WEBVTT 00:00:00.000 --> 00:00:00.496 align:middle line:90% [SQUEAKING] 00:00:00.496 --> 00:00:00.996 align:middle line:90% [RUSTLING] 00:00:00.996 --> 00:00:04.960 align:middle line:90% [CLICKING] 00:00:04.960 --> 00:00:11.430 align:middle line:90% 00:00:11.430 --> 00:00:13.380 align:middle line:84% DAVID KAISER: So for today, we're 00:00:13.380 --> 00:00:18.810 align:middle line:84% going to continue this story, or this unit, 00:00:18.810 --> 00:00:23.100 align:middle line:84% of what we began thinking about together last time, 00:00:23.100 --> 00:00:26.490 align:middle line:84% a body of work, a set of ideas that 00:00:26.490 --> 00:00:30.100 align:middle line:84% came to be grouped together under this title old quantum 00:00:30.100 --> 00:00:30.600 align:middle line:90% theory. 00:00:30.600 --> 00:00:32.225 align:middle line:84% And as I mentioned last time, that only 00:00:32.225 --> 00:00:34.200 align:middle line:84% makes sense once there's a new quantum theory 00:00:34.200 --> 00:00:35.670 align:middle line:90% to contrast it with. 00:00:35.670 --> 00:00:38.250 align:middle line:84% So this is a term not only made up 00:00:38.250 --> 00:00:40.710 align:middle line:84% many, many years after the fact, this was introduced even 00:00:40.710 --> 00:00:43.740 align:middle line:84% by many leading physicists right around the years 00:00:43.740 --> 00:00:44.760 align:middle line:90% that we're describing. 00:00:44.760 --> 00:00:48.090 align:middle line:84% So by the later years of the 1920s, 00:00:48.090 --> 00:00:51.810 align:middle line:84% it already had become common to make this kind of marker 00:00:51.810 --> 00:00:56.640 align:middle line:84% to distinguish between the scattershot developments that 00:00:56.640 --> 00:01:01.650 align:middle line:84% had been unfolding between roughly 1900, and 1924 or '25, 00:01:01.650 --> 00:01:05.459 align:middle line:84% or so, and to bracket those together under this umbrella 00:01:05.459 --> 00:01:07.140 align:middle line:90% term, old quantum theory. 00:01:07.140 --> 00:01:10.200 align:middle line:84% Because as we'll see, starting actually in the next class, 00:01:10.200 --> 00:01:17.140 align:middle line:84% by the mid 1920s, there had been some new bodies of work 00:01:17.140 --> 00:01:19.120 align:middle line:84% put forward that look like this could really 00:01:19.120 --> 00:01:21.640 align:middle line:84% become the new quantum mechanics and not 00:01:21.640 --> 00:01:25.330 align:middle line:84% only a kind of hodgepodge of suggestive ideas 00:01:25.330 --> 00:01:28.040 align:middle line:84% within what then became known as old quantum theory. 00:01:28.040 --> 00:01:30.970 align:middle line:84% So as last time, I just want to remind you these dates 00:01:30.970 --> 00:01:34.810 align:middle line:84% that I include here are convenient and limited. 00:01:34.810 --> 00:01:38.470 align:middle line:84% So as we've seen throughout the entire term so far-- 00:01:38.470 --> 00:01:41.560 align:middle line:84% we'll keep seeing examples of this well beyond even 00:01:41.560 --> 00:01:42.910 align:middle line:90% our quantum theory unit-- 00:01:42.910 --> 00:01:44.710 align:middle line:84% the dates that we assign to these things 00:01:44.710 --> 00:01:47.470 align:middle line:84% have to be taken with some grains of salt. 00:01:47.470 --> 00:01:49.210 align:middle line:90% We have to squint at them a bit. 00:01:49.210 --> 00:01:52.600 align:middle line:84% They're helpful by giving us a rough sense of the flow 00:01:52.600 --> 00:01:56.140 align:middle line:84% and where within this evolving body of work 00:01:56.140 --> 00:01:58.030 align:middle line:84% do these particular developments fit in. 00:01:58.030 --> 00:02:00.130 align:middle line:84% But remember that it's not like someone 00:02:00.130 --> 00:02:02.050 align:middle line:84% conducted a single experiment or published 00:02:02.050 --> 00:02:04.450 align:middle line:90% a single paper with a date. 00:02:04.450 --> 00:02:06.800 align:middle line:84% And then afterwards, everyone agreed and moved on. 00:02:06.800 --> 00:02:10.090 align:middle line:84% And again, we'll find that to be true for these examples today. 00:02:10.090 --> 00:02:14.080 align:middle line:84% We've certainly see it true in previous discussions. 00:02:14.080 --> 00:02:15.880 align:middle line:84% So with those caveats, today, we're 00:02:15.880 --> 00:02:20.050 align:middle line:84% going to look at this more purplish rectangle 00:02:20.050 --> 00:02:22.150 align:middle line:84% to contrast it with this reddish pinkish one. 00:02:22.150 --> 00:02:25.720 align:middle line:84% So last time, we looked at some of these moments of physicists 00:02:25.720 --> 00:02:31.450 align:middle line:84% sometimes very begrudgingly rethinking the nature of light, 00:02:31.450 --> 00:02:33.910 align:middle line:84% not always going into it with that as their plan, 00:02:33.910 --> 00:02:38.023 align:middle line:84% but coming out having rethought how physicists 00:02:38.023 --> 00:02:38.940 align:middle line:90% should describe light. 00:02:38.940 --> 00:02:41.530 align:middle line:84% And we saw instances of more and more attention 00:02:41.530 --> 00:02:44.260 align:middle line:90% to quantization, discreteness. 00:02:44.260 --> 00:02:47.290 align:middle line:84% Maybe light even had a kind of specific particulate 00:02:47.290 --> 00:02:49.420 align:middle line:90% or particle-like behavior. 00:02:49.420 --> 00:02:51.730 align:middle line:84% And today, we're going to look at a kind of inverse 00:02:51.730 --> 00:02:55.210 align:middle line:84% or the other half of those discussions, 00:02:55.210 --> 00:02:58.720 align:middle line:84% as physicists began rethinking the nature of matter. 00:02:58.720 --> 00:03:01.580 align:middle line:84% Again, not always going into that with that in mind, 00:03:01.580 --> 00:03:04.210 align:middle line:84% but that's how these developments really 00:03:04.210 --> 00:03:05.630 align:middle line:90% began to add up. 00:03:05.630 --> 00:03:08.080 align:middle line:84% So today, we'll look at this second half, the mirror 00:03:08.080 --> 00:03:12.670 align:middle line:84% half of the old quantum theory, rethinking matter. 00:03:12.670 --> 00:03:17.410 align:middle line:84% So by the closing years of the 19th century, 00:03:17.410 --> 00:03:19.900 align:middle line:84% really in the last say two or most 00:03:19.900 --> 00:03:23.420 align:middle line:84% three decades of the 19th century, 00:03:23.420 --> 00:03:26.200 align:middle line:84% there really seemed to be a coalescence, a pretty amazing 00:03:26.200 --> 00:03:30.100 align:middle line:84% achievement among physicists and chemists 00:03:30.100 --> 00:03:32.110 align:middle line:84% in many, many parts of the world. 00:03:32.110 --> 00:03:34.480 align:middle line:84% It looked like physicists and chemists, 00:03:34.480 --> 00:03:37.090 align:middle line:84% natural scientists more broadly, had figured out 00:03:37.090 --> 00:03:41.290 align:middle line:84% a really deep regularity to the stuff of which the world is 00:03:41.290 --> 00:03:42.880 align:middle line:90% made. 00:03:42.880 --> 00:03:45.700 align:middle line:84% Here's an illustration of one of the very first published 00:03:45.700 --> 00:03:48.568 align:middle line:84% versions of Dmitri Mendeleev's periodic table. 00:03:48.568 --> 00:03:50.860 align:middle line:84% It doesn't look quite the way we would expect it today. 00:03:50.860 --> 00:03:55.120 align:middle line:84% It's actually oriented in the opposite orientation 00:03:55.120 --> 00:03:56.300 align:middle line:90% than what we're used to. 00:03:56.300 --> 00:03:59.260 align:middle line:84% But this was a remarkable effort at ordering, 00:03:59.260 --> 00:04:02.890 align:middle line:84% ordering the stuff from which all other things seemed 00:04:02.890 --> 00:04:04.960 align:middle line:90% to be made. 00:04:04.960 --> 00:04:09.130 align:middle line:84% And on the strength of work like Mendeleev's and many others, 00:04:09.130 --> 00:04:12.040 align:middle line:84% by the late 19th century, it seemed clear 00:04:12.040 --> 00:04:14.810 align:middle line:84% that matter consisted of chemical elements that 00:04:14.810 --> 00:04:17.910 align:middle line:84% would behave certain ways in chemical reactions. 00:04:17.910 --> 00:04:22.010 align:middle line:84% And a given chemical element-- hydrogen, beryllium, iron, 00:04:22.010 --> 00:04:23.030 align:middle line:90% uranium-- 00:04:23.030 --> 00:04:25.000 align:middle line:90% consisted of physical atoms. 00:04:25.000 --> 00:04:27.830 align:middle line:84% So there was a two-part way of trying 00:04:27.830 --> 00:04:29.930 align:middle line:90% to make sense of the world. 00:04:29.930 --> 00:04:32.060 align:middle line:84% And that seemed really great until suddenly 00:04:32.060 --> 00:04:34.520 align:middle line:84% more complications began to really crowd in. 00:04:34.520 --> 00:04:37.790 align:middle line:84% So not too long after this really amazing, 00:04:37.790 --> 00:04:39.950 align:middle line:84% synthetic achievement to bring together 00:04:39.950 --> 00:04:42.260 align:middle line:84% lots and lots of disparate phenomena 00:04:42.260 --> 00:04:44.600 align:middle line:84% in things like the periodic table 00:04:44.600 --> 00:04:46.910 align:middle line:84% and this association between chemical elements 00:04:46.910 --> 00:04:50.180 align:middle line:84% and physical atoms, pretty soon, there were some new challenges 00:04:50.180 --> 00:04:55.430 align:middle line:84% to that whole scheme, starting really in the mid 1890s 00:04:55.430 --> 00:04:56.990 align:middle line:84% and moving sometimes very quickly. 00:04:56.990 --> 00:04:59.000 align:middle line:84% This caught a lot of people by surprise. 00:04:59.000 --> 00:05:03.170 align:middle line:84% Some of this was accelerated by new types of instruments. 00:05:03.170 --> 00:05:04.850 align:middle line:84% There were whole new kinds of ways 00:05:04.850 --> 00:05:08.360 align:middle line:84% of trying to probe the behavior of matter and radiation-- cloud 00:05:08.360 --> 00:05:11.390 align:middle line:84% chambers, fluorescent screens that would glow 00:05:11.390 --> 00:05:14.120 align:middle line:84% and they interacted with certain matter or energy, 00:05:14.120 --> 00:05:15.560 align:middle line:90% photographic techniques. 00:05:15.560 --> 00:05:17.360 align:middle line:84% Remember, photography of any kind 00:05:17.360 --> 00:05:20.090 align:middle line:84% was still pretty new in the middle decades 00:05:20.090 --> 00:05:21.510 align:middle line:90% of the 19th century. 00:05:21.510 --> 00:05:24.260 align:middle line:84% So trying to make reliable, repeatable use 00:05:24.260 --> 00:05:26.750 align:middle line:84% of photographic plates, that was still pretty new, even 00:05:26.750 --> 00:05:28.580 align:middle line:90% by the 1880s and '90s. 00:05:28.580 --> 00:05:32.790 align:middle line:84% So through this constellation of new techniques, 00:05:32.790 --> 00:05:37.170 align:middle line:84% some accidental incidents in various laboratories, 00:05:37.170 --> 00:05:41.310 align:middle line:84% unexpected, researchers in many parts of the world, 00:05:41.310 --> 00:05:44.130 align:middle line:84% in the 1890s in particular, began 00:05:44.130 --> 00:05:47.340 align:middle line:84% to identify several different kinds of radiations 00:05:47.340 --> 00:05:50.520 align:middle line:84% or emanations, some kind of energy that 00:05:50.520 --> 00:05:52.860 align:middle line:84% could be flowing out of what had once seemed 00:05:52.860 --> 00:05:56.400 align:middle line:90% like stable, boring matter. 00:05:56.400 --> 00:05:58.410 align:middle line:84% And so there are a couple of these points 00:05:58.410 --> 00:06:01.530 align:middle line:84% along the way that became worldwide sensations 00:06:01.530 --> 00:06:02.640 align:middle line:90% in real time. 00:06:02.640 --> 00:06:05.380 align:middle line:84% Not only do we look back and say, oh, that was exciting. 00:06:05.380 --> 00:06:09.630 align:middle line:84% But even at the time, this became literally headline news 00:06:09.630 --> 00:06:11.460 align:middle line:84% in many, many parts of the world-- 00:06:11.460 --> 00:06:13.840 align:middle line:84% I mean, throughout multiple continents. 00:06:13.840 --> 00:06:16.950 align:middle line:84% And so we can again attach names and dates to them, 00:06:16.950 --> 00:06:20.530 align:middle line:84% but understanding these were extended activities. 00:06:20.530 --> 00:06:23.460 align:middle line:84% One of those had to do with what became known as radioactivity 00:06:23.460 --> 00:06:25.920 align:middle line:84% and though there were many people involved in this, very 00:06:25.920 --> 00:06:28.260 align:middle line:84% quickly among the most prominent, 00:06:28.260 --> 00:06:31.730 align:middle line:84% the most famous researchers on this area 00:06:31.730 --> 00:06:35.420 align:middle line:84% included Pierre and Marie Curie, shown here. 00:06:35.420 --> 00:06:38.630 align:middle line:84% Marie Curie, originally Marie Sklodowska, 00:06:38.630 --> 00:06:40.730 align:middle line:84% a young student from Poland, she'd 00:06:40.730 --> 00:06:42.200 align:middle line:90% made her way to study in Paris. 00:06:42.200 --> 00:06:44.180 align:middle line:84% She met Pierre, who was quite a bit older. 00:06:44.180 --> 00:06:45.440 align:middle line:90% They got married. 00:06:45.440 --> 00:06:46.110 align:middle line:90% They teamed up. 00:06:46.110 --> 00:06:48.800 align:middle line:84% They became a remarkable research team, 00:06:48.800 --> 00:06:53.270 align:middle line:84% investigating some of these radiations or radioactive 00:06:53.270 --> 00:06:55.670 align:middle line:84% behaviors of a range of elements-- in fact, 00:06:55.670 --> 00:07:00.140 align:middle line:84% identifying whole new forms of matter and radiation 00:07:00.140 --> 00:07:01.100 align:middle line:90% interaction. 00:07:01.100 --> 00:07:05.810 align:middle line:84% Right around that time, roughly a year later, there 00:07:05.810 --> 00:07:07.790 align:middle line:84% was a distinct set of developments coming, 00:07:07.790 --> 00:07:10.520 align:middle line:84% in this case, out of Cambridge University, 00:07:10.520 --> 00:07:12.890 align:middle line:84% associated with JJ Thompson, who is shown here. 00:07:12.890 --> 00:07:15.313 align:middle line:84% He was experimenting with different kinds of stuff, 00:07:15.313 --> 00:07:17.480 align:middle line:84% and different instruments, and different techniques. 00:07:17.480 --> 00:07:20.630 align:middle line:84% He began identifying what became known as cathode rays. 00:07:20.630 --> 00:07:23.892 align:middle line:84% We would now call those electrons, a different sort 00:07:23.892 --> 00:07:26.180 align:middle line:84% of energetic beam that could come out 00:07:26.180 --> 00:07:28.700 align:middle line:84% of one form of matter and cause effects 00:07:28.700 --> 00:07:30.210 align:middle line:90% on other forms of matter. 00:07:30.210 --> 00:07:34.440 align:middle line:84% So all these activities, which were often quite surprising 00:07:34.440 --> 00:07:37.230 align:middle line:84% when first identified, they suggested 00:07:37.230 --> 00:07:39.570 align:middle line:84% that atoms could fall apart and that they 00:07:39.570 --> 00:07:40.798 align:middle line:90% have internal structure. 00:07:40.798 --> 00:07:42.840 align:middle line:84% And this was a big deal because, as you may know, 00:07:42.840 --> 00:07:46.350 align:middle line:84% the word atom itself was derived from an ancient Greek word that 00:07:46.350 --> 00:07:48.720 align:middle line:84% means indivisible or unbreakable. 00:07:48.720 --> 00:07:53.400 align:middle line:84% And so all this effort from Lavoisier through Mendeleev 00:07:53.400 --> 00:07:56.610 align:middle line:84% to understand the regularity of chemical elements, 00:07:56.610 --> 00:07:58.680 align:middle line:84% associate them with physical atoms, 00:07:58.680 --> 00:08:00.540 align:middle line:84% that was really under some new strain 00:08:00.540 --> 00:08:03.420 align:middle line:84% if atoms themselves were actually not atomic if they 00:08:03.420 --> 00:08:05.100 align:middle line:84% really could be broken apart, if they 00:08:05.100 --> 00:08:07.270 align:middle line:90% have some internal structure. 00:08:07.270 --> 00:08:10.680 align:middle line:84% And so by 1900, with this remarkable series 00:08:10.680 --> 00:08:13.380 align:middle line:84% of developments throughout the 1890s, 00:08:13.380 --> 00:08:15.270 align:middle line:84% researchers had begun to identify 00:08:15.270 --> 00:08:19.140 align:middle line:84% different kinds of stuff that could fly out of matter, 00:08:19.140 --> 00:08:21.270 align:middle line:90% different kinds of radiations. 00:08:21.270 --> 00:08:22.690 align:middle line:84% And they had different properties. 00:08:22.690 --> 00:08:26.100 align:middle line:84% So for example, some of these emanations, or radiations, 00:08:26.100 --> 00:08:28.890 align:middle line:84% were easily deflected by an external magnetic field. 00:08:28.890 --> 00:08:32.000 align:middle line:84% You could actually watch, see the bending path. 00:08:32.000 --> 00:08:35.240 align:middle line:84% Others seemed not to be deflected at all by magnets. 00:08:35.240 --> 00:08:37.309 align:middle line:84% Some of these could fog, could begin 00:08:37.309 --> 00:08:41.360 align:middle line:84% to expose a photographic plate, leave a kind of smudge, 00:08:41.360 --> 00:08:43.280 align:middle line:84% even if the plates were protected, 00:08:43.280 --> 00:08:47.510 align:middle line:84% wrapped up in dark paper in some desk drawer, 00:08:47.510 --> 00:08:49.895 align:middle line:90% not in the direct line of fire. 00:08:49.895 --> 00:08:51.270 align:middle line:84% So they had different properties. 00:08:51.270 --> 00:08:53.030 align:middle line:84% So what researchers began to do was just 00:08:53.030 --> 00:08:56.090 align:middle line:84% try to classify them by different kind 00:08:56.090 --> 00:08:57.750 align:middle line:90% of neutral sounding names. 00:08:57.750 --> 00:09:00.230 align:middle line:84% They just began at the start of the Greek alphabet 00:09:00.230 --> 00:09:03.920 align:middle line:84% and labeled one kind alpha rays, another kind beta rays, 00:09:03.920 --> 00:09:04.910 align:middle line:90% a third type gamma. 00:09:04.910 --> 00:09:06.577 align:middle line:84% And they figured they'd just keep going, 00:09:06.577 --> 00:09:08.160 align:middle line:90% as many letters as needed. 00:09:08.160 --> 00:09:11.240 align:middle line:84% They didn't know what caused these emanations or radiations. 00:09:11.240 --> 00:09:14.270 align:middle line:84% But they could at least begin to classify or distinguish 00:09:14.270 --> 00:09:17.540 align:middle line:84% among them because the radiations themselves really 00:09:17.540 --> 00:09:19.770 align:middle line:84% did seem to have some different properties. 00:09:19.770 --> 00:09:24.890 align:middle line:84% And again, this was remarkably interesting news at the time. 00:09:24.890 --> 00:09:28.910 align:middle line:84% The Curies, in particular, became really media sensations, 00:09:28.910 --> 00:09:31.120 align:middle line:90% especially Marie Curie. 00:09:31.120 --> 00:09:35.470 align:middle line:84% As you may know or can imagine, this was really, really unusual 00:09:35.470 --> 00:09:39.580 align:middle line:84% to have a world class leading researcher in the sciences who 00:09:39.580 --> 00:09:40.810 align:middle line:90% happened to be a woman. 00:09:40.810 --> 00:09:43.630 align:middle line:84% And there was tremendous speculation about was she just 00:09:43.630 --> 00:09:45.580 align:middle line:84% like other women, was she a caring mother 00:09:45.580 --> 00:09:48.980 align:middle line:84% or not, really from today's point of view horribly, 00:09:48.980 --> 00:09:53.740 align:middle line:84% horribly gender stereotyped, often very unfair attributes 00:09:53.740 --> 00:09:57.370 align:middle line:84% attributed to her in the wide press. 00:09:57.370 --> 00:09:59.330 align:middle line:84% When her when Pierre passed away, 00:09:59.330 --> 00:10:01.360 align:middle line:84% she had a relationship with another researcher. 00:10:01.360 --> 00:10:03.790 align:middle line:90% It was a French scandal. 00:10:03.790 --> 00:10:06.130 align:middle line:84% And people wanted to know these scurrilous details 00:10:06.130 --> 00:10:08.180 align:middle line:90% of her private life. 00:10:08.180 --> 00:10:11.470 align:middle line:84% On the other hand, she was constantly in the news. 00:10:11.470 --> 00:10:13.540 align:middle line:90% And people were really curious. 00:10:13.540 --> 00:10:15.220 align:middle line:84% And she was, of course, the first person 00:10:15.220 --> 00:10:16.790 align:middle line:90% to win two Nobel prizes-- 00:10:16.790 --> 00:10:18.657 align:middle line:84% one in chemistry and one in physics. 00:10:18.657 --> 00:10:19.990 align:middle line:90% And I just find this remarkable. 00:10:19.990 --> 00:10:22.582 align:middle line:84% This wasn't only true in turn of the century Paris. 00:10:22.582 --> 00:10:24.040 align:middle line:84% But as recently as last year, there 00:10:24.040 --> 00:10:26.170 align:middle line:84% was a major film some of you might 00:10:26.170 --> 00:10:30.620 align:middle line:84% have seen starring a major film star Rosamund Pike playing, yet 00:10:30.620 --> 00:10:33.990 align:middle line:84% again, yet another film adaptation of the life of Marie 00:10:33.990 --> 00:10:34.490 align:middle line:90% Curie. 00:10:34.490 --> 00:10:38.390 align:middle line:84% So her personal story continues to fascinate as well. 00:10:38.390 --> 00:10:40.400 align:middle line:84% And that was true really from the beginning. 00:10:40.400 --> 00:10:43.760 align:middle line:84% In real time, she was already a kind of media sensation, 00:10:43.760 --> 00:10:46.610 align:middle line:84% as were these findings, things like these mysterious 00:10:46.610 --> 00:10:49.293 align:middle line:84% ghost-like rays that often people's eyes 00:10:49.293 --> 00:10:51.710 align:middle line:84% couldn't register, but could have effects across the room. 00:10:51.710 --> 00:10:54.680 align:middle line:84% It was a really remarkable conjunction. 00:10:54.680 --> 00:10:57.830 align:middle line:84% So one of the younger folks who got really excited about this 00:10:57.830 --> 00:10:59.390 align:middle line:90% was Ernest Rutherford. 00:10:59.390 --> 00:11:00.980 align:middle line:84% He was a bit younger than the Curies. 00:11:00.980 --> 00:11:04.220 align:middle line:84% He was the next generation coming up. 00:11:04.220 --> 00:11:05.600 align:middle line:90% He grew up in New Zealand. 00:11:05.600 --> 00:11:07.940 align:middle line:84% But he was a very promising young student. 00:11:07.940 --> 00:11:10.550 align:middle line:84% And he received a fellowship to come to England, 00:11:10.550 --> 00:11:13.640 align:middle line:84% to Cambridge, to finish his studies there. 00:11:13.640 --> 00:11:16.790 align:middle line:84% He actually studied under JJ Thomson, the person who, 00:11:16.790 --> 00:11:20.240 align:middle line:84% in 1897, was experimenting with these cathode rays 00:11:20.240 --> 00:11:21.950 align:middle line:90% that I mentioned briefly before. 00:11:21.950 --> 00:11:25.070 align:middle line:84% He joined Thompson's group at the Cavendish really right 00:11:25.070 --> 00:11:26.030 align:middle line:90% at that time. 00:11:26.030 --> 00:11:27.740 align:middle line:84% Rutherford was there just in the midst 00:11:27.740 --> 00:11:30.620 align:middle line:84% of this tremendous excitement over some of these new rays, 00:11:30.620 --> 00:11:34.580 align:middle line:90% like Thompson's cathode rays. 00:11:34.580 --> 00:11:37.670 align:middle line:84% Rutherford became fascinated by this topic of radioactivity. 00:11:37.670 --> 00:11:40.100 align:middle line:84% It was all the news at the Cavendish, 00:11:40.100 --> 00:11:41.630 align:middle line:90% in Paris, and beyond. 00:11:41.630 --> 00:11:44.570 align:middle line:84% And he began identifying new sources that 00:11:44.570 --> 00:11:47.120 align:middle line:84% could emit by now familiar rays, meaning 00:11:47.120 --> 00:11:50.390 align:middle line:84% the alpha rays had been identified people now 00:11:50.390 --> 00:11:52.790 align:middle line:84% knew they had different properties than the beta rays 00:11:52.790 --> 00:11:53.700 align:middle line:90% and so on. 00:11:53.700 --> 00:11:58.250 align:middle line:84% But Rutherford found new sources that could give off 00:11:58.250 --> 00:11:59.900 align:middle line:90% that kind of radiation. 00:11:59.900 --> 00:12:02.630 align:middle line:84% And he also began trying to systematize 00:12:02.630 --> 00:12:05.600 align:middle line:84% the study of radioactivity more generally. 00:12:05.600 --> 00:12:09.665 align:middle line:84% It's to Rutherford whom we owe the concept of a half-life. 00:12:09.665 --> 00:12:11.540 align:middle line:84% The Curies were very much involved with this. 00:12:11.540 --> 00:12:13.550 align:middle line:84% Rutherford helped to formalize it-- 00:12:13.550 --> 00:12:15.080 align:middle line:84% the half-life being a term that's 00:12:15.080 --> 00:12:17.300 align:middle line:84% probably quite familiar to us today, 00:12:17.300 --> 00:12:20.510 align:middle line:84% the time during which the radioactivity of a sample 00:12:20.510 --> 00:12:23.030 align:middle line:84% was measured by Geiger counters or other things 00:12:23.030 --> 00:12:25.320 align:middle line:90% would fall by half. 00:12:25.320 --> 00:12:28.077 align:middle line:84% So that's the characteristic time 00:12:28.077 --> 00:12:30.410 align:middle line:84% during which you would measure these kinds of emanations 00:12:30.410 --> 00:12:31.520 align:middle line:90% coming out. 00:12:31.520 --> 00:12:33.340 align:middle line:84% And Rutherford in particular became 00:12:33.340 --> 00:12:36.790 align:middle line:84% fascinated by what we now call decay chains. 00:12:36.790 --> 00:12:39.280 align:middle line:84% So he could start, much as the Curies would do, 00:12:39.280 --> 00:12:43.600 align:middle line:84% with a certain material, and then watch that material decay, 00:12:43.600 --> 00:12:46.750 align:middle line:84% for example, by emitting alpha rays. 00:12:46.750 --> 00:12:49.870 align:middle line:84% And then that original substance would transmute 00:12:49.870 --> 00:12:53.230 align:middle line:84% transform to a new kind of substance that 00:12:53.230 --> 00:12:54.940 align:middle line:90% would later be called radon. 00:12:54.940 --> 00:12:56.920 align:middle line:84% If he began with radium, one of the elements 00:12:56.920 --> 00:13:00.700 align:middle line:84% first scrutinized by the Curies, what 00:13:00.700 --> 00:13:02.470 align:middle line:84% would happen to a sample of radium 00:13:02.470 --> 00:13:04.522 align:middle line:84% after a bunch of alpha particles would come out? 00:13:04.522 --> 00:13:06.730 align:middle line:84% And that was the kind of thing that Rutherford wanted 00:13:06.730 --> 00:13:08.260 align:middle line:90% to study and systematize. 00:13:08.260 --> 00:13:11.830 align:middle line:84% So the decay products from alpha decay of radium 00:13:11.830 --> 00:13:14.140 align:middle line:84% would be identified eventually as radon. 00:13:14.140 --> 00:13:15.400 align:middle line:90% The chain we keep going. 00:13:15.400 --> 00:13:18.310 align:middle line:84% Radon would emit alpha particles, become radium a. 00:13:18.310 --> 00:13:20.530 align:middle line:84% But now, it's called polonium, actually 00:13:20.530 --> 00:13:24.170 align:middle line:84% in honor of Marie Curie's homeland of Poland, and so on. 00:13:24.170 --> 00:13:27.190 align:middle line:84% So Rutherford got very quickly into this game, 00:13:27.190 --> 00:13:29.590 align:middle line:84% into this study of radioactivity. 00:13:29.590 --> 00:13:32.180 align:middle line:84% One of the things he did then, when 00:13:32.180 --> 00:13:35.210 align:middle line:84% he was only a little bit further along, 00:13:35.210 --> 00:13:38.030 align:middle line:84% was to team up with another colleague, Hans Geiger, 00:13:38.030 --> 00:13:41.390 align:middle line:84% originally from Germany, but at this point working in the UK. 00:13:41.390 --> 00:13:43.970 align:middle line:90% We now refer to Geiger counters. 00:13:43.970 --> 00:13:45.890 align:middle line:84% They were actually developed in partnership 00:13:45.890 --> 00:13:49.220 align:middle line:84% between Rutherford and Geiger, in this first decade 00:13:49.220 --> 00:13:50.910 align:middle line:90% of the 20th century. 00:13:50.910 --> 00:13:53.060 align:middle line:84% Here's one of their earliest own illustrations 00:13:53.060 --> 00:13:53.720 align:middle line:90% of how this would work. 00:13:53.720 --> 00:13:55.470 align:middle line:84% This is, of course, a more modern version, 00:13:55.470 --> 00:13:57.140 align:middle line:90% a kind of Wikipedia version. 00:13:57.140 --> 00:13:59.480 align:middle line:84% And the idea was that this was a device 00:13:59.480 --> 00:14:02.330 align:middle line:84% with which to measure these emanations, 00:14:02.330 --> 00:14:06.200 align:middle line:84% especially electrically charged radiations coming out 00:14:06.200 --> 00:14:08.330 align:middle line:90% of these radioactive materials. 00:14:08.330 --> 00:14:11.643 align:middle line:84% Very clever and actually very inexpensive and robust. 00:14:11.643 --> 00:14:13.310 align:middle line:84% That's partly why these things are still 00:14:13.310 --> 00:14:15.740 align:middle line:84% in such widespread use to this day. 00:14:15.740 --> 00:14:23.870 align:middle line:84% Again, in the modern version, you have two conducting coils 00:14:23.870 --> 00:14:25.880 align:middle line:90% or beams-- 00:14:25.880 --> 00:14:27.950 align:middle line:90% the anode and the cathode. 00:14:27.950 --> 00:14:30.500 align:middle line:84% And you have a voltage difference between them. 00:14:30.500 --> 00:14:34.250 align:middle line:84% Inside the chamber, you have inert gas. 00:14:34.250 --> 00:14:36.440 align:middle line:90% It could be a kind of noble gas. 00:14:36.440 --> 00:14:39.530 align:middle line:84% If ionizing radiations, one of these emanations 00:14:39.530 --> 00:14:42.410 align:middle line:84% from some radioactive source, enters the chamber, 00:14:42.410 --> 00:14:45.440 align:middle line:84% it can actually ionize those otherwise neutral and fairly 00:14:45.440 --> 00:14:46.700 align:middle line:90% inert atoms. 00:14:46.700 --> 00:14:49.670 align:middle line:84% It can, as we now know, rip off an electron or something 00:14:49.670 --> 00:14:50.430 align:middle line:90% like that. 00:14:50.430 --> 00:14:53.960 align:middle line:84% So now, you have a charged ion running around in this chamber. 00:14:53.960 --> 00:14:56.747 align:middle line:84% It will be attracted to either the anode or cathode. 00:14:56.747 --> 00:14:57.830 align:middle line:90% You'll complete a circuit. 00:14:57.830 --> 00:14:58.940 align:middle line:90% You'll have a readout. 00:14:58.940 --> 00:15:02.930 align:middle line:84% So you can convert certain kinds of physical interactions 00:15:02.930 --> 00:15:07.520 align:middle line:84% within the chamber into measurable electric outputs 00:15:07.520 --> 00:15:10.440 align:middle line:84% from this otherwise very simple closed device. 00:15:10.440 --> 00:15:14.690 align:middle line:84% So by 1908, this had now become a new kind of tool 00:15:14.690 --> 00:15:16.280 align:middle line:84% in many, many laboratories because it 00:15:16.280 --> 00:15:18.020 align:middle line:90% was both cheap and reliable. 00:15:18.020 --> 00:15:21.800 align:middle line:84% And the idea behind it was pretty easy to convey. 00:15:21.800 --> 00:15:24.450 align:middle line:84% Using these kinds of tools, Rutherford, and Geiger, 00:15:24.450 --> 00:15:27.540 align:middle line:84% and their immediate circle in and around the Cavendish 00:15:27.540 --> 00:15:30.840 align:middle line:84% were able to determine that alpha particles actually 00:15:30.840 --> 00:15:34.560 align:middle line:84% carried twice the electric charge of Thompson's still 00:15:34.560 --> 00:15:37.308 align:middle line:84% pretty new beta particles, but of the opposite side. 00:15:37.308 --> 00:15:39.600 align:middle line:84% Basically, they would go to the anode, not the cathode, 00:15:39.600 --> 00:15:40.630 align:middle line:90% and vice versa. 00:15:40.630 --> 00:15:43.050 align:middle line:84% So you could begin measuring more and more properties 00:15:43.050 --> 00:15:46.470 align:middle line:84% of these different kinds of radiations or emanations. 00:15:46.470 --> 00:15:49.080 align:middle line:84% So very soon after there was a reliable way 00:15:49.080 --> 00:15:51.960 align:middle line:84% to characterize these new rays, these alpha 00:15:51.960 --> 00:15:55.140 align:middle line:84% particles in particular, Rutherford got a new job. 00:15:55.140 --> 00:15:57.810 align:middle line:84% He was now a young professor at Manchester University 00:15:57.810 --> 00:15:58.950 align:middle line:90% in northern England. 00:15:58.950 --> 00:16:01.950 align:middle line:84% He built up a big, big flourishing research group. 00:16:01.950 --> 00:16:04.980 align:middle line:84% And the idea now was not only to study alpha particles 00:16:04.980 --> 00:16:07.230 align:middle line:84% as the subject of research, as he'd 00:16:07.230 --> 00:16:09.390 align:middle line:84% been doing since his student days, 00:16:09.390 --> 00:16:14.010 align:middle line:84% but to flip it around and use alpha particles as a tool 00:16:14.010 --> 00:16:15.730 align:middle line:84% to learn new stuff about other things. 00:16:15.730 --> 00:16:18.840 align:middle line:84% So the alpha particles were domesticated, I think, 00:16:18.840 --> 00:16:21.300 align:middle line:84% really remarkably quickly from being 00:16:21.300 --> 00:16:23.820 align:middle line:84% the topic you'd scrutinize to being 00:16:23.820 --> 00:16:26.190 align:middle line:84% just another tool on your lab bench 00:16:26.190 --> 00:16:27.580 align:middle line:90% to learn about other things. 00:16:27.580 --> 00:16:30.210 align:middle line:84% And Rutherford was very proactive, as others were. 00:16:30.210 --> 00:16:33.700 align:middle line:84% But Rutherford was really very creative in that transition. 00:16:33.700 --> 00:16:37.290 align:middle line:84% So beginning as early as 1909, his group 00:16:37.290 --> 00:16:39.270 align:middle line:90% began directing alpha particles. 00:16:39.270 --> 00:16:41.100 align:middle line:84% They would have a radon source of the kind 00:16:41.100 --> 00:16:43.080 align:middle line:90% he'd been studying for years. 00:16:43.080 --> 00:16:45.970 align:middle line:84% It would be what's called now an alpha emitter. 00:16:45.970 --> 00:16:48.540 align:middle line:84% So the natural form of radioactive decay 00:16:48.540 --> 00:16:52.720 align:middle line:84% of a radon source is to shoot out beams of alpha particles. 00:16:52.720 --> 00:16:54.670 align:middle line:90% So that was in this block here. 00:16:54.670 --> 00:16:56.580 align:middle line:84% And they could kind of collimate the beam. 00:16:56.580 --> 00:16:58.860 align:middle line:84% They could encase the radon source 00:16:58.860 --> 00:17:01.950 align:middle line:84% in lead shielding with a very narrow opening 00:17:01.950 --> 00:17:05.109 align:middle line:84% to have the alpha particles shoot out in one direction. 00:17:05.109 --> 00:17:07.800 align:middle line:84% They would shoot them towards a target of a very, very 00:17:07.800 --> 00:17:11.940 align:middle line:84% thin metallic foil, often gold foil very, very thin, 00:17:11.940 --> 00:17:15.569 align:middle line:84% and then surround almost an entire foil 00:17:15.569 --> 00:17:18.040 align:middle line:90% by this new fluorescent screen. 00:17:18.040 --> 00:17:23.400 align:middle line:84% So when the alpha particles would ricochet off that foil, 00:17:23.400 --> 00:17:26.130 align:middle line:84% they would light up this fluorescent screen. 00:17:26.130 --> 00:17:28.830 align:middle line:84% This was incredibly-- that's very easy to describe. 00:17:28.830 --> 00:17:32.370 align:middle line:84% Even a nice Wikipedia-level cartoon 00:17:32.370 --> 00:17:33.940 align:middle line:84% makes it look so straightforward. 00:17:33.940 --> 00:17:36.910 align:middle line:84% This was incredibly painstaking work. 00:17:36.910 --> 00:17:39.150 align:middle line:84% The researchers had to sit in a darkened room 00:17:39.150 --> 00:17:42.780 align:middle line:84% for like a minimum half an hour just to let their eyes adjust. 00:17:42.780 --> 00:17:46.435 align:middle line:84% Imagine sitting basically in an entirely blackened room-- 00:17:46.435 --> 00:17:48.060 align:middle line:84% your mind starts playing tricks on you. 00:17:48.060 --> 00:17:50.580 align:middle line:84% You start seeing flashes where that might not be any-- 00:17:50.580 --> 00:17:53.610 align:middle line:84% just so that their eyes would be sensitive to these very, very 00:17:53.610 --> 00:17:57.390 align:middle line:84% modest little flickers from the fluorescent screen. 00:17:57.390 --> 00:18:00.600 align:middle line:84% And you basically had to sit there alone in the dark 00:18:00.600 --> 00:18:03.210 align:middle line:84% and count not just how many flickers but, 00:18:03.210 --> 00:18:05.880 align:middle line:84% as I'll say in a moment, where along this circle, 00:18:05.880 --> 00:18:10.200 align:middle line:84% what angle did you see most of these little tiny short flashes 00:18:10.200 --> 00:18:12.330 align:middle line:90% of light appear. 00:18:12.330 --> 00:18:14.970 align:middle line:84% So what they began to find is that most 00:18:14.970 --> 00:18:19.020 align:middle line:84% of these alpha particles would pass right through the foil, 00:18:19.020 --> 00:18:21.240 align:middle line:84% meaning most of the little flashes of light 00:18:21.240 --> 00:18:23.610 align:middle line:84% would line up directly behind the target. 00:18:23.610 --> 00:18:25.200 align:middle line:90% There would be a straight line. 00:18:25.200 --> 00:18:28.290 align:middle line:84% And they began to reason, Rutherford and his team, 00:18:28.290 --> 00:18:30.300 align:middle line:84% that these alpha particles were probably 00:18:30.300 --> 00:18:34.020 align:middle line:84% considerably smaller than the target atoms within that foil. 00:18:34.020 --> 00:18:36.060 align:middle line:84% If that was a gold foil, they would 00:18:36.060 --> 00:18:38.730 align:middle line:84% assume these gold atoms are really 00:18:38.730 --> 00:18:40.680 align:middle line:84% big on the scale of alpha particles 00:18:40.680 --> 00:18:44.290 align:middle line:84% and spread out on the scale of alpha particles. 00:18:44.290 --> 00:18:46.650 align:middle line:84% So most of the time, these little emanations, 00:18:46.650 --> 00:18:48.930 align:middle line:84% these alpha particles, could zoom right 00:18:48.930 --> 00:18:51.270 align:middle line:84% through that thin metal foil and never 00:18:51.270 --> 00:18:53.680 align:middle line:84% get deflected or scattered at all. 00:18:53.680 --> 00:18:55.260 align:middle line:84% So in that case, you'd expect most 00:18:55.260 --> 00:18:59.460 align:middle line:84% of the very faint short flashes on the fluorescent screen 00:18:59.460 --> 00:19:01.920 align:middle line:84% to line up directly behind the source. 00:19:01.920 --> 00:19:03.180 align:middle line:90% There's no deflection. 00:19:03.180 --> 00:19:07.650 align:middle line:84% Sometimes, there'd be a glancing scatter, a small angle scatter, 00:19:07.650 --> 00:19:08.760 align:middle line:90% a few of them over here. 00:19:08.760 --> 00:19:11.410 align:middle line:84% And that is, indeed, what they found most of the time. 00:19:11.410 --> 00:19:14.130 align:middle line:84% But every now and then, in a way that 00:19:14.130 --> 00:19:16.380 align:middle line:84% by doing this over and over and over again over 00:19:16.380 --> 00:19:19.590 align:middle line:84% months in the darkened room, painstakingly-- they 00:19:19.590 --> 00:19:21.210 align:middle line:84% could quantify it was roughly one 00:19:21.210 --> 00:19:24.320 align:middle line:84% out of every 100,000 scattering events. 00:19:24.320 --> 00:19:28.640 align:middle line:84% An alpha particle would actually scatter by very large angles. 00:19:28.640 --> 00:19:30.020 align:middle line:90% It became known as backscatter. 00:19:30.020 --> 00:19:33.590 align:middle line:84% It would scatter almost 180 degrees, coming back almost 00:19:33.590 --> 00:19:35.670 align:middle line:90% towards its own source. 00:19:35.670 --> 00:19:38.600 align:middle line:84% So most of the time, there was either no deflection 00:19:38.600 --> 00:19:40.790 align:middle line:90% or very minimal deflection. 00:19:40.790 --> 00:19:43.580 align:middle line:84% But some small number of times, there 00:19:43.580 --> 00:19:45.470 align:middle line:84% would be large angle scatter instead. 00:19:45.470 --> 00:19:48.380 align:middle line:84% They began making essentially these histograms 00:19:48.380 --> 00:19:51.500 align:middle line:84% of the number of scattering events 00:19:51.500 --> 00:19:53.600 align:middle line:84% as a function of the scattering angle. 00:19:53.600 --> 00:19:58.070 align:middle line:84% And as you can see, small angles is where almost all the events 00:19:58.070 --> 00:19:59.240 align:middle line:90% would cluster. 00:19:59.240 --> 00:20:03.230 align:middle line:84% And very rarely, about one out of every 100,000 approximately, 00:20:03.230 --> 00:20:05.930 align:middle line:84% you'd find a very large angle scatter event. 00:20:05.930 --> 00:20:08.480 align:middle line:84% That was not at all what they expected to find. 00:20:08.480 --> 00:20:10.790 align:middle line:84% Rutherford very famously recalled-- 00:20:10.790 --> 00:20:12.440 align:middle line:90% I love this quotation. 00:20:12.440 --> 00:20:14.480 align:middle line:84% Referring to his experiments, he said, 00:20:14.480 --> 00:20:16.760 align:middle line:84% "It was quite the most incredible event that has ever 00:20:16.760 --> 00:20:18.510 align:middle line:90% happened to me in my life. 00:20:18.510 --> 00:20:21.560 align:middle line:84% It was almost as incredible as if you had fired a 15-inch 00:20:21.560 --> 00:20:24.900 align:middle line:84% artillery shell--" think of it like from a cannon-- 00:20:24.900 --> 00:20:27.840 align:middle line:84% "fired that huge shell at a piece of tissue paper 00:20:27.840 --> 00:20:29.173 align:middle line:90% and it came back and hit you." 00:20:29.173 --> 00:20:31.590 align:middle line:84% That's what it seemed like to have these little tiny alpha 00:20:31.590 --> 00:20:35.310 align:middle line:84% particles ricochet all the way back for very large angle 00:20:35.310 --> 00:20:36.300 align:middle line:90% scatter. 00:20:36.300 --> 00:20:39.600 align:middle line:84% So they were collecting that data starting around 1909 00:20:39.600 --> 00:20:41.820 align:middle line:84% or so over months and months, ultimately 00:20:41.820 --> 00:20:46.140 align:middle line:84% over about two years to really build up lots and lots of data 00:20:46.140 --> 00:20:47.820 align:middle line:90% and statistics. 00:20:47.820 --> 00:20:49.860 align:middle line:84% During which, Rutherford then worked hard 00:20:49.860 --> 00:20:52.560 align:middle line:84% to make sense of the pattern quantitatively, 00:20:52.560 --> 00:20:55.770 align:middle line:84% to work out why it might be that you have not just 00:20:55.770 --> 00:20:58.140 align:middle line:84% rare scattering events at large angle, 00:20:58.140 --> 00:21:00.420 align:middle line:84% most scattering events at small angle, but really 00:21:00.420 --> 00:21:03.690 align:middle line:84% to retrace this particular shape of that curve, 00:21:03.690 --> 00:21:06.420 align:middle line:84% that particular kind of exponential decay 00:21:06.420 --> 00:21:10.110 align:middle line:84% of the scattering rates with angle. 00:21:10.110 --> 00:21:13.800 align:middle line:84% And he finally convinced himself with a pretty short derivation 00:21:13.800 --> 00:21:15.510 align:middle line:84% that this kind of scattering pattern 00:21:15.510 --> 00:21:19.770 align:middle line:84% would only make sense if most of the mass of those target atoms, 00:21:19.770 --> 00:21:22.470 align:middle line:84% the little gold atoms in the thin gold foil, 00:21:22.470 --> 00:21:26.070 align:middle line:84% were concentrated in a very dense nucleus in the center 00:21:26.070 --> 00:21:29.280 align:middle line:84% of those atoms, that most of the mass of the atom 00:21:29.280 --> 00:21:31.710 align:middle line:84% was actually in the very, very center. 00:21:31.710 --> 00:21:34.740 align:middle line:84% And otherwise, most of the rest of the volume that the atom 00:21:34.740 --> 00:21:37.680 align:middle line:90% might take up was empty. 00:21:37.680 --> 00:21:39.730 align:middle line:90% Atoms were mostly empty space. 00:21:39.730 --> 00:21:42.180 align:middle line:84% In fact, about one part in 100,000 00:21:42.180 --> 00:21:45.390 align:middle line:84% was the ratio between the size we might attribute 00:21:45.390 --> 00:21:47.580 align:middle line:84% to an atom and the size we would attribute 00:21:47.580 --> 00:21:50.860 align:middle line:84% to this massive inner core of the nucleus. 00:21:50.860 --> 00:21:54.300 align:middle line:84% The nucleus, much like the alpha particles, he goes on, 00:21:54.300 --> 00:21:55.943 align:middle line:90% must have a positive charge. 00:21:55.943 --> 00:21:57.360 align:middle line:84% They were repelling each other, he 00:21:57.360 --> 00:22:01.020 align:middle line:84% concluded, whereas these lightweight electrons, which 00:22:01.020 --> 00:22:04.650 align:middle line:84% at this point were what Thompson's cathode rays or beta 00:22:04.650 --> 00:22:06.630 align:middle line:84% particles have been identified with, those 00:22:06.630 --> 00:22:08.010 align:middle line:90% must have the opposite charge. 00:22:08.010 --> 00:22:10.530 align:middle line:84% And again, you could get a sense of the size of the charge 00:22:10.530 --> 00:22:12.540 align:middle line:84% from things like Geiger counters. 00:22:12.540 --> 00:22:15.600 align:middle line:84% So the model that Rutherford begins to piece together, 00:22:15.600 --> 00:22:18.720 align:middle line:84% building on these multiple years of data collection, 00:22:18.720 --> 00:22:22.230 align:middle line:84% is a kind of solar system picture of the atom. 00:22:22.230 --> 00:22:26.730 align:middle line:84% There's a very, very tiny massive core, the nucleus, 00:22:26.730 --> 00:22:28.200 align:middle line:90% that's kind of like the sun. 00:22:28.200 --> 00:22:30.600 align:middle line:84% And lighter weight objects are going 00:22:30.600 --> 00:22:31.870 align:middle line:90% to somehow move around it. 00:22:31.870 --> 00:22:34.750 align:middle line:84% And that's what makes up an atom. 00:22:34.750 --> 00:22:39.270 align:middle line:84% So he introduces this solar system model by around 1911. 00:22:39.270 --> 00:22:41.460 align:middle line:84% But of course, that led to several new questions 00:22:41.460 --> 00:22:43.690 align:middle line:90% on its own. 00:22:43.690 --> 00:22:47.370 align:middle line:84% So one question was these electrons, these JJ Thomson 00:22:47.370 --> 00:22:51.030 align:middle line:84% beta particles, would be constantly accelerated as they 00:22:51.030 --> 00:22:52.810 align:middle line:90% moved around the nucleus. 00:22:52.810 --> 00:22:55.620 align:middle line:84% If you thought about them like the Earth in the solar system, 00:22:55.620 --> 00:22:58.470 align:middle line:84% the Earth is constantly being accelerated 00:22:58.470 --> 00:23:00.300 align:middle line:90% as it moves around the sun. 00:23:00.300 --> 00:23:03.090 align:middle line:84% Its direction of travel is changing. 00:23:03.090 --> 00:23:04.875 align:middle line:84% Its velocity, in fact, is changing. 00:23:04.875 --> 00:23:06.540 align:middle line:90% Its velocity vector is changing. 00:23:06.540 --> 00:23:09.000 align:middle line:84% It's suffering constant acceleration. 00:23:09.000 --> 00:23:11.790 align:middle line:84% Wouldn't that be true of these negatively charged 00:23:11.790 --> 00:23:13.710 align:middle line:84% electric particles, the electrons, 00:23:13.710 --> 00:23:17.250 align:middle line:84% as they move around in any old pattern around the positively 00:23:17.250 --> 00:23:18.720 align:middle line:90% charged nucleus? 00:23:18.720 --> 00:23:20.520 align:middle line:84% And then the question comes up, according 00:23:20.520 --> 00:23:23.670 align:middle line:84% to Maxwell's remarkably successful work 00:23:23.670 --> 00:23:26.550 align:middle line:84% on electromagnetism, anytime electrically 00:23:26.550 --> 00:23:29.730 align:middle line:84% charged objects accelerate, they should radiate. 00:23:29.730 --> 00:23:33.490 align:middle line:84% They should give off light or electromagnetic radiation. 00:23:33.490 --> 00:23:36.480 align:middle line:84% So question 1 from this new Rutherford model was, 00:23:36.480 --> 00:23:37.980 align:middle line:90% where's all that light? 00:23:37.980 --> 00:23:43.200 align:middle line:84% If every atom filling every bit of matter in the universe 00:23:43.200 --> 00:23:45.720 align:middle line:84% has its inner parts constantly accelerated, 00:23:45.720 --> 00:23:49.140 align:middle line:84% electric charges accelerated, why don't we see everything 00:23:49.140 --> 00:23:50.800 align:middle line:90% glowing all the time? 00:23:50.800 --> 00:23:53.220 align:middle line:84% And perhaps an even trickier question 00:23:53.220 --> 00:23:56.730 align:middle line:84% was, if those electrons are actually emitting radiation, 00:23:56.730 --> 00:23:58.650 align:middle line:84% if they're giving up some of their own energy 00:23:58.650 --> 00:24:02.760 align:middle line:84% in the form of light, it's going to carry that energy away, then 00:24:02.760 --> 00:24:05.220 align:middle line:90% why are any atoms ever stable? 00:24:05.220 --> 00:24:07.800 align:middle line:84% Wouldn't those electrons be giving up their energy 00:24:07.800 --> 00:24:08.700 align:middle line:90% as they irradiate? 00:24:08.700 --> 00:24:11.940 align:middle line:84% Wouldn't basically their orbits decay, decay, decay? 00:24:11.940 --> 00:24:13.980 align:middle line:84% Wouldn't they just crash into the nucleus? 00:24:13.980 --> 00:24:16.830 align:middle line:84% Why don't atoms fall apart all the time and, in fact, 00:24:16.830 --> 00:24:18.040 align:middle line:90% very quickly? 00:24:18.040 --> 00:24:20.070 align:middle line:84% So these two questions became at least 00:24:20.070 --> 00:24:24.720 align:middle line:84% as challenging as the successes of Rutherford's nuclear model. 00:24:24.720 --> 00:24:27.112 align:middle line:84% Let me pause there and see if there 00:24:27.112 --> 00:24:28.320 align:middle line:90% are any questions about that. 00:24:28.320 --> 00:24:31.470 align:middle line:90% 00:24:31.470 --> 00:24:33.803 align:middle line:84% Alex asks in the chat, were all the detection events 00:24:33.803 --> 00:24:34.470 align:middle line:90% detected by eye? 00:24:34.470 --> 00:24:36.120 align:middle line:84% Yes, in the very first ones, they were. 00:24:36.120 --> 00:24:39.270 align:middle line:90% This is, again, astonishing. 00:24:39.270 --> 00:24:43.920 align:middle line:84% There were no the fancier things we 00:24:43.920 --> 00:24:46.200 align:middle line:84% would use today with, say, CCD cameras 00:24:46.200 --> 00:24:48.030 align:middle line:90% and so on, CCD detectors. 00:24:48.030 --> 00:24:50.340 align:middle line:84% Obviously, those didn't exist yet. 00:24:50.340 --> 00:24:54.390 align:middle line:84% There were early photographic methods. 00:24:54.390 --> 00:24:56.790 align:middle line:84% They didn't have the resolution that people would need. 00:24:56.790 --> 00:24:59.160 align:middle line:84% And they didn't have the timeliness. 00:24:59.160 --> 00:25:01.410 align:middle line:84% If you just set up the photographic plate 00:25:01.410 --> 00:25:04.680 align:middle line:84% and didn't have a way to rapidly take those plates out, 00:25:04.680 --> 00:25:06.760 align:middle line:84% and develop them, and put new ones in, 00:25:06.760 --> 00:25:09.960 align:middle line:84% then you would lose the kind of information 00:25:09.960 --> 00:25:11.640 align:middle line:90% they were looking to find. 00:25:11.640 --> 00:25:15.420 align:middle line:84% And so they really just had to have researchers sitting 00:25:15.420 --> 00:25:20.220 align:middle line:84% in the dark counting for hours, locked in a dark closet, 00:25:20.220 --> 00:25:25.620 align:middle line:84% both because the human eye, once you sensitized it, 00:25:25.620 --> 00:25:27.930 align:middle line:84% was, in its day much, more sensitive 00:25:27.930 --> 00:25:30.580 align:middle line:84% than these photographic techniques at the time, 00:25:30.580 --> 00:25:32.380 align:middle line:84% both in terms of spatial resolution, 00:25:32.380 --> 00:25:34.390 align:middle line:90% but also for temporal response. 00:25:34.390 --> 00:25:38.213 align:middle line:84% Your retina will go back to neutral 00:25:38.213 --> 00:25:40.630 align:middle line:84% much more quickly than these than these large photographic 00:25:40.630 --> 00:25:41.230 align:middle line:90% plates would. 00:25:41.230 --> 00:25:43.180 align:middle line:84% So they would really do basically naked eye 00:25:43.180 --> 00:25:44.950 align:middle line:90% observations. 00:25:44.950 --> 00:25:48.470 align:middle line:84% And I just don't know how they could do that for so long. 00:25:48.470 --> 00:25:50.380 align:middle line:84% Silu asks, did they choose to use gold foil 00:25:50.380 --> 00:25:51.400 align:middle line:90% for a specific reason? 00:25:51.400 --> 00:25:53.452 align:middle line:90% Why not any other metal? 00:25:53.452 --> 00:25:54.410 align:middle line:90% That's a good question. 00:25:54.410 --> 00:25:58.360 align:middle line:84% I think partly it was very pliable. 00:25:58.360 --> 00:26:02.530 align:middle line:84% So they could make very thin gold leaf. 00:26:02.530 --> 00:26:05.740 align:middle line:84% Then as now, bakers can make gold leaf on cakes. 00:26:05.740 --> 00:26:09.580 align:middle line:84% I mean, you can make very, very malleable, very, very thin 00:26:09.580 --> 00:26:12.130 align:middle line:90% layers of gold leaf. 00:26:12.130 --> 00:26:15.880 align:middle line:84% And there were already chemical notions, chemical measurements, 00:26:15.880 --> 00:26:20.320 align:middle line:84% to suggest that the gold atoms should be relatively massive. 00:26:20.320 --> 00:26:23.590 align:middle line:84% They wanted big scattering targets, basically. 00:26:23.590 --> 00:26:26.740 align:middle line:84% Even by the rough estimate of, say, 00:26:26.740 --> 00:26:30.250 align:middle line:84% 1 mole of gold atoms, how much would that weigh, 00:26:30.250 --> 00:26:33.970 align:middle line:84% they knew that had a place on Mendeleev's periodic table 00:26:33.970 --> 00:26:37.210 align:middle line:84% that looked pretty massive compared to other lighter 00:26:37.210 --> 00:26:39.130 align:middle line:90% targets. 00:26:39.130 --> 00:26:40.640 align:middle line:84% So those are the kinds of reasons. 00:26:40.640 --> 00:26:43.240 align:middle line:84% I think they did experiment with multiple types of thin foils. 00:26:43.240 --> 00:26:45.448 align:middle line:84% But they were all choosing them from around that part 00:26:45.448 --> 00:26:49.300 align:middle line:84% of the periodic table and that were both relatively 00:26:49.300 --> 00:26:49.870 align:middle line:90% inexpensive. 00:26:49.870 --> 00:26:52.030 align:middle line:84% They didn't need tons and tons of gold bullion. 00:26:52.030 --> 00:26:54.280 align:middle line:84% They just needed a little trace amounts of gold 00:26:54.280 --> 00:26:59.470 align:middle line:84% that was workable, had the right kind of macroscopic properties, 00:26:59.470 --> 00:27:03.910 align:middle line:84% and that also had a placement within Mendeleev's table, which 00:27:03.910 --> 00:27:07.320 align:middle line:84% already was ordered, roughly speaking, by atomic weight. 00:27:07.320 --> 00:27:09.070 align:middle line:84% So I think those were the kind of criteria 00:27:09.070 --> 00:27:10.903 align:middle line:84% they used, though indeed they did experiment 00:27:10.903 --> 00:27:12.527 align:middle line:90% with multiple types of targets. 00:27:12.527 --> 00:27:13.610 align:middle line:90% Those are great questions. 00:27:13.610 --> 00:27:16.760 align:middle line:90% Any other questions? 00:27:16.760 --> 00:27:20.990 align:middle line:84% I mean, we all have the benefit of many things in 2020, 00:27:20.990 --> 00:27:24.990 align:middle line:84% like high school, including high school chemistry classes. 00:27:24.990 --> 00:27:26.870 align:middle line:84% So the fact that atoms are made up 00:27:26.870 --> 00:27:29.550 align:middle line:84% of nuclei that have a lot of mass and positive charge, 00:27:29.550 --> 00:27:32.510 align:middle line:84% the scales might not yet have fallen from your eyes 00:27:32.510 --> 00:27:34.490 align:middle line:84% because you come in knowing that. 00:27:34.490 --> 00:27:37.400 align:middle line:84% But that was really, really pretty surprising, 00:27:37.400 --> 00:27:39.710 align:middle line:90% very surprising in 1911. 00:27:39.710 --> 00:27:42.350 align:middle line:84% The prevailing models until then had 00:27:42.350 --> 00:27:44.090 align:middle line:84% suggested that atoms really were made up 00:27:44.090 --> 00:27:46.520 align:middle line:90% of different kinds of charges. 00:27:46.520 --> 00:27:50.210 align:middle line:84% It was clear, by this point, that Thompson's cathode 00:27:50.210 --> 00:27:52.700 align:middle line:84% rays carried a negative electric charge. 00:27:52.700 --> 00:27:54.710 align:middle line:84% It was clear that alpha particles carried 00:27:54.710 --> 00:27:56.210 align:middle line:90% a positive electric charge. 00:27:56.210 --> 00:27:58.415 align:middle line:84% It was clear that atoms were electrically neutral. 00:27:58.415 --> 00:28:00.290 align:middle line:84% So people figured there must be equal numbers 00:28:00.290 --> 00:28:03.290 align:middle line:84% of these constituent parts, so the total electric charge 00:28:03.290 --> 00:28:04.440 align:middle line:90% balances out. 00:28:04.440 --> 00:28:06.860 align:middle line:84% But the prevailing model actually at the time, 00:28:06.860 --> 00:28:10.340 align:middle line:84% before Rutherford's experiments, was known as the plum pudding 00:28:10.340 --> 00:28:12.530 align:middle line:90% model, which is very British. 00:28:12.530 --> 00:28:16.340 align:middle line:84% The idea was that atoms might be just like this kind of mush, 00:28:16.340 --> 00:28:19.430 align:middle line:84% like a plum pudding, which I think is actually pretty gross, 00:28:19.430 --> 00:28:23.630 align:middle line:84% of this undifferentiated goo with positive and negative 00:28:23.630 --> 00:28:27.050 align:middle line:84% charges just distributed at random so they average out 00:28:27.050 --> 00:28:29.330 align:middle line:84% within some volume, that they didn't 00:28:29.330 --> 00:28:32.005 align:middle line:84% have a kind of structure, let alone 00:28:32.005 --> 00:28:35.920 align:middle line:84% that the positive charge was associated with such 00:28:35.920 --> 00:28:37.270 align:middle line:90% an imbalance of the mass. 00:28:37.270 --> 00:28:40.150 align:middle line:84% I mean, all those things were really quite unexpected, which 00:28:40.150 --> 00:28:42.580 align:middle line:84% is, I think, why someone like Rutherford says, 00:28:42.580 --> 00:28:45.520 align:middle line:84% it's like firing a cannon shell at tissue paper 00:28:45.520 --> 00:28:46.720 align:middle line:90% and having it smash back. 00:28:46.720 --> 00:28:49.870 align:middle line:84% If you fire a cannon shell at porridge, 00:28:49.870 --> 00:28:52.060 align:middle line:84% you don't expect it to come back in your face. 00:28:52.060 --> 00:28:54.880 align:middle line:84% So the fact that these atoms had very, very 00:28:54.880 --> 00:28:59.110 align:middle line:84% hard, massive scattering sites, these very, very dense nuclei 00:28:59.110 --> 00:29:01.390 align:middle line:84% in the middle, that was genuinely unexpected. 00:29:01.390 --> 00:29:04.600 align:middle line:84% Even though now we're like, oh yeah, I grew up knowing that. 00:29:04.600 --> 00:29:08.890 align:middle line:84% So sometimes, the novelty is hard to put our heads back 00:29:08.890 --> 00:29:10.152 align:middle line:90% into that moment. 00:29:10.152 --> 00:29:11.610 align:middle line:84% Any questions about what Rutherford 00:29:11.610 --> 00:29:14.940 align:middle line:84% was up to or the broader excitement about radioactivity 00:29:14.940 --> 00:29:15.750 align:middle line:90% and all that stuff? 00:29:15.750 --> 00:29:18.900 align:middle line:90% 00:29:18.900 --> 00:29:20.750 align:middle line:84% If not, I think I'll press ahead. 00:29:20.750 --> 00:29:22.460 align:middle line:84% As always, of course, please feel 00:29:22.460 --> 00:29:24.150 align:middle line:90% free to chime in, in the chat. 00:29:24.150 --> 00:29:26.285 align:middle line:84% We'll have another question break pretty soon. 00:29:26.285 --> 00:29:30.090 align:middle line:90% 00:29:30.090 --> 00:29:32.100 align:middle line:84% Oh yeah, Gary asked, why did Rutherford 00:29:32.100 --> 00:29:34.330 align:middle line:84% think the alpha particle is like a cannonball. 00:29:34.330 --> 00:29:34.830 align:middle line:90% Very good. 00:29:34.830 --> 00:29:36.390 align:middle line:90% Thank you, Gary. 00:29:36.390 --> 00:29:40.260 align:middle line:84% So by this point people knew, thanks to some of his own work, 00:29:40.260 --> 00:29:43.110 align:middle line:84% that the alpha particles were unbelievably heavy 00:29:43.110 --> 00:29:45.060 align:middle line:90% compared to the beta particles. 00:29:45.060 --> 00:29:51.390 align:middle line:84% These things were on the order of 10,000 times more massive. 00:29:51.390 --> 00:29:53.400 align:middle line:84% In their artillery minds, it would 00:29:53.400 --> 00:29:56.560 align:middle line:84% be like a BB gun versus a cannon blast. 00:29:56.560 --> 00:29:59.460 align:middle line:84% It really was, in that sense, a huge difference 00:29:59.460 --> 00:30:03.480 align:middle line:90% in just the heft. 00:30:03.480 --> 00:30:07.920 align:middle line:84% People would conduct what soon became called charge 00:30:07.920 --> 00:30:10.023 align:middle line:90% to mass ratio experiments. 00:30:10.023 --> 00:30:11.190 align:middle line:90% Some of you might know this. 00:30:11.190 --> 00:30:15.120 align:middle line:84% You might have even done some of these in junior lab or earlier. 00:30:15.120 --> 00:30:17.468 align:middle line:84% This was building on things that JJ Thompson had 00:30:17.468 --> 00:30:19.260 align:middle line:84% been doing in the 1890s and that Rutherford 00:30:19.260 --> 00:30:20.910 align:middle line:90% learned as a student. 00:30:20.910 --> 00:30:24.450 align:middle line:84% Once it became clear that both beta particles and alpha 00:30:24.450 --> 00:30:26.700 align:middle line:84% particles carried some electric charge, 00:30:26.700 --> 00:30:29.080 align:middle line:84% then people were like, great, let me go mess with them. 00:30:29.080 --> 00:30:31.163 align:middle line:84% One of the best ways to mess with electric charges 00:30:31.163 --> 00:30:34.670 align:middle line:84% is to use magnets, use a strong external magnetic field. 00:30:34.670 --> 00:30:36.910 align:middle line:84% And then you can measure the ratio of basically 00:30:36.910 --> 00:30:38.860 align:middle line:84% how strong an external magnet you 00:30:38.860 --> 00:30:42.820 align:middle line:84% need to get a certain kind of arc in the trajectory of those 00:30:42.820 --> 00:30:43.360 align:middle line:90% particles. 00:30:43.360 --> 00:30:46.300 align:middle line:84% And that will help you learn the ratio of their charge 00:30:46.300 --> 00:30:47.560 align:middle line:90% to their mass. 00:30:47.560 --> 00:30:49.690 align:middle line:84% Then separately, with things like Geiger counters, 00:30:49.690 --> 00:30:53.560 align:middle line:84% you can start measuring the ratio of just their charges. 00:30:53.560 --> 00:30:54.550 align:middle line:90% You combine all that. 00:30:54.550 --> 00:30:57.130 align:middle line:84% You say, oh, the mass of those alpha particles 00:30:57.130 --> 00:31:00.850 align:middle line:84% was, again, on the order of 10,000 times greater or more 00:31:00.850 --> 00:31:02.780 align:middle line:84% than the mass of the beta particles. 00:31:02.780 --> 00:31:05.770 align:middle line:84% So they were using each of these to fire on stuff. 00:31:05.770 --> 00:31:09.010 align:middle line:84% These quickly both became projectiles 00:31:09.010 --> 00:31:10.450 align:middle line:90% to shoot at new targets. 00:31:10.450 --> 00:31:12.160 align:middle line:84% But one of them seemed like it really 00:31:12.160 --> 00:31:15.490 align:middle line:84% was just this monster of the radioactive realm. 00:31:15.490 --> 00:31:18.530 align:middle line:84% And to have that kind of cannonball shell, 00:31:18.530 --> 00:31:21.550 align:middle line:84% artillery shell bounce back if you thought you were firing it 00:31:21.550 --> 00:31:24.160 align:middle line:84% at otherwise undifferentiated porridge, I mean, 00:31:24.160 --> 00:31:27.650 align:middle line:84% I think that's what Rutherford's surprise was coming from. 00:31:27.650 --> 00:31:29.310 align:middle line:90% That's a great question. 00:31:29.310 --> 00:31:32.490 align:middle line:90% Any other questions on that? 00:31:32.490 --> 00:31:32.990 align:middle line:90% OK. 00:31:32.990 --> 00:31:34.430 align:middle line:90% Let me march on now. 00:31:34.430 --> 00:31:36.320 align:middle line:84% We're going to hear about some work 00:31:36.320 --> 00:31:43.170 align:middle line:84% by one of Rutherford's postdocs who was named Niels Bohr. 00:31:43.170 --> 00:31:46.270 align:middle line:84% So Bohr was a young Danish physicist. 00:31:46.270 --> 00:31:48.960 align:middle line:84% He had just finished his PhD in theoretical physics 00:31:48.960 --> 00:31:51.420 align:middle line:84% in his native Copenhagen. He grew up 00:31:51.420 --> 00:31:53.800 align:middle line:84% in an actually relatively well-to-do family. 00:31:53.800 --> 00:31:55.980 align:middle line:84% His father was a very prestigious professor 00:31:55.980 --> 00:31:57.990 align:middle line:84% of physiology at the University of Copenhagen. 00:31:57.990 --> 00:32:00.240 align:middle line:84% He grew up in an academic household. 00:32:00.240 --> 00:32:02.220 align:middle line:84% He remembered from his childhood having 00:32:02.220 --> 00:32:05.670 align:middle line:84% lots and lots of distinguished scholars come visit for dinner 00:32:05.670 --> 00:32:07.200 align:middle line:84% all the time, that kind of thing. 00:32:07.200 --> 00:32:11.550 align:middle line:84% And Niels himself was a very ambitious young physicist. 00:32:11.550 --> 00:32:13.303 align:middle line:90% His younger brother went on to-- 00:32:13.303 --> 00:32:14.970 align:middle line:84% Harald went on to a distinguished career 00:32:14.970 --> 00:32:18.210 align:middle line:84% in pure mathematics, a very elite, academic family 00:32:18.210 --> 00:32:19.680 align:middle line:90% in Copenhagen. 00:32:19.680 --> 00:32:23.520 align:middle line:84% The place he most wanted to go after finishing his PhD 00:32:23.520 --> 00:32:25.130 align:middle line:90% was to join Rutherford's group. 00:32:25.130 --> 00:32:26.880 align:middle line:84% This was right at the time that Rutherford 00:32:26.880 --> 00:32:28.890 align:middle line:84% was doing all these amazing experiments 00:32:28.890 --> 00:32:32.800 align:middle line:84% on things like the scattering that led to the nuclear model. 00:32:32.800 --> 00:32:35.790 align:middle line:84% So Bohr was accepted as a young postdoctoral scholar 00:32:35.790 --> 00:32:36.810 align:middle line:90% with Rutherford's group. 00:32:36.810 --> 00:32:39.900 align:middle line:84% He moved to Manchester and spent about two years there, 00:32:39.900 --> 00:32:42.850 align:middle line:84% typical postdoc time, right at the time 00:32:42.850 --> 00:32:46.340 align:middle line:84% that these scattering results were first being shared. 00:32:46.340 --> 00:32:49.540 align:middle line:84% So Bohr became really fascinated by this new notion, 00:32:49.540 --> 00:32:51.580 align:middle line:84% partly for the reasons I was describing. 00:32:51.580 --> 00:32:54.460 align:middle line:84% It really did seem so unexpected that atoms 00:32:54.460 --> 00:32:58.000 align:middle line:84% would have such a hard, dense, compact scattering 00:32:58.000 --> 00:33:01.180 align:middle line:84% center deep in their middle and other [INAUDIBLE] mostly 00:33:01.180 --> 00:33:02.660 align:middle line:90% empty space. 00:33:02.660 --> 00:33:05.110 align:middle line:84% So that was really cool for Bohr. 00:33:05.110 --> 00:33:07.870 align:middle line:84% But he was puzzled, as many of Rutherford's contemporaries 00:33:07.870 --> 00:33:10.930 align:middle line:84% were, about how to make sense of the stability of matter. 00:33:10.930 --> 00:33:12.700 align:middle line:84% If these electric charges are somehow 00:33:12.700 --> 00:33:15.760 align:middle line:84% whipping around that central mass like planets 00:33:15.760 --> 00:33:18.965 align:middle line:84% around the sun, how come they're not radiating all the time? 00:33:18.965 --> 00:33:20.840 align:middle line:84% How come they're not losing all their energy? 00:33:20.840 --> 00:33:23.050 align:middle line:84% Why do atoms not just collapse on themselves 00:33:23.050 --> 00:33:25.390 align:middle line:90% in very short times? 00:33:25.390 --> 00:33:27.730 align:middle line:84% So Bohr, maybe because he came from this very 00:33:27.730 --> 00:33:31.300 align:middle line:84% elite academic family, he set himself a very modest goal 00:33:31.300 --> 00:33:32.350 align:middle line:90% for his postdoc. 00:33:32.350 --> 00:33:35.020 align:middle line:84% He said, I'll explain the stability of every single kind 00:33:35.020 --> 00:33:36.290 align:middle line:90% of atom forever. 00:33:36.290 --> 00:33:37.880 align:middle line:90% It was remarkable. 00:33:37.880 --> 00:33:40.990 align:middle line:84% He wanted to basically solve for the stability 00:33:40.990 --> 00:33:44.240 align:middle line:84% of every single entry on the periodic table. 00:33:44.240 --> 00:33:47.530 align:middle line:84% And you got a taste of this in the reading for today 00:33:47.530 --> 00:33:49.960 align:middle line:90% by historian John Heilbron. 00:33:49.960 --> 00:33:52.090 align:middle line:84% One of the things that I think we often forget-- 00:33:52.090 --> 00:33:54.472 align:middle line:84% I didn't know when I first learned about the Bohr model. 00:33:54.472 --> 00:33:55.930 align:middle line:84% And I think that's my favorite part 00:33:55.930 --> 00:33:57.700 align:middle line:90% about the piece by Heilbron-- 00:33:57.700 --> 00:33:59.800 align:middle line:84% is that Bohr's first attempt was actually 00:33:59.800 --> 00:34:03.580 align:middle line:84% to focus on multi-electron atoms and even molecules. 00:34:03.580 --> 00:34:05.530 align:middle line:84% He didn't first start with hydrogen, 00:34:05.530 --> 00:34:08.380 align:middle line:84% the way we now usually associate with his work. 00:34:08.380 --> 00:34:10.000 align:middle line:84% He actually figured, maybe there is 00:34:10.000 --> 00:34:15.040 align:middle line:84% some kind of what we now call classical equilibrium, a kind 00:34:15.040 --> 00:34:17.889 align:middle line:84% of compensation mechanism that would allow 00:34:17.889 --> 00:34:24.159 align:middle line:84% these electrons to be outside of a nucleus, 00:34:24.159 --> 00:34:26.409 align:middle line:84% but not constantly accelerated, constantly losing 00:34:26.409 --> 00:34:28.360 align:middle line:90% their energy due to radiation. 00:34:28.360 --> 00:34:30.250 align:middle line:84% So he wanted to find some combination 00:34:30.250 --> 00:34:33.940 align:middle line:84% of electrostatic repulsion between the electrons repelling 00:34:33.940 --> 00:34:37.480 align:middle line:84% each other and the magnetic effect that he thought 00:34:37.480 --> 00:34:41.469 align:middle line:84% could maybe counterbalance and make a kind of equilibrium. 00:34:41.469 --> 00:34:45.190 align:middle line:84% And maybe that would explain both the structure of atoms 00:34:45.190 --> 00:34:48.580 align:middle line:84% and why atoms don't immediately fall apart. 00:34:48.580 --> 00:34:50.920 align:middle line:84% That's quite an ambitious postdoc project. 00:34:50.920 --> 00:34:52.030 align:middle line:90% And it didn't work. 00:34:52.030 --> 00:34:54.340 align:middle line:84% And pretty soon, it became clear he just 00:34:54.340 --> 00:34:58.780 align:middle line:84% could not get this kind of equilibrium compensation thing 00:34:58.780 --> 00:34:59.860 align:middle line:90% to work. 00:34:59.860 --> 00:35:03.010 align:middle line:84% The multi-electron systems were very complicated 00:35:03.010 --> 00:35:03.670 align:middle line:90% mathematically. 00:35:03.670 --> 00:35:06.460 align:middle line:84% Any time you have many things acting on many other things, 00:35:06.460 --> 00:35:08.920 align:middle line:84% as you know to this day, the mathematics quickly 00:35:08.920 --> 00:35:11.230 align:middle line:90% becomes pretty, pretty intense. 00:35:11.230 --> 00:35:16.090 align:middle line:84% So he finally agreed to try a simpler case, which is always 00:35:16.090 --> 00:35:19.180 align:middle line:90% a good tip in physics. 00:35:19.180 --> 00:35:22.840 align:middle line:84% Don't try to tackle the hardest, most complicated case first. 00:35:22.840 --> 00:35:25.100 align:middle line:84% Try to tackle a simpler case first. 00:35:25.100 --> 00:35:28.270 align:middle line:84% So in a desperation, Bohr switches 00:35:28.270 --> 00:35:31.150 align:middle line:84% gears and starts to think hard about the simplest of all 00:35:31.150 --> 00:35:33.640 align:middle line:84% the atoms, the very first placeholder 00:35:33.640 --> 00:35:37.930 align:middle line:84% on Mendeleev's periodic table, the hydrogen atom, which 00:35:37.930 --> 00:35:40.630 align:middle line:84% even by then was known to have one electron 00:35:40.630 --> 00:35:42.850 align:middle line:84% and therefore was assumed to have one compensating 00:35:42.850 --> 00:35:44.560 align:middle line:90% proton in that nucleus. 00:35:44.560 --> 00:35:46.060 align:middle line:84% So that way, you don't have to worry 00:35:46.060 --> 00:35:49.420 align:middle line:84% about multi-electron repulsion within a single atom. 00:35:49.420 --> 00:35:52.660 align:middle line:84% And again, for simplicity, he considered a circular orbit. 00:35:52.660 --> 00:35:54.980 align:middle line:84% It could have been a more complicated motion. 00:35:54.980 --> 00:35:57.820 align:middle line:84% But he said, let me just get started by assuming really 00:35:57.820 --> 00:36:01.450 align:middle line:84% like a simplified version of the solar system, 00:36:01.450 --> 00:36:04.870 align:middle line:84% that the proton, the positive nucleus, sits in the middle. 00:36:04.870 --> 00:36:07.810 align:middle line:84% And the electron orbits in a perfect circle 00:36:07.810 --> 00:36:11.200 align:middle line:84% in a simpler version even than the planet Earth 00:36:11.200 --> 00:36:12.580 align:middle line:90% around the sun. 00:36:12.580 --> 00:36:15.200 align:middle line:84% In that case, now he knew how to start. 00:36:15.200 --> 00:36:17.530 align:middle line:84% And again, this is how I think any of us would start. 00:36:17.530 --> 00:36:19.600 align:middle line:84% He knew there was an attractive force 00:36:19.600 --> 00:36:22.810 align:middle line:84% between the negatively charged electron and the positively 00:36:22.810 --> 00:36:23.830 align:middle line:90% charged proton. 00:36:23.830 --> 00:36:26.500 align:middle line:84% There'd be an electrostatic attraction, 00:36:26.500 --> 00:36:28.540 align:middle line:84% the strength of which would go like the square 00:36:28.540 --> 00:36:30.940 align:middle line:84% of their charges divided by the square 00:36:30.940 --> 00:36:32.770 align:middle line:90% of their distance between them. 00:36:32.770 --> 00:36:35.710 align:middle line:84% There'd also be a kind of mechanical motion 00:36:35.710 --> 00:36:39.310 align:middle line:84% of that electron constantly moving around, undergoing 00:36:39.310 --> 00:36:41.170 align:middle line:90% centrifugal acceleration. 00:36:41.170 --> 00:36:44.060 align:middle line:84% And you could just take the a Newtonian expression for that. 00:36:44.060 --> 00:36:47.430 align:middle line:84% You have the planet Earth moving around the sun or a ball 00:36:47.430 --> 00:36:49.440 align:middle line:84% moving on a string or in a circle. 00:36:49.440 --> 00:36:52.840 align:middle line:84% There'll be an outward-directed effective force, 00:36:52.840 --> 00:36:54.720 align:middle line:90% the centrifugal force. 00:36:54.720 --> 00:36:57.330 align:middle line:84% And he just said, there must be a stable orbit 00:36:57.330 --> 00:37:01.080 align:middle line:84% when that inward directed force of electromagnetic attraction 00:37:01.080 --> 00:37:03.570 align:middle line:84% is perfectly balanced by that outward tendency 00:37:03.570 --> 00:37:05.220 align:middle line:90% of the centrifugal force. 00:37:05.220 --> 00:37:06.900 align:middle line:84% Balance the forces, and now, he can 00:37:06.900 --> 00:37:11.550 align:middle line:84% solve for this speed, the speed squared, associated with one 00:37:11.550 --> 00:37:12.900 align:middle line:90% of those stable orbits. 00:37:12.900 --> 00:37:17.370 align:middle line:84% This is all Newtonian and Maxwellian or even pre-Maxwell, 00:37:17.370 --> 00:37:18.900 align:middle line:90% just Coulomb. 00:37:18.900 --> 00:37:22.720 align:middle line:84% So as far as Bohr was concerned at this stage, both the speed, 00:37:22.720 --> 00:37:26.400 align:middle line:84% the magnitude of the velocity, v, and the average radius, 00:37:26.400 --> 00:37:29.140 align:middle line:84% the distance between the electron and the nucleus, 00:37:29.140 --> 00:37:30.690 align:middle line:84% these were assumed to be variables 00:37:30.690 --> 00:37:34.290 align:middle line:84% that could take any one of a continuous range of values. 00:37:34.290 --> 00:37:38.650 align:middle line:84% It could be at 1 unit, or 1.003 units, or 1.035 units, et 00:37:38.650 --> 00:37:40.260 align:middle line:90% cetera. 00:37:40.260 --> 00:37:43.030 align:middle line:84% Then Bohr says, well, if we just stick with that, 00:37:43.030 --> 00:37:46.450 align:middle line:84% we have all the challenges of Rutherford's model. 00:37:46.450 --> 00:37:49.000 align:middle line:90% Why are these atoms stable? 00:37:49.000 --> 00:37:50.260 align:middle line:90% Why aren't they radiating? 00:37:50.260 --> 00:37:51.140 align:middle line:90% And so on. 00:37:51.140 --> 00:37:55.180 align:middle line:84% So now, Bohr takes inspiration partly from Max Planck. 00:37:55.180 --> 00:37:58.270 align:middle line:84% Remember, this is now 1911, '12, '13. 00:37:58.270 --> 00:38:01.390 align:middle line:84% This was a decade into to Planck's work 00:38:01.390 --> 00:38:02.920 align:middle line:90% on blackbody radiation. 00:38:02.920 --> 00:38:06.340 align:middle line:84% But we know from Bohr's writings and letters at the time, 00:38:06.340 --> 00:38:07.960 align:middle line:84% he was even more directly inspired 00:38:07.960 --> 00:38:09.760 align:middle line:84% by Einstein, who was just a couple of years 00:38:09.760 --> 00:38:11.740 align:middle line:90% older than Bohr himself. 00:38:11.740 --> 00:38:14.830 align:middle line:84% And by this point, Bohr was thinking 00:38:14.830 --> 00:38:18.160 align:middle line:84% about Einstein's re-explanations of things 00:38:18.160 --> 00:38:21.070 align:middle line:84% like blackbody radiation and the photoelectric effect. 00:38:21.070 --> 00:38:23.260 align:middle line:84% And Einstein, even more than Bohr, 00:38:23.260 --> 00:38:25.720 align:middle line:84% had been emphasizing a kind of discreteness, 00:38:25.720 --> 00:38:29.170 align:middle line:84% that we have to break the classical rules, at some point, 00:38:29.170 --> 00:38:32.950 align:middle line:84% and say certain quantities can only take quantized units, 00:38:32.950 --> 00:38:35.710 align:middle line:84% like Einstein's explanation for Planck's work 00:38:35.710 --> 00:38:38.680 align:middle line:84% saying that light quanta could only 00:38:38.680 --> 00:38:41.350 align:middle line:90% hold fixed amounts of energy-- 00:38:41.350 --> 00:38:46.310 align:middle line:84% h times nu or 2h times nu, but not any non-integer value. 00:38:46.310 --> 00:38:48.340 align:middle line:84% So Bohr says, let me try that trick again. 00:38:48.340 --> 00:38:52.370 align:middle line:84% Basically, by now, it's a strategy to try. 00:38:52.370 --> 00:38:57.530 align:middle line:84% So Bohr just gives, again, a heuristic hypothesis. 00:38:57.530 --> 00:38:58.430 align:middle line:90% He doesn't prove it. 00:38:58.430 --> 00:39:01.250 align:middle line:84% He doesn't derive it much, like Einstein 00:39:01.250 --> 00:39:04.250 align:middle line:84% was doing with his heuristic suggestion of light quantum. 00:39:04.250 --> 00:39:08.630 align:middle line:84% Bohr says, what if a quantity that ordinarily we would treat 00:39:08.630 --> 00:39:12.500 align:middle line:84% as having any old value at all, the angular momentum of that 00:39:12.500 --> 00:39:16.070 align:middle line:84% electron's motion in the atom, which classically 00:39:16.070 --> 00:39:19.340 align:middle line:84% for a perfectly circular orbit has a very simple expression-- 00:39:19.340 --> 00:39:23.060 align:middle line:84% the electrons mass times the magnitude of its velocity times 00:39:23.060 --> 00:39:24.230 align:middle line:90% its radius-- 00:39:24.230 --> 00:39:26.810 align:middle line:84% and what if we just impose now a discreteness, 00:39:26.810 --> 00:39:29.330 align:middle line:84% much as Einstein had done in other contexts? 00:39:29.330 --> 00:39:32.390 align:middle line:84% What if we say the angular momentum of that moving 00:39:32.390 --> 00:39:38.150 align:middle line:84% electron can only take integer values of a scale set 00:39:38.150 --> 00:39:39.240 align:middle line:90% by Planck's constant? 00:39:39.240 --> 00:39:42.380 align:middle line:84% And again, as many of you likely have seen already, 00:39:42.380 --> 00:39:45.230 align:middle line:84% there's an abbreviation that very quickly becomes common. 00:39:45.230 --> 00:39:46.730 align:middle line:90% This is called h-bar. 00:39:46.730 --> 00:39:50.690 align:middle line:84% So h, lowercase h, had been introduced by Planck 00:39:50.690 --> 00:39:53.930 align:middle line:84% in his 1900 paper, became soon known as Planck's constant, 00:39:53.930 --> 00:39:57.890 align:middle line:84% had a very particular numerical value in, say, erg/seconds. 00:39:57.890 --> 00:39:59.900 align:middle line:84% And then a very convenient shorthand 00:39:59.900 --> 00:40:01.790 align:middle line:84% is to divide that numerical value 00:40:01.790 --> 00:40:04.670 align:middle line:84% by 2 pi, which comes up a lot if you're thinking about things 00:40:04.670 --> 00:40:05.870 align:middle line:90% like circular orbits. 00:40:05.870 --> 00:40:09.770 align:middle line:84% So Bohr says, what if the total angular momentum of that moving 00:40:09.770 --> 00:40:13.940 align:middle line:84% electron could only take unit values at a scale set 00:40:13.940 --> 00:40:16.100 align:middle line:90% by Planck's constant? 00:40:16.100 --> 00:40:16.910 align:middle line:90% He doesn't say why. 00:40:16.910 --> 00:40:17.780 align:middle line:90% He says what if. 00:40:17.780 --> 00:40:21.620 align:middle line:84% It's a heuristic kind of hypothetical suggestion. 00:40:21.620 --> 00:40:25.310 align:middle line:84% So now, Bohr has two expressions for v. 00:40:25.310 --> 00:40:28.460 align:middle line:84% He has the classical balance of forces expression. 00:40:28.460 --> 00:40:31.250 align:middle line:84% He now has a new quantum condition expression. 00:40:31.250 --> 00:40:32.210 align:middle line:90% That's his term. 00:40:32.210 --> 00:40:35.000 align:middle line:84% He can solve each for v and set them equal to each other. 00:40:35.000 --> 00:40:38.360 align:middle line:84% And then he can solve the resulting single equation 00:40:38.360 --> 00:40:39.440 align:middle line:90% for r. 00:40:39.440 --> 00:40:42.360 align:middle line:84% So now, he has basically two equations with two unknowns. 00:40:42.360 --> 00:40:43.950 align:middle line:90% He wants to know both v and r. 00:40:43.950 --> 00:40:46.410 align:middle line:84% He has two equations-- one here, one here. 00:40:46.410 --> 00:40:50.070 align:middle line:84% Equate them, and then he can solve for the allowable radii, 00:40:50.070 --> 00:40:53.940 align:middle line:84% distances from the nucleus at which an electron should 00:40:53.940 --> 00:40:57.870 align:middle line:84% be found if its angular momentum is subject to this new quantum 00:40:57.870 --> 00:40:58.740 align:middle line:90% condition. 00:40:58.740 --> 00:41:00.840 align:middle line:90% And he finds that the radii-- 00:41:00.840 --> 00:41:03.480 align:middle line:84% the radius can't take any old value. 00:41:03.480 --> 00:41:06.810 align:middle line:84% It no longer falls within a continuum of possible values. 00:41:06.810 --> 00:41:12.420 align:middle line:84% It now snaps into place with n being any positive integer. 00:41:12.420 --> 00:41:17.700 align:middle line:84% So it could be 1 squared, 1 times some basic shortest 00:41:17.700 --> 00:41:18.520 align:middle line:90% length. 00:41:18.520 --> 00:41:22.090 align:middle line:84% It could be 2 squared or 4 times that length, 9, and so on. 00:41:22.090 --> 00:41:25.950 align:middle line:84% But it can't be 2.05 or 8.96, right? 00:41:25.950 --> 00:41:28.110 align:middle line:84% So the radius at which one should 00:41:28.110 --> 00:41:31.080 align:middle line:84% expect to find electrons, if we impose 00:41:31.080 --> 00:41:34.740 align:middle line:84% this new discreteness, this new quantum condition, becomes 00:41:34.740 --> 00:41:37.800 align:middle line:84% set by some new integer, n, which 00:41:37.800 --> 00:41:40.170 align:middle line:84% becomes known as the principal quantum number. 00:41:40.170 --> 00:41:42.240 align:middle line:84% It's just any old positive integer. 00:41:42.240 --> 00:41:45.840 align:middle line:84% And there's now, again, a scale in which 00:41:45.840 --> 00:41:48.600 align:middle line:84% Planck's constant plays a central role. 00:41:48.600 --> 00:41:53.370 align:middle line:84% The combination of these constants of nature, h-bar 00:41:53.370 --> 00:41:55.800 align:middle line:84% squared divided by the mass of the electron 00:41:55.800 --> 00:41:59.250 align:middle line:84% times the square of its charge, that has dimensions of length. 00:41:59.250 --> 00:42:01.440 align:middle line:90% That's the unit radius. 00:42:01.440 --> 00:42:04.980 align:middle line:84% An electron should be found at 1 times that, 4 times 00:42:04.980 --> 00:42:06.810 align:middle line:90% that, 9 times that, et cetera. 00:42:06.810 --> 00:42:10.170 align:middle line:84% The radius itself is about half an angstrom, if you've 00:42:10.170 --> 00:42:11.670 align:middle line:90% heard of the units angstroms. 00:42:11.670 --> 00:42:14.910 align:middle line:84% 1 angstrom is 10 to the minus 10 meters. 00:42:14.910 --> 00:42:17.980 align:middle line:84% And so this is about half of that. 00:42:17.980 --> 00:42:23.010 align:middle line:84% So roughly 0.5 angstroms is what this new unit of length 00:42:23.010 --> 00:42:25.210 align:middle line:90% works out to be. 00:42:25.210 --> 00:42:27.610 align:middle line:84% So now, Bohr has this picture emerging 00:42:27.610 --> 00:42:30.160 align:middle line:84% not just of a nuclear atom, like from Rutherford, 00:42:30.160 --> 00:42:33.250 align:middle line:84% where most of the mass and all the positive charge 00:42:33.250 --> 00:42:36.070 align:middle line:84% are concentrated in this dense central nucleus. 00:42:36.070 --> 00:42:39.880 align:middle line:84% But now, there's a more finely articulated structure 00:42:39.880 --> 00:42:42.870 align:middle line:84% for where one should find the electrons outside 00:42:42.870 --> 00:42:44.710 align:middle line:84% of the nucleus, as the electrons circle 00:42:44.710 --> 00:42:47.410 align:middle line:84% around, at least in a simple atom like hydrogen, 00:42:47.410 --> 00:42:49.060 align:middle line:90% which only has one electron. 00:42:49.060 --> 00:42:51.340 align:middle line:84% As I was saying a moment ago, the electron 00:42:51.340 --> 00:42:55.270 align:middle line:84% can be found at 1 squared times its basic length, a0, 00:42:55.270 --> 00:42:59.270 align:middle line:84% at 2 squared times that length, 3 squared, and so on. 00:42:59.270 --> 00:43:02.050 align:middle line:84% And so you have this series of discrete orbits. 00:43:02.050 --> 00:43:04.330 align:middle line:84% So now, Bohr wants to know, well, 00:43:04.330 --> 00:43:08.620 align:middle line:84% if we have this solar system model where the electron can 00:43:08.620 --> 00:43:13.580 align:middle line:84% only be at certain distances, certain radii from the nucleus, 00:43:13.580 --> 00:43:16.165 align:middle line:84% how would the energy of such a system-- 00:43:16.165 --> 00:43:18.415 align:middle line:84% how could we characterize the energy of such a system? 00:43:18.415 --> 00:43:21.550 align:middle line:90% 00:43:21.550 --> 00:43:24.880 align:middle line:84% So just as he'd done before, he goes back 00:43:24.880 --> 00:43:29.230 align:middle line:84% and starts with the perfectly normal textbook expressions 00:43:29.230 --> 00:43:31.630 align:middle line:90% from both Newton and Maxwell. 00:43:31.630 --> 00:43:35.440 align:middle line:84% You have a charge, a charged object in motion 00:43:35.440 --> 00:43:36.970 align:middle line:84% around some other charged object. 00:43:36.970 --> 00:43:39.160 align:middle line:84% The moving thing has some kinetic energy. 00:43:39.160 --> 00:43:41.200 align:middle line:90% That's always 1/2 mv squared. 00:43:41.200 --> 00:43:43.520 align:middle line:84% There'll be some, in this case, potential energy. 00:43:43.520 --> 00:43:45.610 align:middle line:84% It's an attractive energy because the charge 00:43:45.610 --> 00:43:48.200 align:middle line:84% is-- the electron and the proton have opposite charge. 00:43:48.200 --> 00:43:49.760 align:middle line:84% That's why they attract each other. 00:43:49.760 --> 00:43:53.170 align:middle line:84% So the potential energy has an overall minus sign. 00:43:53.170 --> 00:43:56.260 align:middle line:84% Now, already from his previous classical balance 00:43:56.260 --> 00:43:58.330 align:middle line:84% of forces argument, he already had 00:43:58.330 --> 00:44:00.290 align:middle line:90% an expression for v squared. 00:44:00.290 --> 00:44:03.580 align:middle line:84% So now, we can just sub into this expression for the energy. 00:44:03.580 --> 00:44:05.950 align:middle line:84% He also, from the previous exercise, 00:44:05.950 --> 00:44:08.230 align:middle line:90% had an expression for r. 00:44:08.230 --> 00:44:09.820 align:middle line:84% Now, the energy depends only on r. 00:44:09.820 --> 00:44:11.770 align:middle line:84% Well, he knows he has an expression for r. 00:44:11.770 --> 00:44:16.270 align:middle line:84% This part's newer, once he uses that discrete quantum condition 00:44:16.270 --> 00:44:20.150 align:middle line:84% by quantizing the angular momentum. 00:44:20.150 --> 00:44:23.870 align:middle line:84% And so finally, he can plug in his new basic unit of length. 00:44:23.870 --> 00:44:27.000 align:middle line:84% It soon gets called, in his honor, the Bohr radius. 00:44:27.000 --> 00:44:29.450 align:middle line:84% And now, Bohr has an expression for the energy 00:44:29.450 --> 00:44:33.170 align:middle line:84% of an electron in any of these quantized orbits 00:44:33.170 --> 00:44:35.360 align:middle line:90% or quantized forms of motion. 00:44:35.360 --> 00:44:38.240 align:middle line:84% It depends only on various constants-- the mass 00:44:38.240 --> 00:44:40.790 align:middle line:84% of the electron, its charge, and Planck's constant, 00:44:40.790 --> 00:44:43.730 align:middle line:84% and that integer n, which marks which 00:44:43.730 --> 00:44:48.010 align:middle line:84% of these orbits or states of motion the electron is in. 00:44:48.010 --> 00:44:52.780 align:middle line:84% So the electron now has very particular kinds of motion 00:44:52.780 --> 00:44:53.860 align:middle line:90% it can undertake. 00:44:53.860 --> 00:44:56.710 align:middle line:84% There are quantized amounts of energy associated 00:44:56.710 --> 00:44:58.570 align:middle line:90% with any of those orbits. 00:44:58.570 --> 00:45:01.150 align:middle line:84% So now, that means one could take the difference 00:45:01.150 --> 00:45:04.870 align:middle line:84% in energies between any of those discrete allowable orbits. 00:45:04.870 --> 00:45:07.220 align:middle line:84% What's the difference in energy between, say, 00:45:07.220 --> 00:45:10.060 align:middle line:84% an electron over here with n equals 3-- 00:45:10.060 --> 00:45:12.070 align:middle line:90% so 3 squared is 9-- 00:45:12.070 --> 00:45:14.050 align:middle line:84% versus the energy of an electron here for n 00:45:14.050 --> 00:45:17.590 align:middle line:84% equals 2 or for any two discrete states 00:45:17.590 --> 00:45:20.320 align:middle line:84% of motion labeled by some integer n? 00:45:20.320 --> 00:45:21.890 align:middle line:84% The energy difference between them 00:45:21.890 --> 00:45:25.420 align:middle line:84% then just has this pretty simple expression. 00:45:25.420 --> 00:45:27.970 align:middle line:84% It'll be the difference of the inverse squares 00:45:27.970 --> 00:45:30.610 align:middle line:84% because the energy for either state alone goes like 1 over n 00:45:30.610 --> 00:45:32.570 align:middle line:90% squared. 00:45:32.570 --> 00:45:34.965 align:middle line:84% And now, Bohr starts to get excited. 00:45:34.965 --> 00:45:36.340 align:middle line:84% In fact, this is why anyone began 00:45:36.340 --> 00:45:38.080 align:middle line:90% taking him seriously at all. 00:45:38.080 --> 00:45:39.640 align:middle line:84% Much like with Einstein, he hadn't 00:45:39.640 --> 00:45:41.710 align:middle line:84% proven that the angular momentum should 00:45:41.710 --> 00:45:43.150 align:middle line:90% be quantized and discrete. 00:45:43.150 --> 00:45:45.710 align:middle line:84% He hadn't even really given very good arguments for it. 00:45:45.710 --> 00:45:48.160 align:middle line:84% But he basically says, give me a moment. 00:45:48.160 --> 00:45:51.820 align:middle line:84% Let me show you what we get if we adopt that assumption. 00:45:51.820 --> 00:45:53.350 align:middle line:90% And why was Bohr excited? 00:45:53.350 --> 00:45:56.680 align:middle line:84% Because by taking on that simple looking but otherwise not 00:45:56.680 --> 00:46:00.250 align:middle line:84% well-motivated assumption, this special quantum condition, 00:46:00.250 --> 00:46:03.190 align:middle line:84% he now found that the energy differences 00:46:03.190 --> 00:46:05.320 align:middle line:84% between these discrete states of motion 00:46:05.320 --> 00:46:09.160 align:middle line:84% of an electron in hydrogen should reproduce 00:46:09.160 --> 00:46:11.800 align:middle line:84% the already well measured, well characterized 00:46:11.800 --> 00:46:15.730 align:middle line:84% behavior of the light that comes out of hydrogen atoms when 00:46:15.730 --> 00:46:16.510 align:middle line:90% we excite them. 00:46:16.510 --> 00:46:18.880 align:middle line:84% If you add some energy external energy 00:46:18.880 --> 00:46:21.970 align:middle line:84% to a gas of hydrogen atoms, they will 00:46:21.970 --> 00:46:26.710 align:middle line:84% radiate at very specific colors, the emission spectrum. 00:46:26.710 --> 00:46:30.190 align:middle line:84% The spectral lines that will come out of excited hydrogen 00:46:30.190 --> 00:46:33.720 align:middle line:84% have a very specific pattern to the frequencies. 00:46:33.720 --> 00:46:35.963 align:middle line:90% And this is actually real data. 00:46:35.963 --> 00:46:37.880 align:middle line:84% You can actually see these with the naked eye. 00:46:37.880 --> 00:46:41.540 align:middle line:84% Three of the lines that come out are in the visible range 00:46:41.540 --> 00:46:44.270 align:middle line:90% for ordinary human eyesight. 00:46:44.270 --> 00:46:46.482 align:middle line:84% And they're very discrete emission lines, 00:46:46.482 --> 00:46:47.690 align:middle line:90% the so-called spectral lines. 00:46:47.690 --> 00:46:50.060 align:middle line:84% These have been measured in the 1880s-- 00:46:50.060 --> 00:46:53.100 align:middle line:84% in fact, it turns out, the very year that Bohr was born. 00:46:53.100 --> 00:46:55.230 align:middle line:84% These were measured by a German schoolteacher, 00:46:55.230 --> 00:46:57.590 align:middle line:84% a German language-speaking schoolteacher named 00:46:57.590 --> 00:46:59.330 align:middle line:90% Johann Balmer. 00:46:59.330 --> 00:47:01.730 align:middle line:84% These were known as the Balmer series. 00:47:01.730 --> 00:47:03.440 align:middle line:84% After that, there were other series 00:47:03.440 --> 00:47:06.260 align:middle line:84% that had been measured that were in either the infrared 00:47:06.260 --> 00:47:07.220 align:middle line:90% or the ultraviolet. 00:47:07.220 --> 00:47:09.020 align:middle line:84% But the three characteristic lines 00:47:09.020 --> 00:47:11.840 align:middle line:84% to which our eyes are usually sensitive 00:47:11.840 --> 00:47:13.700 align:middle line:84% is a simple series of three lines. 00:47:13.700 --> 00:47:17.252 align:middle line:84% And these had a numerical regularity to them 00:47:17.252 --> 00:47:18.710 align:middle line:84% that had otherwise been pretty much 00:47:18.710 --> 00:47:21.140 align:middle line:90% unexamined and unexplained. 00:47:21.140 --> 00:47:24.530 align:middle line:84% But it became clear you could identify 00:47:24.530 --> 00:47:27.920 align:middle line:84% each of these parts of the Balmer spectrum 00:47:27.920 --> 00:47:31.520 align:middle line:84% as being a transition between one integer 00:47:31.520 --> 00:47:32.870 align:middle line:90% squared and another. 00:47:32.870 --> 00:47:34.730 align:middle line:84% And there was some overall constant called 00:47:34.730 --> 00:47:36.230 align:middle line:84% R named for a different researcher, 00:47:36.230 --> 00:47:39.050 align:middle line:84% Rydberg, that set, again, the quantitative scale 00:47:39.050 --> 00:47:42.050 align:middle line:84% for the actual frequencies of that shade of purple, 00:47:42.050 --> 00:47:44.490 align:middle line:84% that shade of blue, and this shade of red. 00:47:44.490 --> 00:47:47.810 align:middle line:84% And so the Balmer series would come about 00:47:47.810 --> 00:47:51.110 align:middle line:84% if you simply said there's some overall empirical constant, R, 00:47:51.110 --> 00:47:52.400 align:middle line:90% the Rydberg constant. 00:47:52.400 --> 00:47:54.830 align:middle line:84% And the light that we see would correspond 00:47:54.830 --> 00:47:57.740 align:middle line:84% to a transition between, say, n equals 3 to n equals 2. 00:47:57.740 --> 00:48:02.060 align:middle line:84% That would be the red one, relatively long wavelength, 00:48:02.060 --> 00:48:03.050 align:middle line:90% lower energy. 00:48:03.050 --> 00:48:05.780 align:middle line:84% There could be a transition from n equals 4 to n equals 2. 00:48:05.780 --> 00:48:09.350 align:middle line:84% That would light up to our eyes like this nice turquoisey blue. 00:48:09.350 --> 00:48:11.570 align:middle line:84% Or from n equals 5 to n equals 2, that would give us 00:48:11.570 --> 00:48:12.720 align:middle line:90% the deeper purple. 00:48:12.720 --> 00:48:14.780 align:middle line:84% So now, Bohr could say, well, there's 00:48:14.780 --> 00:48:17.120 align:middle line:84% an energy difference between these discrete states 00:48:17.120 --> 00:48:18.050 align:middle line:90% of motion. 00:48:18.050 --> 00:48:21.650 align:middle line:84% When an electron moved, made a transition from an excited 00:48:21.650 --> 00:48:23.750 align:middle line:84% state, and we had to add external energy 00:48:23.750 --> 00:48:25.850 align:middle line:84% to these hydrogen atoms, maybe, Bohr 00:48:25.850 --> 00:48:30.110 align:middle line:84% says, that bumps them up to an excited state of motion. n 00:48:30.110 --> 00:48:31.370 align:middle line:90% gets larger. 00:48:31.370 --> 00:48:34.160 align:middle line:84% At some point, the atom will relax back down 00:48:34.160 --> 00:48:36.020 align:middle line:90% to a lower state of energy. 00:48:36.020 --> 00:48:39.410 align:middle line:84% And maybe the light that gets submitted, this emission 00:48:39.410 --> 00:48:42.170 align:middle line:84% spectral line, is simply the difference in energy 00:48:42.170 --> 00:48:46.550 align:middle line:84% between the excited state of the electron's motion and the lower 00:48:46.550 --> 00:48:47.730 align:middle line:90% energy state. 00:48:47.730 --> 00:48:51.860 align:middle line:84% So the energy that comes out in the form of light, the energy 00:48:51.860 --> 00:48:53.360 align:middle line:84% difference is exactly the difference 00:48:53.360 --> 00:48:57.620 align:middle line:84% between these otherwise stable, quantum stable states 00:48:57.620 --> 00:48:58.680 align:middle line:90% of the electron. 00:48:58.680 --> 00:49:02.750 align:middle line:84% So not only did Bohr find the same form for the difference 00:49:02.750 --> 00:49:05.060 align:middle line:84% between the energies of those two states, 00:49:05.060 --> 00:49:07.520 align:middle line:84% he can now calculate this empirical constant, 00:49:07.520 --> 00:49:10.110 align:middle line:84% the Rydberg constant, from first principles. 00:49:10.110 --> 00:49:11.540 align:middle line:84% And when he plugged in the values 00:49:11.540 --> 00:49:13.820 align:middle line:84% for the mass of the electron, the charge, and Planck's 00:49:13.820 --> 00:49:17.630 align:middle line:84% constant, he got a remarkable match to this empirical value 00:49:17.630 --> 00:49:18.950 align:middle line:90% for the Rydberg constant. 00:49:18.950 --> 00:49:20.780 align:middle line:84% If you have trouble keeping that in mind, 00:49:20.780 --> 00:49:24.860 align:middle line:84% I recommend this historian's way to remember the Balmer series. 00:49:24.860 --> 00:49:28.010 align:middle line:84% Many, many years later, well after Bohr's death, 00:49:28.010 --> 00:49:31.160 align:middle line:84% his collections of his most important works 00:49:31.160 --> 00:49:33.980 align:middle line:84% were republished in a three-volume set. 00:49:33.980 --> 00:49:37.040 align:middle line:84% And the editors very, very amusingly 00:49:37.040 --> 00:49:39.080 align:middle line:84% colored the books to match the Balmer series. 00:49:39.080 --> 00:49:40.490 align:middle line:90% So volume 1 is the red. 00:49:40.490 --> 00:49:42.230 align:middle line:90% Volume 2 is the turquoisey blue. 00:49:42.230 --> 00:49:44.580 align:middle line:90% And volume 3 is the purple. 00:49:44.580 --> 00:49:45.080 align:middle line:90% OK. 00:49:45.080 --> 00:49:47.450 align:middle line:84% So at first, Bohr was actually reluctant to publish 00:49:47.450 --> 00:49:48.440 align:middle line:90% those results. 00:49:48.440 --> 00:49:50.690 align:middle line:84% Partly, remember, he'd only treated hydrogen. 00:49:50.690 --> 00:49:52.820 align:middle line:84% And he set out at the start of his postdoc trying 00:49:52.820 --> 00:49:55.760 align:middle line:84% to explain every single atom on the periodic table, 00:49:55.760 --> 00:49:58.970 align:middle line:84% every single element, which is pretty ridiculous. 00:49:58.970 --> 00:50:01.790 align:middle line:84% So he had fallen approximately 100 steps short 00:50:01.790 --> 00:50:03.830 align:middle line:84% of his goal, 90 some-odd steps short. 00:50:03.830 --> 00:50:06.800 align:middle line:84% Happily, his postdoc advisor, Ernest Rutherford, 00:50:06.800 --> 00:50:10.273 align:middle line:84% said, explaining hydrogen is pretty good. 00:50:10.273 --> 00:50:11.690 align:middle line:84% And you should publish because you 00:50:11.690 --> 00:50:15.350 align:middle line:84% have this remarkable, unexpected agreement, an accounting 00:50:15.350 --> 00:50:18.720 align:middle line:84% now for things like the Balmer series of these spectral lines. 00:50:18.720 --> 00:50:21.230 align:middle line:84% So Rutherford convinced the young Bohr to publish. 00:50:21.230 --> 00:50:24.590 align:middle line:84% And Bohr actually published his trilogy of related articles 00:50:24.590 --> 00:50:29.310 align:middle line:84% in 1913, On the Constitution of Atoms and Molecules. 00:50:29.310 --> 00:50:33.470 align:middle line:84% So what really became central was this new kind of hypothesis 00:50:33.470 --> 00:50:35.420 align:middle line:90% of this quantum condition. 00:50:35.420 --> 00:50:37.520 align:middle line:84% For reasons that still weren't at all clear, 00:50:37.520 --> 00:50:41.210 align:middle line:84% they were not proven, they weren't even really derived 00:50:41.210 --> 00:50:46.970 align:middle line:84% or motivated, but if one takes a heuristic suggestion that maybe 00:50:46.970 --> 00:50:50.870 align:middle line:84% the angular momentum associated with the motion of electrons 00:50:50.870 --> 00:50:55.250 align:middle line:84% could only take on quantized or discrete values and h-bar, 00:50:55.250 --> 00:50:57.110 align:middle line:84% then that would immediately restrict 00:50:57.110 --> 00:51:00.620 align:middle line:84% the locations, the distances between the electrons 00:51:00.620 --> 00:51:02.340 align:middle line:90% and the positive nucleus. 00:51:02.340 --> 00:51:05.000 align:middle line:84% Now, you have a discrete series of states of motion. 00:51:05.000 --> 00:51:08.780 align:middle line:84% Only for those, for some reason, would the atom remains stable. 00:51:08.780 --> 00:51:10.910 align:middle line:84% There's some new ingredient that had 00:51:10.910 --> 00:51:13.910 align:middle line:84% been missing in Rutherford's own picture that now might account 00:51:13.910 --> 00:51:16.460 align:middle line:90% for the stability of matter. 00:51:16.460 --> 00:51:19.910 align:middle line:84% When an electron is in one of these special quantized units, 00:51:19.910 --> 00:51:21.020 align:middle line:90% it won't radiate. 00:51:21.020 --> 00:51:24.350 align:middle line:84% It will only radiate when it jumps between these levels. 00:51:24.350 --> 00:51:28.690 align:middle line:84% And that will account for the emission spectrum. 00:51:28.690 --> 00:51:30.920 align:middle line:84% Now, of course, some questions still remained. 00:51:30.920 --> 00:51:32.860 align:middle line:84% Why don't we see this kind of discreteness 00:51:32.860 --> 00:51:34.580 align:middle line:90% in ordinary experience? 00:51:34.580 --> 00:51:38.780 align:middle line:84% So one of the next things that Bohr occupied himself with-- 00:51:38.780 --> 00:51:41.750 align:middle line:84% and it actually went over the next four or five years. 00:51:41.750 --> 00:51:44.020 align:middle line:90% It was a non-trivial exercise-- 00:51:44.020 --> 00:51:46.710 align:middle line:84% became known as the correspondence principle. 00:51:46.710 --> 00:51:48.460 align:middle line:84% Again, this was something that Bohr really 00:51:48.460 --> 00:51:50.440 align:middle line:84% championed, and worked out, and then 00:51:50.440 --> 00:51:53.020 align:middle line:84% became enormously influential in these kind 00:51:53.020 --> 00:51:57.190 align:middle line:84% of later years of what we call the old quantum theory. 00:51:57.190 --> 00:52:00.250 align:middle line:84% These quantum ideas seemed to impose some new break 00:52:00.250 --> 00:52:01.180 align:middle line:90% from experience. 00:52:01.180 --> 00:52:03.760 align:middle line:84% Something that we usually think of as continuous 00:52:03.760 --> 00:52:05.170 align:middle line:90% can only be discrete. 00:52:05.170 --> 00:52:08.050 align:middle line:84% In our ordinary experience, we don't see that kind of lock 00:52:08.050 --> 00:52:09.460 align:middle line:90% in step discreteness. 00:52:09.460 --> 00:52:13.060 align:middle line:84% And so Bohr wanted to make sense of the two different regimes 00:52:13.060 --> 00:52:16.900 align:middle line:84% and see if there was a way one could slide over 00:52:16.900 --> 00:52:18.292 align:middle line:90% into the other. 00:52:18.292 --> 00:52:20.500 align:middle line:84% And so that's what became known as the correspondence 00:52:20.500 --> 00:52:23.890 align:middle line:84% principle, which was to say, in the limit of very large quantum 00:52:23.890 --> 00:52:27.130 align:middle line:84% numbers, for very highly excited atoms in this case, where 00:52:27.130 --> 00:52:29.150 align:middle line:90% n is much, much larger than 1-- 00:52:29.150 --> 00:52:31.460 align:middle line:84% still an integer, but much larger than 1-- 00:52:31.460 --> 00:52:33.410 align:middle line:84% these quantum systems should begin 00:52:33.410 --> 00:52:36.020 align:middle line:84% to reproduce the more expected continuous 00:52:36.020 --> 00:52:38.300 align:middle line:90% or classical behavior. 00:52:38.300 --> 00:52:41.000 align:middle line:84% And again, if these next few steps 00:52:41.000 --> 00:52:44.330 align:middle line:84% don't make immediate sense, you're in good company. 00:52:44.330 --> 00:52:45.410 align:middle line:90% Don't worry. 00:52:45.410 --> 00:52:46.940 align:middle line:84% The slides are on the Canvas site. 00:52:46.940 --> 00:52:51.060 align:middle line:84% You can go through these steps, the algebra on your own. 00:52:51.060 --> 00:52:53.820 align:middle line:84% I just want to make sure that we understand his reasoning here. 00:52:53.820 --> 00:52:56.278 align:middle line:84% So I to go through his main argument for the correspondence 00:52:56.278 --> 00:52:56.854 align:middle line:90% principle. 00:52:56.854 --> 00:52:59.640 align:middle line:90% 00:52:59.640 --> 00:53:03.330 align:middle line:84% According to Maxwell's, again, highly successful work 00:53:03.330 --> 00:53:07.770 align:middle line:84% on electromagnetism, the frequency of light, 00:53:07.770 --> 00:53:10.050 align:middle line:84% or of any electromagnetic wave that's emitted-- 00:53:10.050 --> 00:53:11.730 align:middle line:84% so we'll call that new radiation. 00:53:11.730 --> 00:53:15.120 align:middle line:84% That's the frequency of the electromagnetic waves 00:53:15.120 --> 00:53:16.590 align:middle line:90% that come out-- 00:53:16.590 --> 00:53:19.285 align:middle line:84% that should be equal to the mechanical motion, 00:53:19.285 --> 00:53:20.910 align:middle line:84% the frequency of the mechanical motion. 00:53:20.910 --> 00:53:23.880 align:middle line:84% If you think about a dipole antenna, 00:53:23.880 --> 00:53:28.080 align:middle line:84% if you shake an electric charge up and down on a conducting 00:53:28.080 --> 00:53:30.630 align:middle line:84% wire, the electromagnetic waves that 00:53:30.630 --> 00:53:33.570 align:middle line:84% come from accelerating an electric charge 00:53:33.570 --> 00:53:36.120 align:middle line:84% should be directly related to the motion 00:53:36.120 --> 00:53:37.240 align:middle line:90% of the charge itself. 00:53:37.240 --> 00:53:39.390 align:middle line:84% So the frequency of radiation should be equal to 00:53:39.390 --> 00:53:43.105 align:middle line:90% or maybe a higher multiple. 00:53:43.105 --> 00:53:44.730 align:middle line:84% But it should be basically proportional 00:53:44.730 --> 00:53:47.940 align:middle line:84% to, if not directly equal to, the mechanical motion 00:53:47.940 --> 00:53:51.870 align:middle line:84% of the charge whose acceleration is emitting that radiation. 00:53:51.870 --> 00:53:54.152 align:middle line:84% That comes directly out of Maxwell's work. 00:53:54.152 --> 00:53:56.610 align:middle line:84% And we use that all the time in things like antenna theory. 00:53:56.610 --> 00:53:58.710 align:middle line:90% It still works to this day. 00:53:58.710 --> 00:54:01.360 align:middle line:84% So Bohr said, OK, well, let's figure out these two 00:54:01.360 --> 00:54:04.030 align:middle line:84% different quantities and see how they relate to each other. 00:54:04.030 --> 00:54:06.970 align:middle line:84% He begins by thinking about the mechanical motion, 00:54:06.970 --> 00:54:11.200 align:middle line:84% the frequency of that electron constantly whirling 00:54:11.200 --> 00:54:12.980 align:middle line:90% around the nucleus. 00:54:12.980 --> 00:54:16.000 align:middle line:84% So the frequency would be 1 over the period-- how long does 00:54:16.000 --> 00:54:18.810 align:middle line:84% it take the electron to complete an orbit, just like the Earth 00:54:18.810 --> 00:54:20.650 align:middle line:84% taking a year to go around the sun. 00:54:20.650 --> 00:54:25.300 align:middle line:84% So the mechanical frequency is 1 over the orbital period. 00:54:25.300 --> 00:54:27.580 align:middle line:84% And that, for a perfectly circular orbit 00:54:27.580 --> 00:54:30.610 align:middle line:84% to keep things simple, would be the orbital velocity, 00:54:30.610 --> 00:54:33.730 align:middle line:84% the magnitude of the velocity, so the speed divided 00:54:33.730 --> 00:54:35.260 align:middle line:84% by the distance it has to travel. 00:54:35.260 --> 00:54:38.410 align:middle line:84% It has to travel one circumference, 2 pi r. 00:54:38.410 --> 00:54:40.480 align:middle line:84% It does so at a speed, v. That's how 00:54:40.480 --> 00:54:44.320 align:middle line:84% we determine the inverse period, or the frequency. 00:54:44.320 --> 00:54:46.540 align:middle line:84% Well, once again, from the balance of forces, 00:54:46.540 --> 00:54:50.950 align:middle line:84% he has an expression for v, from balancing the classical forces 00:54:50.950 --> 00:54:53.390 align:middle line:84% with the quantized angular momentum. 00:54:53.390 --> 00:54:55.390 align:middle line:84% So he can substitute in for v. He 00:54:55.390 --> 00:54:57.730 align:middle line:84% has a new expression for the mechanical frequency. 00:54:57.730 --> 00:55:01.560 align:middle line:84% This is now of the electron in motion around the atom. 00:55:01.560 --> 00:55:04.080 align:middle line:84% And now, he wants to turn to that other thing he wants 00:55:04.080 --> 00:55:06.780 align:middle line:84% to compare it to, the frequency of the radiation that 00:55:06.780 --> 00:55:07.950 align:middle line:90% comes out. 00:55:07.950 --> 00:55:10.500 align:middle line:84% Now, in his model, the radiation frequency 00:55:10.500 --> 00:55:14.670 align:middle line:84% is not given in that earlier derivation by anything 00:55:14.670 --> 00:55:19.350 align:middle line:84% having to do with the mechanical motion around the nucleus 00:55:19.350 --> 00:55:20.400 align:middle line:90% of the electron. 00:55:20.400 --> 00:55:23.430 align:middle line:84% It actually comes from the energy differences when 00:55:23.430 --> 00:55:27.060 align:middle line:84% an electron in an excited state will emit some of that energy 00:55:27.060 --> 00:55:29.070 align:middle line:84% and drop down to a lower energy state, 00:55:29.070 --> 00:55:31.712 align:middle line:84% rather than having anything to do with this mechanical motion. 00:55:31.712 --> 00:55:33.420 align:middle line:84% That's why it looks like it's in conflict 00:55:33.420 --> 00:55:35.970 align:middle line:90% with Maxwell's electrodynamics. 00:55:35.970 --> 00:55:39.030 align:middle line:84% So we saw Bohr had derived this expression for the energy, 00:55:39.030 --> 00:55:42.900 align:middle line:84% for the frequency of the light that comes out as radiated. 00:55:42.900 --> 00:55:45.180 align:middle line:84% But again, he can start plugging in things he knows. 00:55:45.180 --> 00:55:49.830 align:middle line:84% He can use the definition of this radius, the Bohr radius. 00:55:49.830 --> 00:55:52.310 align:middle line:84% And now, he can consider not the regime of n 00:55:52.310 --> 00:55:55.700 align:middle line:84% equals 1, or 2, or 3 of small principle quantum 00:55:55.700 --> 00:55:59.450 align:middle line:84% numbers for states of motion that are near the lowest energy 00:55:59.450 --> 00:56:00.200 align:middle line:90% state. 00:56:00.200 --> 00:56:03.110 align:middle line:84% But he wants to think about large quantum numbers, 00:56:03.110 --> 00:56:06.650 align:middle line:84% away from the most quantumness of the behavior 00:56:06.650 --> 00:56:07.940 align:middle line:90% of this hydrogen atom. 00:56:07.940 --> 00:56:09.650 align:middle line:90% Is there a regime? 00:56:09.650 --> 00:56:12.500 align:middle line:84% Is there a different regime in which 00:56:12.500 --> 00:56:17.450 align:middle line:84% the behavior predicted by this quantum theoretic description 00:56:17.450 --> 00:56:21.260 align:middle line:84% will carry over to the behavior of the expected classical 00:56:21.260 --> 00:56:22.110 align:middle line:90% system? 00:56:22.110 --> 00:56:26.240 align:middle line:84% So let's consider a very large principle number 00:56:26.240 --> 00:56:28.340 align:middle line:90% n, a very highly excited state. 00:56:28.340 --> 00:56:30.110 align:middle line:84% And now, let's consider the radiation 00:56:30.110 --> 00:56:34.610 align:middle line:84% that would come out between two neighboring, but very large 00:56:34.610 --> 00:56:36.080 align:middle line:90% high n states. 00:56:36.080 --> 00:56:40.430 align:middle line:84% So consider both n1 and n2 to be very larger 00:56:40.430 --> 00:56:42.480 align:middle line:90% than 1 and near each other. 00:56:42.480 --> 00:56:44.840 align:middle line:84% Let's say the difference between n2 and n1 00:56:44.840 --> 00:56:47.840 align:middle line:84% is small compared to either them alone. 00:56:47.840 --> 00:56:51.823 align:middle line:84% Then we can expand this 1 over n1 squared minus 1 00:56:51.823 --> 00:56:53.240 align:middle line:84% over n2 squared-- just do a Taylor 00:56:53.240 --> 00:56:56.270 align:middle line:84% expansion-- to first order in this tiny difference. 00:56:56.270 --> 00:56:58.290 align:middle line:84% We get an expression that looks like this. 00:56:58.290 --> 00:57:02.000 align:middle line:84% Now, we can begin comparing the frequency of the light that 00:57:02.000 --> 00:57:04.250 align:middle line:84% comes out, the electromagnetic radiation, 00:57:04.250 --> 00:57:06.770 align:middle line:84% compare that to, indeed, the mechanical motion, 00:57:06.770 --> 00:57:09.950 align:middle line:84% motion of the electron itself in one of these very high n, 00:57:09.950 --> 00:57:11.870 align:middle line:90% large n orbits. 00:57:11.870 --> 00:57:15.218 align:middle line:84% And now, we just take the ratio of these expressions, once 00:57:15.218 --> 00:57:17.510 align:middle line:84% again using other things that we've already worked hard 00:57:17.510 --> 00:57:18.350 align:middle line:90% to learn. 00:57:18.350 --> 00:57:20.900 align:middle line:84% Now, you find that in that regime, 00:57:20.900 --> 00:57:23.488 align:middle line:84% not near the lowest energy state, where 00:57:23.488 --> 00:57:25.280 align:middle line:84% we expect the quantumness, the discreteness 00:57:25.280 --> 00:57:30.920 align:middle line:84% to be most on display, but at some very highly excited state, 00:57:30.920 --> 00:57:33.810 align:middle line:84% the ratio should, in fact, go back to 1. 00:57:33.810 --> 00:57:36.240 align:middle line:84% Maxwell said that ratio should be identically 1. 00:57:36.240 --> 00:57:39.450 align:middle line:84% In the limit of large principle quantum number, 00:57:39.450 --> 00:57:41.820 align:middle line:84% that ratio, once again, goes back to 1, 00:57:41.820 --> 00:57:44.760 align:middle line:84% even though the way we account for it is totally different. 00:57:44.760 --> 00:57:47.040 align:middle line:84% We don't say, according to Bohr's model, 00:57:47.040 --> 00:57:49.932 align:middle line:84% that the radiation comes out with frequency nu 00:57:49.932 --> 00:57:52.140 align:middle line:84% because that's the frequency at which the electron is 00:57:52.140 --> 00:57:53.490 align:middle line:90% physically spinning. 00:57:53.490 --> 00:57:57.000 align:middle line:84% But it turns out the difference between neighboring highly 00:57:57.000 --> 00:58:01.200 align:middle line:84% excited states obeys basically the Maxwellian relation 00:58:01.200 --> 00:58:02.220 align:middle line:90% after all. 00:58:02.220 --> 00:58:04.920 align:middle line:84% This becomes known as the correspondence principle, 00:58:04.920 --> 00:58:07.530 align:middle line:84% that the behavior should smoothly 00:58:07.530 --> 00:58:11.910 align:middle line:84% morph onto the classical Newtonian Maxwellian behavior 00:58:11.910 --> 00:58:13.680 align:middle line:90% in an appropriate limit. 00:58:13.680 --> 00:58:15.570 align:middle line:84% It might break from that expectation 00:58:15.570 --> 00:58:19.810 align:middle line:84% dramatically in a different regime-- 00:58:19.810 --> 00:58:22.200 align:middle line:84% in this case, small principle quantum numbers, 00:58:22.200 --> 00:58:23.910 align:middle line:90% when n is 1, 2, 3, or 4. 00:58:23.910 --> 00:58:26.310 align:middle line:84% But there should be some smooth, almost 00:58:26.310 --> 00:58:29.640 align:middle line:84% like an asymptotic matching because, 00:58:29.640 --> 00:58:32.100 align:middle line:84% then as now, Maxwell's equations work really 00:58:32.100 --> 00:58:34.680 align:middle line:84% well for understanding things like the radiation coming off 00:58:34.680 --> 00:58:36.000 align:middle line:90% of a dipole antenna. 00:58:36.000 --> 00:58:39.570 align:middle line:84% So Bohr didn't want to lose all the extraordinary successes 00:58:39.570 --> 00:58:43.230 align:middle line:84% of Maxwell or Newton, but wanted to have an account for why 00:58:43.230 --> 00:58:45.060 align:middle line:84% things might not always only look 00:58:45.060 --> 00:58:49.390 align:middle line:84% like that when you get really down to the scale of atoms. 00:58:49.390 --> 00:58:51.270 align:middle line:84% So for large quantum numbers, quantum systems 00:58:51.270 --> 00:58:53.940 align:middle line:84% really do start to behave like classical ones. 00:58:53.940 --> 00:58:57.300 align:middle line:84% In more modern language, we'd say the emission spectrum looks 00:58:57.300 --> 00:59:01.440 align:middle line:84% basically continuous, even though it looks highly discrete 00:59:01.440 --> 00:59:03.210 align:middle line:90% far away from that regime. 00:59:03.210 --> 00:59:03.850 align:middle line:90% OK. 00:59:03.850 --> 00:59:04.980 align:middle line:84% I'm going to wrap up the Bohr part. 00:59:04.980 --> 00:59:07.090 align:middle line:84% We'll pause for discussion in just in a moment. 00:59:07.090 --> 00:59:10.470 align:middle line:84% So Bohr further developed Rutherford's solar system 00:59:10.470 --> 00:59:12.840 align:middle line:84% or nuclear model of atomic structure. 00:59:12.840 --> 00:59:17.070 align:middle line:84% He remarkably was able to account for empirical results, 00:59:17.070 --> 00:59:19.350 align:middle line:84% like the emission spectrum from hydrogen. 00:59:19.350 --> 00:59:20.940 align:middle line:84% But much like Rutherford's work, this 00:59:20.940 --> 00:59:22.740 align:middle line:84% starts raising several new questions, 00:59:22.740 --> 00:59:24.750 align:middle line:84% even as it starts to answer some. 00:59:24.750 --> 00:59:28.440 align:middle line:84% For one thing, again, despite Bohr's remarkable ambition, 00:59:28.440 --> 00:59:32.130 align:middle line:84% this whole scheme only seemed to work for single electron atoms 00:59:32.130 --> 00:59:33.160 align:middle line:90% or ions-- 00:59:33.160 --> 00:59:35.850 align:middle line:84% so a hydrogen atom, which is electrically neutral, 00:59:35.850 --> 00:59:41.250 align:middle line:84% or an ionized atom of helium, which one of its two electrons 00:59:41.250 --> 00:59:44.370 align:middle line:84% has stripped away, you only have one electron in orbit, 00:59:44.370 --> 00:59:48.050 align:middle line:84% or doubly ionized lithium, that idea. 00:59:48.050 --> 00:59:50.180 align:middle line:84% Moreover, again as I've tried to emphasize, 00:59:50.180 --> 00:59:51.740 align:middle line:84% Bohr really didn't have any answer 00:59:51.740 --> 00:59:56.540 align:middle line:84% for why we might impose this brand new seemingly ad 00:59:56.540 --> 00:59:59.690 align:middle line:84% hoc quantum condition that the angular momentum should only 00:59:59.690 --> 01:00:03.452 align:middle line:84% appear in integer units of h-bar. 01:00:03.452 --> 01:00:04.910 align:middle line:84% Another question, when people began 01:00:04.910 --> 01:00:07.760 align:middle line:84% to try to visualize these warring 01:00:07.760 --> 01:00:10.700 align:middle line:84% electrons in these discrete states of motion, 01:00:10.700 --> 01:00:13.430 align:middle line:84% what happens to electrons between stable orbits? 01:00:13.430 --> 01:00:16.850 align:middle line:84% Are they literally falling from some large, excited state 01:00:16.850 --> 01:00:18.740 align:middle line:90% towards another one? 01:00:18.740 --> 01:00:21.140 align:middle line:84% What determined when an electron would make one 01:00:21.140 --> 01:00:23.570 align:middle line:90% of these sudden discrete jumps? 01:00:23.570 --> 01:00:26.780 align:middle line:84% How did an electron know how much energy to radiate? 01:00:26.780 --> 01:00:30.710 align:middle line:84% It has to give up a delta E exactly equal to the energy 01:00:30.710 --> 01:00:32.210 align:middle line:90% to be radiated away. 01:00:32.210 --> 01:00:35.360 align:middle line:84% And yet, if the electron can only 01:00:35.360 --> 01:00:39.260 align:middle line:84% land at a particular value of its lower energy state, 01:00:39.260 --> 01:00:41.743 align:middle line:84% how does it know, so to speak, in advance 01:00:41.743 --> 01:00:43.410 align:middle line:84% where it's going to land and, therefore, 01:00:43.410 --> 01:00:44.840 align:middle line:90% how much energy to radiate? 01:00:44.840 --> 01:00:49.350 align:middle line:84% How come it never messes up and radiates a different amount 01:00:49.350 --> 01:00:53.460 align:middle line:84% of energy for which it could no longer land at a stable orbit? 01:00:53.460 --> 01:00:55.770 align:middle line:90% And then another question was-- 01:00:55.770 --> 01:00:58.590 align:middle line:84% it became clear well before Bohr's time 01:00:58.590 --> 01:01:01.110 align:middle line:84% that, in addition to a very particular pattern 01:01:01.110 --> 01:01:04.440 align:middle line:84% of the colors, the frequencies of these emitted 01:01:04.440 --> 01:01:07.020 align:middle line:84% spectral lines, they also came with different brightnesses, 01:01:07.020 --> 01:01:07.980 align:middle line:90% different intensities. 01:01:07.980 --> 01:01:11.100 align:middle line:84% Not every line that you could measure of these emission lines 01:01:11.100 --> 01:01:12.690 align:middle line:90% was equally bright. 01:01:12.690 --> 01:01:15.120 align:middle line:84% And Bohr's model didn't seem to have any way of accounting 01:01:15.120 --> 01:01:19.020 align:middle line:84% for that other kind of equally salient set of measurements 01:01:19.020 --> 01:01:20.440 align:middle line:90% about the spectral lines. 01:01:20.440 --> 01:01:25.200 align:middle line:84% So some remarkable and surprising positive 01:01:25.200 --> 01:01:26.940 align:middle line:90% steps from this Bohr model. 01:01:26.940 --> 01:01:30.070 align:middle line:84% But again, opening up a whole new set of questions as well. 01:01:30.070 --> 01:01:32.700 align:middle line:84% So I'll pause there and ask if there's any questions on that. 01:01:32.700 --> 01:01:40.950 align:middle line:90% 01:01:40.950 --> 01:01:41.770 align:middle line:90% Oh, very good. 01:01:41.770 --> 01:01:44.460 align:middle line:84% So there's a question, as you can see in the chat, 01:01:44.460 --> 01:01:46.210 align:middle line:84% we have this reading, which I like a lot-- 01:01:46.210 --> 01:01:48.335 align:middle line:84% and we'll talk a little bit more about this reading 01:01:48.335 --> 01:01:50.190 align:middle line:84% in the next class as well, the reading 01:01:50.190 --> 01:01:54.610 align:middle line:84% by Megan Shields Formato who, by the way, used to TA this class. 01:01:54.610 --> 01:01:57.210 align:middle line:84% So it's a nice homegrown body of work. 01:01:57.210 --> 01:01:58.357 align:middle line:90% Megan is a great colleague. 01:01:58.357 --> 01:01:59.940 align:middle line:84% And when she was still a grad student, 01:01:59.940 --> 01:02:00.960 align:middle line:90% she worked with this question. 01:02:00.960 --> 01:02:02.490 align:middle line:84% And Megan has this really, I think, 01:02:02.490 --> 01:02:12.150 align:middle line:84% very lovely, very eye-opening essay about what kinds of work 01:02:12.150 --> 01:02:13.980 align:middle line:90% got credited then or now. 01:02:13.980 --> 01:02:16.642 align:middle line:84% So we always talk about Bohr did this, Bohr did that. 01:02:16.642 --> 01:02:17.850 align:middle line:90% And Bohr did a lot of things. 01:02:17.850 --> 01:02:19.813 align:middle line:84% But he was almost never doing them on his own. 01:02:19.813 --> 01:02:21.480 align:middle line:84% And we'll see a lot of examples of that, 01:02:21.480 --> 01:02:22.980 align:middle line:84% again, actually in the next lecture. 01:02:22.980 --> 01:02:24.560 align:middle line:90% I placed it in the wrong slot. 01:02:24.560 --> 01:02:26.310 align:middle line:84% And I think that reading works even better 01:02:26.310 --> 01:02:27.690 align:middle line:90% for Wednesday's class. 01:02:27.690 --> 01:02:30.150 align:middle line:84% But Bohr was not only always, always 01:02:30.150 --> 01:02:32.880 align:middle line:84% talking with younger postdocs and younger students 01:02:32.880 --> 01:02:34.700 align:middle line:84% of his own, people who would come 01:02:34.700 --> 01:02:36.450 align:middle line:84% to be like Werner Heisenberg, and Wolfgang 01:02:36.450 --> 01:02:37.660 align:middle line:90% Pauli, and the whole circle. 01:02:37.660 --> 01:02:41.610 align:middle line:84% He was always talking with his very, very patient and talented 01:02:41.610 --> 01:02:44.070 align:middle line:84% wife, Margrethe, who did not have 01:02:44.070 --> 01:02:46.290 align:middle line:84% a formal training in physics, but could certainly 01:02:46.290 --> 01:02:47.910 align:middle line:90% follow a logical argument. 01:02:47.910 --> 01:02:50.520 align:middle line:84% And she seems to have been a very steadying force 01:02:50.520 --> 01:02:54.450 align:middle line:84% to help discipline Bohr's own unfolding syllogisms-- if 01:02:54.450 --> 01:02:55.860 align:middle line:90% A then B kind of thing. 01:02:55.860 --> 01:02:59.415 align:middle line:84% She was his constant sounding board and a kind of like 01:02:59.415 --> 01:03:02.950 align:middle line:84% a-- not debate coach, but just his-- 01:03:02.950 --> 01:03:04.390 align:middle line:90% he would try things out. 01:03:04.390 --> 01:03:06.580 align:middle line:84% And they would talk about things very actively. 01:03:06.580 --> 01:03:10.570 align:middle line:84% And then he would write them up because she 01:03:10.570 --> 01:03:13.450 align:middle line:84% had helped him crystallize or clarify 01:03:13.450 --> 01:03:16.000 align:middle line:84% the order of his arguments and say this is a red Herring, 01:03:16.000 --> 01:03:17.000 align:middle line:90% this doesn't make sense. 01:03:17.000 --> 01:03:21.430 align:middle line:84% So Margrethe was doing, as we now know, a ton of unseen, 01:03:21.430 --> 01:03:26.637 align:middle line:84% behind the scenes work, actual, conceptual work for which we 01:03:26.637 --> 01:03:28.720 align:middle line:84% would then usually just credit Niels Bohr himself. 01:03:28.720 --> 01:03:30.928 align:middle line:84% It would be written up usually only with Bohr's name, 01:03:30.928 --> 01:03:33.970 align:middle line:84% not Bohr and Margrethe, not Niels and Margrethe Bohr. 01:03:33.970 --> 01:03:36.320 align:middle line:84% And I think Megan's piece really draws it out very, 01:03:36.320 --> 01:03:38.218 align:middle line:84% very evocatively with some pretty cool use 01:03:38.218 --> 01:03:39.010 align:middle line:90% of primary sources. 01:03:39.010 --> 01:03:40.177 align:middle line:90% I think she's exactly right. 01:03:40.177 --> 01:03:42.468 align:middle line:84% So we'll see that again and again, especially with Bohr 01:03:42.468 --> 01:03:43.400 align:middle line:90% himself next week. 01:03:43.400 --> 01:03:45.850 align:middle line:84% So the question here is, did Einstein 01:03:45.850 --> 01:03:48.310 align:middle line:84% have a similar relationship with his own partner? 01:03:48.310 --> 01:03:50.900 align:middle line:84% His first wife, Mileva, I've mentioned a few times, 01:03:50.900 --> 01:03:52.360 align:middle line:90% had also been trained-- 01:03:52.360 --> 01:03:54.970 align:middle line:84% in fact, they met as university students. 01:03:54.970 --> 01:03:58.180 align:middle line:84% Mileva was studying physics and mathematics at the ETH. 01:03:58.180 --> 01:04:00.160 align:middle line:90% And they were classmates. 01:04:00.160 --> 01:04:01.970 align:middle line:84% And here, it's really complicated. 01:04:01.970 --> 01:04:04.130 align:middle line:84% I won't spend too long on this because if I 01:04:04.130 --> 01:04:06.620 align:middle line:84% don't watch myself, I'll talk about it for the next eight 01:04:06.620 --> 01:04:06.920 align:middle line:90% hours. 01:04:06.920 --> 01:04:08.837 align:middle line:84% And you all have things to do with your lives. 01:04:08.837 --> 01:04:11.930 align:middle line:84% But I would be glad to direct you to lots of readings. 01:04:11.930 --> 01:04:15.320 align:middle line:84% The short answer is they began talking together 01:04:15.320 --> 01:04:17.780 align:middle line:84% all the time, very much like we now 01:04:17.780 --> 01:04:21.110 align:middle line:84% know that Niels and Margretha Bohr were doing. 01:04:21.110 --> 01:04:24.470 align:middle line:84% Einstein and Mileva Maric were doing that absolutely all 01:04:24.470 --> 01:04:25.340 align:middle line:90% through college. 01:04:25.340 --> 01:04:29.390 align:middle line:84% They have their charming, almost sappy sweet love letters 01:04:29.390 --> 01:04:31.100 align:middle line:84% between them when they would be apart. 01:04:31.100 --> 01:04:33.020 align:middle line:84% I can't wait to talk about my problem set 01:04:33.020 --> 01:04:34.325 align:middle line:90% with you, my dear cherub. 01:04:34.325 --> 01:04:36.890 align:middle line:84% They were very sweet and geeky in a way 01:04:36.890 --> 01:04:39.050 align:middle line:84% that might appeal to this group in particular. 01:04:39.050 --> 01:04:41.630 align:middle line:84% They were study buddies, as well as developing 01:04:41.630 --> 01:04:43.503 align:middle line:90% a real deep relationship. 01:04:43.503 --> 01:04:45.920 align:middle line:84% And as I mentioned before, Einstein would cut his classes. 01:04:45.920 --> 01:04:47.840 align:middle line:84% Mileva was a more diligent student. 01:04:47.840 --> 01:04:50.580 align:middle line:84% She would often take notes and let him study them. 01:04:50.580 --> 01:04:52.760 align:middle line:84% And so there's plenty of evidence of them also 01:04:52.760 --> 01:04:55.250 align:middle line:84% actively talking through questions about, for example, 01:04:55.250 --> 01:05:01.640 align:middle line:84% electrodynamics from like 1896 through 1901, 1902. 01:05:01.640 --> 01:05:04.670 align:middle line:84% Then their path begins to be different, 01:05:04.670 --> 01:05:06.230 align:middle line:84% at least from all we can reconstruct 01:05:06.230 --> 01:05:08.570 align:middle line:84% from the historical documentation, 01:05:08.570 --> 01:05:12.560 align:middle line:84% different than that between, say, Niels and Margretha Bohr. 01:05:12.560 --> 01:05:15.290 align:middle line:84% What happens in the Einstein marriage case 01:05:15.290 --> 01:05:16.855 align:middle line:90% is that they have a young child. 01:05:16.855 --> 01:05:19.073 align:middle line:84% In fact, they have a first child out of wedlock, 01:05:19.073 --> 01:05:21.740 align:middle line:84% a little girl named Lieserl, who then was given up for adoption. 01:05:21.740 --> 01:05:23.157 align:middle line:84% And no one knows what came of her. 01:05:23.157 --> 01:05:26.480 align:middle line:84% So they first have a first child they don't raise on their own. 01:05:26.480 --> 01:05:28.070 align:middle line:84% Then they very quickly get married. 01:05:28.070 --> 01:05:30.320 align:middle line:84% Then they have another child and eventually two. 01:05:30.320 --> 01:05:34.460 align:middle line:84% And then Mileva starts doing what was very typical, 01:05:34.460 --> 01:05:39.260 align:middle line:84% gender-typed family responsibilities 01:05:39.260 --> 01:05:43.770 align:middle line:84% expected of the time and with very little variation 01:05:43.770 --> 01:05:44.270 align:middle line:90% at the time. 01:05:44.270 --> 01:05:46.062 align:middle line:84% Even though they both considered themselves 01:05:46.062 --> 01:05:48.450 align:middle line:84% radical bohemians, who cares what people think, 01:05:48.450 --> 01:05:50.810 align:middle line:84% I don't have to live by society's rules, pretty soon, 01:05:50.810 --> 01:05:54.470 align:middle line:84% they began living by pretty typical Central European rules 01:05:54.470 --> 01:05:55.640 align:middle line:90% or norms. 01:05:55.640 --> 01:05:59.060 align:middle line:84% And that meant Mileva did not pursue her scientific career. 01:05:59.060 --> 01:06:01.820 align:middle line:84% In fact, I think she didn't ever complete her degree. 01:06:01.820 --> 01:06:03.828 align:middle line:84% She dropped out, I'm pretty sure. 01:06:03.828 --> 01:06:04.620 align:middle line:90% I can look that up. 01:06:04.620 --> 01:06:06.110 align:middle line:84% But she either barely got through 01:06:06.110 --> 01:06:07.460 align:middle line:84% with her degree after some interruptions 01:06:07.460 --> 01:06:09.060 align:middle line:84% or perhaps had to interrupt her studies. 01:06:09.060 --> 01:06:09.768 align:middle line:90% I can't remember. 01:06:09.768 --> 01:06:10.580 align:middle line:90% I'll look it up. 01:06:10.580 --> 01:06:13.130 align:middle line:84% She becomes basically a full-time homemaker, 01:06:13.130 --> 01:06:16.190 align:middle line:84% is what we would now say, raising their children 01:06:16.190 --> 01:06:19.070 align:middle line:84% while Einstein then had the full-time job at the patent 01:06:19.070 --> 01:06:19.610 align:middle line:90% office. 01:06:19.610 --> 01:06:22.430 align:middle line:84% And then they seemed not to have talked with anything 01:06:22.430 --> 01:06:25.700 align:middle line:84% like the same intensity about the scientific work, 01:06:25.700 --> 01:06:28.783 align:middle line:84% starting a couple of years before 1905. 01:06:28.783 --> 01:06:30.200 align:middle line:84% So there have been all these kinds 01:06:30.200 --> 01:06:33.650 align:middle line:84% of efforts to tie relativity, in particular, 01:06:33.650 --> 01:06:35.720 align:middle line:90% to a joint conversation. 01:06:35.720 --> 01:06:38.510 align:middle line:84% Maybe Mileva was a key thought partner. 01:06:38.510 --> 01:06:40.830 align:middle line:84% And I would love for that story to be true. 01:06:40.830 --> 01:06:42.980 align:middle line:84% I mean, it would cap off this college romance. 01:06:42.980 --> 01:06:44.300 align:middle line:90% It would just be thrilling. 01:06:44.300 --> 01:06:46.342 align:middle line:84% And I've been convinced by the work 01:06:46.342 --> 01:06:48.050 align:middle line:84% by historians who've looked very squarely 01:06:48.050 --> 01:06:50.960 align:middle line:84% at this, including a lot of women's history, gender 01:06:50.960 --> 01:06:53.720 align:middle line:84% and science scholars, who were very attuned to partnerships 01:06:53.720 --> 01:06:57.080 align:middle line:84% that don't often get a lot of credit, people whose work 01:06:57.080 --> 01:06:58.430 align:middle line:90% we'll read this term. 01:06:58.430 --> 01:07:01.460 align:middle line:84% And I'm convinced by their argument that that seemed not 01:07:01.460 --> 01:07:04.610 align:middle line:84% to have been the nature of the Einstein marriage relationship, 01:07:04.610 --> 01:07:08.150 align:middle line:84% starting in like 1902, 1903, let alone '05. 01:07:08.150 --> 01:07:11.150 align:middle line:84% They quickly became really embittered. 01:07:11.150 --> 01:07:14.810 align:middle line:84% And so by the later 19-teens, they 01:07:14.810 --> 01:07:17.240 align:middle line:90% were basically in open warfare. 01:07:17.240 --> 01:07:18.950 align:middle line:84% And they couldn't wait to get divorced. 01:07:18.950 --> 01:07:20.867 align:middle line:84% And so Einstein couldn't afford to divorce her 01:07:20.867 --> 01:07:22.190 align:middle line:90% until he won the Nobel Prize. 01:07:22.190 --> 01:07:25.790 align:middle line:84% He was so sure he'd win the Nobel Prize that he promised 01:07:25.790 --> 01:07:28.970 align:middle line:84% his Prize winnings to be the divorce settlement before he 01:07:28.970 --> 01:07:32.810 align:middle line:84% won the Prize, like four years before he won the Prize. 01:07:32.810 --> 01:07:34.490 align:middle line:90% Then the Prize came through. 01:07:34.490 --> 01:07:35.480 align:middle line:90% They got divorced. 01:07:35.480 --> 01:07:36.980 align:middle line:84% Einstein, by that point, was already 01:07:36.980 --> 01:07:40.070 align:middle line:84% seeing his second cousin, Elsa, who soon became his wife. 01:07:40.070 --> 01:07:44.330 align:middle line:84% So the story seems actually pretty different than this very 01:07:44.330 --> 01:07:47.450 align:middle line:84% lifelong intellectual partnership between Niels 01:07:47.450 --> 01:07:49.760 align:middle line:84% and Margretha, which, nonetheless, never really got 01:07:49.760 --> 01:07:53.090 align:middle line:84% credited the way that today, I think, we would find much more 01:07:53.090 --> 01:07:53.878 align:middle line:90% appropriate. 01:07:53.878 --> 01:07:55.920 align:middle line:84% That was a long answer to a really good question. 01:07:55.920 --> 01:07:56.920 align:middle line:90% I'd be glad to say more. 01:07:56.920 --> 01:08:00.320 align:middle line:84% There's really a lot, especially in the Einstein marriage 01:08:00.320 --> 01:08:01.430 align:middle line:90% relationship. 01:08:01.430 --> 01:08:05.070 align:middle line:84% But I'm glad that you raised a question about Meghan's piece 01:08:05.070 --> 01:08:06.460 align:middle line:90% about Neil's marriage as well. 01:08:06.460 --> 01:08:07.360 align:middle line:90% That's a great point. 01:08:07.360 --> 01:08:10.570 align:middle line:90% Any other questions on that? 01:08:10.570 --> 01:08:12.450 align:middle line:84% Let me jump in to the last part for today. 01:08:12.450 --> 01:08:13.680 align:middle line:90% The last part is shorter. 01:08:13.680 --> 01:08:15.730 align:middle line:84% We have plenty of time to do this last part. 01:08:15.730 --> 01:08:17.670 align:middle line:84% We saw, with Bohr's work, there were 01:08:17.670 --> 01:08:21.670 align:middle line:84% all these dangling questions about the Bohr model. 01:08:21.670 --> 01:08:24.810 align:middle line:84% And so we're going to see this last moment that really helps 01:08:24.810 --> 01:08:28.770 align:middle line:84% to at least better motivate some of these open questions 01:08:28.770 --> 01:08:32.550 align:middle line:84% from the Bohr model comes fully 10 or 11 years later. 01:08:32.550 --> 01:08:35.700 align:middle line:84% It's introduced by literally a French Prince-- 01:08:35.700 --> 01:08:38.490 align:middle line:84% we don't often get to talk about royalty in this class-- 01:08:38.490 --> 01:08:41.189 align:middle line:84% a French aristocrat named Louis de Broglie. 01:08:41.189 --> 01:08:42.810 align:middle line:84% He was actually the younger brother 01:08:42.810 --> 01:08:45.000 align:middle line:84% of Maurice de Broglie, who also, by this point, 01:08:45.000 --> 01:08:47.490 align:middle line:84% was a very accomplished experimental physicist. 01:08:47.490 --> 01:08:50.100 align:middle line:84% They had a laboratory in the basement 01:08:50.100 --> 01:08:52.560 align:middle line:90% of their enormous castle. 01:08:52.560 --> 01:08:54.960 align:middle line:84% So Louis had first studied history, 01:08:54.960 --> 01:08:57.779 align:middle line:84% like a good aristocrat, and all the rich humanities, 01:08:57.779 --> 01:09:00.029 align:middle line:84% and then stubbornly said that, like his older brother, 01:09:00.029 --> 01:09:02.380 align:middle line:84% he'd like to study this grubby physics stuff instead. 01:09:02.380 --> 01:09:06.359 align:middle line:84% So he finished his PhD in 1924 in theoretical physics, 01:09:06.359 --> 01:09:09.180 align:middle line:84% I think at the Sorbonne or some very elite Paris School. 01:09:09.180 --> 01:09:11.170 align:middle line:84% And here, he began to wonder, is there 01:09:11.170 --> 01:09:15.729 align:middle line:84% a way to account for Bohr's powerful yet as yet unexplained 01:09:15.729 --> 01:09:18.040 align:middle line:84% hypothesis about the quantum condition, 01:09:18.040 --> 01:09:19.840 align:middle line:84% that the angular momentum of an electron 01:09:19.840 --> 01:09:24.040 align:middle line:84% should take integer units set by h-bar? 01:09:24.040 --> 01:09:27.160 align:middle line:84% So de Broglie tries to make an explicit symmetry. 01:09:27.160 --> 01:09:29.620 align:middle line:84% He really has a this happened here, 01:09:29.620 --> 01:09:32.200 align:middle line:84% can I make the same thing happen here kind of framework. 01:09:32.200 --> 01:09:33.890 align:middle line:90% He's very explicit about that. 01:09:33.890 --> 01:09:37.810 align:middle line:84% He also returns to Einstein's work on light quanta, 01:09:37.810 --> 01:09:40.180 align:middle line:84% which, by this point, people are now taking seriously. 01:09:40.180 --> 01:09:44.350 align:middle line:84% This is now fully two years after Compton's results 01:09:44.350 --> 01:09:45.880 align:middle line:90% with X-ray scattering. 01:09:45.880 --> 01:09:49.540 align:middle line:84% The notion of returning to Einstein's work in 1924 01:09:49.540 --> 01:09:51.279 align:middle line:84% was no longer controversial the way 01:09:51.279 --> 01:09:54.140 align:middle line:84% it would have been in 1905, or 1910, and so on. 01:09:54.140 --> 01:09:56.830 align:middle line:84% So for de Broglie, that looks like a pretty sensible place 01:09:56.830 --> 01:09:57.680 align:middle line:90% to start. 01:09:57.680 --> 01:10:00.160 align:middle line:84% And as we saw in the previous class, 01:10:00.160 --> 01:10:03.040 align:middle line:84% there's a Maxwellian expression for the momentum 01:10:03.040 --> 01:10:05.950 align:middle line:84% of a light wave related to its energy and its speed. 01:10:05.950 --> 01:10:09.972 align:middle line:84% We can then take on Einstein's light quantum hypothesis. 01:10:09.972 --> 01:10:11.680 align:middle line:84% The energy of that light quantum can only 01:10:11.680 --> 01:10:16.650 align:middle line:84% take certain units set, again, by Planck's constant, h. 01:10:16.650 --> 01:10:20.430 align:middle line:84% And so then as we saw, Compton himself used this relation. 01:10:20.430 --> 01:10:23.250 align:middle line:84% The momentum for an individual particle of light, 01:10:23.250 --> 01:10:25.920 align:middle line:84% a light quantum, should be inversely proportional 01:10:25.920 --> 01:10:28.620 align:middle line:84% to its wavelength with a proportionality set 01:10:28.620 --> 01:10:29.640 align:middle line:90% by Planck's constant. 01:10:29.640 --> 01:10:32.460 align:middle line:84% That, by now, had become pretty familiar, 01:10:32.460 --> 01:10:34.800 align:middle line:84% even to people who were grudging in that. 01:10:34.800 --> 01:10:37.380 align:middle line:84% What de Broglie says is simply assert-- 01:10:37.380 --> 01:10:38.250 align:middle line:90% he doesn't derive. 01:10:38.250 --> 01:10:38.958 align:middle line:90% He doesn't prove. 01:10:38.958 --> 01:10:41.460 align:middle line:84% He simply asserts whether the same thing happens 01:10:41.460 --> 01:10:42.790 align:middle line:90% for particles of matter. 01:10:42.790 --> 01:10:44.830 align:middle line:84% This is all about the behavior of light. 01:10:44.830 --> 01:10:46.830 align:middle line:84% So de Broglie says, what if we relate 01:10:46.830 --> 01:10:50.040 align:middle line:84% the momentum of a little electron, for example, moving 01:10:50.040 --> 01:10:53.980 align:middle line:90% around the nucleus in an atom? 01:10:53.980 --> 01:10:55.380 align:middle line:84% So there would be some expression 01:10:55.380 --> 01:10:57.450 align:middle line:84% for the momentum of that particle coming just, 01:10:57.450 --> 01:10:59.670 align:middle line:90% say, from Newtonian mechanics. 01:10:59.670 --> 01:11:02.910 align:middle line:84% What if we also relate that to an inverse wavelength, 01:11:02.910 --> 01:11:05.190 align:middle line:84% just as Einstein had by this point 01:11:05.190 --> 01:11:08.042 align:middle line:84% convinced many physicists to try for light? 01:11:08.042 --> 01:11:10.000 align:middle line:84% In that case, you can rearrange this expression 01:11:10.000 --> 01:11:13.170 align:middle line:84% and say, what if there's some waviness associated even 01:11:13.170 --> 01:11:17.650 align:middle line:84% with chunks of matter, particulate solid matter? 01:11:17.650 --> 01:11:21.040 align:middle line:84% de Broglie says, what if there's an inherent waviness 01:11:21.040 --> 01:11:24.160 align:middle line:84% of a scale set inversely by the momentum, 01:11:24.160 --> 01:11:26.930 align:middle line:84% just like you'd expect here, and proportional to Planck's 01:11:26.930 --> 01:11:27.430 align:middle line:90% constant? 01:11:27.430 --> 01:11:30.640 align:middle line:84% Why would anyone ever take this crazy French Prince's word 01:11:30.640 --> 01:11:31.690 align:middle line:90% for it? 01:11:31.690 --> 01:11:35.740 align:middle line:84% We never see this in real life, in ordinary life. 01:11:35.740 --> 01:11:38.230 align:middle line:84% This is now after things like Bohr's correspondence 01:11:38.230 --> 01:11:40.150 align:middle line:84% principle. de Broglie knows to wonder 01:11:40.150 --> 01:11:43.090 align:middle line:84% about the scales at which one might ever see such 01:11:43.090 --> 01:11:44.900 align:middle line:90% a strange sounding phenomenon. 01:11:44.900 --> 01:11:46.570 align:middle line:84% So if you imagine a fastball-- he 01:11:46.570 --> 01:11:49.690 align:middle line:84% didn't use this example, we can, for those more familiar 01:11:49.690 --> 01:11:51.160 align:middle line:84% with American baseball, or cricket, 01:11:51.160 --> 01:11:55.720 align:middle line:84% or fill in your favorite human-sized ball throwing game. 01:11:55.720 --> 01:11:59.050 align:middle line:84% If you imagine a fastball pitched in a baseball game 01:11:59.050 --> 01:12:03.070 align:middle line:84% and calculate 1 over its momentum scaled by h, 01:12:03.070 --> 01:12:05.240 align:middle line:84% the waviness associated with that, 01:12:05.240 --> 01:12:06.760 align:middle line:84% if we took de Broglie at his word, 01:12:06.760 --> 01:12:11.320 align:middle line:84% would be unbelievably small, 10 to the minus 32nd of a meter. 01:12:11.320 --> 01:12:14.960 align:middle line:84% That's smaller than the smallest known elementary particles. 01:12:14.960 --> 01:12:17.980 align:middle line:84% So of course, we don't see this somehow inherent waviness 01:12:17.980 --> 01:12:19.870 align:middle line:90% on everyday scales. 01:12:19.870 --> 01:12:22.970 align:middle line:84% But de Broglie goes on and says, for an electron, 01:12:22.970 --> 01:12:25.960 align:middle line:84% if we plug in a typical momentum that we estimate 01:12:25.960 --> 01:12:28.150 align:middle line:84% for its motion, say, in a hydrogen atom, 01:12:28.150 --> 01:12:31.900 align:middle line:84% the waviness, the actual wavelength somehow associated 01:12:31.900 --> 01:12:34.210 align:middle line:84% with that electron, is on the same length 01:12:34.210 --> 01:12:38.230 align:middle line:84% scale as its own radius, as its own orbital path, 01:12:38.230 --> 01:12:40.480 align:middle line:90% that Bohr radius, a0. 01:12:40.480 --> 01:12:45.520 align:middle line:84% For an electron, this new, hypothetical quantum waviness 01:12:45.520 --> 01:12:48.550 align:middle line:84% is on the same scale as its own mechanical motion. 01:12:48.550 --> 01:12:51.010 align:middle line:84% So maybe, de Broglie says, we shouldn't ignore it. 01:12:51.010 --> 01:12:54.760 align:middle line:84% We can absolutely ignore this somehow hypothetical quantum 01:12:54.760 --> 01:12:58.030 align:middle line:84% waviness when playing cricket, or baseball, 01:12:58.030 --> 01:12:59.080 align:middle line:90% or any kind of sport. 01:12:59.080 --> 01:13:01.258 align:middle line:84% But maybe it's actually really critical 01:13:01.258 --> 01:13:02.800 align:middle line:84% when we're talking about the behavior 01:13:02.800 --> 01:13:05.000 align:middle line:90% of atoms and parts of atoms. 01:13:05.000 --> 01:13:08.440 align:middle line:84% So if there really were some inherent wavelike structure, 01:13:08.440 --> 01:13:11.650 align:middle line:84% wavelike feature associated with the motion 01:13:11.650 --> 01:13:14.500 align:middle line:84% of an electron in an atom, could that 01:13:14.500 --> 01:13:17.080 align:middle line:84% begin to address this biggest as yet unanswered 01:13:17.080 --> 01:13:19.750 align:middle line:84% question about the Bohr model, why 01:13:19.750 --> 01:13:23.500 align:middle line:84% certain configurations or certain discrete states 01:13:23.500 --> 01:13:26.980 align:middle line:84% of motion for an electron would lead to stability of matter 01:13:26.980 --> 01:13:29.590 align:middle line:90% rather than unstable behavior? 01:13:29.590 --> 01:13:31.390 align:middle line:84% And he says, what if there is a kind 01:13:31.390 --> 01:13:33.490 align:middle line:90% of constructive interference? 01:13:33.490 --> 01:13:36.430 align:middle line:84% And what if the only stable states for an electron 01:13:36.430 --> 01:13:41.050 align:middle line:84% are those for which there's an integer number of wavelengths 01:13:41.050 --> 01:13:43.400 align:middle line:90% that can wrap around the orbit? 01:13:43.400 --> 01:13:45.850 align:middle line:84% So the wave, in some sense, joins back on itself 01:13:45.850 --> 01:13:49.360 align:middle line:84% and constructively interferes to make a stable standing wave, 01:13:49.360 --> 01:13:50.830 align:middle line:90% basically a standing wave. 01:13:50.830 --> 01:13:52.660 align:middle line:84% Whereas if the radius of that orbit 01:13:52.660 --> 01:13:55.360 align:middle line:84% were ever so slightly different, you would no longer 01:13:55.360 --> 01:13:58.270 align:middle line:84% be able to wrap an integer number of wavelengths 01:13:58.270 --> 01:13:59.050 align:middle line:90% around the radius. 01:13:59.050 --> 01:14:02.300 align:middle line:84% And you'd start getting the wave out of phase with itself. 01:14:02.300 --> 01:14:04.780 align:middle line:84% So the crests would actually start meeting up with troughs. 01:14:04.780 --> 01:14:07.150 align:middle line:84% And the whole wave would basically fall apart. 01:14:07.150 --> 01:14:11.680 align:middle line:84% So de Broglie is saying, if we grant this hypothetical as yet 01:14:11.680 --> 01:14:14.290 align:middle line:84% unseen waviness to things like electrons, 01:14:14.290 --> 01:14:17.980 align:middle line:84% could we start accounting for that stability of matter? 01:14:17.980 --> 01:14:19.960 align:middle line:84% What would be the criterion then? 01:14:19.960 --> 01:14:23.080 align:middle line:84% You have to have an integer number of these wavelengths 01:14:23.080 --> 01:14:25.120 align:middle line:84% fit around the circumference, fit around 2 01:14:25.120 --> 01:14:27.320 align:middle line:90% pi r of that circular orbit. 01:14:27.320 --> 01:14:30.600 align:middle line:84% Well, now, he has an idea for what that wavelength should be. 01:14:30.600 --> 01:14:33.380 align:middle line:84% He's now working directly in analogy to Einstein's work 01:14:33.380 --> 01:14:34.130 align:middle line:90% with light quanta. 01:14:34.130 --> 01:14:36.410 align:middle line:84% So plug in what he thinks lambda would be. 01:14:36.410 --> 01:14:39.620 align:middle line:84% And then presto chango, he's now derived, or at least 01:14:39.620 --> 01:14:42.290 align:middle line:84% found, an expression that exactly matches 01:14:42.290 --> 01:14:46.280 align:middle line:84% the form for what Bohr had put in by hand in a totally 01:14:46.280 --> 01:14:48.720 align:middle line:90% unexplained and ad hoc manner. 01:14:48.720 --> 01:14:51.860 align:middle line:84% So now, this might account for why this quantity Bohr had 01:14:51.860 --> 01:14:54.230 align:middle line:84% begun with, the angular momentum of an electron 01:14:54.230 --> 01:14:56.540 align:middle line:84% moving in a circular orbit, could only 01:14:56.540 --> 01:15:00.830 align:middle line:90% take on integer values of h-bar. 01:15:00.830 --> 01:15:05.090 align:middle line:84% That arises from this physical criterion of stability, 01:15:05.090 --> 01:15:07.220 align:middle line:84% of constructive interference to get 01:15:07.220 --> 01:15:10.190 align:middle line:84% the waves to line up into basically a standing wave 01:15:10.190 --> 01:15:10.820 align:middle line:90% pattern. 01:15:10.820 --> 01:15:12.500 align:middle line:90% That's pretty astonishing. 01:15:12.500 --> 01:15:15.050 align:middle line:84% Einstein reads a thesis, and is immediately impressed, 01:15:15.050 --> 01:15:17.780 align:middle line:84% and helps to draw news to it, draw attention to it. 01:15:17.780 --> 01:15:19.850 align:middle line:84% It's still, again, merely hypothetical. 01:15:19.850 --> 01:15:23.210 align:middle line:84% It's clever, but it's not like it's been proven. 01:15:23.210 --> 01:15:26.360 align:middle line:84% And so quite remarkably-- and the pace of this 01:15:26.360 --> 01:15:29.490 align:middle line:84% I find just astonishing-- just within three years 01:15:29.490 --> 01:15:33.840 align:middle line:84% of that clever suggestion in a French aristocrat's PhD thesis, 01:15:33.840 --> 01:15:37.110 align:middle line:84% there was some pretty compelling new empirical evidence 01:15:37.110 --> 01:15:39.870 align:middle line:84% to start taking that seriously, in this case coming from what 01:15:39.870 --> 01:15:41.160 align:middle line:90% would soon become Bell Labs. 01:15:41.160 --> 01:15:44.340 align:middle line:84% It wasn't quite Bell Labs yet, but from an industrial research 01:15:44.340 --> 01:15:47.430 align:middle line:84% laboratory here in the United States, 01:15:47.430 --> 01:15:53.770 align:middle line:84% work led by Clinton Davison and Lester Germer as early as 1927. 01:15:53.770 --> 01:15:56.550 align:middle line:84% So they were actually firing electron 01:15:56.550 --> 01:15:59.280 align:middle line:84% beams in a souped-up version of JJ Thompson's experiment. 01:15:59.280 --> 01:16:01.650 align:middle line:84% They had basically a cathode ray from which 01:16:01.650 --> 01:16:05.670 align:middle line:84% they could beam electrons at a certain crystal 01:16:05.670 --> 01:16:08.280 align:middle line:84% by other techniques they new, characteristics 01:16:08.280 --> 01:16:11.550 align:middle line:84% of the crystal structure of that nickel, what 01:16:11.550 --> 01:16:14.400 align:middle line:84% was the spacing, for example, between layers of atoms. 01:16:14.400 --> 01:16:19.050 align:middle line:84% And then they could measure the amount of scattered electrons 01:16:19.050 --> 01:16:20.920 align:middle line:90% as a function of angle. 01:16:20.920 --> 01:16:24.180 align:middle line:84% So as they moved their detector to different angles, 01:16:24.180 --> 01:16:26.640 align:middle line:84% they could measure how large an intensity 01:16:26.640 --> 01:16:29.340 align:middle line:84% they would measure of the rescattered electron beam. 01:16:29.340 --> 01:16:32.520 align:middle line:84% And they found exactly this wavelike interference pattern, 01:16:32.520 --> 01:16:36.180 align:middle line:84% that there would be a criterion for these two scattered waves 01:16:36.180 --> 01:16:40.590 align:middle line:84% from scattering off distinct layers within that crystal 01:16:40.590 --> 01:16:42.780 align:middle line:84% to line up with an integer number of wavelengths 01:16:42.780 --> 01:16:45.450 align:middle line:84% between them that changes with the scattering angle. 01:16:45.450 --> 01:16:48.270 align:middle line:84% They just did a kind of classical wave interference 01:16:48.270 --> 01:16:52.110 align:middle line:84% analysis, not having known things like the lattice spacing 01:16:52.110 --> 01:16:54.270 align:middle line:90% for that crystal. 01:16:54.270 --> 01:16:57.450 align:middle line:84% And they found exactly this kind of waviness interference 01:16:57.450 --> 01:17:02.310 align:middle line:84% pattern on exactly the scale to expect given de Broglie's 01:17:02.310 --> 01:17:04.720 align:middle line:90% surprising hypothesis. 01:17:04.720 --> 01:17:06.690 align:middle line:90% So let me wrap up. 01:17:06.690 --> 01:17:10.890 align:middle line:84% Between roughly 1900 and 1924, '25-- 01:17:10.890 --> 01:17:14.040 align:middle line:84% we'll see even a little bit more of this in the coming lecture-- 01:17:14.040 --> 01:17:17.130 align:middle line:84% in this period that comes to be called old quantum theory, 01:17:17.130 --> 01:17:20.730 align:middle line:84% physicists really went through a pretty dramatic series 01:17:20.730 --> 01:17:23.910 align:middle line:84% of new ideas and assumptions about both light 01:17:23.910 --> 01:17:28.300 align:middle line:84% and matter, almost interwoven among each other. 01:17:28.300 --> 01:17:31.320 align:middle line:84% So in contrast with these great triumphs of 19th century 01:17:31.320 --> 01:17:34.073 align:middle line:84% physics-- the wave theory of light that we've looked 01:17:34.073 --> 01:17:35.490 align:middle line:84% at in the beginning of the class-- 01:17:35.490 --> 01:17:38.550 align:middle line:84% several physicists for several lines of reasoning 01:17:38.550 --> 01:17:40.770 align:middle line:84% begin to explore a kind of discreteness 01:17:40.770 --> 01:17:43.200 align:middle line:84% or particle-like attribute of light. 01:17:43.200 --> 01:17:46.260 align:middle line:84% We saw several steps along that way during last class. 01:17:46.260 --> 01:17:50.970 align:middle line:84% Meanwhile, in parallel, there's an inverse motion 01:17:50.970 --> 01:17:53.430 align:middle line:84% led ultimately by people like de Broglie 01:17:53.430 --> 01:17:57.450 align:middle line:84% to salvage this other new form of discreteness, Bohr's quantum 01:17:57.450 --> 01:18:01.440 align:middle line:84% condition, by suggesting that just as wavelike light could 01:18:01.440 --> 01:18:03.630 align:middle line:84% actually be thought of as particle-like, what 01:18:03.630 --> 01:18:07.680 align:middle line:84% if particle-like matter had some wavelike attributes? 01:18:07.680 --> 01:18:11.670 align:middle line:84% And so by the early 1920s, as each of these partial successes 01:18:11.670 --> 01:18:14.577 align:middle line:84% begins to draw attention, many, many physicists 01:18:14.577 --> 01:18:16.410 align:middle line:84% were convinced that something had to change. 01:18:16.410 --> 01:18:19.140 align:middle line:84% There was some quantumness that simply was not 01:18:19.140 --> 01:18:22.960 align:middle line:84% consistent with either Newton's physics or Maxwell's physics. 01:18:22.960 --> 01:18:24.420 align:middle line:84% In fact, they began to use the term 01:18:24.420 --> 01:18:28.080 align:middle line:84% classical now to speak about what was not this new quantum 01:18:28.080 --> 01:18:28.770 align:middle line:90% stuff. 01:18:28.770 --> 01:18:31.130 align:middle line:90% They used that new label. 01:18:31.130 --> 01:18:33.060 align:middle line:90% And the pattern seems familiar. 01:18:33.060 --> 01:18:36.270 align:middle line:84% Start with the textbook classical expressions 01:18:36.270 --> 01:18:39.510 align:middle line:84% for force, or energy, or distance, or speed, and then 01:18:39.510 --> 01:18:44.250 align:middle line:84% somehow just plug in, staple in some as yet unexplained 01:18:44.250 --> 01:18:46.890 align:middle line:84% new discreteness condition-- either the energy, 01:18:46.890 --> 01:18:49.120 align:middle line:84% or the angular momentum, or some wavelength. 01:18:49.120 --> 01:18:53.010 align:middle line:84% So you have this ad hoc stapling onto otherwise perfectly 01:18:53.010 --> 01:18:55.080 align:middle line:90% familiar classical expressions. 01:18:55.080 --> 01:18:57.180 align:middle line:84% That began to really upset a bunch of people. 01:18:57.180 --> 01:18:59.970 align:middle line:84% There's a marvelous book I used to assign in this class. 01:18:59.970 --> 01:19:01.060 align:middle line:90% I dropped it this year. 01:19:01.060 --> 01:19:03.000 align:middle line:84% But I encourage you, you might enjoy it. 01:19:03.000 --> 01:19:06.720 align:middle line:84% It's a novel by historian Russell McCormmach shown here 01:19:06.720 --> 01:19:08.910 align:middle line:84% called Night Thoughts of a Classical Physicist. 01:19:08.910 --> 01:19:11.070 align:middle line:84% What McCormmach does is try to really, 01:19:11.070 --> 01:19:14.520 align:middle line:84% I think, very movingly, very compellingly recreate 01:19:14.520 --> 01:19:16.740 align:middle line:84% what it felt like to be a physicist living 01:19:16.740 --> 01:19:20.070 align:middle line:84% through this period of conceptual disruption. 01:19:20.070 --> 01:19:22.740 align:middle line:84% What it really felt like is the solidity of the world 01:19:22.740 --> 01:19:24.030 align:middle line:90% began to shake. 01:19:24.030 --> 01:19:25.350 align:middle line:90% And it didn't just shake. 01:19:25.350 --> 01:19:26.340 align:middle line:90% It looked ugly. 01:19:26.340 --> 01:19:29.040 align:middle line:90% It looked piecemeal and ad hoc. 01:19:29.040 --> 01:19:32.610 align:middle line:84% So McCormmach, who had poured over just literally 01:19:32.610 --> 01:19:35.640 align:middle line:84% tens of thousands of letters, and laboratory notes, 01:19:35.640 --> 01:19:38.820 align:middle line:84% and publications from a whole generation of these mostly 01:19:38.820 --> 01:19:41.970 align:middle line:84% German-based physicists during this period of change, 01:19:41.970 --> 01:19:46.710 align:middle line:84% he distills that into a 160-page novel of a composite character 01:19:46.710 --> 01:19:49.020 align:middle line:84% named Victor Jakob, to watch Jakob 01:19:49.020 --> 01:19:51.570 align:middle line:84% react to this kind of like-- that kind of makes sense. 01:19:51.570 --> 01:19:53.340 align:middle line:84% But it's disjointed from over there. 01:19:53.340 --> 01:19:54.370 align:middle line:90% I can follow you here. 01:19:54.370 --> 01:19:55.650 align:middle line:90% But this looks really weird. 01:19:55.650 --> 01:19:57.570 align:middle line:90% It just starts to feel broken. 01:19:57.570 --> 01:20:00.150 align:middle line:84% It starts to feel disorganized and ad hoc. 01:20:00.150 --> 01:20:03.390 align:middle line:84% And so when people began calling this old quantum theory, 01:20:03.390 --> 01:20:06.600 align:middle line:84% it was both to say this happened before something new, 01:20:06.600 --> 01:20:08.310 align:middle line:84% but also to try to bracket it saying, 01:20:08.310 --> 01:20:09.910 align:middle line:90% it's old and kind of broken. 01:20:09.910 --> 01:20:12.420 align:middle line:84% It just felt conceptually dissatisfying to a number 01:20:12.420 --> 01:20:13.050 align:middle line:90% of people. 01:20:13.050 --> 01:20:14.592 align:middle line:84% And people were pretty well convinced 01:20:14.592 --> 01:20:17.400 align:middle line:84% that couldn't be the last way these things will stand. 01:20:17.400 --> 01:20:19.380 align:middle line:84% So I know we're just about at time. 01:20:19.380 --> 01:20:21.060 align:middle line:84% I see there's a question from Iabo. 01:20:21.060 --> 01:20:23.783 align:middle line:84% How did de Broglie waves impact the wave particle debate? 01:20:23.783 --> 01:20:24.450 align:middle line:90% Thank you, Iabo. 01:20:24.450 --> 01:20:26.980 align:middle line:84% So basically, it heightened this even further. 01:20:26.980 --> 01:20:29.380 align:middle line:84% I mean, the short answer is it made it even harder 01:20:29.380 --> 01:20:33.850 align:middle line:84% to ignore this strange, unsteady, and unstable 01:20:33.850 --> 01:20:36.490 align:middle line:84% combination of concepts which otherwise 01:20:36.490 --> 01:20:38.980 align:middle line:90% had seemed clear, but separate. 01:20:38.980 --> 01:20:41.775 align:middle line:84% And that's the kind of thing that this novel I just 01:20:41.775 --> 01:20:43.900 align:middle line:84% mentioned, Night Thoughts of a Classical Physicist, 01:20:43.900 --> 01:20:47.560 align:middle line:84% is actually really beautifully helping us appreciate, 01:20:47.560 --> 01:20:49.270 align:middle line:90% that it looked dizzying. 01:20:49.270 --> 01:20:51.970 align:middle line:84% People would have like a physiological reaction. 01:20:51.970 --> 01:20:53.650 align:middle line:90% What's solid? 01:20:53.650 --> 01:20:55.390 align:middle line:90% I know what a wave is. 01:20:55.390 --> 01:20:58.060 align:middle line:84% And by this point, think about the Wranglers, or Lorenz, 01:20:58.060 --> 01:21:01.690 align:middle line:84% or anyone else, there was a huge, highly successful 01:21:01.690 --> 01:21:05.680 align:middle line:84% quantitative series of tools with which to characterize 01:21:05.680 --> 01:21:08.680 align:middle line:84% wave phenomena-- interference, refraction, diffraction, wave 01:21:08.680 --> 01:21:09.980 align:middle line:90% equations, and all the rest. 01:21:09.980 --> 01:21:12.490 align:middle line:84% And then people would say, I know what particles are. 01:21:12.490 --> 01:21:14.980 align:middle line:84% And they could use Newton's laws to study ballistics 01:21:14.980 --> 01:21:17.240 align:middle line:84% and so on to extraordinary accuracy. 01:21:17.240 --> 01:21:19.960 align:middle line:84% And now, it looked like they had to somehow mush these together 01:21:19.960 --> 01:21:21.040 align:middle line:90% in a way that didn't-- 01:21:21.040 --> 01:21:22.960 align:middle line:84% without any rules, in a way that didn't 01:21:22.960 --> 01:21:24.910 align:middle line:90% seem to have any roadmap. 01:21:24.910 --> 01:21:27.910 align:middle line:84% And so the de Broglie hypothesis, especially 01:21:27.910 --> 01:21:31.000 align:middle line:84% after 1927 with his Davisson-Germer work-- 01:21:31.000 --> 01:21:33.010 align:middle line:84% and they received the Nobel Prize instantly. 01:21:33.010 --> 01:21:35.350 align:middle line:84% This, again, was seen as immediately important work 01:21:35.350 --> 01:21:36.880 align:middle line:90% when they did those experiments. 01:21:36.880 --> 01:21:40.480 align:middle line:84% That was just heightening this clash and made the stakes, 01:21:40.480 --> 01:21:42.520 align:middle line:84% the conceptual stakes seem even higher. 01:21:42.520 --> 01:21:43.518 align:middle line:90% It's a great question. 01:21:43.518 --> 01:21:45.310 align:middle line:84% And we'll see how that plays out, actually, 01:21:45.310 --> 01:21:47.290 align:middle line:90% in the next several classes. 01:21:47.290 --> 01:21:48.700 align:middle line:90% It doesn't get resolved. 01:21:48.700 --> 01:21:51.340 align:middle line:84% What happens is physicists resolve themselves 01:21:51.340 --> 01:21:53.830 align:middle line:84% to keep dealing with this strange connectedness as 01:21:53.830 --> 01:21:56.500 align:middle line:84% opposed to saying, now, it's one or the other, as many of you 01:21:56.500 --> 01:21:58.643 align:middle line:90% likely know from other classes. 01:21:58.643 --> 01:21:59.810 align:middle line:90% Any other questions on that? 01:21:59.810 --> 01:22:02.273 align:middle line:90% 01:22:02.273 --> 01:22:03.690 align:middle line:84% I don't want to keep you too long. 01:22:03.690 --> 01:22:05.148 align:middle line:84% I'm sure you have a full afternoon. 01:22:05.148 --> 01:22:06.710 align:middle line:90% Anyways, good to see you all. 01:22:06.710 --> 01:22:10.720 align:middle line:84% We'll pick up the story again on Wednesday. 01:22:10.720 --> 01:22:17.000 align:middle line:90%