29.020 --> 00:13:31.090 Because this is not to scale. 00:13:31.090 --> 00:13:34.210 These n equal 4, n equal 5 are closer and closer to closer 00:13:34.210 --> 00:13:36.800 together in terms of energy. 00:13:36.800 --> 00:13:40.360 They're farther and farther apart in terms of spacing, but 00:13:40.360 --> 00:13:42.510 they're closer and closer together in terms of energy. 00:13:42.510 --> 00:13:43.930 Because they're farther from the nucleus. 00:13:43.930 --> 00:13:45.710 You say, gee, shouldn't it cost more 00:13:45.710 --> 00:13:47.010 energy to go farther? 00:13:47.010 --> 00:13:47.500 Uh-uh. 00:13:47.500 --> 00:13:50.350 Because you're farther from the positive nucleus. 00:13:50.350 --> 00:13:51.040 Be careful. 00:13:51.040 --> 00:13:53.980 Don't let your intuition send you in the wrong direction. 00:13:53.980 --> 00:13:55.830 It's all about Coulombics. 00:13:55.830 --> 00:13:59.160 Anyway, so the Lyman series ends at n equals 1. 00:13:59.160 --> 00:14:00.370 And these are different scientists. 00:14:00.370 --> 00:14:03.020 Paschen, Bracket, Pfund, Humphreys, and so on. 00:14:03.020 --> 00:14:05.870 So maybe, I don't know, if somebody hasn't claimed n 00:14:05.870 --> 00:14:08.870 equals 214, all the lines that end there, you know, maybe 00:14:08.870 --> 00:14:11.760 that could be your name on the series. 00:14:11.760 --> 00:14:13.485 As if anybody cares. 00:14:19.620 --> 00:14:22.100 Looks like this quantum condition is validated. 00:14:22.100 --> 00:14:25.220 See this is really important because this was the big break 00:14:25.220 --> 00:14:27.380 away from classical theory. 00:14:27.380 --> 00:14:33.000 That the motion of a body, something with mass, could be 00:14:33.000 --> 00:14:37.720 quantized in its behavior shook this physics community. 00:14:37.720 --> 00:14:41.080 But this reconciliation of the data says that 00:14:41.080 --> 00:14:42.330 assumption is valid. 00:14:46.810 --> 00:14:48.730 There's more that happens. 00:14:48.730 --> 00:14:55.210 So in 1913 in Berlin-- 00:14:55.210 --> 00:14:57.960 remember 1913 is when Bohr published the paper-- 00:14:57.960 --> 00:15:03.860 1913 in Berlin there was James Franck and Gustav Hertz. 00:15:03.860 --> 00:15:08.490 James Franck and Gustav Hertz. 00:15:08.490 --> 00:15:10.110 And they were conducting experiments on 00:15:10.110 --> 00:15:11.270 gas discharge tubes. 00:15:11.270 --> 00:15:14.080 Only they filled a gas discharge tube, instead of 00:15:14.080 --> 00:15:16.640 with hydrogen, they filled it with mercury vapor. 00:15:16.640 --> 00:15:19.430 So gas discharge tube-- 00:15:19.430 --> 00:15:20.250 GDT-- 00:15:20.250 --> 00:15:26.010 gas discharge tube containing mercury vapor. 00:15:26.010 --> 00:15:27.260 The same thing. 00:15:29.740 --> 00:15:33.200 Put the electrodes, connect on a power supply, and started 00:15:33.200 --> 00:15:35.230 varying the potential. 00:15:35.230 --> 00:15:38.610 So I'm going to show you what they found. 00:15:38.610 --> 00:15:42.550 This is the Planck voltage, and this is the current 00:15:42.550 --> 00:15:48.180 between electrodes, or if you like, across the tube. 00:15:48.180 --> 00:15:51.000 Between the electrodes, or through the tube. 00:15:51.000 --> 00:15:53.630 Or if you like, tube current. 00:15:53.630 --> 00:15:56.100 Meaning from one electrode to the other. 00:15:56.100 --> 00:15:57.110 The tube current. 00:15:57.110 --> 00:15:59.500 Well, low voltage, low current. 00:15:59.500 --> 00:16:00.950 High voltage, high currently. 00:16:00.950 --> 00:16:03.610 They get up to a certain value of voltage, all of sudden the 00:16:03.610 --> 00:16:07.210 tube starts glowing blindly and the current falls to 0. 00:16:10.600 --> 00:16:13.200 Then they continued to raise the voltage. 00:16:13.200 --> 00:16:15.800 More voltage, more current, up, up, up, up, up. 00:16:15.800 --> 00:16:19.160 And then they get to another critical value of voltage, 00:16:19.160 --> 00:16:21.180 even more intensity. 00:16:21.180 --> 00:16:24.960 And then the current falls to 0. 00:16:24.960 --> 00:16:27.560 So you look at those data and say, well, what's that got to 00:16:27.560 --> 00:16:28.650 do with the Bohr Model? 00:16:28.650 --> 00:16:31.250 Because mercury is not a 1 electron atom. 00:16:31.250 --> 00:16:33.020 It's got a boat load of electrons. 00:16:33.020 --> 00:16:35.370 This is not a 1 electron atom. 00:16:35.370 --> 00:16:36.530 So you say, I know what it is. 00:16:36.530 --> 00:16:37.540 It's ionization energy. 00:16:37.540 --> 00:16:38.990 Must be ionizing the mercury. 00:16:38.990 --> 00:16:41.740 So you go to the periodic table and you look up the 00:16:41.740 --> 00:16:46.430 ionization energy of mercury and you discover that that's 00:16:46.430 --> 00:16:48.230 10.4 volts. 00:16:48.230 --> 00:16:51.370 10.4 electron volts is the ionization energy. 00:16:51.370 --> 00:16:56.470 And this first null is at 4.9 volts. 00:16:56.470 --> 00:16:59.390 Well, 4.9 is a long way from 10.4. 00:16:59.390 --> 00:17:04.250 And this second null occurs at 6.7 volts. 00:17:04.250 --> 00:17:06.730 6.7 volts. 00:17:06.730 --> 00:17:08.490 So what's this telling us? 00:17:08.490 --> 00:17:11.320 What this is telling us is that when you get to a value 00:17:11.320 --> 00:17:16.290 of 4.9 volts, you've hit a certain value that allows you 00:17:16.290 --> 00:17:21.290 to promote electrons within mercury between one level and 00:17:21.290 --> 00:17:22.370 the next level. 00:17:22.370 --> 00:17:24.980 And those electrons are being promoted and 00:17:24.980 --> 00:17:26.330 then cascading down. 00:17:26.330 --> 00:17:28.510 And they're cascading down and they're emitting in the 00:17:28.510 --> 00:17:31.600 visible and it's blinding you. 00:17:31.600 --> 00:17:33.400 Say, OK, so what does that mean? 00:17:33.400 --> 00:17:37.350 Well, it means that the Bohr Model, which is for a 1 00:17:37.350 --> 00:17:40.330 electron atom, assumes that energy levels 00:17:40.330 --> 00:17:42.130 within it are quantized. 00:17:42.130 --> 00:17:46.760 These data indicate that on the basis the behavior of this 00:17:46.760 --> 00:17:50.260 gas discharge tube, there must be quantized energy levels 00:17:50.260 --> 00:17:54.820 inside of mercury, which means all atoms have quantized 00:17:54.820 --> 00:17:56.342 energy levels. 00:17:56.342 --> 00:17:57.670 You understand? 00:17:57.670 --> 00:17:59.840 Everything is quantized. 00:17:59.840 --> 00:18:01.050 That's really powerful. 00:18:01.050 --> 00:18:04.350 It starts off with this nerdy little 1 electron atom, and 00:18:04.350 --> 00:18:06.900 now he's applying it across matter. 00:18:06.900 --> 00:18:10.550 And this is gas, this is more elaborate gas. 00:18:10.550 --> 00:18:13.750 Heaven forbid, it might exist in liquids and solids. 00:18:16.850 --> 00:18:19.110 So that's the Franck, Hertz experiment. 00:18:19.110 --> 00:18:23.590 So his stock goes way, way up as a result of that. 00:18:23.590 --> 00:18:26.700 And they win a Nobel Prize. 00:18:26.700 --> 00:18:28.220 Here's James Franck. 00:18:28.220 --> 00:18:29.000 Here's Gustav Hertz. 00:18:29.000 --> 00:18:30.570 You know what the Hertz is. 00:18:30.570 --> 00:18:32.120 200 kilohertz, so on. 00:18:32.120 --> 00:18:32.690 That's Hertz. 00:18:32.690 --> 00:18:38.060 James Franck was at Gottingen when he won this, but he 00:18:38.060 --> 00:18:41.210 ultimately came to the United States when the political 00:18:41.210 --> 00:18:44.780 changes started occurring in the thirties in Germany. 00:18:44.780 --> 00:18:49.100 Franck decided to seek safer surroundings and ended up at 00:18:49.100 --> 00:18:52.090 the University of Chicago, where there is to this day the 00:18:52.090 --> 00:18:54.400 James Franck Institute of Physics. 00:18:54.400 --> 00:18:57.310 Very, very high-end physics institution. 00:19:00.240 --> 00:19:02.350 So this is good. 00:19:02.350 --> 00:19:05.320 But all good things come to an end. 00:19:05.320 --> 00:19:09.000 So 1913 was a bittersweet year for Bohr. 00:19:09.000 --> 00:19:13.180 Because he got some good news, but he also got some bad news. 00:19:13.180 --> 00:19:17.670 So now I want to move over to limitations of the Bohr Model. 00:19:17.670 --> 00:19:19.370 Limitations of the Bohr Model. 00:19:22.810 --> 00:19:24.460 So I know what you're going to say-- well, it only talks 00:19:24.460 --> 00:19:26.430 about 1 electron atoms, so that's a limitation. 00:19:26.430 --> 00:19:28.120 No, there's more to it than that. 00:19:28.120 --> 00:19:33.340 Even the 1 electron atom model doesn't capture everything. 00:19:33.340 --> 00:19:37.350 I'm going to summarize the limitations. 00:19:37.350 --> 00:19:42.160 I'm going to show you three, and they all fall under the 00:19:42.160 --> 00:19:45.520 general umbrella of fine structure. 00:19:45.520 --> 00:19:46.320 Fine structure. 00:19:46.320 --> 00:19:49.100 In other words, the Bohr Model is good, give us the big 00:19:49.100 --> 00:19:52.530 lines, but when you start looking more carefully it 00:19:52.530 --> 00:19:54.090 fails to capture some of the physics. 00:19:54.090 --> 00:19:57.450 So first of all, let's go back to some earlier data. 00:19:57.450 --> 00:19:59.460 1887. 00:19:59.460 --> 00:20:01.940 1887, there were already data out there that were going to 00:20:01.940 --> 00:20:04.020 give heartburn to the Bohr Model. 00:20:04.020 --> 00:20:07.650 And those data were taken by Michelson and Morley. 00:20:07.650 --> 00:20:08.900 Michelson and Morley. 00:20:11.830 --> 00:20:14.820 Everything I've taught you so far, with one exception, has 00:20:14.820 --> 00:20:16.680 been European science. 00:20:16.680 --> 00:20:18.870 Americans were not active in science because this was a 00:20:18.870 --> 00:20:19.560 young country. 00:20:19.560 --> 00:20:22.800 We were really good engineers because we were blockaded by 00:20:22.800 --> 00:20:23.670 the rest of the world. 00:20:23.670 --> 00:20:25.550 We had to live by our wits-- that's where you get the term 00:20:25.550 --> 00:20:28.420 "yankee ingenuity." Science was hifalutin stuff. 00:20:28.420 --> 00:20:29.560 We didn't have time for it. 00:20:29.560 --> 00:20:33.200 But towards the latter half of the 19th century, we started 00:20:33.200 --> 00:20:35.012 moving into fundamental science. 00:20:35.012 --> 00:20:38.770 The first American to win the Nobel Prize was Michelson. 00:20:38.770 --> 00:20:43.040 Michelson was doing work at Case in Cleveland, which 00:20:43.040 --> 00:20:47.130 eventually became Case Western Reserve University. 00:20:47.130 --> 00:20:51.740 So he was at Case in Cleveland and he was studying optics. 00:20:51.740 --> 00:20:56.720 And he was a brilliant experimentalist. In fact, he 00:20:56.720 --> 00:21:00.270 made the first reliable measure of the speed of light. 00:21:00.270 --> 00:21:04.470 Back before 1900. 00:21:04.470 --> 00:21:06.720 What they were doing is they were looking at Angstrom's 00:21:06.720 --> 00:21:09.230 lines and they noticed something peculiar. 00:21:09.230 --> 00:21:11.990 If you take a look at even this drawing, you notice the 00:21:11.990 --> 00:21:14.830 red line is a little bit fatter than the others. 00:21:14.830 --> 00:21:17.230 Now you might just say, well, that's just the artist taking 00:21:17.230 --> 00:21:20.480 liberties and somebody didn't catch it in proof reading. 00:21:20.480 --> 00:21:26.670 But in point of fact, what he found was that if you look at 00:21:26.670 --> 00:21:31.440 that line, which is really the line for the 3-2 transition-- 00:21:31.440 --> 00:21:36.890 the 3-2 transition in the Balmer series-- 00:21:36.890 --> 00:21:41.480 what you find is that if you look at the photographic plate 00:21:41.480 --> 00:21:45.980 more carefully, you find that this thing in fact is a pair 00:21:45.980 --> 00:21:49.010 of lines, but very, very closely spaced. 00:21:49.010 --> 00:21:51.890 This is known as a doublet. 00:21:51.890 --> 00:21:57.200 Two lines very closely spaced, centered at 656 nanometers. 00:21:57.200 --> 00:22:02.500 And with his interferometer he gets super, super good data. 00:22:02.500 --> 00:22:03.970 And he could split the doublet. 00:22:03.970 --> 00:22:06.130 Well, what's that mean for Bohr? 00:22:06.130 --> 00:22:08.180 Bohr has no way of explaining this. 00:22:08.180 --> 00:22:12.000 If you look at the Bohr Model, you've got n equals 2, you've 00:22:12.000 --> 00:22:14.230 got n equals 3, alright? 00:22:14.230 --> 00:22:19.230 So this is energy 2, energy 3, right? 00:22:19.230 --> 00:22:23.380 And so when the electron falls from 3 to 2, we get a photon 00:22:23.380 --> 00:22:24.920 of a certain value. 00:22:24.920 --> 00:22:27.750 It's going to be nu 3 to 2. 00:22:27.750 --> 00:22:31.800 That's the frequency or wave number, what have you. 00:22:31.800 --> 00:22:34.530 Now, the fact that you've got a doublet here means that 00:22:34.530 --> 00:22:38.600 there must be two transitions, but darn close. 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 00:22:43.410 --> 00:22:47.790 primed, but it's not simply 3 and 2. 00:22:47.790 --> 00:22:50.260 So that piece of information runs 00:22:50.260 --> 00:22:51.670 counter to the Bohr Model. 00:22:51.670 --> 00:22:53.250 Bohr Model is silent about it. 00:22:53.250 --> 00:22:56.040 It gets the big picture, but if you look more carefully it 00:22:56.040 --> 00:22:58.300 can't capture the doublet. 00:22:58.300 --> 00:23:01.950 And Michelson ultimately gets the Nobel Price. 00:23:01.950 --> 00:23:04.940 And I think I've got him here. 00:23:04.940 --> 00:23:05.960 There he is. 00:23:05.960 --> 00:23:08.430 The Nobel Prize. 00:23:08.430 --> 00:23:11.240 By the time he got the Nobel Prize he was at the University 00:23:11.240 --> 00:23:14.620 of Chicago, but he did the work that won the Nobel Prize 00:23:14.620 --> 00:23:16.000 for him at Case. 00:23:16.000 --> 00:23:18.430 So sometimes when you see even Millikan, Millikan did his 00:23:18.430 --> 00:23:21.250 work at University of Chicago, but eventually took a position 00:23:21.250 --> 00:23:22.320 at Caltech. 00:23:22.320 --> 00:23:25.460 So the Nobel Prize says, Robert Millikan, Caltech. 00:23:25.460 --> 00:23:27.035 But he didn't do that work at Caltech. 00:23:27.035 --> 00:23:28.750 He did it at Chicago. 00:23:28.750 --> 00:23:31.320 Anyways, you can go to the Nobel website. 00:23:31.320 --> 00:23:32.920 You can read about these people. 00:23:32.920 --> 00:23:36.540 And what's really cool is when you win the Nobel Prize-- you 00:23:36.540 --> 00:23:37.700 notice I didn't say if-- 00:23:37.700 --> 00:23:42.020 I say, when you win the Nobel Prize, what you do is you get 00:23:42.020 --> 00:23:45.330 on an airplane, you go to Stockholm, and then you go and 00:23:45.330 --> 00:23:47.310 you have dinner in this beautiful hall. 00:23:47.310 --> 00:23:51.070 I've been there and it's gorgeous, gilded and so on. 00:23:51.070 --> 00:23:54.370 Very nice kitchen, excellent wine list. And-- 00:23:54.370 --> 00:23:57.540 yes-- and you can go there and they serve meals. 00:23:57.540 --> 00:24:02.620 the menu is taken from previous Nobel Prize dinners. 00:24:02.620 --> 00:24:04.480 So you can sit and-- 00:24:04.480 --> 00:24:07.830 whatever it is, it could be the Nobel Prizes of 1927 and 00:24:07.830 --> 00:24:10.560 that's what's going to be on the menu today-- 00:24:10.560 --> 00:24:15.660 and after the dinner they have a presentation ceremony with 00:24:15.660 --> 00:24:16.870 the King of Sweden. 00:24:16.870 --> 00:24:18.730 You get your Nobel Prize, and then people 00:24:18.730 --> 00:24:20.750 listen to your lecture. 00:24:20.750 --> 00:24:24.750 And those Nobel lectures are really, really expository. 00:24:24.750 --> 00:24:27.750 So if you want to go and read the Nobel lecture that 00:24:27.750 --> 00:24:31.320 Michelson gave on the occasion of winning the Nobel Prize, 00:24:31.320 --> 00:24:34.570 you'll probably learn all of about this and more. 00:24:34.570 --> 00:24:37.680 It's really, really good, so go there and read. 00:24:37.680 --> 00:24:40.010 Now back to the story. 00:24:40.010 --> 00:24:42.800 Second problem with the Bohr Model. 00:24:42.800 --> 00:24:44.520 1896-- 00:24:44.520 --> 00:24:46.850 see, all this data had been accumulating-- 00:24:46.850 --> 00:24:51.330 1896, there was a postdoc by the name of Zeeman. 00:24:51.330 --> 00:24:52.430 Piet Zeeman. 00:24:52.430 --> 00:24:55.530 He was a postdoc at Leiden. 00:24:55.530 --> 00:24:58.400 Leiden in Holland under Lorentz. 00:25:01.970 --> 00:25:07.400 You'll learn about the Lorentz force when you study 802. 00:25:07.400 --> 00:25:10.010 What he was doing-- 00:25:10.010 --> 00:25:11.940 again, gas discharge tube. 00:25:11.940 --> 00:25:17.080 So this was gas discharge tube, and what Zeeman was 00:25:17.080 --> 00:25:20.195 doing on his postdoc was in a magnetic field. 00:25:23.730 --> 00:25:26.420 These people were doing all sorts of experiments. 00:25:26.420 --> 00:25:29.400 They were trying to block out the whole experimental space. 00:25:29.400 --> 00:25:32.470 So one guy, his specialty is high energy. 00:25:32.470 --> 00:25:33.990 One guy's specialty is low pressure. 00:25:33.990 --> 00:25:36.620 These people are taking a gas discharge tube and putting in 00:25:36.620 --> 00:25:38.920 the jaws of a powerful, permanent magnet and then 00:25:38.920 --> 00:25:40.390 measuring the spectrum. 00:25:40.390 --> 00:25:44.690 And what he found was that for certain lines, 00:25:44.690 --> 00:25:47.130 this was the rest-- 00:25:47.130 --> 00:25:49.460 b, I'm going to use as magnetic field-- 00:25:49.460 --> 00:25:51.650 in the absence of applied magnetic 00:25:51.650 --> 00:25:54.330 field you have a line. 00:25:54.330 --> 00:25:56.050 And this is not a doublet, triplet-- 00:25:56.050 --> 00:25:58.270 it's just a plain old line. 00:25:58.270 --> 00:25:59.770 Well behaved line. 00:25:59.770 --> 00:26:03.040 But when they take that gas discharge tube and put it into 00:26:03.040 --> 00:26:09.660 a magnetic field, they see a plurality of lines. 00:26:09.660 --> 00:26:14.940 And furthermore, the spacing-- 00:26:14.940 --> 00:26:16.500 I'm going to use c here-- 00:26:16.500 --> 00:26:20.990 the spacing in the lines is proportional to the intensity 00:26:20.990 --> 00:26:22.550 of the magnetic field. 00:26:22.550 --> 00:26:25.100 No magnetic field, single line. 00:26:25.100 --> 00:26:28.250 Modest magnetic field, modest amount of what 00:26:28.250 --> 00:26:29.960 is called line splitting. 00:26:32.720 --> 00:26:35.770 So a modest amount of applied magnetic 00:26:35.770 --> 00:26:37.220 field, modest splitting. 00:26:37.220 --> 00:26:41.270 Intense magnetic field, intense splitting. 00:26:41.270 --> 00:26:43.160 Bohr Model is silent about that. 00:26:43.160 --> 00:26:45.340 Because you know, if you've got different lines, it means 00:26:45.340 --> 00:26:46.910 you must have different energy levels. 00:26:46.910 --> 00:26:51.180 It's as though the energy level diagrams opens up in a 00:26:51.180 --> 00:26:52.780 magnetic field. 00:26:52.780 --> 00:26:56.420 The Bohr Model can't account for that. 00:26:56.420 --> 00:27:02.190 And parenthetically, they got the Nobel Prize, too. 00:27:02.190 --> 00:27:03.560 So there's Piet Zeeman. 00:27:03.560 --> 00:27:06.810 Got his PhD in 1896. 00:27:06.810 --> 00:27:08.330 He's got his Noble Prize, 1902. 00:27:08.330 --> 00:27:10.010 He's off to a good start, I'd say. 00:27:10.010 --> 00:27:11.580 And there's Lorentz. 00:27:11.580 --> 00:27:14.040 Two of them. 00:27:14.040 --> 00:27:15.700 We'll get to him in a second. 00:27:15.700 --> 00:27:20.070 So third piece of bad news for the Bohr Model. 00:27:20.070 --> 00:27:23.560 And that comes, again, in 1913 in November. 00:27:23.560 --> 00:27:27.050 In November of 1913 there was a man by the 00:27:27.050 --> 00:27:32.340 name of Stark in Germany. 00:27:32.340 --> 00:27:35.300 And Stark was doing analogous experiments. 00:27:35.300 --> 00:27:39.710 He was studying gas discharge tube in electric fields. 00:27:44.620 --> 00:27:46.450 Obviously, you've got an electric field across the 00:27:46.450 --> 00:27:50.370 electrodes to excite the electrons. 00:27:50.370 --> 00:27:52.720 But he's taking a whole gas discharge tube and putting it 00:27:52.720 --> 00:27:56.050 between flights and then applying an electric field. 00:27:56.050 --> 00:27:57.150 And what did he find? 00:27:57.150 --> 00:27:58.680 He found the same sort of thing. 00:27:58.680 --> 00:28:07.940 He got line splitting in an E field, and furthermore that 00:28:07.940 --> 00:28:12.443 extent of splitting, extent dependent upon the intensity. 00:28:16.220 --> 00:28:17.360 E intensity. 00:28:17.360 --> 00:28:19.150 So no field, no splitting. 00:28:19.150 --> 00:28:21.200 Modest field, modest splitting. 00:28:21.200 --> 00:28:22.990 Intense field, intense splitting. 00:28:22.990 --> 00:28:26.230 Well, again, that's a headache for the Bohr Model. 00:28:26.230 --> 00:28:31.120 So this is all three problems, and it's all under aegis of 00:28:31.120 --> 00:28:33.820 fine structure. 00:28:33.820 --> 00:28:35.630 So we know the Bohr Model has its limitations. 00:28:35.630 --> 00:28:36.460 OK, Stark. 00:28:36.460 --> 00:28:38.580 I know he's got his Nobel Prize. 00:28:38.580 --> 00:28:39.830 There he is. 00:28:42.120 --> 00:28:47.060 So 1913 ends on a sour note. 00:28:47.060 --> 00:28:48.640 But people don't give up. 00:28:48.640 --> 00:28:56.440 1916, Arnold Sommerfeld in Munich. 00:28:56.440 --> 00:29:00.270 He was a professor of physics and he proposed modifications. 00:29:00.270 --> 00:29:02.110 Modifications to Bohr Model. 00:29:05.780 --> 00:29:08.450 It's a patch, we would call it a patch. 00:29:08.450 --> 00:29:08.570 going? 00:29:08.570 --> 00:29:10.790 To put a patch on the Bohr Model. 00:29:10.790 --> 00:29:11.520 And what's he going to do? 00:29:11.520 --> 00:29:13.590 What's the gist of his idea? 00:29:13.590 --> 00:29:18.990 Well, he retains the planetary structure. 00:29:18.990 --> 00:29:20.910 He liked that idea-- 00:29:20.910 --> 00:29:23.570 nice orbits, so on. 00:29:23.570 --> 00:29:27.370 But he took a page out of Kepler's book. 00:29:27.370 --> 00:29:31.050 The planets in the Kepler model, when they revolve 00:29:31.050 --> 00:29:33.475 around the sun their orbit is not circular. 00:29:33.475 --> 00:29:35.300 It's elliptical. 00:29:35.300 --> 00:29:39.150 So Sommerfeld said, why don't we give that a try? 00:29:39.150 --> 00:29:45.710 What if we said the electronic orbit can be 00:29:45.710 --> 00:29:49.835 elliptical or circular? 00:29:53.700 --> 00:29:54.850 And he was quite specific. 00:29:54.850 --> 00:29:56.660 He said, suppose-- 00:29:56.660 --> 00:30:03.980 and this, again, is not to scale, but to emphasize this 00:30:03.980 --> 00:30:09.090 is going to be elliptical or circular, but very, very mild 00:30:09.090 --> 00:30:10.550 eccentricity. 00:30:10.550 --> 00:30:14.380 What I'm going to draw for you is extreme eccentricity to 00:30:14.380 --> 00:30:15.060 make a point. 00:30:15.060 --> 00:30:18.990 But suppose we had the circular orbit as I'm drawing 00:30:18.990 --> 00:30:24.680 it now, and then we had an elliptical orbit that is 00:30:24.680 --> 00:30:27.640 centered on that circle. 00:30:27.640 --> 00:30:29.960 So it's mild eccentricity. 00:30:29.960 --> 00:30:33.130 We might have another one-- let's do one more. 00:30:33.130 --> 00:30:34.790 This is good enough. 00:30:34.790 --> 00:30:37.740 The gist here is that we have a circular orbit and an 00:30:37.740 --> 00:30:41.690 elliptical orbit, but the bandwidth here 00:30:41.690 --> 00:30:43.780 is very, very narrow. 00:30:43.780 --> 00:30:48.240 So this is very, very thin. 00:30:48.240 --> 00:30:50.570 And it's sort of like an egg shell. 00:30:50.570 --> 00:30:53.550 So if I asked you, what's the dimension of an egg? 00:30:53.550 --> 00:30:55.770 You'd say, well, it's dimension of the 00:30:55.770 --> 00:30:56.390 surface of the egg. 00:30:56.390 --> 00:30:57.900 Then I'd say, but the egg shell has 00:30:57.900 --> 00:30:58.970 some thickness, right? 00:30:58.970 --> 00:31:01.580 But that thickness is relatively small in comparison 00:31:01.580 --> 00:31:03.550 to the total dimension of the egg. 00:31:03.550 --> 00:31:04.750 So an analogy. 00:31:04.750 --> 00:31:09.040 He said that the range of distance from the nucleus, 00:31:09.040 --> 00:31:11.440 whether it's circular or elliptical, 00:31:11.440 --> 00:31:12.580 is very, very narrow. 00:31:12.580 --> 00:31:17.200 So we can say the set of circular and elliptical orbits 00:31:17.200 --> 00:31:20.690 lie within a shell, as in egg shell. 00:31:20.690 --> 00:31:22.890 So this is a shell model. 00:31:22.890 --> 00:31:26.170 It's a shell model. 00:31:26.170 --> 00:31:31.070 So now how do you designate the different orbits? 00:31:31.070 --> 00:31:32.740 You've got some that are circular, some that are 00:31:32.740 --> 00:31:33.530 elliptical. 00:31:33.530 --> 00:31:35.560 He needs to distinguish them and he needs to be able to 00:31:35.560 --> 00:31:36.270 label them. 00:31:36.270 --> 00:31:40.600 So he introduces new quantum numbers to 00:31:40.600 --> 00:31:42.050 allow us to name them. 00:31:42.050 --> 00:31:46.320 So let's go and take a look at the quantum numbers that 00:31:46.320 --> 00:31:47.670 Sommerfeld gave us. 00:31:47.670 --> 00:31:49.140 So he starts off with n. 00:31:49.140 --> 00:31:52.410 He retains that from the Bohr Model and he calls that the 00:31:52.410 --> 00:31:54.280 principal quantum number. 00:31:54.280 --> 00:31:58.740 And it's primary attribute is size. 00:31:58.740 --> 00:32:03.900 It captures the distance, the principal r from the nucleus. 00:32:03.900 --> 00:32:08.910 And it takes values 1, 2, 3, all the way up to infinity. 00:32:08.910 --> 00:32:12.650 So n equals 1, small radius. 00:32:12.650 --> 00:32:15.560 n equals 10, large radius. 00:32:15.560 --> 00:32:19.050 Oh, by the way, there's another numbering system. 00:32:19.050 --> 00:32:23.880 This is what we use, but the spectroscopists use letters. 00:32:23.880 --> 00:32:25.910 The spectroscopists use letters-- why? 00:32:25.910 --> 00:32:28.220 Because remember the Balmer series? 00:32:28.220 --> 00:32:30.480 Everybody was hooked on the Balmer series and it ended up 00:32:30.480 --> 00:32:31.330 being n equals 2. 00:32:31.330 --> 00:32:33.050 And then later with better detectors we find 00:32:33.050 --> 00:32:34.320 there's an n equals 1. 00:32:34.320 --> 00:32:36.060 So the spectroscopists said, we're going 00:32:36.060 --> 00:32:37.150 to get fooled again. 00:32:37.150 --> 00:32:38.730 So we're going use letters. 00:32:38.730 --> 00:32:41.420 And we're going to start with the letter k. 00:32:41.420 --> 00:32:43.680 It's in the middle of the alphabet. 00:32:43.680 --> 00:32:47.210 That way if we discover even lower energies, we've got some 00:32:47.210 --> 00:32:49.220 head room here, we can label those. 00:32:49.220 --> 00:32:51.090 But we never found any. 00:32:51.090 --> 00:32:53.960 So if you go over to Building Thirteen and you do some x-ray 00:32:53.960 --> 00:32:57.220 refraction and you use the line that emanates from a 00:32:57.220 --> 00:33:00.150 copper target, n equals 1-- it's called the k 00:33:00.150 --> 00:33:01.420 alpha line of copper. 00:33:01.420 --> 00:33:02.270 To this day. 00:33:02.270 --> 00:33:05.030 So k, l, m, and so on. 00:33:05.030 --> 00:33:07.620 You can't get to infinity, obviously. 00:33:07.620 --> 00:33:10.720 You know, I didn't think this thing through. 00:33:10.720 --> 00:33:11.830 Now the l. 00:33:11.830 --> 00:33:13.210 l is, what's his name? 00:33:13.210 --> 00:33:14.060 Sommerfeld. 00:33:14.060 --> 00:33:17.830 And it's called the orbital quantum number. 00:33:17.830 --> 00:33:18.170 Why? 00:33:18.170 --> 00:33:21.480 Because he said that the electron is in an orbital 00:33:21.480 --> 00:33:22.520 instead of an orbit. 00:33:22.520 --> 00:33:26.400 Orbit is Bohr, orbital is Bohr-Sommerfeld. 00:33:26.400 --> 00:33:29.950 And it speaks to the shape. 00:33:29.950 --> 00:33:32.300 Somehow, I've got to distinguish between elliptical 00:33:32.300 --> 00:33:34.470 and circular. 00:33:34.470 --> 00:33:39.260 And it takes values 0, 1, up to n minus 1. 00:33:39.260 --> 00:33:43.480 So the n number controls the range of l. 00:33:43.480 --> 00:33:47.100 And again, the spectroscopists, they're real 00:33:47.100 --> 00:33:48.280 number weenies, they're afraid, 00:33:48.280 --> 00:33:50.580 so they use s, lowercase. 00:33:50.580 --> 00:33:52.360 See this is uppercase, this is lowercase. 00:33:52.360 --> 00:33:56.070 s, p, d, f. 00:33:56.070 --> 00:33:59.480 For sharp, this is the sharpest line from the l 00:33:59.480 --> 00:34:03.860 equals 0-- then the principal because as you go to z they 00:34:03.860 --> 00:34:07.050 all seem to converge and look like hydrogen-- 00:34:07.050 --> 00:34:10.260 d is diffuse, f is fine, and then after that they ran out 00:34:10.260 --> 00:34:13.460 of ideas so g and h. 00:34:13.460 --> 00:34:17.820 So you'll talk about the one s-orbital, meaning n equals 1, 00:34:17.820 --> 00:34:20.680 l equals 0. 00:34:20.680 --> 00:34:24.100 And there are some values here for shapes. 00:34:24.100 --> 00:34:25.730 I'm going to put that right above it. 00:34:25.730 --> 00:34:29.420 When l equals 0, l equals 0 means you 00:34:29.420 --> 00:34:31.610 have a circular orbit. 00:34:31.610 --> 00:34:36.010 And when l equals 1 it's elliptical. 00:34:36.010 --> 00:34:43.820 And when l equals 2 it's much more complex, and we'll just 00:34:43.820 --> 00:34:44.700 leave it at that. 00:34:44.700 --> 00:34:46.710 1, 2, and 3. 00:34:46.710 --> 00:34:48.440 So there's l values. 00:34:48.440 --> 00:34:51.390 And then m is the magnetic quantum number. 00:34:55.060 --> 00:34:56.386 And it talks about orientation. 00:35:00.770 --> 00:35:02.870 I'll show you what I mean by that in a second. 00:35:02.870 --> 00:35:06.090 The values are governed by l, which is governed by n. 00:35:06.090 --> 00:35:10.330 Starts at l, l minus 1, goes down through 0, goes to minus 00:35:10.330 --> 00:35:13.300 values and ends at minus l. 00:35:13.300 --> 00:35:17.155 So for example, we could do something like this-- 00:35:20.570 --> 00:35:25.010 when n equals 1, then l most equal 0, so therefore 00:35:25.010 --> 00:35:26.830 m must equals 0. 00:35:26.830 --> 00:35:30.330 So this means for n equals 1, it's only a circular orbit and 00:35:30.330 --> 00:35:32.760 this thing is going to be immune to line splitting in a 00:35:32.760 --> 00:35:35.140 magnetic field. 00:35:35.140 --> 00:35:41.480 When n equals 2, l can equals 0 or l can equal 1. 00:35:41.480 --> 00:35:44.050 When l equals 0, m equals 0. 00:35:44.050 --> 00:35:45.480 That's boring, that's circular. 00:35:45.480 --> 00:35:47.600 But here's another possibility. 00:35:47.600 --> 00:35:52.580 And that is, when l equals 1 then m can equal 1, 00:35:52.580 --> 00:35:55.020 0, and minus 1. 00:35:55.020 --> 00:35:57.160 Now I said it has something to do with orientation. 00:35:57.160 --> 00:36:00.960 Most of quantum mechanics doesn't translate into the 00:36:00.960 --> 00:36:03.970 Cartesian world, but this one does, mercifully, and I think 00:36:03.970 --> 00:36:05.320 it's a cute analogy. 00:36:05.320 --> 00:36:09.060 If I were to tell you that I've got three different 00:36:09.060 --> 00:36:12.160 quantum numbers and I've got an elliptical thing-- and one 00:36:12.160 --> 00:36:16.400 way to think, see, the number 0 looks like a circle and the 00:36:16.400 --> 00:36:19.910 number 1 has some asperity associated with it, so you can 00:36:19.910 --> 00:36:21.330 think of that as the ellipse-- 00:36:21.330 --> 00:36:27.020 so I know that I can, with no prior knowledge of where the 00:36:27.020 --> 00:36:31.100 true origin of the universe it is, I can arbitrarily define a 00:36:31.100 --> 00:36:33.800 set of rectangular coordinates, orthogonal 00:36:33.800 --> 00:36:35.270 coordinates, x, y, and z. 00:36:35.270 --> 00:36:40.260 And that means I could put one orbital here, one orbital 00:36:40.260 --> 00:36:41.640 here, and one orbital here. 00:36:41.640 --> 00:36:47.010 So those are three orthogonal orientations, which I think is 00:36:47.010 --> 00:36:50.620 consistent with the fact that m takes on three values. 00:36:50.620 --> 00:36:52.230 OK, that's cute. 00:36:52.230 --> 00:36:57.720 So that's as far as Sommerfeld went. 00:36:57.720 --> 00:36:59.960 I'm going to go and do something as a retronym. 00:36:59.960 --> 00:37:02.530 I want to get the fourth quantum number up here now, 00:37:02.530 --> 00:37:04.670 but we're going to pause the story. 00:37:04.670 --> 00:37:08.690 We're going to fast forward to 1925 so I can get the last 00:37:08.690 --> 00:37:10.020 quantum number up here. 00:37:10.020 --> 00:37:12.120 And that's called the spin quantum number. 00:37:14.810 --> 00:37:18.680 And it takes values plus or minus a half. 00:37:18.680 --> 00:37:20.990 Where did that come from? 00:37:20.990 --> 00:37:25.950 Well, in 1922-- 00:37:25.950 --> 00:37:28.250 oh, you know everybody's getting Nobel Prizes and I 00:37:28.250 --> 00:37:35.060 didn't give Niels Bohr his proper recognition. 00:37:35.060 --> 00:37:36.450 He gets the Noble Prize, as well. 00:37:39.240 --> 00:37:42.200 Oh, when Sommerfeld turned 80, they had a symposium in his 00:37:42.200 --> 00:37:44.480 honor and they published a book. 00:37:44.480 --> 00:37:47.490 And the book had papers and well-wishes, papers that were 00:37:47.490 --> 00:37:49.140 given at the symposium. 00:37:49.140 --> 00:37:53.720 And in the front they had Sommerfeld's picture and they 00:37:53.720 --> 00:37:58.450 also had this twin picture, this diptych. 00:37:58.450 --> 00:38:01.490 So on the right is Sommerfeld, and on the left is the same 00:38:01.490 --> 00:38:03.630 picture but they've morphed it. 00:38:03.630 --> 00:38:05.870 Now remember, there's no Photoshop. 00:38:05.870 --> 00:38:08.290 Horrors, there's no Photoshop. 00:38:08.290 --> 00:38:09.190 Can you imagine? 00:38:09.190 --> 00:38:10.240 So how could they do this? 00:38:10.240 --> 00:38:13.120 They had to take the negative, which was a photographic 00:38:13.120 --> 00:38:16.690 plate, and when they were printing the negative using a 00:38:16.690 --> 00:38:19.740 light box they had to hold the negative on an angle to get 00:38:19.740 --> 00:38:21.340 the distortion. 00:38:21.340 --> 00:38:24.340 And in holding it on an angle to get the distortion, they 00:38:24.340 --> 00:38:27.720 turned this image into something that was a little 00:38:27.720 --> 00:38:28.610 more spread out. 00:38:28.610 --> 00:38:33.470 And the caption that went with this, "To Arnold Sommerfeld, 00:38:33.470 --> 00:38:37.400 who taught us that the circle is the degenerate form of the 00:38:37.400 --> 00:38:41.520 ellipse." Now that's geek humor. 00:38:41.520 --> 00:38:42.720 I mean, they laughed. 00:38:42.720 --> 00:38:44.200 They thought that was so funny, hahaha. 00:38:44.200 --> 00:38:46.210 You know. 00:38:46.210 --> 00:38:47.320 They were having a great time. 00:38:47.320 --> 00:38:49.970 It was Germany, and nineteen twenties. 00:38:49.970 --> 00:38:52.640 And there he is. 00:38:52.640 --> 00:38:54.550 OK, so now let's go to 1922. 00:38:54.550 --> 00:38:56.250 This is the Stern-Gerlach experiment. 00:38:56.250 --> 00:38:57.990 Very interesting experiment. 00:38:57.990 --> 00:39:00.110 This is really physical vapor deposition. 00:39:00.110 --> 00:39:02.500 Over here I've got a crucible and it's 00:39:02.500 --> 00:39:04.240 full of molten silver. 00:39:04.240 --> 00:39:08.280 So Stern and Gerlach were studying the magnetic behavior 00:39:08.280 --> 00:39:11.090 of liquid metals. 00:39:11.090 --> 00:39:13.690 So what they were doing is they had this-- 00:39:13.690 --> 00:39:15.720 over here you see it's red even though it's silver, 00:39:15.720 --> 00:39:18.290 because this is that about 1,000 centigrade. 00:39:18.290 --> 00:39:20.200 Silver melts at about 960. 00:39:20.200 --> 00:39:22.000 Everything, I don't care what it's color is at room 00:39:22.000 --> 00:39:24.340 temperature, at 1,000 degrees it's red. 00:39:24.340 --> 00:39:26.200 It's called red hot. 00:39:26.200 --> 00:39:26.590 All right. 00:39:26.590 --> 00:39:29.370 So this is red hot silver and there's a vapor here and 00:39:29.370 --> 00:39:32.010 there's a slit and the silver atoms come out of the slit. 00:39:32.010 --> 00:39:35.290 And they go across over here to a substrate and then they 00:39:35.290 --> 00:39:36.970 pause it on the substrate. 00:39:36.970 --> 00:39:40.040 So making little band of silver on the substrate. 00:39:40.040 --> 00:39:43.150 And furthermore, he sometimes put them 00:39:43.150 --> 00:39:44.700 through a magnetic field. 00:39:44.700 --> 00:39:49.190 So he's got a slit here that narrows the beam, and then he 00:39:49.190 --> 00:39:53.730 sends it through a magnetic field that is asymmetric. 00:39:53.730 --> 00:39:54.570 It's divergent. 00:39:54.570 --> 00:39:55.330 Can you see here? 00:39:55.330 --> 00:39:56.280 Look at the end. 00:39:56.280 --> 00:39:59.030 The south pole as a tip and the north pole is 00:39:59.030 --> 00:40:00.670 this arc, this cup. 00:40:00.670 --> 00:40:03.920 So the field lines don't go just directly from tip to tip, 00:40:03.920 --> 00:40:05.910 they go from tip off to the side. 00:40:05.910 --> 00:40:08.210 So you can see the divergence of the magnetic field. 00:40:08.210 --> 00:40:11.910 And so he looked at what kind of deposits he got as a 00:40:11.910 --> 00:40:17.460 function of the magnetic field. 00:40:17.460 --> 00:40:20.470 Here's what the observed. 00:40:20.470 --> 00:40:22.250 Very puzzling. 00:40:22.250 --> 00:40:24.020 The whole thing was about Maxwell's equation. 00:40:24.020 --> 00:40:26.183 So he's got a silver beam. 00:40:29.070 --> 00:40:35.330 And when it went directly from the furnace to the substrate 00:40:35.330 --> 00:40:37.200 he just got the shadow of the slit. 00:40:40.780 --> 00:40:44.490 And they have the split crosswise with respect to the 00:40:44.490 --> 00:40:45.910 divergent magnetic field. 00:40:45.910 --> 00:40:50.750 So if you look at the substrate you just see a band. 00:40:50.750 --> 00:40:53.590 So this is a band of silver and you can imagine there was 00:40:53.590 --> 00:40:56.260 a slit out here and it just cast a shadow and that's the 00:40:56.260 --> 00:40:57.650 band of silver. 00:40:57.650 --> 00:41:01.340 This is PVD, physical vapor deposition of silver. 00:41:01.340 --> 00:41:05.580 Now when b is not equal 0, what would you expect? 00:41:05.580 --> 00:41:08.160 You'd think the beam would bend, right? 00:41:08.160 --> 00:41:09.610 So what do you think happens? 00:41:09.610 --> 00:41:11.100 The beam bends up? 00:41:11.100 --> 00:41:12.910 The beam bends down? 00:41:12.910 --> 00:41:16.790 Or beam bends to the right or to the left? 00:41:16.790 --> 00:41:17.560 Think about it. 00:41:17.560 --> 00:41:18.870 I don't want to hear your answer. 00:41:18.870 --> 00:41:20.710 Think about it. 00:41:20.710 --> 00:41:22.070 What do they observe? 00:41:22.070 --> 00:41:27.050 What they observe is, if this is where the original one is. 00:41:27.050 --> 00:41:28.970 Two. 00:41:28.970 --> 00:41:31.100 The beam splits in two. 00:41:31.100 --> 00:41:33.670 And it gets two deposits, one above, one 00:41:33.670 --> 00:41:36.520 below, of equal intensity. 00:41:36.520 --> 00:41:38.700 That's a problem. 00:41:38.700 --> 00:41:39.940 Beam splitting. 00:41:39.940 --> 00:41:42.605 But now it's a beam of matter. 00:41:47.040 --> 00:41:48.670 Beam splitting. 00:41:48.670 --> 00:41:52.230 Boy, they had them scratching their heads on that one. 00:41:52.230 --> 00:41:55.570 No way to explain that. 00:41:55.570 --> 00:41:57.830 So along come a couple of graduate students. 00:41:57.830 --> 00:42:00.270 1925, couple of graduates. 00:42:00.270 --> 00:42:03.230 So this is 1992 in Frankfurt. 00:42:03.230 --> 00:42:08.070 1925, two graduate students in Leiden, again. 00:42:08.070 --> 00:42:11.000 Gaudsmit and Uhlenbeck. 00:42:15.420 --> 00:42:16.960 They're just like my TA's. 00:42:16.960 --> 00:42:18.740 Grad students. 00:42:18.740 --> 00:42:22.000 And they looked at this thing, I don't know, maybe sitting 00:42:22.000 --> 00:42:24.180 around over a beer one night, and they said, you know, so 00:42:24.180 --> 00:42:28.700 far what we've been saying is the electron revolves around 00:42:28.700 --> 00:42:30.230 the nucleus. 00:42:30.230 --> 00:42:33.400 And sometimes it revolves in a circular orbit, and sometimes 00:42:33.400 --> 00:42:35.920 it revolves in an elliptical orbit, but here's 00:42:35.920 --> 00:42:37.280 the electron revolving. 00:42:37.280 --> 00:42:41.590 And they said, what if in addition to revolve, the 00:42:41.590 --> 00:42:45.320 electron rotated so that it's going like this? 00:42:45.320 --> 00:42:46.570 [GESTURES] 00:42:48.690 --> 00:42:50.580 But there's two choices. 00:42:50.580 --> 00:42:53.310 It can be going like this, or can be going like this. 00:42:53.310 --> 00:42:55.730 [GESTURES] 00:42:55.730 --> 00:43:00.880 Now, it's a charged species and it's rotating, which means 00:43:00.880 --> 00:43:03.670 that it's going to have a magnetic moment 00:43:03.670 --> 00:43:05.580 depending on rotation. 00:43:05.580 --> 00:43:07.120 And now I'm going to send it through a 00:43:07.120 --> 00:43:08.550 divergent magnetic field. 00:43:08.550 --> 00:43:12.170 Doesn't it follow to reason that if I put it through a 00:43:12.170 --> 00:43:15.320 magnetic field and I've got some of them doing this and 00:43:15.320 --> 00:43:17.460 some of them doing that, they're going to go in 00:43:17.460 --> 00:43:18.550 different directions? 00:43:18.550 --> 00:43:20.380 Opposite directions? 00:43:20.380 --> 00:43:22.150 And what do you think the numbers are? 00:43:22.150 --> 00:43:25.420 If I give you Avogadro's number of silvers, you think 00:43:25.420 --> 00:43:28.630 I'm going to get a dominant clockwise and a minority 00:43:28.630 --> 00:43:29.980 anti-clockwise? 00:43:29.980 --> 00:43:30.560 No. 00:43:30.560 --> 00:43:32.180 We're going to get equal numbers. 00:43:32.180 --> 00:43:33.520 Some are going to spin like this, some are going 00:43:33.520 --> 00:43:34.340 to spin like that. 00:43:34.340 --> 00:43:36.320 And you're going say, but electrons don't spin, they're 00:43:36.320 --> 00:43:37.150 not doing this. 00:43:37.150 --> 00:43:42.050 But if you model them as though they are doing this, 00:43:42.050 --> 00:43:44.690 you get those results. 00:43:44.690 --> 00:43:46.930 Those results make sense. 00:43:46.930 --> 00:43:51.530 And so they introduced the spin quantum numbers. 00:43:51.530 --> 00:43:54.675 And I think these are the ones that have been erased. 00:43:57.230 --> 00:43:58.270 Such is education. 00:43:58.270 --> 00:43:58.550 OK. 00:43:58.550 --> 00:43:59.080 So you know it. 00:43:59.080 --> 00:44:00.750 S plus or minus a half. 00:44:00.750 --> 00:44:03.060 By the way, Gaudsmit and Uhlenbeck were here during 00:44:03.060 --> 00:44:04.260 World War Two. 00:44:04.260 --> 00:44:05.900 They worked in Building Four. 00:44:05.900 --> 00:44:08.270 You go down the corridor, Building Four just off the 00:44:08.270 --> 00:44:11.140 Infinite Corridor, there's a plaque there for the Radiation 00:44:11.140 --> 00:44:11.780 Laboratory. 00:44:11.780 --> 00:44:13.180 That's where they worked, in the Rad Lab. 00:44:13.180 --> 00:44:16.150 That's where radar was first engineered. 00:44:16.150 --> 00:44:17.630 There was work in the UK, there was 00:44:17.630 --> 00:44:18.570 work in other places. 00:44:18.570 --> 00:44:22.050 But this is the Radiation Laboratory, started here and 00:44:22.050 --> 00:44:24.300 they were both here at the time. 00:44:24.300 --> 00:44:27.440 OK, well, I think that's a-- 00:44:27.440 --> 00:44:30.090 So this is a plate from the paper. 00:44:30.090 --> 00:44:32.692 No magnetic field with the magnetic field. 00:44:32.692 --> 00:44:35.870 And by the way, why did they choose silver? 00:44:35.870 --> 00:44:39.670 They chose silver because it's atomic number is 47-- 00:44:39.670 --> 00:44:41.240 it has an odd number of electrons. 00:44:41.240 --> 00:44:43.270 You're going to learn later that you get two electrons in 00:44:43.270 --> 00:44:45.780 an orbital, and if you have two electrons, one will be 00:44:45.780 --> 00:44:47.660 spin up, one will be spin down. 00:44:47.660 --> 00:44:49.020 There's no magnetic moment. 00:44:49.020 --> 00:44:51.720 So they were clever about choosing an element that had 00:44:51.720 --> 00:44:56.360 an odd number of electrons so that there would, at the end, 00:44:56.360 --> 00:44:58.260 be an unpaired electron. 00:44:58.260 --> 00:45:00.920 And there's Otto Stern with his Nobel Prize. 00:45:00.920 --> 00:45:03.310 And he came to the United States, as well. 00:45:03.310 --> 00:45:05.530 And you're going to see the ascendancy of American Science 00:45:05.530 --> 00:45:07.940 as people flee Europe up in the nineteen thirties. 00:45:07.940 --> 00:45:10.630 And America is the beneficiary, and then you see 00:45:10.630 --> 00:45:12.340 American science rise. 00:45:12.340 --> 00:45:15.570 But for now it's European science. 00:45:15.570 --> 00:45:17.370 OK, so I'm going to talk a little bit about hydrogen and 00:45:17.370 --> 00:45:18.760 transportation. 00:45:18.760 --> 00:45:20.780 And we're going to talk about the Hindenburg because it was 00:45:20.780 --> 00:45:21.940 full of hydrogen. 00:45:21.940 --> 00:45:24.470 And to give you a sense of scale, this is what a 747 00:45:24.470 --> 00:45:26.960 would look like and is what the Titanic would look like. 00:45:26.960 --> 00:45:29.880 It was almost as long as the Titanic. 00:45:29.880 --> 00:45:32.920 It was built in Germany by the Zeppelin company. 00:45:32.920 --> 00:45:37.490 And the Titanic, the Hindenburg rather, was LZ129 00:45:37.490 --> 00:45:38.080 serial number. 00:45:38.080 --> 00:45:42.120 That's Luftschiff Zeppelin. 00:45:42.120 --> 00:45:43.090 Airship Zeppelin. 00:45:43.090 --> 00:45:44.810 135 feet in diameter. 00:45:44.810 --> 00:45:47.860 804 feet long. 00:45:47.860 --> 00:45:49.170 How long is a football field? 00:45:52.320 --> 00:45:55.510 So that's a big boat. 00:45:55.510 --> 00:46:00.590 Seven million cubic feet of gas, giving you 112 tons of 00:46:00.590 --> 00:46:01.480 useful lift. 00:46:01.480 --> 00:46:03.950 You ever have to lift something very heavy, there's 00:46:03.950 --> 00:46:05.200 your sky crane. 00:46:07.770 --> 00:46:10.010 So why are they using hydrogen? 00:46:10.010 --> 00:46:12.620 Well, when the Nazis came to power in Germany, Congress 00:46:12.620 --> 00:46:14.200 passed the Helium Control Act. 00:46:14.200 --> 00:46:16.480 The dominant supplier of helium to the world was the 00:46:16.480 --> 00:46:17.520 United States. 00:46:17.520 --> 00:46:21.190 Helium comes from helium wells in the earth. 00:46:21.190 --> 00:46:25.410 And so as of 1933 the United States refused to sell Helium 00:46:25.410 --> 00:46:29.850 to Germany, so the engineers were forced to use hydrogen. 00:46:29.850 --> 00:46:32.690 Next best thing. 00:46:32.690 --> 00:46:33.640 Here are some posters. 00:46:33.640 --> 00:46:36.550 "Only 2 1/2 half days to Europe." And here one, a 00:46:36.550 --> 00:46:37.490 German one. 00:46:37.490 --> 00:46:39.960 "And now over the North Atlantic." That's Manhattan. 00:46:39.960 --> 00:46:41.280 That's the lower tip of Manhattan. 00:46:41.280 --> 00:46:45.710 There's the Chrysler Building, look at that. 00:46:45.710 --> 00:46:46.960 Now look at that picture, isn't that magnificent? 00:46:49.400 --> 00:46:52.170 10 transatlantic flights, 1936. 00:46:52.170 --> 00:46:55.080 1002 passengers. 00:46:55.080 --> 00:46:57.220 Cruising speed, 78 miles an hour. 00:46:57.220 --> 00:46:59.650 Took two and a half days. 00:46:59.650 --> 00:47:02.940 By the way, 100 feet in diameter-- 00:47:02.940 --> 00:47:05.440 when people traveled, they traveled in style. 00:47:05.440 --> 00:47:08.390 They had a ballroom there and a grand piano. 00:47:08.390 --> 00:47:09.550 People didn't sit like this. 00:47:09.550 --> 00:47:09.950 [CROUCHES] 00:47:09.950 --> 00:47:13.230 With a plastic knife and fork. 00:47:13.230 --> 00:47:16.480 That's progress, right? 00:47:16.480 --> 00:47:21.040 Two and a half dancing, tux, tails, champagne. 00:47:21.040 --> 00:47:22.150 Now, like this. 00:47:22.150 --> 00:47:24.920 [CROUCHES] 00:47:24.920 --> 00:47:27.020 May sixth, 1937. 00:47:27.020 --> 00:47:30.520 Arrival of first flight to the U.S. while docking in 00:47:30.520 --> 00:47:31.340 Lakehurst, New Jersey. 00:47:31.340 --> 00:47:33.370 Why were they docking in Lakehurst, New Jersey? 00:47:33.370 --> 00:47:36.370 If you go to the top of the Empire State Building, look 00:47:36.370 --> 00:47:39.980 and you will see at the corners moorings. 00:47:39.980 --> 00:47:41.770 Moorings sticking out. 00:47:41.770 --> 00:47:46.400 The plan was to dock airships at the Empire State Building. 00:47:46.400 --> 00:47:50.150 So you'd come in from Europe, you'd dock at Fifth Avenue, 00:47:50.150 --> 00:47:53.010 get on the elevator, and there you were. 00:47:53.010 --> 00:47:55.990 When they tried to dock the air currents were so violent 00:47:55.990 --> 00:47:57.690 that they couldn't safely dock the ship. 00:47:57.690 --> 00:48:00.780 So then they moved across to the fair grounds at Lakehurst, 00:48:00.780 --> 00:48:03.960 New Jersey, where obviously this mooring is much closer to 00:48:03.960 --> 00:48:05.980 the ground than the top of the Empire State Building. 00:48:05.980 --> 00:48:07.810 The wild currents, they're bad, but 00:48:07.810 --> 00:48:08.970 they're manageably bad. 00:48:08.970 --> 00:48:12.680 At the top of the Empire State Building, impossible. 00:48:12.680 --> 00:48:14.720 There's another image. 00:48:14.720 --> 00:48:17.410 So what happened? 00:48:17.410 --> 00:48:19.270 It did not explode. 00:48:19.270 --> 00:48:21.430 It did not explode. 00:48:21.430 --> 00:48:22.650 It couldn't explode. 00:48:22.650 --> 00:48:25.580 Seven million cubic feet of hydrogen to explode requires 00:48:25.580 --> 00:48:29.040 seven million cubic feet of oxygen instantaneously. 00:48:29.040 --> 00:48:32.170 And air is 20% oxygen. 00:48:32.170 --> 00:48:36.910 So it was a very violent fire, roman candle from the point of 00:48:36.910 --> 00:48:38.490 egress of the hydrogen. 00:48:38.490 --> 00:48:43.050 Most of the people on board walked off the Hindenburg. 00:48:43.050 --> 00:48:45.770 Most of the people walked off the Hindenburg uninjured. 00:48:48.630 --> 00:48:51.110 They think it was electrical discharge in the vicinity of a 00:48:51.110 --> 00:48:52.400 hydrogen leak. 00:48:52.400 --> 00:48:56.000 Recent research has indicated the skin was made of resin 00:48:56.000 --> 00:48:57.700 finished with a lacquer dope. 00:48:57.700 --> 00:49:00.380 And then to make it shiny they put aluminum powder. 00:49:00.380 --> 00:49:03.680 And why they put iron oxide on the inside I don't know, but 00:49:03.680 --> 00:49:07.610 this is what NASA uses for solid rocket motor grains. 00:49:07.610 --> 00:49:10.620 So when this thing catches fire, this is a thermite 00:49:10.620 --> 00:49:12.495 reaction and could be very violent. 00:49:15.330 --> 00:49:17.280 And this spelled the end of rigid error ships in 00:49:17.280 --> 00:49:20.290 commercial air transportation. 00:49:20.290 --> 00:49:22.840 Now this a U.S. Navy airship filled with helium. 00:49:22.840 --> 00:49:25.420 And there was a small gasoline fire, look what happened. 00:49:25.420 --> 00:49:26.735 Again, it was the skin. 00:49:31.890 --> 00:49:33.580 That's a blow up of that one. 00:49:33.580 --> 00:49:35.280 So I looked at that and I thought, geez, that looks 00:49:35.280 --> 00:49:37.540 Lichtenstein, doesn't it? 00:49:37.540 --> 00:49:38.940 You know this one? 00:49:38.940 --> 00:49:39.520 This one. 00:49:39.520 --> 00:49:40.470 Look at that. 00:49:40.470 --> 00:49:42.560 Look at that. 00:49:42.560 --> 00:49:45.430 So you know, I can be an artist, too, right? 00:49:45.430 --> 00:49:47.450 OK, I'm going to tell you one more story. 00:49:47.450 --> 00:49:49.140 Another Niels Bohr story. 00:49:49.140 --> 00:49:53.660 So in 1896 there was a guy, and astronomer at Harvard 00:49:53.660 --> 00:49:55.530 called Pickering. 00:49:55.530 --> 00:50:00.190 Pickering at Harvard, 1896, and he was studying the lines 00:50:00.190 --> 00:50:01.360 in star light. 00:50:01.360 --> 00:50:05.910 And he attributed to some of the spectra that he was 00:50:05.910 --> 00:50:11.480 getting, he said he was seeing atomic hydrogen in star light. 00:50:11.480 --> 00:50:15.300 And then there was a fellow in London called Fowler. 00:50:15.300 --> 00:50:19.750 And Fowler, in 1912, reproduced the experiments in 00:50:19.750 --> 00:50:20.235 the laboratory. 00:50:20.235 --> 00:50:25.640 He put gas in a tube and got the same thing in the lab. 00:50:25.640 --> 00:50:31.680 So this guy's at Harvard and the other guy is at London. 00:50:31.680 --> 00:50:33.220 Well, Bohr looks at this stuff and he says, 00:50:33.220 --> 00:50:34.820 you guys are wrong. 00:50:34.820 --> 00:50:36.435 You guys are wrong-- your lines are off 00:50:36.435 --> 00:50:38.540 by a factor of 4x. 00:50:38.540 --> 00:50:41.280 You've got the right series, but you got the wrong element. 00:50:41.280 --> 00:50:43.860 What you guys are looking at is helium plus. 00:50:43.860 --> 00:50:46.455 You're not looking at hydrogen, and you know, from-- 00:50:46.455 --> 00:50:48.100 it goes to z squared. 00:50:48.100 --> 00:50:50.370 So the lines are going to be shifted by factor of four 00:50:50.370 --> 00:50:52.670 because this z is equal to 2. 00:50:52.670 --> 00:50:55.120 So Fowler was a pompous ass and he didn't like being 00:50:55.120 --> 00:50:57.190 called on his bad science. 00:50:57.190 --> 00:51:00.360 So he does a calculation and he looks more carefully and he 00:51:00.360 --> 00:51:01.760 says, Bohr, you're wrong. 00:51:01.760 --> 00:51:06.260 In fact, our lines are off by 4.0016. 00:51:06.260 --> 00:51:08.440 Now don't laugh. 00:51:08.440 --> 00:51:12.130 The reason is the spectroscopy was so precise that they could 00:51:12.130 --> 00:51:14.530 go to five significant figures. 00:51:14.530 --> 00:51:16.730 So Bohr says, hmm. 00:51:16.730 --> 00:51:18.670 And he goes back and he says, you know, we've been doing all 00:51:18.670 --> 00:51:22.040 these calculations with a one electron atom just neglecting 00:51:22.040 --> 00:51:22.980 the center. 00:51:22.980 --> 00:51:25.990 So he redoes the calculations for the entire Bohr model, 00:51:25.990 --> 00:51:29.430 including considerations of the mass of the nucleus and 00:51:29.430 --> 00:51:32.260 the mass of the electron in the form of the reduced mass. 00:51:32.260 --> 00:51:37.740 The reduced mass is-- you're learning this in-- 00:51:37.740 --> 00:51:40.020 the reciprocal of the sum of the reciprocals. 00:51:40.020 --> 00:51:43.890 And when he does that, he gets that the value of the line 00:51:43.890 --> 00:51:49.730 shift should be 4.00163. 00:51:49.730 --> 00:51:52.190 So he says, you guys are wrong. 00:51:52.190 --> 00:51:55.050 It should be 4.0016. 00:51:55.050 --> 00:51:57.500 You got 4.0016, you idiots. 00:51:57.500 --> 00:52:00.750 You're looking at helium plus. 00:52:00.750 --> 00:52:02.300 That was Bohr. 00:52:02.300 --> 00:52:04.840 Did not want to get into an argument with Bohr. 00:52:04.840 --> 00:52:05.850 All right. 00:52:05.850 --> 00:52:07.530 Have a nice weekend.