WEBVTT 00:00:00.030 --> 00:00:02.535 The following content is provided under a Creative 00:00:02.535 --> 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. 00:00:20.670 --> 00:00:22.060 PROFESSOR: Let's get right into it. 00:00:22.060 --> 00:00:25.160 So last day, we started looking at Roentgen again and 00:00:25.160 --> 00:00:28.800 the generation of x-rays, which we saw occurred when we 00:00:28.800 --> 00:00:33.780 operate the gas discharge tube at high voltage and low 00:00:33.780 --> 00:00:36.640 pressure and this is the image that we saw 00:00:36.640 --> 00:00:39.370 of his wife's hand. 00:00:39.370 --> 00:00:42.510 Birth of medical radiography. 00:00:42.510 --> 00:00:47.060 And we started looking at the origin of x-rays and we 00:00:47.060 --> 00:00:51.970 started looking at the energy level diagram of the target 00:00:51.970 --> 00:00:58.620 anode in the gas discharge tube and this is the energy 00:00:58.620 --> 00:01:00.310 level diagram of the target. 00:01:00.310 --> 00:01:03.550 So the ballistic electron-- 00:01:03.550 --> 00:01:04.950 I'm calling it incident-- 00:01:04.950 --> 00:01:08.810 this is the electron that's making its journey across the 00:01:08.810 --> 00:01:10.500 x-ray generating tube. 00:01:10.500 --> 00:01:14.500 It left the cathode and it's moving across and crashing 00:01:14.500 --> 00:01:15.490 into the anode. 00:01:15.490 --> 00:01:18.660 So this is the target or the anode. 00:01:18.660 --> 00:01:20.876 So let's label it as such. 00:01:20.876 --> 00:01:25.250 So we're looking at one of these mixed metaphors, where 00:01:25.250 --> 00:01:32.150 we've got both a Cartesian image here of the electron and 00:01:32.150 --> 00:01:33.330 we've got an energy image. 00:01:33.330 --> 00:01:38.970 So this is the target or it's the anode and it's charged 00:01:38.970 --> 00:01:40.980 positively and so the electrons are 00:01:40.980 --> 00:01:41.990 crashing into it. 00:01:41.990 --> 00:01:45.635 And we reason that what would happen is, if the electrons, 00:01:45.635 --> 00:01:48.260 the ballistic electrons, had high enough energy, they could 00:01:48.260 --> 00:01:54.390 actually dislodge 1s electrons and when they do so, they make 00:01:54.390 --> 00:01:56.150 the conditions for a cascade. 00:01:56.150 --> 00:01:59.730 So you can see electrons falling from n equals 2 to n 00:01:59.730 --> 00:02:02.820 equals 1 and when they do so, they emit radiation. 00:02:02.820 --> 00:02:06.330 They emit photons and these photons are called K alpha. 00:02:06.330 --> 00:02:09.975 K because the final shell number was n equals 1. 00:02:09.975 --> 00:02:11.850 And remember, the spectroscopists 00:02:11.850 --> 00:02:13.450 prefer to use letters. 00:02:13.450 --> 00:02:17.540 So when the electron ends at n equals 1, that's n final, we 00:02:17.540 --> 00:02:21.380 call it a K photon. 00:02:21.380 --> 00:02:26.670 And furthermore, the subscript alpha means that the delta, 00:02:26.670 --> 00:02:30.510 the n initial to n final is only one. 00:02:30.510 --> 00:02:33.780 So when you go from 2 to 1, you get the K alpha. 00:02:33.780 --> 00:02:37.580 And less likely but still possible is the transition 00:02:37.580 --> 00:02:39.180 from 3 down to 1. 00:02:39.180 --> 00:02:42.750 So it's still called a K photon because the electron 00:02:42.750 --> 00:02:45.930 that generated the photon ended in the K shell, but it 00:02:45.930 --> 00:02:50.140 traveled from a delta n of 2, went from 3 to 1 00:02:50.140 --> 00:02:51.760 so that's a K beta. 00:02:51.760 --> 00:02:54.435 Over here, obviously if we have enough energy to kick out 00:02:54.435 --> 00:02:57.800 K shell electrons, we have enough energy to kick out L 00:02:57.800 --> 00:02:59.120 shell electrons. 00:02:59.120 --> 00:03:01.550 And so if we lose an L shell electron and we have a 00:03:01.550 --> 00:03:06.100 cascade, then anything that ends in n equals 2 will be 00:03:06.100 --> 00:03:08.120 called an L photon. 00:03:08.120 --> 00:03:10.910 If it comes from 3 to 2, that's a delta of 1. 00:03:10.910 --> 00:03:12.240 That's the L alpha. 00:03:12.240 --> 00:03:14.390 It it falls 4 to 2, that's a delta of 2. 00:03:14.390 --> 00:03:15.520 That's the L beta. 00:03:15.520 --> 00:03:17.325 And so you can see you get a set of lines. 00:03:20.150 --> 00:03:22.790 And that set of lines looks like this. 00:03:22.790 --> 00:03:26.370 We can plot a spectrum of this entire set of lines, which 00:03:26.370 --> 00:03:30.185 will be characteristic of the identity of the target. 00:03:34.520 --> 00:03:37.360 And I think I showed you last day that it's going to look 00:03:37.360 --> 00:03:45.650 like this, where we will plot intensity and the intensity on 00:03:45.650 --> 00:03:49.410 a spectrum is related to the frequency of occurrence and on 00:03:49.410 --> 00:03:52.930 the abscissa, we're going to have some kind of energy 00:03:52.930 --> 00:03:53.520 coordinate. 00:03:53.520 --> 00:03:57.300 We can put lambda increasing from left to right, which 00:03:57.300 --> 00:04:00.020 means energy increases from right to left. 00:04:00.020 --> 00:04:02.420 And we saw that we have this family of lines where we have 00:04:02.420 --> 00:04:07.610 a discrete line at the energy of K alpha and a second line 00:04:07.610 --> 00:04:12.860 at the energy associated with K beta and K beta has a higher 00:04:12.860 --> 00:04:15.780 energy, therefore, a lower wavelength, and the relative 00:04:15.780 --> 00:04:19.450 heights related to the relative frequency, again, not 00:04:19.450 --> 00:04:24.470 to scale, but still the general 00:04:24.470 --> 00:04:25.870 relationship is correct. 00:04:25.870 --> 00:04:29.040 The likelihood of falling from 2 to 1 is higher than falling 00:04:29.040 --> 00:04:32.700 from 3 to 1 and so you'd expect to have the intensity 00:04:32.700 --> 00:04:35.060 of the K alpha line greater than the intensity of the K 00:04:35.060 --> 00:04:39.040 beta line and the L lines have to be of lower energy because 00:04:39.040 --> 00:04:43.570 transitions 3 to 2 are less energy than 2 to 1 so we 00:04:43.570 --> 00:04:47.960 expect those lines to be out here and again, a relative 00:04:47.960 --> 00:04:52.460 frequency where the L alpha has a slightly lower energy 00:04:52.460 --> 00:04:56.220 and L beta has a slightly lower frequency of a current. 00:04:56.220 --> 00:04:59.645 So that's the spectrum and this we call characteristic. 00:05:03.380 --> 00:05:04.730 Characteristic of what? 00:05:04.730 --> 00:05:11.240 Of the identity of the anode or the target. 00:05:14.470 --> 00:05:16.510 This is generating the x-rays. 00:05:16.510 --> 00:05:20.500 So if I want x-rays of this value of wavelength, I choose 00:05:20.500 --> 00:05:22.450 the target appropriately. 00:05:22.450 --> 00:05:25.240 That's why we have the relationship here. 00:05:25.240 --> 00:05:27.410 And then the other thing is that-- 00:05:27.410 --> 00:05:29.920 it's obvious, but I just want to make sure that 00:05:29.920 --> 00:05:32.020 we put it up here-- 00:05:32.020 --> 00:05:36.330 it's quantized because we're looking at the photons coming 00:05:36.330 --> 00:05:40.160 at discrete values of energy. 00:05:40.160 --> 00:05:42.910 So that's what we speculated on. 00:05:42.910 --> 00:05:44.230 Are there any data? 00:05:44.230 --> 00:05:48.130 The answer is yes and the data come from a young man by the 00:05:48.130 --> 00:05:49.380 name of Henry Moseley. 00:05:52.230 --> 00:05:55.670 He was doing his PhD up in Manchester. 00:05:55.670 --> 00:05:57.820 He was is working for Rutherford. 00:05:57.820 --> 00:06:06.450 Rutherford was his PhD thesis supervisor and 1913, 1914, he 00:06:06.450 --> 00:06:09.600 was making systematic measurements. 00:06:09.600 --> 00:06:16.170 He was conducting a systematic study of the characteristic 00:06:16.170 --> 00:06:20.750 spectra of no fewer than 38 elements of 00:06:20.750 --> 00:06:22.560 the Periodic Table. 00:06:22.560 --> 00:06:26.910 And what did we learn from his measurements? 00:06:26.910 --> 00:06:30.170 Learned from his measurements that there's was a pattern 00:06:30.170 --> 00:06:34.730 here and here's what the pattern is that Moseley found. 00:06:34.730 --> 00:06:39.300 He found that if he took the value of-- 00:06:39.300 --> 00:06:41.120 I'm going to just take one line. 00:06:41.120 --> 00:06:46.170 If he took all of the K alpha lines from 1K alpha per 00:06:46.170 --> 00:06:50.810 element and he plotted the value of the wave number of a 00:06:50.810 --> 00:06:55.670 particular line, he found that the value of the wave number 00:06:55.670 --> 00:06:59.160 of a particular line scaled with the identity of the 00:06:59.160 --> 00:07:02.720 element by the square of the proton number. 00:07:07.470 --> 00:07:10.420 So, for example, we would have, say here we 00:07:10.420 --> 00:07:12.300 started with aluminum. 00:07:12.300 --> 00:07:15.890 So aluminum proton numbers 13 so 13 squared. 00:07:15.890 --> 00:07:18.030 And he went all the way up to gold. 00:07:18.030 --> 00:07:20.670 Didn't do all of them but he did, as I say, 38 00:07:20.670 --> 00:07:21.740 from one to the other. 00:07:21.740 --> 00:07:23.230 And these are discrete values. 00:07:23.230 --> 00:07:26.150 You have different elements here and gold is up here and 00:07:26.150 --> 00:07:31.340 he found that he could take the set of data for, say, all 00:07:31.340 --> 00:07:34.700 the K alphas and they lie on a line-- 00:07:34.700 --> 00:07:36.260 new bar-- 00:07:36.260 --> 00:07:40.440 as if proportional to the square of the proton number 00:07:40.440 --> 00:07:45.520 and he did the same with other lines-- 00:07:45.520 --> 00:07:47.470 say, L alpha and so on-- 00:07:47.470 --> 00:07:50.700 found that they lie on a line. 00:07:50.700 --> 00:07:54.400 So what does all of this mean? 00:07:54.400 --> 00:07:56.090 Well, let's take a look. 00:07:56.090 --> 00:07:59.690 Here's the image of the paper. 00:07:59.690 --> 00:08:01.740 High-frequency spectra elements. 00:08:04.420 --> 00:08:08.040 Henry Moseley, Master's degree, so he's working on his 00:08:08.040 --> 00:08:11.970 PhD, and the data were taken as follows in 00:08:11.970 --> 00:08:13.780 photographic plates. 00:08:13.780 --> 00:08:18.090 And so by trigonometry, you can figure out what the 00:08:18.090 --> 00:08:21.120 wavelength would be of the line that would go to this 00:08:21.120 --> 00:08:23.760 degree of distortion, et cetera, et cetera. 00:08:23.760 --> 00:08:25.120 It's a beautiful set of lines. 00:08:25.120 --> 00:08:26.460 Look at how these date are posed. 00:08:26.460 --> 00:08:27.700 So there's calcium. 00:08:27.700 --> 00:08:29.530 Scandium is frightfully expensive so you 00:08:29.530 --> 00:08:30.270 don't see it here. 00:08:30.270 --> 00:08:32.990 Then there's titanium, vanadium, chromium, manganese, 00:08:32.990 --> 00:08:37.120 and as you change the element, the wave number, the 00:08:37.120 --> 00:08:40.820 wavelength, the energy of all of these lines changes 00:08:40.820 --> 00:08:44.650 systematically in accordance with the square of the proton 00:08:44.650 --> 00:08:47.610 number, and we got over here to copper. 00:08:47.610 --> 00:08:51.870 Next one is zinc. Zinc melts at 420 degrees Celsius, which 00:08:51.870 --> 00:08:53.320 is relatively low melting. 00:08:53.320 --> 00:08:56.530 And under the bombardment of electrons-- 00:08:56.530 --> 00:09:00.450 the bombardment of zinc would cause it to melt and so rather 00:09:00.450 --> 00:09:03.460 than work with zinc, he instead worked with brass 00:09:03.460 --> 00:09:05.750 because brass is an alloy of copper and zinc-- 00:09:05.750 --> 00:09:06.890 and look carefully. 00:09:06.890 --> 00:09:10.480 You can see that brass has four lines, two lines 00:09:10.480 --> 00:09:13.670 identical to the lines of copper and these two new lines 00:09:13.670 --> 00:09:16.670 are the lines associated with zinc. And I mentioned last day 00:09:16.670 --> 00:09:21.490 that you could actually deconvolve the complex spectra 00:09:21.490 --> 00:09:24.920 and identify the constituent elements. 00:09:24.920 --> 00:09:29.130 So this was really fantastic, really fantastic. 00:09:29.130 --> 00:09:31.580 Si what did we learn from all of this? 00:09:31.580 --> 00:09:35.210 What did we learn by these data? 00:09:35.210 --> 00:09:44.530 well, first of all, corrected Mendeleyev What 00:09:44.530 --> 00:09:45.700 do I mean by that? 00:09:45.700 --> 00:09:48.570 Not here to say bad things about Mendeleyev, but 00:09:48.570 --> 00:10:00.240 Mendeleyev had told us that periodicity is a function of 00:10:00.240 --> 00:10:03.900 the atomic mass. 00:10:03.900 --> 00:10:05.670 That's what Mendeleyev said. 00:10:05.670 --> 00:10:08.510 Periodicity is a function of atomic mass. 00:10:08.510 --> 00:10:11.460 And now Moseley says no. 00:10:11.460 --> 00:10:14.480 Moseley says that periodicity is a 00:10:14.480 --> 00:10:16.040 function of proton number. 00:10:21.980 --> 00:10:24.080 And you can see here-- 00:10:26.730 --> 00:10:28.470 I wanted to show you the-- 00:10:28.470 --> 00:10:30.810 this is an image taken from his paper. 00:10:30.810 --> 00:10:31.970 He worked for Rutherford. 00:10:31.970 --> 00:10:34.770 These people were brilliant experimentalists and 00:10:34.770 --> 00:10:36.130 so here he's got-- 00:10:36.130 --> 00:10:38.500 the cathode is up here at the top. 00:10:38.500 --> 00:10:41.007 You see cathode of x-ray tube and the feed through and so 00:10:41.007 --> 00:10:44.740 on, so the anode is down here and it's connected and so on, 00:10:44.740 --> 00:10:49.020 and rather than take the x-ray tube apart in order to change 00:10:49.020 --> 00:10:52.850 the target, he went to the toy store and he bought-- 00:10:52.850 --> 00:10:57.330 this is the train from the toy store and he's got different 00:10:57.330 --> 00:11:03.080 elements seated next to each other on the flat car of the 00:11:03.080 --> 00:11:06.750 train and he's got feedthroughs with silk fishing 00:11:06.750 --> 00:11:10.180 line so that after he's done the experiment with one 00:11:10.180 --> 00:11:16.790 element, he can pull the train car over and change the anode 00:11:16.790 --> 00:11:20.002 without having to take the apparatus apart. 00:11:20.002 --> 00:11:23.160 These guys were very, very good experimentalists. 00:11:23.160 --> 00:11:25.620 So here's from his paper. 00:11:25.620 --> 00:11:28.620 The author intends first to make a general survey of the 00:11:28.620 --> 00:11:31.440 principal types of high-frequency radiation and 00:11:31.440 --> 00:11:34.060 then to examine the spectra of a few elements in greater 00:11:34.060 --> 00:11:36.120 detail with greater accuracy. 00:11:36.120 --> 00:11:39.210 The results already obtained show that such data have an 00:11:39.210 --> 00:11:40.840 important bearing on the question of the internal 00:11:40.840 --> 00:11:43.700 structure of the atom and strongly support the views of 00:11:43.700 --> 00:11:45.420 Rutherford and Bohr. 00:11:45.420 --> 00:11:46.670 It's 1913. 00:11:46.670 --> 00:11:48.510 Remember, that's when Bohr paper came out. 00:11:48.510 --> 00:11:51.270 All these people were working in the lab at the same time, 00:11:51.270 --> 00:11:52.800 supporting each other. 00:11:52.800 --> 00:11:55.680 You see, this doesn't make any sense with a Plum Pudding 00:11:55.680 --> 00:11:58.380 Model, does it? 00:11:58.380 --> 00:12:01.640 See, he continues: "We have here a proof that there isn't 00:12:01.640 --> 00:12:04.910 the atom of fundamental quantity, which increases by 00:12:04.910 --> 00:12:08.370 regular steps as we pass from one element to the next. 00:12:08.370 --> 00:12:12.340 This quantity can only be the charge on the central positive 00:12:12.340 --> 00:12:16.840 nucleus on the existence of which we already have definite 00:12:16.840 --> 00:12:18.470 proof." 00:12:18.470 --> 00:12:21.090 See, not only-- remember, the Plum Pudding Model has this 00:12:21.090 --> 00:12:23.800 big blob of positive charge nests. 00:12:23.800 --> 00:12:25.770 There are no protons. 00:12:25.770 --> 00:12:28.890 In the nuclear model, we have a nucleus that has positive 00:12:28.890 --> 00:12:32.430 charge and he's saying, I know there's positive charge, and 00:12:32.430 --> 00:12:35.150 it increases as you go from one element to the next. 00:12:35.150 --> 00:12:37.610 We are therefore led by experiment to view that N-- we 00:12:37.610 --> 00:12:40.210 use the letter Z today. 00:12:40.210 --> 00:12:41.560 He's using capital N. 00:12:41.560 --> 00:12:45.460 N is the same as the number of the place occupied by the 00:12:45.460 --> 00:12:47.740 element in the periodic system. 00:12:47.740 --> 00:12:50.720 This atomic number-- for the first time, the term atomic 00:12:50.720 --> 00:12:51.450 number is used. 00:12:51.450 --> 00:12:54.350 That's why I was being coy here and I kept saying proton 00:12:54.350 --> 00:12:57.410 number, because that's the way they knew it. 00:12:57.410 --> 00:12:59.480 Now he's say, this is the social security 00:12:59.480 --> 00:13:01.630 number of the element. 00:13:01.630 --> 00:13:05.560 Proton number is then for hydrogen 1, helium 2, lithium 00:13:05.560 --> 00:13:08.310 3, calcium 20, zinc 30, et cetera. 00:13:08.310 --> 00:13:10.310 We can confidently predict-- 00:13:10.310 --> 00:13:13.940 look at-- this is the masters student and 00:13:13.940 --> 00:13:14.770 he's going on a limb. 00:13:14.770 --> 00:13:17.680 He says: "We can confidently predict that in the few cases 00:13:17.680 --> 00:13:21.230 in which the order of the atomic weights A clashes with 00:13:21.230 --> 00:13:24.190 the chemical order of the periodic system, the chemical 00:13:24.190 --> 00:13:29.850 properties are governed by N, while A itself is probably a 00:13:29.850 --> 00:13:34.700 complicated function of N." He's right. 00:13:34.700 --> 00:13:36.160 You look at the Periodic Table. 00:13:36.160 --> 00:13:38.530 You say, yeah, yeah, they just go in descending mass or 00:13:38.530 --> 00:13:39.990 ascending proton number. 00:13:39.990 --> 00:13:41.240 Look carefully. 00:13:43.090 --> 00:13:46.180 Potassium has a lower mass than argon. 00:13:46.180 --> 00:13:47.070 And nobody's to-- 00:13:47.070 --> 00:13:48.620 well, if you were Mendeleyev, you'd say, go back 00:13:48.620 --> 00:13:49.340 and measure it again. 00:13:49.340 --> 00:13:50.310 Well, they have measured it. 00:13:50.310 --> 00:13:53.520 These are the accurate values and no one's going to put 00:13:53.520 --> 00:13:57.820 potassium underneath neon, but it comes next in the order of 00:13:57.820 --> 00:14:00.550 ascending atomic mass. 00:14:00.550 --> 00:14:02.290 Cobalt and nickel-- nickel actually 00:14:02.290 --> 00:14:04.090 weighs less than cobalt. 00:14:04.090 --> 00:14:06.390 But they're transition elements so who cares if you 00:14:06.390 --> 00:14:08.760 get those two mixed up? 00:14:08.760 --> 00:14:10.080 You find them in stainless steel. 00:14:10.080 --> 00:14:11.610 It doesn't matter. 00:14:11.610 --> 00:14:12.960 This is a good one. 00:14:12.960 --> 00:14:15.350 Iodine is lower mass than tellurium. 00:14:15.350 --> 00:14:17.040 Iodine is a halogen. 00:14:17.040 --> 00:14:20.420 It belongs under fluorine, chlorine and bromine. 00:14:20.420 --> 00:14:21.590 You're not going to put it under 00:14:21.590 --> 00:14:25.280 oxygen, sulfur, selenium. 00:14:25.280 --> 00:14:29.310 But look, there's the data. 00:14:29.310 --> 00:14:33.340 And then last one that Moseley couldn't have known about is 00:14:33.340 --> 00:14:37.090 transuranic synthetic element, but that's just the fourth 00:14:37.090 --> 00:14:38.390 case in the periodic table. 00:14:38.390 --> 00:14:40.580 So that gets you the last wedge in Trivial Pursuit. 00:14:40.580 --> 00:14:42.960 What are the four pairs of elements 00:14:42.960 --> 00:14:46.460 that are out of sequence? 00:14:46.460 --> 00:14:47.470 OK. 00:14:47.470 --> 00:14:56.630 So now we can say that proton number is the atomic number. 00:14:56.630 --> 00:14:58.200 It's the identity. 00:14:58.200 --> 00:15:01.710 So that comes out of Moseley, comes out of his work. 00:15:01.710 --> 00:15:07.260 The second thing that he did as a result of his study of 38 00:15:07.260 --> 00:15:09.420 elements is he figured out what to do with the 00:15:09.420 --> 00:15:11.160 lanthanides. 00:15:11.160 --> 00:15:12.410 Remember our friends, the lanthanides. 00:15:15.680 --> 00:15:19.650 Place the lanthanides correctly in 00:15:19.650 --> 00:15:20.900 the Periodic Table. 00:15:25.290 --> 00:15:29.240 Many of the lanthanides have a valence 3 so people were 00:15:29.240 --> 00:15:29.840 struggling. 00:15:29.840 --> 00:15:33.600 They were putting them underneath aluminum. 00:15:33.600 --> 00:15:36.590 They didn't know what to do with them. 00:15:36.590 --> 00:15:38.450 He placed the lanthanides correctly in 00:15:38.450 --> 00:15:39.680 the Periodic Table. 00:15:39.680 --> 00:15:41.350 And it's not as though these were brand new. 00:15:41.350 --> 00:15:46.650 Lanthanum itself had been first isolated in 1839, and 00:15:46.650 --> 00:15:48.970 all through the 1800s, they were picking them up and 00:15:48.970 --> 00:15:53.600 finally, lutetium was the last one discovered, 00:15:53.600 --> 00:15:57.390 categorized in 1907. 00:15:57.390 --> 00:15:59.500 But people didn't know what to do with them and remember, 00:15:59.500 --> 00:16:02.360 they were obsessed with atomic mass measurements. 00:16:02.360 --> 00:16:03.300 So I'm going to give you this. 00:16:03.300 --> 00:16:05.190 I'll give you this piece of information. 00:16:05.190 --> 00:16:08.340 There's the atomic mass of lanthanum, and the atomic mass 00:16:08.340 --> 00:16:13.350 of lutetium is 174.97. 00:16:13.350 --> 00:16:14.940 So what? 00:16:14.940 --> 00:16:16.790 I don't know what to do with that information. 00:16:16.790 --> 00:16:18.430 That doesn't help me at all. 00:16:18.430 --> 00:16:21.720 But now comes Moseley and he says, we're not talking about 00:16:21.720 --> 00:16:22.710 atomic mass. 00:16:22.710 --> 00:16:24.450 We're talking about atomic number. 00:16:24.450 --> 00:16:28.460 So now I tell you this atomic number is 57. 00:16:28.460 --> 00:16:30.090 So where do you put it? 00:16:30.090 --> 00:16:33.150 Duh, you put it right next to barium. 00:16:33.150 --> 00:16:34.830 There's no debate. 00:16:34.830 --> 00:16:38.800 And furthermore, this one is 71-- 00:16:38.800 --> 00:16:40.310 atomic number. 00:16:40.310 --> 00:16:43.850 Well, if this is 71 and this is 57, I can 00:16:43.850 --> 00:16:45.210 tell you with impunity-- 00:16:45.210 --> 00:16:47.980 how many lanthanides are there? 00:16:47.980 --> 00:16:50.650 There's 14 of them from here to there. 00:16:50.650 --> 00:16:51.370 OK. 00:16:51.370 --> 00:16:58.390 14 elements, which makes sense because in s we've got one 00:16:58.390 --> 00:17:02.790 orbital, in p we've got three orbitals, and d we've got 5 00:17:02.790 --> 00:17:05.690 orbitals and these are f and there's 7 orbitals. 00:17:05.690 --> 00:17:07.360 7 times 2 is 14. 00:17:07.360 --> 00:17:08.610 Everything makes sense. 00:17:11.980 --> 00:17:17.110 And the last thing that's a corollary to the item two-- 00:17:17.110 --> 00:17:20.470 we were able to give uranium its proper 00:17:20.470 --> 00:17:24.110 atomic number is 92. 00:17:24.110 --> 00:17:27.930 So now I ask you, how many elements are there up to 00:17:27.930 --> 00:17:29.910 uranium starting with hydrogen? 00:17:29.910 --> 00:17:31.090 92. 00:17:31.090 --> 00:17:36.180 All of this comes as the result of Moseley's 00:17:36.180 --> 00:17:36.890 experiments. 00:17:36.890 --> 00:17:39.420 But it's not over yet because he worked for Rutherford, and 00:17:39.420 --> 00:17:42.040 Rutherford pushed his people really hard. 00:17:42.040 --> 00:17:45.160 He wasn't abusive, but he brought out the best in them. 00:17:45.160 --> 00:17:47.130 So who else was in the building? 00:17:47.130 --> 00:17:49.260 Bohr, and what were they doing? 00:17:49.260 --> 00:17:54.000 They were doing theory and so he said, well, that's nice, 00:17:54.000 --> 00:17:56.960 but he says, I want those things fit to an equation. 00:17:56.960 --> 00:17:59.610 So Moseley said, all right. 00:17:59.610 --> 00:18:00.400 I'm going to use-- 00:18:00.400 --> 00:18:03.090 there's already an equation in the building for a new bar. 00:18:03.090 --> 00:18:04.390 It's the Rydberg equation. 00:18:04.390 --> 00:18:07.200 So I'm going to use a Rydberg-like equation. 00:18:07.200 --> 00:18:08.320 So this is what he does. 00:18:08.320 --> 00:18:09.550 This is Moseley's fit. 00:18:09.550 --> 00:18:14.490 He goes the wave number of whatever the line is-- whether 00:18:14.490 --> 00:18:17.550 it's K alpha, L alpha, what have you-- is going to go as 00:18:17.550 --> 00:18:20.790 the product of the Rydberg constant-- 00:18:20.790 --> 00:18:25.760 1/NF squared minus 1/NI squared. 00:18:25.760 --> 00:18:28.700 So far that's just the Rydberg equation. 00:18:28.700 --> 00:18:31.730 But now comes Moseley's contribution. 00:18:31.730 --> 00:18:38.260 We're going to put z squared, but one more piece. 00:18:38.260 --> 00:18:39.970 Notice the way I've drawn those lines. 00:18:39.970 --> 00:18:42.100 They don't go through the origin, do they? 00:18:42.100 --> 00:18:44.830 There's an offset. 00:18:44.830 --> 00:18:47.140 So he said, let's allow for the offset-- 00:18:47.140 --> 00:18:50.120 z minus sigma quantity square. 00:18:50.120 --> 00:18:52.120 And this is known as Moseley's Law. 00:18:58.440 --> 00:19:02.160 And you've got values for sigma. 00:19:02.160 --> 00:19:16.270 sigma for K alpha equals 1 and for L alpha equals 7.4. 00:19:16.270 --> 00:19:17.860 So now I can-- 00:19:17.860 --> 00:19:21.030 with impunity, you give me the wavelength. 00:19:21.030 --> 00:19:23.670 I can get the wave number-- it's 1 over the wavelength and 00:19:23.670 --> 00:19:27.260 I can plug into this equation and identify the element or 00:19:27.260 --> 00:19:31.495 turn it around if I want to get wavelength radiation of, 00:19:31.495 --> 00:19:35.910 say, 1.25 angstroms, I can plug into this equation and 00:19:35.910 --> 00:19:38.640 come up with the z, which will tell me what the target 00:19:38.640 --> 00:19:40.890 element choice should be. 00:19:40.890 --> 00:19:44.020 So let's go and plug this in because we're only going to 00:19:44.020 --> 00:19:45.390 look at these two. 00:19:45.390 --> 00:19:49.390 So we can say that the wave number for K alpha-- 00:19:49.390 --> 00:19:53.780 it's always going to be 1/2 squared minus 1/1 squared, 00:19:53.780 --> 00:19:55.900 which is always going to come up 3/4. 00:19:55.900 --> 00:20:01.600 So it's 3/4 times Rydberg z minus 1 squared. 00:20:01.600 --> 00:20:09.150 So this is for the 2:1 or, if you like, L to K transition 00:20:09.150 --> 00:20:12.670 and then the other one of interest here 00:20:12.670 --> 00:20:15.670 is nu bar of L alpha. 00:20:15.670 --> 00:20:19.060 nu bar of L alpha's going to be 1/3 squared minus 1/2 00:20:19.060 --> 00:20:26.270 squared, which becomes 536 times the Rydberg constant z 00:20:26.270 --> 00:20:31.540 minus 7.4 squared and this is for the transition 3:2 00:20:31.540 --> 00:20:38.100 or KLM, M to L. 00:20:38.100 --> 00:20:39.150 OK. 00:20:39.150 --> 00:20:41.480 So there it is. 00:20:41.480 --> 00:20:44.430 And now, what's the significance of all of this? 00:20:47.720 --> 00:20:51.960 I try to give a physical significance of this sigma, 00:20:51.960 --> 00:20:55.940 which is known as the screening factor. 00:20:55.940 --> 00:21:00.590 We're going to call sigma here the screening factor. 00:21:00.590 --> 00:21:02.840 You'll see why in a second. 00:21:02.840 --> 00:21:04.740 Why are we calling it the screening factor? 00:21:11.620 --> 00:21:15.620 So let's consider what's happening in the case of the K 00:21:15.620 --> 00:21:17.190 alpha lines. 00:21:17.190 --> 00:21:20.010 Let's look at K alpha generation. 00:21:20.010 --> 00:21:22.115 So not to scale. 00:21:25.420 --> 00:21:27.480 Let's draw-- 00:21:27.480 --> 00:21:32.840 here's the nucleus with all of its z positive charges and 00:21:32.840 --> 00:21:37.640 then I'm going to draw the K shell, and its got two 00:21:37.640 --> 00:21:41.480 electrons in it, and I'm going to show there's a hole here. 00:21:41.480 --> 00:21:43.350 Because without this hole, there's no 00:21:43.350 --> 00:21:45.060 reason for the cascade. 00:21:45.060 --> 00:21:49.490 And then I'm going to draw the L shell and it's got-- what? 00:21:49.490 --> 00:21:54.920 There's 2 from the s, 2s, and then 6 from the 2p. 00:21:54.920 --> 00:21:57.860 At most. I know this is a terrible model. 00:21:57.860 --> 00:22:00.820 It violates all kinds of things, but it's as complex as 00:22:00.820 --> 00:22:03.530 it needs to be for the explanation I'm about to give 00:22:03.530 --> 00:22:05.900 and I don't want to load you down with a whole bunch of 00:22:05.900 --> 00:22:07.540 extraneous information. 00:22:07.540 --> 00:22:11.210 So consider the electrons in the L shell. 00:22:11.210 --> 00:22:15.380 They see the electron vacancy in the K shell and they're 00:22:15.380 --> 00:22:16.570 going to fall down. 00:22:16.570 --> 00:22:20.330 What's the Coulombic pull of the nucleus 00:22:20.330 --> 00:22:22.620 on the L shell electrons? 00:22:22.620 --> 00:22:27.110 Can you see that it's not z plus, but at z plus screened 00:22:27.110 --> 00:22:29.200 by 1 minus. 00:22:29.200 --> 00:22:32.900 So the nuclear charge is mediated-- 00:22:32.900 --> 00:22:37.210 in other words, it's reduced by 1 thanks to the presence of 00:22:37.210 --> 00:22:39.360 the one negative charge here. 00:22:39.360 --> 00:22:44.000 So these electrons in L shell feel z less 1 and hence, we 00:22:44.000 --> 00:22:46.850 get z minus 1 as screening factor. 00:22:46.850 --> 00:22:48.180 It's plausible. 00:22:48.180 --> 00:22:50.360 It's at least physically consistent. 00:22:50.360 --> 00:22:51.780 Now let's look at the next one. 00:22:51.780 --> 00:22:55.230 That's the transition from M to L. 00:22:55.230 --> 00:22:55.850 OK. 00:22:55.850 --> 00:22:56.660 So we get to M. 00:22:56.660 --> 00:23:01.270 We've got 18 electrons, up to maximum of 18, and if they're 00:23:01.270 --> 00:23:05.740 going to fall down to n equals 2, there needs to be at least 00:23:05.740 --> 00:23:07.810 one vacancy here. 00:23:07.810 --> 00:23:10.000 So now let's use the same logic. 00:23:10.000 --> 00:23:14.120 So an electron in the m shell sees the positive charge of 00:23:14.120 --> 00:23:19.890 the nucleus mediated by the electrons between the shell n 00:23:19.890 --> 00:23:22.030 equals 3 and the nucleus. 00:23:22.030 --> 00:23:24.210 Now, I don't know how many electrons there are. 00:23:24.210 --> 00:23:27.080 What's the extreme case here? 00:23:27.080 --> 00:23:32.700 Two, four, six, seven, maybe eight, nine. 00:23:32.700 --> 00:23:35.910 Because this would still give me the conditions to generate 00:23:35.910 --> 00:23:37.360 the transition 3 to 2. 00:23:37.360 --> 00:23:38.980 I need a vacancy in two. 00:23:38.980 --> 00:23:41.050 I don't need a vacancy in one. 00:23:41.050 --> 00:23:42.640 So this is the maximum. 00:23:42.640 --> 00:23:45.620 so that would be two, four, six, eight, nine. 00:23:45.620 --> 00:23:49.990 So it could be z minus nine, but that would mean that all 00:23:49.990 --> 00:23:54.080 of these electrons are on the same side and I don't have any 00:23:54.080 --> 00:23:55.000 vacancies lower. 00:23:55.000 --> 00:23:56.620 I only have one vacancy here. 00:23:56.620 --> 00:23:57.265 That's an extreme. 00:23:57.265 --> 00:23:58.880 It's not observed. 00:23:58.880 --> 00:24:02.920 And the other extreme is, we blow away all the electrons. 00:24:02.920 --> 00:24:07.130 So somewhere in between 9 and 0, it turns out it's 7.4. 00:24:07.130 --> 00:24:11.670 I can't predict that it's 7.4, but 7.4 makes sense. 00:24:11.670 --> 00:24:16.490 If the number were greater than 9, I would be distressed. 00:24:16.490 --> 00:24:18.063 So it makes sense, rationalizes. 00:24:20.920 --> 00:24:22.320 OK. 00:24:22.320 --> 00:24:28.570 And by the way, if you use this formula, Moseley's Law-- 00:24:28.570 --> 00:24:30.380 let's bring that back down. 00:24:30.380 --> 00:24:33.520 Remember, I told you I can still wake up in the middle of 00:24:33.520 --> 00:24:37.540 the night and quote you the wavelength of copper K alpha 00:24:37.540 --> 00:24:39.590 radiation of five significant figures. 00:24:39.590 --> 00:24:41.690 I had it drilled into me in my junior year. 00:24:41.690 --> 00:24:46.550 It's 1.5418 angstroms. That's the lambda. 00:24:46.550 --> 00:24:50.660 So you can use this formula for new bar and you know that 00:24:50.660 --> 00:24:54.520 new bar is equal to 1 over lambda. 00:24:54.520 --> 00:24:57.170 So I can use Moseley's Law. 00:24:57.170 --> 00:25:00.030 But true value, lambda-- 00:25:00.030 --> 00:25:00.910 I love this one. 00:25:00.910 --> 00:25:01.340 Watch. 00:25:01.340 --> 00:25:03.360 I'm going to do a triple subscript. 00:25:03.360 --> 00:25:05.790 Lambda of copper K alpha. 00:25:05.790 --> 00:25:06.640 Isn't that cool? 00:25:06.640 --> 00:25:13.880 Lambda of copper K alpha is equal to 1.5418 angstroms. And 00:25:13.880 --> 00:25:19.165 if you use Moseley's law, you get 1.546 and the delta here 00:25:19.165 --> 00:25:20.600 is 1/3 of 1%. 00:25:24.970 --> 00:25:29.800 This man was a positive genius. 00:25:29.800 --> 00:25:34.210 He was heading pell-mell for the Nobel Prize, but 00:25:34.210 --> 00:25:35.530 he never got it. 00:25:35.530 --> 00:25:37.530 Why not? 00:25:37.530 --> 00:25:42.190 World War I broke out in 1914 and Moseley was passionately 00:25:42.190 --> 00:25:44.420 concerned about World War I. 00:25:44.420 --> 00:25:45.460 He wanted to fight. 00:25:45.460 --> 00:25:48.710 He wanted to fight for the Allied cause and he enlisted 00:25:48.710 --> 00:25:49.250 in the Army. 00:25:49.250 --> 00:25:50.990 Rutherford was furious. 00:25:50.990 --> 00:25:55.850 Rutherford called the Minister of War, which is analogous to 00:25:55.850 --> 00:25:58.850 the Secretary of Defense and said, give him a desk job. 00:25:58.850 --> 00:26:03.570 Put him up in Oxford at a military laboratory. 00:26:03.570 --> 00:26:05.400 And Moseley said, no, I refuse. 00:26:05.400 --> 00:26:06.580 I'm going to fight. 00:26:06.580 --> 00:26:08.440 And so he was sent to Gallipoli. 00:26:08.440 --> 00:26:12.040 Gallipoli, as you may know, was one of the bloodiest sites 00:26:12.040 --> 00:26:12.950 of World War I. 00:26:12.950 --> 00:26:16.300 A quarter of a million Allied troops and 1/3 sort of a 00:26:16.300 --> 00:26:20.650 million Turkish troops were killed at Gallipoli. 00:26:20.650 --> 00:26:25.190 Almost 2/3 of a million people died for that 00:26:25.190 --> 00:26:27.080 little piece of land. 00:26:27.080 --> 00:26:32.850 And on August 10th, 1915, at the age of 27, Henry Moseley 00:26:32.850 --> 00:26:37.910 was killed in the battle of Suvla Bay, and they don't give 00:26:37.910 --> 00:26:44.250 Nobel Prizes posthumously, and so that was the way it ended. 00:26:44.250 --> 00:26:48.920 There's a shot of Henry Moseley with one of his books. 00:26:48.920 --> 00:26:51.150 The tributes poured in from all over the world. 00:26:51.150 --> 00:26:53.620 The physics community was devastated because they knew 00:26:53.620 --> 00:26:56.620 all of this stuff. 00:26:56.620 --> 00:27:01.100 This is the one that really, I think, says it best. This was 00:27:01.100 --> 00:27:03.520 written by Robert Milliken, an American. 00:27:03.520 --> 00:27:08.880 He's the one that gave us the elementary charge of the 00:27:08.880 --> 00:27:12.620 electron, from the University of Chicago at the time. 00:27:12.620 --> 00:27:14.780 This is what Milliken wrote-- wrote this to 00:27:14.780 --> 00:27:16.920 Rutherford to read. 00:27:16.920 --> 00:27:19.520 "In a research which is destined to rank as one of the 00:27:19.520 --> 00:27:22.590 dozen most brilliant in conception, skillful in 00:27:22.590 --> 00:27:27.140 execution, and illuminating in results, a young man 26 years 00:27:27.140 --> 00:27:30.410 old threw open the windows through which we can glimpse 00:27:30.410 --> 00:27:35.030 the subatomic world with a definiteness and a certainty 00:27:35.030 --> 00:27:36.880 never dreamed before. 00:27:36.880 --> 00:27:40.750 Had the European War no other result than the snuffing out 00:27:40.750 --> 00:27:43.600 of this young life, that alone would make it one of the most 00:27:43.600 --> 00:27:47.330 hideous and most irreparable crimes in history." That's 00:27:47.330 --> 00:27:49.870 when American scientists knew to write. 00:27:49.870 --> 00:27:51.490 It's beautiful writing. 00:27:51.490 --> 00:27:54.470 What a tribute. 00:27:54.470 --> 00:27:54.850 OK. 00:27:54.850 --> 00:27:56.630 So let's move on. 00:27:56.630 --> 00:27:58.555 Now that we've got Moseley's Law, we've straightened out 00:27:58.555 --> 00:28:00.910 the Periodic Table. 00:28:00.910 --> 00:28:01.750 So we keep moving. 00:28:01.750 --> 00:28:09.280 And I say, well, I gave you the drawing of the spectrum. 00:28:09.280 --> 00:28:10.890 Remember the spectrum? 00:28:10.890 --> 00:28:12.140 The spectrum was here. 00:28:15.710 --> 00:28:16.670 You see it? 00:28:16.670 --> 00:28:18.400 I'll put it up real quick again. 00:28:18.400 --> 00:28:19.650 This was the spectrum. 00:28:22.850 --> 00:28:23.140 OK. 00:28:23.140 --> 00:28:31.350 This is intensity and this is wavelength and this is K alpha 00:28:31.350 --> 00:28:35.800 and this is K beta and this is L alpha and this is L beta. 00:28:35.800 --> 00:28:39.920 These are the data coming from the x-ray tube. 00:28:39.920 --> 00:28:42.030 This happens to be a molybdenum target. 00:28:42.030 --> 00:28:45.970 Well, it doesn't quite look like what I've drawn, does it? 00:28:45.970 --> 00:28:49.340 It looks a little bit like it, but not quite. 00:28:49.340 --> 00:28:51.500 This is definitely there. 00:28:51.500 --> 00:28:54.070 You can see some of these lines so I'm going to call 00:28:54.070 --> 00:28:59.220 this spectrum A and it looks like spectrum A has been added 00:28:59.220 --> 00:29:01.370 on top of something else. 00:29:01.370 --> 00:29:04.440 I'm going to call the something else spectrum B and 00:29:04.440 --> 00:29:05.980 the spectrum B looks like this. 00:29:10.200 --> 00:29:12.100 And in New England-- 00:29:12.100 --> 00:29:14.180 this curve has a shape because it's New England. 00:29:14.180 --> 00:29:17.790 This is called whale-shaped. 00:29:17.790 --> 00:29:20.780 I don't know what they call it in the rest of the country, 00:29:20.780 --> 00:29:22.170 but it even looks like a whale. 00:29:22.170 --> 00:29:24.440 So you can go on a whale watch. 00:29:24.440 --> 00:29:25.990 So it starts-- 00:29:25.990 --> 00:29:29.840 it's a sharp front, goes straight up, hits the maximum 00:29:29.840 --> 00:29:30.810 and then-- are you ready for this? 00:29:30.810 --> 00:29:32.780 It tails off, all right? 00:29:32.780 --> 00:29:36.480 Whales have tails, yes. 00:29:36.480 --> 00:29:38.160 So what's the difference here? 00:29:38.160 --> 00:29:43.820 Well, the spectrum A, we already observed is quantized, 00:29:43.820 --> 00:29:44.790 whereas this one isn't. 00:29:44.790 --> 00:29:47.800 This one's continuous. 00:29:47.800 --> 00:29:53.330 It has continuous values up to this minimum value or, if you 00:29:53.330 --> 00:29:57.320 like, maximum value of energy, minimum value of wavelengths. 00:29:57.320 --> 00:29:59.650 So we got that. 00:29:59.650 --> 00:30:00.650 It's not quantized. 00:30:00.650 --> 00:30:03.830 And the other thing that's interesting is-- 00:30:03.830 --> 00:30:08.250 spectrum A, we said, is a function of the identity of 00:30:08.250 --> 00:30:08.910 the target. 00:30:08.910 --> 00:30:13.030 z of the target, whereas this one, it's a function of the 00:30:13.030 --> 00:30:14.270 plate voltage. 00:30:14.270 --> 00:30:17.080 So you can see in the diagram I've shown you, as the plate 00:30:17.080 --> 00:30:24.730 voltage changes, we get a series of enveloping curves. 00:30:24.730 --> 00:30:28.080 So this is V1 and this is V2-- 00:30:28.080 --> 00:30:29.780 greater than V1. 00:30:29.780 --> 00:30:31.980 So this whale-shaped thing is somehow 00:30:31.980 --> 00:30:33.245 related to plate voltage. 00:30:35.770 --> 00:30:38.770 And then beyond a certain critical value, can you see 00:30:38.770 --> 00:30:43.410 when you're down here at 15 or 20,000 volts, all you got is 00:30:43.410 --> 00:30:44.780 the whale-shaped curve? 00:30:44.780 --> 00:30:48.510 But somewhere between 20 and 25,000 volts, you hit a 00:30:48.510 --> 00:30:53.070 threshold and now you switch on the characteristic lines. 00:30:53.070 --> 00:30:56.170 So with low voltage, you don't get the characteristic lines. 00:30:56.170 --> 00:30:58.260 You only get the whale-shaped curve. 00:30:58.260 --> 00:31:01.320 And then beyond a certain critical value of V, it's as 00:31:01.320 --> 00:31:04.020 though all of a sudden these lines appear. 00:31:04.020 --> 00:31:05.650 Low voltage, no lines. 00:31:05.650 --> 00:31:08.015 High voltage, you get the characteristic lines. 00:31:11.520 --> 00:31:13.960 And what can we do here? 00:31:13.960 --> 00:31:19.840 Well, we can compute K alpha, L alpha by Moseley's Law. 00:31:24.150 --> 00:31:27.000 The continuous spectrum can't do anything with that, with 00:31:27.000 --> 00:31:28.560 one exception-- 00:31:28.560 --> 00:31:29.430 here. 00:31:29.430 --> 00:31:38.460 So let's look inside and figure out what's going on. 00:31:38.460 --> 00:31:42.860 We have a proposal here of what's going on inside that 00:31:42.860 --> 00:31:43.800 target atom. 00:31:43.800 --> 00:31:44.830 So I'm going to make-- 00:31:44.830 --> 00:31:47.460 this could be the molybdenum target up there. 00:31:47.460 --> 00:31:53.760 So these are molybdenum atoms. And just as 00:31:53.760 --> 00:31:55.520 in Moseley's figure-- 00:31:55.520 --> 00:31:56.990 so this is body centered cubic-- 00:31:56.990 --> 00:31:59.030 I can look that up on the Periodic Table. 00:31:59.030 --> 00:32:02.990 I know this is BCC crystal structure, molybdenum atom 00:32:02.990 --> 00:32:03.940 sitting here. 00:32:03.940 --> 00:32:04.950 This is the anode. 00:32:04.950 --> 00:32:08.230 It's charged positive and way up top, I get the cathode. 00:32:08.230 --> 00:32:13.080 So the cathode is shooting off ballistic electrons and they 00:32:13.080 --> 00:32:17.510 go zooming across the gap and crash into anode, but up until 00:32:17.510 --> 00:32:19.800 now, we've just said the anode is some material. 00:32:19.800 --> 00:32:22.580 Now we're going to take one more peel off the onion and 00:32:22.580 --> 00:32:26.020 say that these are discrete atoms. It's not continuous 00:32:26.020 --> 00:32:27.470 molybdenum. 00:32:27.470 --> 00:32:28.530 It's molybdenum atoms. 00:32:28.530 --> 00:32:31.440 And what do we know the molybdenum atom looks like? 00:32:31.440 --> 00:32:35.030 It's got a dense nucleus where all the positive charge 00:32:35.030 --> 00:32:40.460 resides and then there's this almost vacuum-like zone with 00:32:40.460 --> 00:32:41.760 the negative charge. 00:32:41.760 --> 00:32:45.440 So when the electron comes in, this electron sees the 00:32:45.440 --> 00:32:47.560 negative charge around the molybdenum atom. 00:32:47.560 --> 00:32:48.850 What happens? 00:32:48.850 --> 00:32:50.610 It's deflected. 00:32:50.610 --> 00:32:56.360 Maybe it comes in on a closer angle and it's scattered 00:32:56.360 --> 00:32:57.790 through a higher angle. 00:32:57.790 --> 00:33:00.550 Maybe it comes in almost in between and it 00:33:00.550 --> 00:33:02.030 hardly moves at all. 00:33:02.030 --> 00:33:05.740 Now can you see that when you have a charged species that 00:33:05.740 --> 00:33:09.330 changes direction, that's called an acceleration, and an 00:33:09.330 --> 00:33:13.140 acceleration gives rise to an emission of radiation? 00:33:13.140 --> 00:33:17.580 So because the angle of deflection-- 00:33:17.580 --> 00:33:24.660 so this is low-angle deflection, this is high-angle 00:33:24.660 --> 00:33:25.170 deflection. 00:33:25.170 --> 00:33:31.020 So low-angle deflection means low energy emission. 00:33:31.020 --> 00:33:35.590 High angle means high-energy emission, and the result is 00:33:35.590 --> 00:33:40.580 this continue spectrum that I've shown you here. 00:33:40.580 --> 00:33:45.800 So this is the result of low-angle scattering of the 00:33:45.800 --> 00:33:47.130 ballistic electrons. 00:33:47.130 --> 00:33:52.580 This is the result of high-angle scattering of the 00:33:52.580 --> 00:33:55.230 ballistic electrons, and somewhere in the middle here 00:33:55.230 --> 00:33:58.670 is the dominant angle. 00:33:58.670 --> 00:34:01.880 I can't calculate this curve with one exception. 00:34:01.880 --> 00:34:06.150 Imagine the electron comes from the cathode, and with all 00:34:06.150 --> 00:34:11.750 of its energy is dead on and stops, gives up all of its 00:34:11.750 --> 00:34:14.070 kinetic energy to a photon. 00:34:14.070 --> 00:34:17.440 That's the maximum amount of energy possible. 00:34:17.440 --> 00:34:18.590 Let's look at that. 00:34:18.590 --> 00:34:24.420 That's the case where an electron comes in, stops dead 00:34:24.420 --> 00:34:28.930 here and then emits the photon. 00:34:28.930 --> 00:34:31.370 Sp the kinetic energy is translated 00:34:31.370 --> 00:34:34.420 into the photon energy. 00:34:34.420 --> 00:34:36.420 So we can do that one. 00:34:36.420 --> 00:34:38.150 That's a straightforward calculation. 00:34:38.150 --> 00:34:44.280 So the energy of the incident electron-- 00:34:44.280 --> 00:34:49.720 E of the incident electron is equal to product of the charge 00:34:49.720 --> 00:34:51.950 on the electron and the plate voltage. 00:34:51.950 --> 00:34:54.440 Well, the charge on the electron is the elementary 00:34:54.440 --> 00:34:57.300 charge and the plate voltage is whatever it is, and I'm 00:34:57.300 --> 00:35:04.740 going to equate that with the energy of the emitted photon, 00:35:04.740 --> 00:35:08.520 and that's equal to hc over lambda. 00:35:08.520 --> 00:35:12.730 So now I can cross multiply and I can call this the lambda 00:35:12.730 --> 00:35:16.250 of the shortest wavelength. 00:35:16.250 --> 00:35:19.120 That's the shortest wavelength on the whale-shaped curve. 00:35:19.120 --> 00:35:22.100 So by algebra, you're going to get the product of the plane 00:35:22.100 --> 00:35:24.550 constant times the speed of light divided by the 00:35:24.550 --> 00:35:27.930 elementary charge times the plate voltage, which turns out 00:35:27.930 --> 00:35:33.140 to be 12,400 divided by plate voltage where the wavelength's 00:35:33.140 --> 00:35:36.470 given in angstroms. 00:35:36.470 --> 00:35:37.130 Just try it. 00:35:37.130 --> 00:35:40.520 If you put 10,000 volts, you're going to get 1.24 00:35:40.520 --> 00:35:44.460 angstroms, which is smack dab in the middle of the x-region 00:35:44.460 --> 00:35:49.930 of the spectrum, and this is called the Duane-Hunt Law. 00:35:49.930 --> 00:35:54.343 That's the only thing we can compute in 00:35:54.343 --> 00:35:57.020 the continuous spectrum. 00:35:57.020 --> 00:35:58.060 So I can get this one. 00:35:58.060 --> 00:36:02.030 Lambda shortest wavelength, because shortest wavelength is 00:36:02.030 --> 00:36:05.380 maximum energy. 00:36:05.380 --> 00:36:11.660 Now there's a fancier name for this whale-shaped curve, and 00:36:11.660 --> 00:36:14.300 it's the scientific community's term, and it's a 00:36:14.300 --> 00:36:15.010 German word. 00:36:15.010 --> 00:36:16.260 It's called bremsstrahlung. 00:36:21.070 --> 00:36:22.320 I love it. 00:36:24.360 --> 00:36:25.750 You need to know this. 00:36:25.750 --> 00:36:29.350 You can impress your friends at parties. 00:36:29.350 --> 00:36:31.060 What does bremsstrahlung mean? 00:36:31.060 --> 00:36:35.650 Brems is the German word for brake, as when you put on the 00:36:35.650 --> 00:36:37.180 brakes of a car. 00:36:37.180 --> 00:36:42.230 And strahl, strahl is the word for ray. 00:36:42.230 --> 00:36:44.910 And ung is like ing. 00:36:44.910 --> 00:36:47.950 So this is raying radiation and this is the 00:36:47.950 --> 00:36:50.250 radiation of braking. 00:36:50.250 --> 00:36:53.080 So the electrons are coming in and when they come up against 00:36:53.080 --> 00:36:57.450 the negative charge of the outer shell the target atom, 00:36:57.450 --> 00:36:59.820 they are slamming on the brakes and skidding 00:36:59.820 --> 00:37:00.330 everywhere. 00:37:00.330 --> 00:37:04.020 So this is what bremsstrahlung means: braking radiation. 00:37:07.940 --> 00:37:08.620 So we're going to call-- 00:37:08.620 --> 00:37:10.840 I'm going to put a B here-- 00:37:10.840 --> 00:37:11.340 see that? 00:37:11.340 --> 00:37:12.170 I was thinking ahead. 00:37:12.170 --> 00:37:13.420 B is bremsstrahlung. 00:37:15.910 --> 00:37:16.620 OK. 00:37:16.620 --> 00:37:20.900 So we've got a lot going here. for us. 00:37:20.900 --> 00:37:23.020 I think we've explained a fair bit. 00:37:23.020 --> 00:37:25.700 Now I want to talk about modern x-ray tubes. 00:37:25.700 --> 00:37:29.030 What do modern x-ray tubes have that these primitive ones 00:37:29.030 --> 00:37:33.900 that Moseley worked with and Roentgen 00:37:33.900 --> 00:37:36.480 worked with didn't have? 00:37:36.480 --> 00:37:40.300 So I want to show you that the modern x-ray tube is the 00:37:40.300 --> 00:37:44.890 result of improvements made by an MIT alum. 00:37:44.890 --> 00:37:53.880 His name was William Coolidge, and he's the class of '96-- 00:37:53.880 --> 00:37:59.490 1896. 00:37:59.490 --> 00:38:04.260 And he made a number of improvements. 00:38:04.260 --> 00:38:07.680 He actually taught for awhile then eventually spent a good 00:38:07.680 --> 00:38:09.940 part of his professional career working as a research 00:38:09.940 --> 00:38:13.030 scientist at the General Electric Labs out in 00:38:13.030 --> 00:38:13.850 Schenectady. 00:38:13.850 --> 00:38:17.470 If you go down to the lobby of Building 6, on the south side 00:38:17.470 --> 00:38:19.910 of the lobby, there's a showcase. 00:38:19.910 --> 00:38:21.130 Look inside the showcase. 00:38:21.130 --> 00:38:27.780 You'll see there's a little display in honor of Coolidge. 00:38:27.780 --> 00:38:29.630 So what's the first thing Coolidge did? 00:38:29.630 --> 00:38:31.640 He was an engineer so he was thinking about making things 00:38:31.640 --> 00:38:32.250 more efficient. 00:38:32.250 --> 00:38:35.270 First thing he did is he turned the discharge tube into 00:38:35.270 --> 00:38:38.010 a vacuum tube. 00:38:38.010 --> 00:38:40.090 Remember, Roentgen worked at low pressure, but there was 00:38:40.090 --> 00:38:42.910 still gas, and he was blinded by the light and so on. 00:38:42.910 --> 00:38:45.730 This means you don't get any visible light, and secondly, 00:38:45.730 --> 00:38:50.650 it's more efficient because if you've got the tube like this 00:38:50.650 --> 00:38:53.510 with the two electrodes, the feedthroughs and you've got 00:38:53.510 --> 00:38:56.190 gas inside, some of the electrons are crashing into 00:38:56.190 --> 00:38:58.310 the gas molecules, and we don't care 00:38:58.310 --> 00:38:59.290 about the gas molecules. 00:38:59.290 --> 00:39:03.130 We want to get the electrons crashing into the target. 00:39:03.130 --> 00:39:05.575 So by going to vacuum, this improves the efficiency. 00:39:09.590 --> 00:39:13.485 No glow in the visible and higher energy efficiency. 00:39:18.770 --> 00:39:22.930 More x-rays out per unit power put in. 00:39:22.930 --> 00:39:24.410 What's the second thing he did? 00:39:24.410 --> 00:39:26.887 Second think he did was hot cathode. 00:39:30.590 --> 00:39:32.610 Remember, you're trying to rip the electrons out of the 00:39:32.610 --> 00:39:34.690 cathode and send them on their journey. 00:39:34.690 --> 00:39:37.670 So Coolidge reasoned that if you heated the cathode, you'd 00:39:37.670 --> 00:39:41.110 weaken the bonds, and the electrons would come off. 00:39:41.110 --> 00:39:44.780 They'd boil off much more readily, OK? 00:39:44.780 --> 00:39:54.630 Raise temperature to reduce bond energy, to reduce binding 00:39:54.630 --> 00:39:58.284 energy of the electrons. 00:39:58.284 --> 00:40:04.450 The electrons in the cathode makes them easier to boil off. 00:40:04.450 --> 00:40:06.200 Think I've got a cartoon of that. 00:40:06.200 --> 00:40:07.310 Yeah, here it is. 00:40:07.310 --> 00:40:09.490 So here's the tube lying on its side. 00:40:09.490 --> 00:40:11.300 So the cathode is over here to the left. 00:40:11.300 --> 00:40:12.120 It's negative. 00:40:12.120 --> 00:40:13.430 Here's the anode to the right. 00:40:13.430 --> 00:40:16.770 That's this purple thing here and the electrons are moving 00:40:16.770 --> 00:40:18.590 from left to right and so he's got-- 00:40:18.590 --> 00:40:21.090 see, you can have multiple electrical signals going 00:40:21.090 --> 00:40:23.070 through the same conductor. 00:40:23.070 --> 00:40:23.750 It's not the same. 00:40:23.750 --> 00:40:25.860 You can't have an AC waveform and a DC 00:40:25.860 --> 00:40:27.410 waveform in the same conductor. 00:40:27.410 --> 00:40:30.950 So you've got a big DC voltage between the cathode and the 00:40:30.950 --> 00:40:34.440 anode and you'd got a separate little circuit going through 00:40:34.440 --> 00:40:37.990 the cathode, running almost like a toaster to 00:40:37.990 --> 00:40:39.790 make it super hot. 00:40:39.790 --> 00:40:43.860 So the potential between here and here is 35,000 volts. 00:40:43.860 --> 00:40:46.860 The potential along this stretch of real estate might 00:40:46.860 --> 00:40:49.250 be several hundred volts, and furthermore, this 00:40:49.250 --> 00:40:52.200 could be an AC signal. 00:40:52.200 --> 00:40:52.720 It's Coolidge. 00:40:52.720 --> 00:40:53.940 He was smart. 00:40:53.940 --> 00:40:57.530 So this makes this hot and now for per given voltage, you get 00:40:57.530 --> 00:41:00.610 much more yield of the electrons. 00:41:00.610 --> 00:41:01.810 So that was pretty good. 00:41:01.810 --> 00:41:03.610 I like that. 00:41:03.610 --> 00:41:05.210 Smart. 00:41:05.210 --> 00:41:10.160 Third thing he did was he heated the cathode and he 00:41:10.160 --> 00:41:11.720 cooled the anode. 00:41:11.720 --> 00:41:12.970 Water-cooled anode. 00:41:18.190 --> 00:41:18.675 Why? 00:41:18.675 --> 00:41:20.280 You got to dissipate the heat. 00:41:20.280 --> 00:41:22.830 All these electrons crashing into the anode. 00:41:22.830 --> 00:41:25.250 You raise the temperature of that anode so high you'll melt 00:41:25.250 --> 00:41:29.010 it and so they had to run the tubes intermittently. 00:41:29.010 --> 00:41:31.480 They just get a decent signal. 00:41:31.480 --> 00:41:33.400 You have to take these x-ray measurements over a long 00:41:33.400 --> 00:41:35.510 period of time because the amount of x-rays you get is 00:41:35.510 --> 00:41:37.680 small, but you have to keep shutting the thing down. 00:41:37.680 --> 00:41:39.260 Otherwise, you melt through the anode. 00:41:39.260 --> 00:41:42.840 So he put that on a water-cooled copper hearth and 00:41:42.840 --> 00:41:44.990 was able to run continuous. 00:41:44.990 --> 00:41:46.240 Continuous operation. 00:41:50.400 --> 00:41:51.650 No more pulse current. 00:41:51.650 --> 00:41:53.870 But sometimes when nature hands you a 00:41:53.870 --> 00:41:55.450 lemon, you make lemonade. 00:41:55.450 --> 00:41:56.730 So I'm going to turn this thing around. 00:41:56.730 --> 00:41:57.790 I'll say, hey, wait a minute. 00:41:57.790 --> 00:42:00.070 I don't want any water-cooled copper anode. 00:42:00.070 --> 00:42:02.300 Suppose I want to weld some titanium. 00:42:02.300 --> 00:42:06.240 Titanium melts at 1675 degrees Centigrade and it's got a 00:42:06.240 --> 00:42:08.190 voracious appetite for oxygen. 00:42:08.190 --> 00:42:10.270 Well, this thing's a vacuum tube. 00:42:10.270 --> 00:42:12.950 So what if I were to take my part and I put the two pieces 00:42:12.950 --> 00:42:16.940 of titanium in the path of an electron beam and I don't cool 00:42:16.940 --> 00:42:17.710 the titanium? 00:42:17.710 --> 00:42:20.320 Eventually, I get the temperature so high that I can 00:42:20.320 --> 00:42:22.010 weld titanium. 00:42:22.010 --> 00:42:25.060 This is the birth of electron beam welding. 00:42:25.060 --> 00:42:27.130 And that's how you weld refracting metals. 00:42:27.130 --> 00:42:30.260 You get one of those titanium bicycle frames 00:42:30.260 --> 00:42:32.210 that cost about $4,000. 00:42:32.210 --> 00:42:34.030 It might be tungsten inert gas. 00:42:34.030 --> 00:42:36.910 It might be electron beam, depending. 00:42:36.910 --> 00:42:39.430 So that's the flip side of the technology. 00:42:39.430 --> 00:42:44.830 By the way, if you were in attendance observing 00:42:44.830 --> 00:42:47.450 electronic beam welding, what do you think is being 00:42:47.450 --> 00:42:51.460 generated in the electron beam welding apparatus? 00:42:51.460 --> 00:42:56.320 X-rays, by the boatload 00:42:56.320 --> 00:42:59.240 So there's a fourth thing-- maybe the most important thing 00:42:59.240 --> 00:43:01.660 that Coolidge came up with-- shielding. 00:43:01.660 --> 00:43:03.050 You see the yellow here? 00:43:03.050 --> 00:43:04.350 That's lead shielding. 00:43:14.840 --> 00:43:18.200 Why did he choose lead? 00:43:18.200 --> 00:43:24.620 Well, it's got a very high z. 00:43:24.620 --> 00:43:26.900 That means it's got many energy levels. 00:43:31.820 --> 00:43:35.300 So that if you start looking at the energy level diagram of 00:43:35.300 --> 00:43:41.640 lead, you've got lots of action up in here. 00:43:41.640 --> 00:43:42.930 So what can happen? 00:43:42.930 --> 00:43:50.470 When the x-rays come with their high energy, the x-rays 00:43:50.470 --> 00:43:54.720 from the tube on their way out to get you, and everybody 00:43:54.720 --> 00:43:57.160 standing observing this marvel. 00:43:57.160 --> 00:43:59.950 They excite electrons inside. 00:43:59.950 --> 00:44:02.970 So these x-rays are absorbed. 00:44:02.970 --> 00:44:07.410 The electrons inside the lead rise, cascade down and now 00:44:07.410 --> 00:44:08.380 they come out. 00:44:08.380 --> 00:44:10.240 And what's the difference in energy between 00:44:10.240 --> 00:44:12.590 the x-ray and these? 00:44:12.590 --> 00:44:16.250 The ones up here are much lower energy. 00:44:16.250 --> 00:44:18.870 So this is, if you like, a frequency shifter 00:44:18.870 --> 00:44:20.260 or an energy shifter. 00:44:20.260 --> 00:44:23.220 So now we're using photons to excite 00:44:23.220 --> 00:44:25.650 electrons to generate photons. 00:44:25.650 --> 00:44:30.000 And that's how the shielding works. 00:44:30.000 --> 00:44:32.570 So you want to absorb and re-emit. 00:44:38.720 --> 00:44:41.690 And while we're on the topic, he gave us lead shielding and 00:44:41.690 --> 00:44:44.030 he gave us beryllium windows because they were using 00:44:44.030 --> 00:44:47.690 silicate glass, just as you use in your home, but the 00:44:47.690 --> 00:44:50.930 silicate glass was absorbing some of the x-rays. 00:44:50.930 --> 00:44:53.440 So to get higher efficiency, he chose beryllium. 00:44:53.440 --> 00:44:54.820 Why did he choose beryllium? 00:44:54.820 --> 00:44:58.350 Well, it's got a low z. 00:44:58.350 --> 00:45:01.840 So that means it has few energy levels. 00:45:06.640 --> 00:45:10.880 So therefore, there's less absorption and re-emission-- 00:45:10.880 --> 00:45:12.130 again, higher efficiency. 00:45:18.050 --> 00:45:20.400 I think this was taken from one of the other readings. 00:45:20.400 --> 00:45:21.700 So they flipped it around. 00:45:21.700 --> 00:45:26.250 See, here you can see the cathode here, the anode. 00:45:26.250 --> 00:45:28.390 That's one of these things. 00:45:28.390 --> 00:45:28.720 All right. 00:45:28.720 --> 00:45:29.820 So the window is up here. 00:45:29.820 --> 00:45:33.860 You don't use lithium because lithium is unstable in the air 00:45:33.860 --> 00:45:38.950 unless you had a giant room of humidity set at a dew point of 00:45:38.950 --> 00:45:40.560 minus 38 degrees, see, and then you can 00:45:40.560 --> 00:45:42.090 use a lithium window. 00:45:42.090 --> 00:45:44.580 Otherwise, you use beryllium and lead down here. 00:45:44.580 --> 00:45:45.600 Why'd he choose lead? 00:45:45.600 --> 00:45:48.690 Well, you're pretty much at the bottom of the naturally 00:45:48.690 --> 00:45:50.390 occurring elements in the Periodic Table. 00:45:50.390 --> 00:45:52.340 So it's the cheapest of all of these heavies. 00:45:54.940 --> 00:45:55.410 All right. 00:45:55.410 --> 00:45:58.240 So now let's take a few minutes and talk about the use 00:45:58.240 --> 00:46:02.820 of x-rays in characterizing art. 00:46:02.820 --> 00:46:06.570 So this painting here at once time was arguably one of the 00:46:06.570 --> 00:46:08.950 most recognizable paintings in the western world. 00:46:08.950 --> 00:46:11.270 It's The Angelus by Jean-Francois Millet. 00:46:11.270 --> 00:46:16.430 It was painted at 1857 to 1859 on commission for an insurance 00:46:16.430 --> 00:46:18.870 company here in Boston. 00:46:18.870 --> 00:46:24.490 The Boston Brahmins loved BA's paintings of rural life in 00:46:24.490 --> 00:46:26.800 19th century France. 00:46:26.800 --> 00:46:31.680 And this is couple of peasants who are giving thanks to God. 00:46:31.680 --> 00:46:35.160 The Angelus is a prayer, and they're thanking God for this 00:46:35.160 --> 00:46:38.790 pitiful bounty of potatoes evident. 00:46:38.790 --> 00:46:42.300 Salvador Dali, as an art student, was required to paint 00:46:42.300 --> 00:46:43.600 this as part of training. 00:46:43.600 --> 00:46:47.340 You know how when you learn to play the piano, you reproduce 00:46:47.340 --> 00:46:48.660 the works of the Grand Masters. 00:46:48.660 --> 00:46:50.390 So when you go to art school, you have to paint. 00:46:50.390 --> 00:46:53.170 He hated this painting. 00:46:53.170 --> 00:46:55.460 For many years, it was here in Boston, and then it was 00:46:55.460 --> 00:46:59.160 repatriated around World War I, it hung in the Louvre, and 00:46:59.160 --> 00:47:01.305 then ultimately, now it's in the Musee d'Orsay. 00:47:01.305 --> 00:47:04.880 In 1963 when Dali was at the peak of his career, he asked 00:47:04.880 --> 00:47:07.060 the curator of the Louvre if she would have 00:47:07.060 --> 00:47:08.460 this painting x-rayed. 00:47:08.460 --> 00:47:10.160 He said this painting spooks him. 00:47:10.160 --> 00:47:12.480 He doesn't like this painting. 00:47:12.480 --> 00:47:13.820 And they x-rayed the painting. 00:47:13.820 --> 00:47:14.600 What did they find? 00:47:14.600 --> 00:47:17.640 They found that it had been painted over down here. 00:47:17.640 --> 00:47:21.870 Wasn't an art forgery, Millet himself had painted it over. 00:47:21.870 --> 00:47:24.630 You may have heard two years ago there was this art find. 00:47:24.630 --> 00:47:26.560 It was a van Gogh painting. 00:47:26.560 --> 00:47:28.930 They found that van Gogh had painted over one of his own 00:47:28.930 --> 00:47:31.770 paintings that had never been seen before even though the 00:47:31.770 --> 00:47:34.370 pencil sketches survived, so they assumed that maybe the 00:47:34.370 --> 00:47:36.290 painting was destroyed in World War II 00:47:36.290 --> 00:47:37.160 or some such thing. 00:47:37.160 --> 00:47:41.070 It turns out that van Gogh was so poor at one point that he 00:47:41.070 --> 00:47:44.580 valued the canvas over the art, and he took his previous 00:47:44.580 --> 00:47:46.570 painting, and he painted over it. 00:47:46.570 --> 00:47:46.830 OK. 00:47:46.830 --> 00:47:48.140 So this was going on here. 00:47:48.140 --> 00:47:49.420 This is the truth. 00:47:49.420 --> 00:47:51.620 Now my speculation begins. 00:47:51.620 --> 00:47:56.800 So what was underneath here initially? 00:47:56.800 --> 00:48:01.230 It was the casket of a baby. 00:48:01.230 --> 00:48:02.290 Look at the pose. 00:48:02.290 --> 00:48:05.140 These people don't look like they're happy with their 00:48:05.140 --> 00:48:08.620 bounty of harvest. They're grieving. 00:48:08.620 --> 00:48:11.200 This was this futility of peasant life. 00:48:11.200 --> 00:48:14.530 It was a hard life and they lost their baby. 00:48:14.530 --> 00:48:18.000 So imagine Millet paints this, puts it on a boat, it comes 00:48:18.000 --> 00:48:21.820 over to Boston, they unveil it, and the directors of the 00:48:21.820 --> 00:48:25.090 insurance company go, we can't hang this in the lobby of an 00:48:25.090 --> 00:48:28.010 insurance company. 00:48:28.010 --> 00:48:29.550 That's my speculation. 00:48:29.550 --> 00:48:31.990 It didn't take him three years to paint this thing. 00:48:31.990 --> 00:48:33.920 I think it spent most of its time on the boat. 00:48:33.920 --> 00:48:35.680 They sent it back and said fix it. 00:48:35.680 --> 00:48:38.080 So he put the basket of potatoes. 00:48:38.080 --> 00:48:39.200 That's my theory. 00:48:39.200 --> 00:48:40.490 All right, look at the pose. 00:48:40.490 --> 00:48:43.990 This is from the Galleria Borghese in Rome. 00:48:43.990 --> 00:48:46.810 I was there about two years ago and saw this and went, 00:48:46.810 --> 00:48:48.010 wow, referential. 00:48:48.010 --> 00:48:51.460 You see, everything's been said. 00:48:51.460 --> 00:48:52.720 All of art has been said. 00:48:52.720 --> 00:48:55.940 Now we're just recasting it. 00:48:55.940 --> 00:48:57.560 So now here's Dali's revenge. 00:48:57.560 --> 00:49:00.160 Now this is what he paints. 00:49:00.160 --> 00:49:02.090 You see the man is shorter than the woman. 00:49:02.090 --> 00:49:05.070 His hat is down a little bit below the waistline. 00:49:05.070 --> 00:49:07.540 There's all sorts of psychosexual things going on 00:49:07.540 --> 00:49:09.020 here, but we're running out of time. 00:49:09.020 --> 00:49:13.790 So here's Dali and his father and his dad is saying, see, 00:49:13.790 --> 00:49:15.360 this is life, et cetera, et cetera. 00:49:15.360 --> 00:49:17.120 So you can see the reference. 00:49:17.120 --> 00:49:20.810 See, man taller here, woman taller, et cetera, et cetera. 00:49:20.810 --> 00:49:21.640 Have you seen this one? 00:49:21.640 --> 00:49:24.000 The Hallucinogenic Toreador. 00:49:24.000 --> 00:49:27.690 OK, he went outside one day in Manhattan to buy some pencils. 00:49:27.690 --> 00:49:30.870 There was a company called the Venus Pencil Company, you see. 00:49:30.870 --> 00:49:33.220 And so he came back and made this trompe l'oeil. 00:49:33.220 --> 00:49:34.360 So this is the toreador. 00:49:34.360 --> 00:49:38.900 Do you see the breast here is the nose? 00:49:38.900 --> 00:49:40.390 There is the face. 00:49:40.390 --> 00:49:42.940 There are the flies of the Thames and here is 00:49:42.940 --> 00:49:44.545 the cape and so on. 00:49:48.960 --> 00:49:51.860 Symmetry plane-- all of those Venuses facing back, these 00:49:51.860 --> 00:49:54.690 Venuses facing forward. 00:49:54.690 --> 00:49:55.830 There's the bull. 00:49:55.830 --> 00:49:58.910 The life force of the bull is a crystal. 00:49:58.910 --> 00:50:00.970 What is the crystal structure? 00:50:00.970 --> 00:50:03.560 It's one of the 14 Bravais lattices. 00:50:03.560 --> 00:50:07.230 If you ignore color, it's simple cubic, isn't it? 00:50:07.230 --> 00:50:09.080 And if you don't believe me, check. 00:50:09.080 --> 00:50:11.310 And if you don't appreciate it, study. 00:50:11.310 --> 00:50:14.360 Here's the symmetry plane. 00:50:14.360 --> 00:50:17.770 Atoms, atoms, fly, fly et cetera, et cetera. 00:50:17.770 --> 00:50:18.630 What else do we have here? 00:50:18.630 --> 00:50:22.900 Oh, this is the one he painted on the occasion of the 00:50:22.900 --> 00:50:24.610 revelation of the structure of DNA. 00:50:24.610 --> 00:50:25.990 It's hard to see, but over here is the 00:50:25.990 --> 00:50:28.230 double helix of DNA. 00:50:28.230 --> 00:50:35.770 This is his wife Gaia and here are people standing in cubic 00:50:35.770 --> 00:50:37.600 arrays with guns pointing at each other. 00:50:37.600 --> 00:50:40.540 And the point that he's making is that now that we've 00:50:40.540 --> 00:50:47.420 discovered the instruction set for reproduction of life, not 00:50:47.420 --> 00:50:51.160 just human life, but life, we are still at a point where we 00:50:51.160 --> 00:50:52.770 can't resist killing each other. 00:50:52.770 --> 00:50:56.820 So this was the point and he chose to use cubic arrays, and 00:50:56.820 --> 00:50:59.090 I would venture to say this is simple cubic. 00:50:59.090 --> 00:51:02.060 If you put a fifth person here, it would be-- are you 00:51:02.060 --> 00:51:02.570 ready for this? 00:51:02.570 --> 00:51:03.820 Body-centered cubic. 00:51:07.320 --> 00:51:08.750 Oh, yes! 00:51:08.750 --> 00:51:11.260 And there's more, but I think we're running out of time so I 00:51:11.260 --> 00:51:14.610 think at this point we will dismiss the class.