1 00:00:03,250 --> 00:00:06,990 Hello everyone welcome back, I am Charles Clark we'll continue now by completing 2 00:00:06,990 --> 00:00:11,740 our discussion with Bohr model and looking at some of its applications. 3 00:00:15,810 --> 00:00:20,835 Let me remind you again that there is some original literature available on the 4 00:00:20,835 --> 00:00:24,520 subject we'll discuss today in case you have, want to have a deeper 5 00:00:24,520 --> 00:00:29,050 understanding. And the two relevant things are the, 6 00:00:29,050 --> 00:00:33,240 accounts for the discovery of deuterium that are found in the usual location. 7 00:00:35,880 --> 00:00:41,015 So, to recall where we left off Bohr by quantizing the angular momentum of a 8 00:00:41,015 --> 00:00:46,624 circular orbit in the hydrogen atom found a series of discreet energy levels with 9 00:00:46,624 --> 00:00:54,543 energies given by this formula. Most conveniently in my opinion, 10 00:00:54,543 --> 00:00:58,140 expressed in terms of the redbird constant. 11 00:00:59,540 --> 00:01:03,480 And so now what does this imply for the interaction of atoms with light? 12 00:01:03,480 --> 00:01:09,778 Well the the photon is absorbed or emitted in a transitions between n1 and 13 00:01:09,778 --> 00:01:16,076 n2 so if this is, if this is energy in this direction then transition from n1 to 14 00:01:16,076 --> 00:01:22,844 n2 corresponds to abortion of the photon, a transition from n2 to n1 corresponds to 15 00:01:22,844 --> 00:01:31,640 emission. In any event the frequency of, of the 16 00:01:31,640 --> 00:01:37,460 photon is just, we take a convenient passive definition. 17 00:01:37,460 --> 00:01:44,138 the energy difference is h nu, which is hc over lambda, and now you see why 18 00:01:44,138 --> 00:01:54,173 there's this expression HC in the the, the ex, expression for the energy. 19 00:01:54,173 --> 00:02:00,683 Because we can now go in and substitute the energies for the wavelength and we 20 00:02:00,683 --> 00:02:08,696 get this convenient expression. So the inverse of the wavelength is just 21 00:02:08,696 --> 00:02:14,806 the Rydberg constant times the the difference in in the inverse squares of 22 00:02:14,806 --> 00:02:22,700 the principle quantum members. I think I made that notation clear. 23 00:02:22,700 --> 00:02:34,573 N is called the principle quantum number. Principal with an a I guess, quantum 24 00:02:34,573 --> 00:02:41,765 number. That's a notation that still used in in 25 00:02:41,765 --> 00:02:46,467 modern wave mechanics. And this is an, this is an expression 26 00:02:46,467 --> 00:02:51,075 that's good for that's valid for when the nuclear masses is infidently large 27 00:02:51,075 --> 00:02:57,903 compared to the electronic mass. if one wants more detailed description, 28 00:02:57,903 --> 00:03:03,346 more accurate description then one must use the reduced mass. 29 00:03:04,660 --> 00:03:09,682 And then the result for a finite mass is just again the infinite Ryd, has the 30 00:03:09,682 --> 00:03:16,090 infinite Rydberg constants modified by the ratio of mu over m. 31 00:03:19,599 --> 00:03:24,099 So in the turns in which we describe things, it turns out at the, There's a 32 00:03:24,099 --> 00:03:30,083 Balmer series which corresponds to the value of n1 equal to 2. 33 00:03:30,083 --> 00:03:34,201 there's something else we'll come across in a minute, the Lyman series, which has 34 00:03:34,201 --> 00:03:38,815 n1 equal to 1. But in this case the the low, the Balmer 35 00:03:38,815 --> 00:03:44,376 series that we see in the visible is associated with transitions that all 36 00:03:44,376 --> 00:03:51,812 terminate or originate on n1 equal to 2. So here are the first, we can see the 37 00:03:51,812 --> 00:03:56,232 first 4 members of that series, n equal 3, so the Balmer alpha, 4 Balmer beta and 38 00:03:56,232 --> 00:04:01,326 so on, 5 and 6. Now there are an infinite number of other 39 00:04:01,326 --> 00:04:06,304 terms, other lines in this series. We believe but you don't see them here, 40 00:04:06,304 --> 00:04:09,698 because they're not perceptible to the eye. 41 00:04:09,698 --> 00:04:15,160 They lie, the, the, they lie in the ultraviolet region of the spectrum. 42 00:04:18,170 --> 00:04:22,010 When Bohr published his paper, it produced something quite remarkable. 43 00:04:22,010 --> 00:04:27,428 It was the first sort of rational and quantitative theory that actually 44 00:04:27,428 --> 00:04:33,620 predicted accurately the existence of known spectral lines. 45 00:04:33,620 --> 00:04:38,657 So in particular all known members of the Balmer series for which n1 is equal to 2 46 00:04:38,657 --> 00:04:44,132 and lie in visible. And the Paschen series which are lie in 47 00:04:44,132 --> 00:04:52,070 the infrared were described to within the experimental uncertainties. 48 00:04:52,070 --> 00:04:56,490 Furthermore, there was something called the Pickering series which was a series 49 00:04:56,490 --> 00:05:00,414 of lines in helium plus. That's a hydrogen-like system like the 50 00:05:00,414 --> 00:05:03,895 one that we've been talking about during these past few lectures. 51 00:05:03,895 --> 00:05:10,720 so this I think, particularly significant in that the Bohr theory applies not just 52 00:05:10,720 --> 00:05:16,726 to hydrogen, but to another chemical element, admittedly still a one electron 53 00:05:16,726 --> 00:05:22,828 one. But then, what really set the pace was 54 00:05:22,828 --> 00:05:28,925 the discovery in the following year by Theodore Lyman of Harvard University of a 55 00:05:28,925 --> 00:05:35,386 new lines that on the far ultraviolet spectrum of the hydrogen atom, there to, 56 00:05:35,386 --> 00:05:45,700 around 100, the longest wavelength one is around 121 nanometers. 57 00:05:45,700 --> 00:05:51,289 these are the, these are the, the series associated with the ground state of 58 00:05:51,289 --> 00:05:56,684 hydrogen. So again those are found to be exactly 59 00:05:56,684 --> 00:06:05,190 where Bohr's theory replace them, then there was a spell of two years. 60 00:06:05,190 --> 00:06:11,745 At Johns-Hopkins university in which Fredrick Brackett found the, the series 61 00:06:11,745 --> 00:06:16,370 with n1 equal to 4. Which is the next one after Paschen. 62 00:06:16,370 --> 00:06:23,918 And then his PHD thesis supervisor August Pfund reported a series with the 63 00:06:23,918 --> 00:06:32,250 principal quantum number five. So you can impress your physicist friends 64 00:06:32,250 --> 00:06:38,270 if you memorize the sequence Lyman Balmer, Paschen, Brackett, Pfund. 65 00:06:39,440 --> 00:06:47,237 Most of them won't get it and somewhat later the next series for n 1 equals to 6 66 00:06:47,237 --> 00:06:53,042 is observed. This is the last series exactly named for 67 00:06:53,042 --> 00:06:57,200 anyone because by this time 1953, there was no doubt that under the right 68 00:06:57,200 --> 00:07:01,547 conditions you would be able to get more highly excited states of hydrogen that 69 00:07:01,547 --> 00:07:07,872 had been seen here to form. We'll see a moment of that, an example of 70 00:07:07,872 --> 00:07:12,384 that in the next slide. But this was a what do you call it, 71 00:07:12,384 --> 00:07:18,124 technical triumph, because these the transitions between these states lie off 72 00:07:18,124 --> 00:07:23,603 in the far infrared region of the spectrum. 73 00:07:23,603 --> 00:07:29,179 And so getting some standard wavelengths in, in a region like that is a very 74 00:07:29,179 --> 00:07:35,538 useful thing, indeed. Now here we have what I think is just an 75 00:07:35,538 --> 00:07:42,162 amazing example of the existence of these very highly excited quantized states of 76 00:07:42,162 --> 00:07:47,946 atoms. This is a paper by a team from, Ukraine 77 00:07:47,946 --> 00:07:53,926 and India published in the monthly notices of the royal astronomical society 78 00:07:53,926 --> 00:07:59,457 in 2007. And this spectrum that are, that are 79 00:07:59,457 --> 00:08:05,502 dealt with you see here that are they are, these are absorption lines in the 80 00:08:05,502 --> 00:08:13,340 radio band, in a radio frequency, of around 26 megahertz. 81 00:08:13,340 --> 00:08:19,346 And these absorption lines are associated with transitions of the type delta n 82 00:08:19,346 --> 00:08:30,556 equal plus 1 in principle quantum number. So there's something like transitions n 83 00:08:30,556 --> 00:08:39,944 equal 1,009, going to n equal 1,010. these, so where, where do, where do atoms 84 00:08:39,944 --> 00:08:44,432 in the interstellar medium get these extraordinary, large principle quantum 85 00:08:44,432 --> 00:08:49,534 numbers? Do recall that the, the radius of an 86 00:08:49,534 --> 00:08:55,192 atomic state in the Bohr model increases as the square of the principle quantum 87 00:08:55,192 --> 00:09:00,440 number. So these atoms are a million times larger 88 00:09:00,440 --> 00:09:03,990 than the ordinary atoms, which were familiar. 89 00:09:03,990 --> 00:09:07,608 You could, you could, you could, see them with your eye, if they were solid, which 90 00:09:07,608 --> 00:09:13,062 of course they're not. And the way that they're produced is that 91 00:09:13,062 --> 00:09:18,444 there are electrons in the interstellar medium that are cap slow electrons are 92 00:09:18,444 --> 00:09:23,952 captured into these very highly excited states. 93 00:09:23,952 --> 00:09:29,100 And then those states this is sufficient number of them you can see this regular 94 00:09:29,100 --> 00:09:34,887 series of absorption lines. So now we see that the again there given 95 00:09:34,887 --> 00:09:40,283 by the board transition frequencies so we see this Bohr like behavior starting in 96 00:09:40,283 --> 00:09:45,603 the far ultraviolet with the, the Lyman alpha transition going up into the radio 97 00:09:45,603 --> 00:09:52,014 wave region. So there's eight decades of frequency 98 00:09:52,014 --> 00:09:56,478 over which this theory renders very useful predictions. 99 00:09:56,478 --> 00:10:02,244 Now we're going to look at one of the most important applications ever made of 100 00:10:02,244 --> 00:10:07,812 Bohr's theory. In fact it was a, perhaps the only case 101 00:10:07,812 --> 00:10:13,206 in which a new isotope of an element was discovered by the use of atomic 102 00:10:13,206 --> 00:10:20,180 spectroscopy. Now back in the early part of the 20th 103 00:10:20,180 --> 00:10:26,105 century it was discovered that a number of the chemical elements had constituents 104 00:10:26,105 --> 00:10:32,950 that seemed to be chemically similar but had different masses. 105 00:10:32,950 --> 00:10:37,610 So one of the first was neon which was found by J.J. 106 00:10:37,610 --> 00:10:43,004 Thompson to have 2 isotopes, one of a mass number 20 and the other was mass of 107 00:10:43,004 --> 00:10:47,864 22. Now these mass numbers are, their mass is 108 00:10:47,864 --> 00:10:53,658 in the units of the protons mass. And so we know today where that the 109 00:10:53,658 --> 00:11:01,020 origin of, of these different masses but at the time, it was a mystery. 110 00:11:01,020 --> 00:11:05,308 And most of these discoveries were made by the use of mass spectrometry where 111 00:11:05,308 --> 00:11:09,931 you'd put a, a charged particle through a combination of electric magnetic fields 112 00:11:09,931 --> 00:11:14,420 and then you'd get a a trajectory that dependent upon the charge to mass ratio 113 00:11:14,420 --> 00:11:21,341 so you could separate out the the different isotopes. 114 00:11:24,310 --> 00:11:27,730 Today we understand the origin of the isotopes and the, well, the easy to 115 00:11:27,730 --> 00:11:31,720 explain way there's the proton, which is the carry of charge in the atom, and then 116 00:11:31,720 --> 00:11:35,368 we know of the, the neutron which is a neutral particle that's almost exactly 117 00:11:35,368 --> 00:11:42,275 the same mass as the proton. In some senses it's considered to be a, a 118 00:11:42,275 --> 00:11:46,260 partner of the proton in a two level quantum system. 119 00:11:46,260 --> 00:11:52,240 Maybe we'll talk about that a bit in the lectures on symmetries. 120 00:11:52,240 --> 00:11:56,400 But the story that we're going to discuss now starts in 1931, a time in which the 121 00:11:56,400 --> 00:12:03,443 neutron had not yet been discovered. And most people in those days thought 122 00:12:03,443 --> 00:12:08,755 that isotopes were due to having different numbers of protons of the same 123 00:12:08,755 --> 00:12:16,500 element and then a and then something called nuclear electrons. 124 00:12:16,500 --> 00:12:21,380 So the idea which is first stated by Rutherford. 125 00:12:21,380 --> 00:12:28,928 Was that for some reason what we, what we think of now as helium 4, for example, 4 126 00:12:28,928 --> 00:12:38,180 helium which is equal to, we would say 2 protons and 2 neutrons. 127 00:12:41,190 --> 00:12:58,013 Rutherford would say 4 protons plus 2 nuclear electrons. 128 00:13:00,110 --> 00:13:03,685 But once again, the underlying, there wasn't a good understanding of what the 129 00:13:03,685 --> 00:13:07,480 so-called nuclear electrons were or why they would be bound inside the nucleus 130 00:13:07,480 --> 00:13:11,970 versus the, the electrons in the Bohr, the Bohr model. 131 00:13:13,720 --> 00:13:19,013 now here is a picture of a little road map that was constructed by a man name 132 00:13:19,013 --> 00:13:24,701 Harold Urey, Harold Clayton Urey then a Junior Professor at Columbia University, 133 00:13:24,701 --> 00:13:30,495 in New York. And it shows a map, this is a chart in 134 00:13:30,495 --> 00:13:35,565 terms of this proton and nuclear electron schematic that shows the, the solid 135 00:13:35,565 --> 00:13:40,902 circles here. some which are labeled, are known 136 00:13:40,902 --> 00:13:43,771 isotopes. And you see there is this tendency 137 00:13:43,771 --> 00:13:49,082 downward. and then there are some empty circles 138 00:13:49,082 --> 00:13:59,880 that suggest places where there might be isotopes that have not yet been observed. 139 00:13:59,880 --> 00:14:05,505 And the, the target, principal target of Urey's investigation was hydrogen 2 the, 140 00:14:05,505 --> 00:14:10,905 the, the hydrogen isotope of mass 2 as it was called today we call that Deuterium 141 00:14:10,905 --> 00:14:18,633 or the nucleus we call the Deuteron. there were clues from Chemical from 142 00:14:18,633 --> 00:14:24,410 atomic weights analysis that a heavy isotope of hydrogen might exist. 143 00:14:26,020 --> 00:14:31,268 But it couldn't be seen in mass spectrometry because when, when hydrogen 144 00:14:31,268 --> 00:14:38,661 gas is ionized, there's always a large quantity of the molecular ion h2 plus. 145 00:14:38,661 --> 00:14:44,073 And that has the essential the same chart to mass ratio as an isotope of mass 2 146 00:14:44,073 --> 00:14:48,588 graph. Here we have the idea that it might be 147 00:14:48,588 --> 00:14:53,590 possible to see the heavy isotopes of hydrogen in the optical spectrum of 148 00:14:53,590 --> 00:15:01,920 hydrogen that we've been looking at for a little while during these lectures. 149 00:15:01,920 --> 00:15:09,580 And here is how he presents the idea in his Nobel lecture. 150 00:15:09,580 --> 00:15:15,660 He was awarded the Nobel prize in 1934, for this discovery of heavy hydrogen, 151 00:15:15,660 --> 00:15:22,975 which was published on January 1st 1932 in the physical review. 152 00:15:22,975 --> 00:15:28,840 Here he says Bohr's theory, given some 20 years ago, permits the calculation of the 153 00:15:28,840 --> 00:15:34,620 Balmer spectrum of the heavier, heavier isotopes of hydrogen from this spectrum 154 00:15:34,620 --> 00:15:44,160 of hydrogen by the well known theoretical formula for the Rydberg constant. 155 00:15:44,160 --> 00:15:49,704 So I'd just like to note that Urey was the first American, or one of the two 156 00:15:49,704 --> 00:15:56,550 first Americans to co-author a book on wave mechanics. 157 00:15:56,550 --> 00:16:01,198 And he knew very well that Bohr's theory was obsolete in the light of 158 00:16:01,198 --> 00:16:07,225 Schrodinger's equation. Nevertheless, he choose to present his 159 00:16:07,225 --> 00:16:11,580 motivation and justification for the way the experiment was done in terms of the 160 00:16:11,580 --> 00:16:15,870 Bohr model. That shows the, the influence and respect 161 00:16:15,870 --> 00:16:22,576 that it, had. Now, we're going to have a little 162 00:16:22,576 --> 00:16:31,316 in-video quiz here, which I'm, I'm not asking you to repeat Urey's calculations. 163 00:16:31,316 --> 00:16:38,106 But I've set up, discussion of where the isotope shift, what effects give rise to 164 00:16:38,106 --> 00:16:44,799 the isotope shift, and you are invited to answer some well, sort of qualitative 165 00:16:44,799 --> 00:16:51,340 questions. So I hope that most of you were able to 166 00:16:51,340 --> 00:16:56,440 develop the feeling that it's the heavier isotope. 167 00:16:57,460 --> 00:17:03,463 to which the electron is more tightly bound and therefore the wavelength of the 168 00:17:03,463 --> 00:17:08,665 transition is lower for the heavier isotope. 169 00:17:08,665 --> 00:17:14,581 you know by a small amount and its the, the deviation the wavelength is just 170 00:17:14,581 --> 00:17:21,970 linear int he ratio of the lectern mass to the mass of the isotope. 171 00:17:24,740 --> 00:17:29,574 How was Urey idea implemented? His concept was to get the, a 172 00:17:29,574 --> 00:17:38,660 concentrated form of the heavy hydrogen, heavy isotope hydrogen, if any existed. 173 00:17:38,660 --> 00:17:43,106 By taking just regular molecular hydrogen, liquefying it at low 174 00:17:43,106 --> 00:17:50,210 temperatures and then evaporating the, the liquid off by by heating. 175 00:17:50,210 --> 00:17:57,728 presumably in this process the heavier isotope will be less likely to evaporate. 176 00:17:57,728 --> 00:18:04,856 Volatile. And so the liquid that's left in the in, 177 00:18:04,856 --> 00:18:13,280 in the residue might be concentrated in any heavier isotope. 178 00:18:13,280 --> 00:18:18,320 So he sought out colleague a man whom he'd known as a young professor at Johns 179 00:18:18,320 --> 00:18:24,424 Hopkins University, Ferdinand Brickwedde. Brickwedde was the head of the low 180 00:18:24,424 --> 00:18:29,244 temperature physics laboratory at the National Bureau of Standards. 181 00:18:29,244 --> 00:18:33,212 And earlier in the year 1931 he was, he led a team that was the first American 182 00:18:33,212 --> 00:18:39,690 effort to produce liquid helium. So he was he had a very well equipped 183 00:18:39,690 --> 00:18:44,240 laboratory. Able to to, to take large quantities of 184 00:18:44,240 --> 00:18:49,784 liquid hydrogen. So he evidently started with about five 185 00:18:49,784 --> 00:18:56,613 to six liter of liquid nit- hydrogen. And boiled away all but 2 cubic 186 00:18:56,613 --> 00:19:01,460 centimeters of it. So very heavily evaporated. 187 00:19:01,460 --> 00:19:05,000 And it was sent up to Columbia University where it was looked at in Urey's 188 00:19:05,000 --> 00:19:14,079 spectrometer. Here is the original data from, a second 189 00:19:14,079 --> 00:19:20,990 paper by Ur-, by Urey, and, Brickwedde and Murphy. 190 00:19:20,990 --> 00:19:27,400 Published in Physical Review in 1932. And this shows, this shows the photo 191 00:19:27,400 --> 00:19:33,458 emission spectrum. which is, I mean, it's, it's, the 192 00:19:33,458 --> 00:19:39,039 notation here is h1 beta. This is the Balmer beta line, this is, 193 00:19:39,039 --> 00:19:43,380 this, this line here. And this central peak. 194 00:19:43,380 --> 00:19:47,640 You see, what's going on here, is these are, this is photographic film. 195 00:19:47,640 --> 00:19:51,480 It's strongly saturated by the strong central line. 196 00:19:51,480 --> 00:19:56,355 And then according to the predictions we see the fee, the predicted value, 197 00:19:56,355 --> 00:20:02,657 predicted wavelength of an isotope of mass two is shown here h2 beta. 198 00:20:02,657 --> 00:20:07,319 And what you are seeing here are three different samples of distillate with 199 00:20:07,319 --> 00:20:11,981 increasing constant, increasing concentration of any heavy isotope that 200 00:20:11,981 --> 00:20:17,610 might be in there based on the degree of distillation. 201 00:20:17,610 --> 00:20:22,307 And so this shows conclusively that there's a line that grows with the 202 00:20:22,307 --> 00:20:28,630 expected increase in concentration of the mass two isotope. 203 00:20:28,630 --> 00:20:33,730 Now, as you can see there are many other features in this spectrum. 204 00:20:33,730 --> 00:20:37,374 Some are called ghosts. Maybe you've heard of ghosts. 205 00:20:37,374 --> 00:20:41,700 people in those days believe in ghosts, we still do in spectroscopy. 206 00:20:41,700 --> 00:20:48,190 And and then there are other, other things going on. 207 00:20:48,190 --> 00:20:54,770 These are dealt with in the paper they're artifacts of of spectrosity. 208 00:20:54,770 --> 00:21:01,267 so note that there's, there's no apparent no apparent feature associated with a 209 00:21:01,267 --> 00:21:10,236 mass three isotope even though there is. We know there is a, mass 3 isotope called 210 00:21:10,236 --> 00:21:15,985 Tritium which is radioactive. It has a half life of about 12 years, if 211 00:21:15,985 --> 00:21:19,794 I recall correctly. It's not present in any great abundance 212 00:21:19,794 --> 00:21:24,635 in the earth's atmosphere. But nevertheless, there are a sufficient 213 00:21:24,635 --> 00:21:29,189 number of artifacts In this spectrum that it was really essential for the use of 214 00:21:29,189 --> 00:21:35,590 this distillate to show that they increase with concentration. 215 00:21:35,590 --> 00:21:40,840 But it also suggests that maybe deuterium isn't such a big deal after all. 216 00:21:40,840 --> 00:21:44,104 I mean it's, it's seems to be you know very I think the natural abundance of 217 00:21:44,104 --> 00:21:47,750 deuterium is about a part in 10 to the 4th. 218 00:21:47,750 --> 00:21:56,009 So you might ask well why bother? Why should such a little bump be such a 219 00:21:56,009 --> 00:21:59,878 big deal?. Well it turned out to be a huge deal, and 220 00:21:59,878 --> 00:22:03,014 you can read more about this in the literature in the supplemental materials 221 00:22:03,014 --> 00:22:10,079 section. it became a, it became a big deal, not 222 00:22:10,079 --> 00:22:16,174 because of the, that little bump that was seen in the spectrum. 223 00:22:16,174 --> 00:22:21,569 But because that once people knew that the heavy isotope of hydrogen existed, 224 00:22:21,569 --> 00:22:26,632 there were very clever ideas that were developed to figure out how, how to 225 00:22:26,632 --> 00:22:34,620 acquire it more easily than by boiling off all this liquid hydrogen. 226 00:22:34,620 --> 00:22:38,820 And the the breakthrough was made and this was something done jointly by Urey 227 00:22:38,820 --> 00:22:42,720 and Edward Wight Washburn, who was the chief chemist of the National Bureau of 228 00:22:42,720 --> 00:22:49,210 Standards at the time, Together they developed a means for 229 00:22:49,210 --> 00:22:53,181 producing deuterium efficiently by electrolysis. 230 00:22:53,181 --> 00:22:56,839 So you know, this striking thing that on Thanksgiving Day which is when the 231 00:22:56,839 --> 00:23:00,674 experiments were done in New York City, Thanksgiving Day of 1931, making Urey 232 00:23:00,674 --> 00:23:08,350 late for his Thanksgiving dinner. You know, up to that moment no one had 233 00:23:08,350 --> 00:23:11,885 any evidence for this, this mass two isotope at all. 234 00:23:11,885 --> 00:23:17,960 But just a few months later there was a method that was developed by Washburn and 235 00:23:17,960 --> 00:23:23,427 Urey to produce it efficiently by electroloysis. 236 00:23:23,427 --> 00:23:28,152 And this was rapidly taken up on an industrial basis by Norsk Hydro, the main 237 00:23:28,152 --> 00:23:33,520 electricity generating company in, in Norway. 238 00:23:33,520 --> 00:23:40,488 And by 1935 so really just three years later they were shipping 99% pure heavy 239 00:23:40,488 --> 00:23:48,576 water at a price of 50 cents, 50 American cents per gram. 240 00:23:48,576 --> 00:23:53,679 And there was a wide demand for this for a, a large number of uses in chemistry 241 00:23:53,679 --> 00:23:59,184 and biology. Well furthermore, it turns out that the 242 00:23:59,184 --> 00:24:05,388 only suitable moderators for a nuclear chain reaction are deuterium and ultra 243 00:24:05,388 --> 00:24:12,973 pure graphite. And there was a Nazi nuclear power 244 00:24:12,973 --> 00:24:18,700 project that was started during the second World War. 245 00:24:18,700 --> 00:24:24,670 And they made the decision to go with with Deuterium. 246 00:24:24,670 --> 00:24:30,328 So the Nazis had invaded Norway in 1940, they took over this, the heavy water 247 00:24:30,328 --> 00:24:36,642 plant to use the the Deuterium to develop nuclear power perhaps even a nuclear 248 00:24:36,642 --> 00:24:42,822 weapon. And well, I don't have time for this, but 249 00:24:42,822 --> 00:24:46,852 there's a very striking set of events involving great individual heroism and 250 00:24:46,852 --> 00:24:52,750 sacrifice that are told in a book and the movie The Heroes of Telemark. 251 00:24:52,750 --> 00:24:57,374 They're dealt with to some extent in the, the the supplementary material with 252 00:24:57,374 --> 00:25:01,890 [INAUDIBLE]. Okay, well that's it for the Bohr model. 253 00:25:01,890 --> 00:25:05,580 I hope you found it entertaining and interesting and learned something. 254 00:25:05,580 --> 00:25:09,240 And in the next lecture we'll start on the use of wave mechanics to discuss 255 00:25:09,240 --> 00:25:11,670 simple material systems.