WEBVTT 00:00:00.090 --> 00:00:02.430 The following content is provided under a Creative 00:00:02.430 --> 00:00:03.820 Commons license. 00:00:03.820 --> 00:00:06.060 Your support will help MIT OpenCourseWare 00:00:06.060 --> 00:00:10.150 continue to offer high quality educational resources for free. 00:00:10.150 --> 00:00:12.690 To make a donation or to view additional materials 00:00:12.690 --> 00:00:16.650 from hundreds of MIT courses, visit MIT OpenCourseWare 00:00:16.650 --> 00:00:17.850 at ocw.mit.edu. 00:00:36.414 --> 00:00:37.330 CATHERINE DRENNAN: OK. 00:00:37.330 --> 00:00:38.980 We're going to take 10 more seconds. 00:00:56.030 --> 00:00:57.350 OK. 00:00:57.350 --> 00:01:01.510 Does someone want to explain how they got the right answer? 00:01:01.510 --> 00:01:07.600 We have a Faculty of 1,000 research bag for them. 00:01:11.390 --> 00:01:13.570 Do you want to hand that up and the bag, too? 00:01:13.570 --> 00:01:14.070 We're just-- 00:01:18.460 --> 00:01:22.150 AUDIENCE: So the theme of light gives enough 00:01:22.150 --> 00:01:24.880 energy for the electrons to be ejected. 00:01:24.880 --> 00:01:29.770 And the amount of energy for that is 4.3 eV. 00:01:29.770 --> 00:01:32.890 And then it also has kinetic energy of 7.9 eV. 00:01:32.890 --> 00:01:34.210 So you just add the two. 00:01:34.210 --> 00:01:38.543 So 4.3 plus 7.9 is 12.2 eV. 00:01:38.543 --> 00:01:39.626 CATHERINE DRENNAN: Thanks. 00:01:39.626 --> 00:01:41.631 Let's bring it back. 00:01:41.631 --> 00:01:42.130 OK. 00:01:42.130 --> 00:01:42.890 Thank you. 00:01:42.890 --> 00:01:43.390 All right. 00:01:43.390 --> 00:01:48.610 We'll have lots more practice with this today, 00:01:48.610 --> 00:01:51.230 and we'll get the hang of doing these problems. 00:01:51.230 --> 00:01:53.650 So let's just jump in and get started. 00:01:53.650 --> 00:01:56.830 We're still continuing to think about the photoelectric effect, 00:01:56.830 --> 00:01:58.660 and think about light as a particle. 00:01:58.660 --> 00:02:01.450 So we're going to finish up with the photoelectric effect, 00:02:01.450 --> 00:02:04.357 and we're going to have a little demo on that in a few minutes. 00:02:04.357 --> 00:02:05.440 Then we're going to go on. 00:02:05.440 --> 00:02:11.320 If light is, in fact, quantized, and you have these photons, 00:02:11.320 --> 00:02:13.930 then photons should have momentum. 00:02:13.930 --> 00:02:15.600 And so we'll talk about that. 00:02:15.600 --> 00:02:19.700 Then we've talked about white as a particle. 00:02:19.700 --> 00:02:23.530 And most of you are probably pretty OK with matter 00:02:23.530 --> 00:02:24.340 being a particle. 00:02:24.340 --> 00:02:26.110 But what about matter being a wave? 00:02:26.110 --> 00:02:28.660 So we're going to talk about matter being a wave. 00:02:28.660 --> 00:02:30.420 And if we have time at the end, we're 00:02:30.420 --> 00:02:32.461 going to start on the Schrodinger equation, which 00:02:32.461 --> 00:02:34.390 we're going to continue with on Friday. 00:02:34.390 --> 00:02:39.370 So I'll just say that sometimes, I am a little overly ambitious, 00:02:39.370 --> 00:02:41.710 and I put things on the handout that I'm not really 00:02:41.710 --> 00:02:43.120 sure I'm going to get to. 00:02:43.120 --> 00:02:44.860 Just because I've never gotten into it 00:02:44.860 --> 00:02:48.100 before doesn't mean that I won't get into it this time. 00:02:48.100 --> 00:02:50.680 So if I don't finish everything on a handout, 00:02:50.680 --> 00:02:52.602 bring your handout to the next class, 00:02:52.602 --> 00:02:54.060 and we'll just continue from there. 00:02:54.060 --> 00:02:56.530 And there'll be a new handout then as well, so 00:02:56.530 --> 00:02:58.220 just a heads up on that. 00:02:58.220 --> 00:02:58.720 All right. 00:02:58.720 --> 00:03:02.800 So let's continue with the photoelectric effect 00:03:02.800 --> 00:03:05.360 and get good at doing these kinds of problems. 00:03:05.360 --> 00:03:09.580 So let's look at these particular examples. 00:03:09.580 --> 00:03:11.770 We have three different examples here. 00:03:11.770 --> 00:03:14.920 We have the energy of an incoming photon 00:03:14.920 --> 00:03:19.960 must be equal or greater to that threshold energy or that work 00:03:19.960 --> 00:03:23.200 function, in order for an electron to be ejected. 00:03:23.200 --> 00:03:28.810 So in this case, the energy is greater than the work function. 00:03:28.810 --> 00:03:32.350 So tell me whether an electron will be ejected 00:03:32.350 --> 00:03:33.470 or will not be ejected. 00:03:33.470 --> 00:03:34.690 And you can just yell it out. 00:03:34.690 --> 00:03:35.662 What do you think? 00:03:35.662 --> 00:03:36.640 AUDIENCE: Will. 00:03:36.640 --> 00:03:37.598 CATHERINE DRENNAN: Yes. 00:03:37.598 --> 00:03:38.950 So an electron is ejected. 00:03:38.950 --> 00:03:41.260 It will be ejected. 00:03:41.260 --> 00:03:43.780 What about this scenario over here, 00:03:43.780 --> 00:03:48.310 where the energy is less than that threshold energy? 00:03:48.310 --> 00:03:50.520 Is or is not ejected? 00:03:50.520 --> 00:03:51.820 AUDIENCE: Is not. 00:03:51.820 --> 00:03:52.900 CATHERINE DRENNAN: Yes. 00:03:52.900 --> 00:03:56.210 OK now we have another scenario. 00:03:56.210 --> 00:03:58.660 We have three photons, each of which 00:03:58.660 --> 00:04:02.800 have half of the energy needed, half of that threshold energy. 00:04:02.800 --> 00:04:05.090 But you have three of them. 00:04:05.090 --> 00:04:10.864 So will an electron is or is not ejected? 00:04:10.864 --> 00:04:11.572 AUDIENCE: Is not. 00:04:14.350 --> 00:04:16.000 CATHERINE DRENNAN: Is not. 00:04:16.000 --> 00:04:16.959 OK. 00:04:16.959 --> 00:04:21.160 So three photons each that have half the energy 00:04:21.160 --> 00:04:22.660 does not add up. 00:04:22.660 --> 00:04:23.490 You cannot add it. 00:04:23.490 --> 00:04:25.420 It will not eject an electron. 00:04:25.420 --> 00:04:27.170 So let's just think about it for a minute. 00:04:27.170 --> 00:04:29.920 Suppose the threshold knowledge for passing 00:04:29.920 --> 00:04:34.180 an exam is answering three specific questions correctly. 00:04:34.180 --> 00:04:38.440 Suppose over here, we have the answer to one of the questions, 00:04:38.440 --> 00:04:40.360 but not to the other two. 00:04:40.360 --> 00:04:42.580 Over here, we have an answer to the middle one, 00:04:42.580 --> 00:04:44.252 but not the first or the second. 00:04:44.252 --> 00:04:46.210 And over here, we have the answer to the third, 00:04:46.210 --> 00:04:47.740 but not the first or the second. 00:04:47.740 --> 00:04:51.910 So everyone knows the answer to a different question. 00:04:51.910 --> 00:04:55.930 Will there be the threshold energy, a threshold knowledge, 00:04:55.930 --> 00:04:58.010 to pass this test? 00:04:58.010 --> 00:04:59.490 No. 00:04:59.490 --> 00:05:02.730 Everyone needs to have the threshold knowledge 00:05:02.730 --> 00:05:05.580 themselves to be able to pass. 00:05:05.580 --> 00:05:09.240 Everyone has to overcome that critical amount of knowledge 00:05:09.240 --> 00:05:11.250 to be able to pass the test. 00:05:11.250 --> 00:05:13.440 So that's the same thing here. 00:05:13.440 --> 00:05:15.140 You can't add it up. 00:05:15.140 --> 00:05:19.230 Now, with the test here at MIT, if everyone has that threshold 00:05:19.230 --> 00:05:21.420 knowledge, and a really high level of the threshold 00:05:21.420 --> 00:05:25.470 knowledge, everyone can get an A. So the more people 00:05:25.470 --> 00:05:29.550 with the threshold knowledge, the more tests that are passed, 00:05:29.550 --> 00:05:32.350 and the more the course is passed by people. 00:05:32.350 --> 00:05:36.030 So the more photons coming in with that threshold 00:05:36.030 --> 00:05:39.270 energy, the more electrons being ejected. 00:05:39.270 --> 00:05:41.940 But you can't add up if you have photons 00:05:41.940 --> 00:05:44.310 that don't have enough, if they're not greater 00:05:44.310 --> 00:05:45.720 than, the threshold energy. 00:05:45.720 --> 00:05:47.250 You won't eject an electron. 00:05:47.250 --> 00:05:51.000 So everyone needs to meet that threshold criteria. 00:05:51.000 --> 00:05:53.800 You can't add things up. 00:05:53.800 --> 00:05:55.800 OK. 00:05:55.800 --> 00:05:58.830 So here's just some useful terminology 00:05:58.830 --> 00:06:01.410 for solving problems on this problem set. 00:06:01.410 --> 00:06:04.050 And there will also be problems on problems set two 00:06:04.050 --> 00:06:06.990 related to this topic. 00:06:06.990 --> 00:06:09.390 So photons-- also called light, also 00:06:09.390 --> 00:06:12.270 called electric magnetic radiation-- 00:06:12.270 --> 00:06:17.070 may be described by their energy, by their wavelength, 00:06:17.070 --> 00:06:20.430 or by their frequency. 00:06:20.430 --> 00:06:23.880 Whereas electrons, which are sometimes also called 00:06:23.880 --> 00:06:28.590 photoelectrons, may be described by their kinetic energy, 00:06:28.590 --> 00:06:34.150 their velocity, and, as you'll see later, by their wavelength. 00:06:34.150 --> 00:06:36.480 So you'll be given problems where, 00:06:36.480 --> 00:06:38.399 given different pieces of information, 00:06:38.399 --> 00:06:40.690 you have to think about how you're going to convert it. 00:06:40.690 --> 00:06:42.940 You've got to think about am I talking about a photon? 00:06:42.940 --> 00:06:44.940 Am I talking about an electron? 00:06:44.940 --> 00:06:47.800 And you also want to think about units. 00:06:47.800 --> 00:06:51.780 You'll sometimes be told about energy in eVs 00:06:51.780 --> 00:06:54.660 and sometimes be told about energies in joules. 00:06:54.660 --> 00:06:56.520 So this is a conversion factor. 00:06:56.520 --> 00:06:59.085 All conversion factors are given to you on the exam. 00:06:59.085 --> 00:07:03.160 You do not need to memorize any kind of conversion factor. 00:07:03.160 --> 00:07:05.250 But you need to be aware, when someone 00:07:05.250 --> 00:07:09.090 said joules, what's that a unit for, or eV, what's that a unit 00:07:09.090 --> 00:07:10.990 for. 00:07:10.990 --> 00:07:11.490 All right. 00:07:11.490 --> 00:07:14.730 So now we're going to do and in-class demonstration 00:07:14.730 --> 00:07:16.430 of the photoelectric effect. 00:07:16.430 --> 00:07:19.200 But before we actually do the experiment, 00:07:19.200 --> 00:07:23.160 we're going to predict what the experiment will show. 00:07:23.160 --> 00:07:25.050 Always dangerous to do that, so we'll 00:07:25.050 --> 00:07:27.461 hope it works after we do the prediction. 00:07:27.461 --> 00:07:27.960 All right. 00:07:27.960 --> 00:07:31.020 So we're going to be looking at whether we're 00:07:31.020 --> 00:07:36.750 going to get an injection of an electron from a zinc surface. 00:07:36.750 --> 00:07:42.510 And we're given the threshold energy, or the work function, 00:07:42.510 --> 00:07:44.520 of zinc. 00:07:44.520 --> 00:07:47.490 Every metal-- this is a property of metals. 00:07:47.490 --> 00:07:49.620 They're different, as we saw last time. 00:07:49.620 --> 00:07:54.390 So this is 6.9 times 10 to the minus 19th joules. 00:07:54.390 --> 00:07:56.400 And we're going to use two different light 00:07:56.400 --> 00:08:00.420 sources that are going to have different wavelengths. 00:08:00.420 --> 00:08:04.440 And we'll predict whether they have enough energy 00:08:04.440 --> 00:08:07.660 to meet this threshold to go over the threshold 00:08:07.660 --> 00:08:09.270 and inject an electron. 00:08:09.270 --> 00:08:12.660 So the two different sources, we have a UV lamp 00:08:12.660 --> 00:08:16.480 with a wavelength of 254 nanometers 00:08:16.480 --> 00:08:19.650 and a red laser pointer with a wavelength 00:08:19.650 --> 00:08:22.631 of about 700 nanometers. 00:08:22.631 --> 00:08:23.130 OK. 00:08:23.130 --> 00:08:25.650 So before we do the experiment, let's 00:08:25.650 --> 00:08:29.250 do some calculations to see what we expect. 00:08:29.250 --> 00:08:31.860 So first, we want to see what the energy, 00:08:31.860 --> 00:08:34.470 or calculate what the energy, of the photon 00:08:34.470 --> 00:08:38.909 will be that's a emitted by the UV lamp. 00:08:38.909 --> 00:08:43.049 And I will write this down. 00:08:43.049 --> 00:08:44.190 So what do we know? 00:08:44.190 --> 00:08:46.230 We know a bunch of things already. 00:08:46.230 --> 00:08:51.420 We know that energy is equal to Planck's constant times 00:08:51.420 --> 00:08:52.980 the frequency. 00:08:52.980 --> 00:08:57.720 We also know that the frequency is related to wavelength 00:08:57.720 --> 00:09:00.360 by c, the speed of light. 00:09:00.360 --> 00:09:03.120 And then we can put those two things together 00:09:03.120 --> 00:09:08.070 to say the energy, then, is also the Planck's constant times 00:09:08.070 --> 00:09:12.750 the speed of light divided by the wavelength. 00:09:12.750 --> 00:09:16.710 So we can use that last equation to do a calculation, 00:09:16.710 --> 00:09:19.620 and figure out the energy that's associated 00:09:19.620 --> 00:09:22.710 with that particular wavelength of light. 00:09:22.710 --> 00:09:24.810 So here we have energy. 00:09:24.810 --> 00:09:32.910 We're going to write in Planck's constant, 6.626 times 10 00:09:32.910 --> 00:09:35.530 to the minus 34. 00:09:35.530 --> 00:09:39.000 And the units are joules times seconds 00:09:39.000 --> 00:09:46.200 and the speed of light, 2.998 times 10 00:09:46.200 --> 00:09:51.130 to the 8 meters per second. 00:09:51.130 --> 00:09:56.770 And we want to divide this, then, by the wavelength. 00:09:56.770 --> 00:09:59.580 So we have the wavelength here that we're 00:09:59.580 --> 00:10:11.130 using first is a 254 times 10 to the minus 19 meters. 00:10:13.690 --> 00:10:17.200 Oh sorry-- 9 meters. 00:10:17.200 --> 00:10:19.720 Thank you. 00:10:19.720 --> 00:10:20.630 I wrote down 19. 00:10:20.630 --> 00:10:21.630 I'm like, wait a minute. 00:10:21.630 --> 00:10:23.250 That's not right. 00:10:23.250 --> 00:10:24.850 OK. 00:10:24.850 --> 00:10:26.170 OK. 00:10:26.170 --> 00:10:28.410 So then we can do the calculation out. 00:10:28.410 --> 00:10:31.720 And here is where I got excited about 19. 00:10:31.720 --> 00:10:41.130 We have 7.82 times 10 to the minus 19 joules. 00:10:41.130 --> 00:10:42.940 And if we look at the equation, we'll 00:10:42.940 --> 00:10:44.890 see that the meters are going to cancel. 00:10:44.890 --> 00:10:46.540 The seconds cancel, and we're left 00:10:46.540 --> 00:10:48.990 with joules, which is good, because we want an energy. 00:10:48.990 --> 00:10:52.030 So joules is a good thing to have. 00:10:52.030 --> 00:10:54.940 So there, we can do a simple calculation. 00:10:54.940 --> 00:11:00.100 And we can look and say, OK, if the energy, then, associated 00:11:00.100 --> 00:11:03.430 with that wavelength is 7.82 times 10 00:11:03.430 --> 00:11:08.410 to the minus 19th joules, then we ask, is this greater or less 00:11:08.410 --> 00:11:11.560 than the threshold energy? 00:11:11.560 --> 00:11:13.720 And it's greater than that. 00:11:13.720 --> 00:11:16.420 So it does have enough energy. 00:11:16.420 --> 00:11:18.100 It should eject an electron. 00:11:18.100 --> 00:11:20.800 So we can try that out and see. 00:11:20.800 --> 00:11:24.580 Now we can look at what happens with the red laser pointer 00:11:24.580 --> 00:11:27.870 and see whether that should have the energy that's needed. 00:11:27.870 --> 00:11:32.540 And so I will just write these things down here 00:11:32.540 --> 00:11:33.990 instead of writing it again. 00:11:33.990 --> 00:11:36.220 So that was our UV. 00:11:36.220 --> 00:11:42.520 So now our red light, we have 700 times 10 to the minus 9 00:11:42.520 --> 00:11:45.520 meters, or 700 nanometers. 00:11:45.520 --> 00:11:48.490 And so here is our answer for the UV. 00:11:48.490 --> 00:11:57.160 And our answer for the red light should be 2.84 times 10 00:11:57.160 --> 00:12:00.340 to the minus 19 joules. 00:12:00.340 --> 00:12:04.820 And I'll move this up a little so people can see that. 00:12:04.820 --> 00:12:09.700 So does that have enough energy to eject an electron? 00:12:09.700 --> 00:12:12.437 AUDIENCE: [INAUDIBLE] 00:12:12.437 --> 00:12:14.020 CATHERINE DRENNAN: No, that should not 00:12:14.020 --> 00:12:17.530 work, because that's less than the threshold energy that's 00:12:17.530 --> 00:12:18.790 needed. 00:12:18.790 --> 00:12:19.530 All right. 00:12:19.530 --> 00:12:22.530 So we'll do one more calculation just for fun. 00:12:22.530 --> 00:12:24.400 And then we'll do the experiment. 00:12:24.400 --> 00:12:26.740 So the last calculation we'll do is 00:12:26.740 --> 00:12:28.900 we'll think about the number of photons 00:12:28.900 --> 00:12:32.410 that are emitted by a laser in 60 seconds 00:12:32.410 --> 00:12:38.860 if you have an intensity of one milliwatt. 00:12:38.860 --> 00:12:43.720 And a milliwatt is equal to 10 to the minus 3 joules 00:12:43.720 --> 00:12:45.160 per second. 00:12:45.160 --> 00:12:49.370 So we can just do that calculation over here. 00:12:49.370 --> 00:13:00.730 So we have 1.00 times 10 to the minus 3 joules per second, 00:13:00.730 --> 00:13:07.410 1 photon, and here, this is for the red laser. 00:13:07.410 --> 00:13:11.480 So we'll use the number that we just calculated over here. 00:13:11.480 --> 00:13:17.650 So we have 2.84 times 10 to the minus 19th joules 00:13:17.650 --> 00:13:24.400 for the red laser and times 60 seconds. 00:13:24.400 --> 00:13:32.200 And we should get 2.1 times 10 to the 17 photons. 00:13:32.200 --> 00:13:35.080 So that's how much photons, if we hold it 00:13:35.080 --> 00:13:40.900 for 60 seconds, that were going to be shooting at our metal's 00:13:40.900 --> 00:13:42.030 surface. 00:13:42.030 --> 00:13:43.720 So these are the kind of calculations 00:13:43.720 --> 00:13:46.270 that you'll be doing on these kind of problems. 00:13:46.270 --> 00:13:49.139 And now let's see how well the experiment works. 00:13:49.139 --> 00:13:51.430 So we're going to bring out our demo TAs, who are going 00:13:51.430 --> 00:13:53.186 to tell you about this demo. 00:13:53.186 --> 00:13:55.060 And we're going to try to do some fancy stuff 00:13:55.060 --> 00:13:57.660 with this document camera to project it on the screen. 00:13:57.660 --> 00:13:59.580 So this is all very exciting. 00:13:59.580 --> 00:14:01.310 Oh, I guess I should put that down, 00:14:01.310 --> 00:14:02.810 the number, in case you couldn't see 00:14:02.810 --> 00:14:06.260 it-- 2.1 times 10 to the 17. 00:14:06.260 --> 00:14:06.760 All right. 00:14:06.760 --> 00:14:08.385 So let's bring-- you've got the mic. 00:14:12.607 --> 00:14:13.440 GUEST SPEAKER 1: OK. 00:14:13.440 --> 00:14:15.784 So we've got our metal plate here 00:14:15.784 --> 00:14:16.950 that Eric's got in his hand. 00:14:16.950 --> 00:14:19.020 And what he's doing right now is he's 00:14:19.020 --> 00:14:21.722 rubbing it with a little bit of-- what is that, actually? 00:14:21.722 --> 00:14:23.320 ERIC: It's just steel wool. 00:14:23.320 --> 00:14:24.570 CATHERINE DRENNAN: Steel wool. 00:14:24.570 --> 00:14:24.810 GUEST SPEAKER 1: OK. 00:14:24.810 --> 00:14:26.476 So that's just going to get the aluminum 00:14:26.476 --> 00:14:28.780 oxide, because sometimes-- you guys will get to it. 00:14:28.780 --> 00:14:32.100 But sometimes you can get a reaction of aluminum 00:14:32.100 --> 00:14:36.250 with the moisture in the air, and that's 00:14:36.250 --> 00:14:37.500 going to cause aluminum oxide. 00:14:37.500 --> 00:14:39.230 So he's getting get rid of that. 00:14:39.230 --> 00:14:43.704 And now we've put this on a-- what is this? 00:14:43.704 --> 00:14:44.580 ERIC: [INAUDIBLE]. 00:14:44.580 --> 00:14:45.470 GUEST SPEAKER 1: What do you call it? 00:14:45.470 --> 00:14:46.570 A detector of some kind. 00:14:46.570 --> 00:14:49.620 So basically, when he charges this, what's going to happen 00:14:49.620 --> 00:14:54.660 is that you have this plate, and you have this joint. 00:14:54.660 --> 00:14:58.290 And they're both going to be electrically negative, 00:14:58.290 --> 00:15:00.230 because you've introduced some electrons. 00:15:00.230 --> 00:15:02.160 And they're going to repel each other, 00:15:02.160 --> 00:15:03.000 because they're both negative. 00:15:03.000 --> 00:15:04.583 Two negative charges repel each other. 00:15:04.583 --> 00:15:08.190 So you're going to see some space develop as Eric's done. 00:15:08.190 --> 00:15:10.760 Now, what he's doing is he's got a plastic rod here 00:15:10.760 --> 00:15:13.440 that he's charging with the fur. 00:15:13.440 --> 00:15:16.637 And he's introducing those electrons onto the plate. 00:15:16.637 --> 00:15:18.470 So now we've got a negatively charged plate, 00:15:18.470 --> 00:15:20.460 and you can see that by the fact that you 00:15:20.460 --> 00:15:23.220 see some repulsion between that rod and the rest 00:15:23.220 --> 00:15:25.670 of the detector, which is actually working out 00:15:25.670 --> 00:15:27.860 pretty nicely. 00:15:27.860 --> 00:15:28.360 So once-- 00:15:28.360 --> 00:15:30.068 CATHERINE DRENNAN: So say this experiment 00:15:30.068 --> 00:15:31.340 is very weather-dependent. 00:15:31.340 --> 00:15:36.410 If it's really humid or too dry, it doesn't work nearly as well. 00:15:36.410 --> 00:15:37.910 But today, today's good weather. 00:15:37.910 --> 00:15:39.618 Today's good weather for this experiment, 00:15:39.618 --> 00:15:42.320 not so much good for sunbathing outside, but good 00:15:42.320 --> 00:15:43.885 weather for this experiment. 00:15:43.885 --> 00:15:47.810 GUEST SPEAKER 1: Although we have UV lamps, so maybe. 00:15:47.810 --> 00:15:49.217 CATHERINE DRENNAN: That's true. 00:15:49.217 --> 00:15:50.050 GUEST SPEAKER 1: OK. 00:15:50.050 --> 00:15:51.487 So now we've got a charge. 00:15:51.487 --> 00:15:53.570 CATHERINE DRENNAN: That's the green laser pointer. 00:15:53.570 --> 00:15:54.992 Let's get the red. 00:15:54.992 --> 00:15:56.950 GUEST SPEAKER 1: It's underneath here, I think. 00:15:56.950 --> 00:15:58.317 CATHERINE DRENNAN: Oh, yeah. 00:15:58.317 --> 00:15:59.150 GUEST SPEAKER 1: OK. 00:15:59.150 --> 00:15:59.960 So now-- 00:15:59.960 --> 00:16:01.340 CATHERINE DRENNAN: We could do the calculation for the green. 00:16:01.340 --> 00:16:03.770 If you want to do the calculation for the green, 00:16:03.770 --> 00:16:04.740 we can try it later. 00:16:04.740 --> 00:16:06.200 GUEST SPEAKER 1: Eric's got a red laser pointer in his hand. 00:16:06.200 --> 00:16:07.158 He's going to shine it. 00:16:07.158 --> 00:16:11.450 And we're going to see that nothing happens, 00:16:11.450 --> 00:16:15.170 because as we calculated, the energy of these photons 00:16:15.170 --> 00:16:17.069 is not enough to get over the threshold 00:16:17.069 --> 00:16:18.110 of this particular metal. 00:16:18.110 --> 00:16:20.600 CATHERINE DRENNAN: So if electrons were being ejected, 00:16:20.600 --> 00:16:23.599 you should see it move. 00:16:23.599 --> 00:16:25.640 GUEST SPEAKER 1: And we'll do that one more time. 00:16:25.640 --> 00:16:26.889 Maybe the green one will work. 00:16:26.889 --> 00:16:28.242 It doesn't. 00:16:28.242 --> 00:16:29.450 CATHERINE DRENNAN: All right. 00:16:29.450 --> 00:16:31.310 Well, now we have to see if the UV-- we built it up. 00:16:31.310 --> 00:16:31.970 The UV should-- 00:16:31.970 --> 00:16:32.440 GUEST SPEAKER 1: So hopefully this works. 00:16:32.440 --> 00:16:32.900 CATHERINE DRENNAN: --work. 00:16:32.900 --> 00:16:33.637 Let's see. 00:16:33.637 --> 00:16:36.167 GUEST SPEAKER 2: [INAUDIBLE] 00:16:36.167 --> 00:16:37.000 GUEST SPEAKER 1: OK. 00:16:37.000 --> 00:16:38.877 So oh-- maybe-- 00:16:38.877 --> 00:16:39.752 AUDIENCE: [INAUDIBLE] 00:16:39.752 --> 00:16:40.668 CATHERINE DRENNAN: Oh. 00:16:40.668 --> 00:16:42.740 GUEST SPEAKER 1: Oh, well, I guess it worked. 00:16:42.740 --> 00:16:44.410 CATHERINE DRENNAN: It did work. 00:16:44.410 --> 00:16:45.580 You could sort of see that. 00:16:45.580 --> 00:16:47.330 GUEST SPEAKER 1: So maybe we can charge it 00:16:47.330 --> 00:16:48.690 up again while I talk about it. 00:16:48.690 --> 00:16:48.995 CATHERINE DRENNAN: Yeah, sometimes 00:16:48.995 --> 00:16:49.953 the charge [INAUDIBLE]. 00:16:49.953 --> 00:16:51.710 GUEST SPEAKER 1: The UV lamp, obviously, 00:16:51.710 --> 00:16:54.050 has enough energy in each of these photons. 00:16:54.050 --> 00:16:58.250 So when you shine that light at the metal, 00:16:58.250 --> 00:16:59.900 you have the electrons on the surface, 00:16:59.900 --> 00:17:01.850 which are being ejected. 00:17:01.850 --> 00:17:03.650 And if those electrons get ejected, 00:17:03.650 --> 00:17:06.010 then the whole system becomes neutral. 00:17:06.010 --> 00:17:09.050 If the systems become neutral, then that rod can go back 00:17:09.050 --> 00:17:13.060 and is no longer feels a repulsion, 00:17:13.060 --> 00:17:15.410 because the two parts are no longer negative. 00:17:15.410 --> 00:17:17.450 So once we charge this up again, maybe we 00:17:17.450 --> 00:17:19.859 can go to the other side and-- I think it's good. 00:17:19.859 --> 00:17:20.359 It's good. 00:17:20.359 --> 00:17:21.096 CATHERINE DRENNAN: Yeah, that's good. 00:17:21.096 --> 00:17:21.869 Oh-- 00:17:21.869 --> 00:17:23.801 GUEST SPEAKER 1: It will be fine. 00:17:23.801 --> 00:17:25.292 GUEST SPEAKER 2: Wavering. 00:17:25.292 --> 00:17:26.750 CATHERINE DRENNAN: OK. 00:17:26.750 --> 00:17:27.960 GUEST SPEAKER 1: OK. 00:17:27.960 --> 00:17:29.720 Now we're just going to try it again. 00:17:29.720 --> 00:17:34.182 And yay. 00:17:34.182 --> 00:17:35.140 CATHERINE DRENNAN: Yay. 00:17:35.140 --> 00:17:36.265 GUEST SPEAKER 1: We got it. 00:17:36.265 --> 00:17:39.550 [APPLAUSE] 00:17:39.550 --> 00:17:40.990 CATHERINE DRENNAN: OK. 00:17:40.990 --> 00:17:41.490 Great. 00:17:41.490 --> 00:17:43.520 We can just leave this here. 00:17:43.520 --> 00:17:45.070 All right. 00:17:45.070 --> 00:17:47.360 And I think he held it for 60 seconds, so you 00:17:47.360 --> 00:17:49.400 know how many photons were coming off, 00:17:49.400 --> 00:17:51.860 too, if you want to do that calculation. 00:17:51.860 --> 00:17:55.220 So again, the photoelectric effect 00:17:55.220 --> 00:17:58.850 was really important at this time 00:17:58.850 --> 00:18:03.140 in understanding the properties that were being observed, 00:18:03.140 --> 00:18:07.370 to help us understand about this quantized energy of particles, 00:18:07.370 --> 00:18:10.290 that light had this particle-like property. 00:18:10.290 --> 00:18:12.290 It had this quantized energy. 00:18:12.290 --> 00:18:15.110 And you needed a certain amount of it 00:18:15.110 --> 00:18:17.900 to eject an electron from a metal surface. 00:18:17.900 --> 00:18:21.530 So we all know that light is a wave. 00:18:21.530 --> 00:18:23.240 But now there's this evidence that, 00:18:23.240 --> 00:18:27.590 even though it's pretty much this massless particle, 00:18:27.590 --> 00:18:31.070 that it still has particle-like properties. 00:18:31.070 --> 00:18:34.887 So light is a really amazing thing. 00:18:34.887 --> 00:18:36.470 This doesn't really show up very well. 00:18:36.470 --> 00:18:37.803 It's a view of the Stata Center. 00:18:37.803 --> 00:18:41.360 Stata Center always has some really spectacular sunlight 00:18:41.360 --> 00:18:43.200 coming around it sometimes. 00:18:43.200 --> 00:18:43.700 All right. 00:18:43.700 --> 00:18:47.900 So now, if this is true, that means 00:18:47.900 --> 00:18:51.530 that photons that have this quantized energy 00:18:51.530 --> 00:18:53.980 should have momentum as well. 00:18:53.980 --> 00:18:56.390 And so Einstein was thinking about that. 00:18:56.390 --> 00:18:59.450 And so he reasoned that this had to be true. 00:18:59.450 --> 00:19:03.650 There had to be some kind of momentum associated with them. 00:19:03.650 --> 00:19:07.490 And so momentum, or p, here is equal to Planck's 00:19:07.490 --> 00:19:11.840 constant times the frequency divided by the speed of light, 00:19:11.840 --> 00:19:12.740 c. 00:19:12.740 --> 00:19:16.250 And since the speed of light is equal to the frequency 00:19:16.250 --> 00:19:18.770 times the wavelength of the light, 00:19:18.770 --> 00:19:22.280 then the momentum should be equal to Planck's constant 00:19:22.280 --> 00:19:24.530 divided by the wavelength. 00:19:24.530 --> 00:19:27.050 So this is really-- we're talking about momentum 00:19:27.050 --> 00:19:31.470 in terms of wavelength, this inverse relationship here. 00:19:31.470 --> 00:19:33.590 This was just a kind of a crazy idea 00:19:33.590 --> 00:19:35.570 to be thinking about momentum, when 00:19:35.570 --> 00:19:37.560 you're talking about light. 00:19:37.560 --> 00:19:41.120 And this really came out of the photoelectric effect. 00:19:41.120 --> 00:19:43.700 And also, there were some experiments 00:19:43.700 --> 00:19:48.560 done by Arthur Compton that also showed that you could 00:19:48.560 --> 00:19:51.110 sort of transfer this momentum. 00:19:51.110 --> 00:19:54.170 And so that's again the particle-like property. 00:19:54.170 --> 00:19:57.050 So it's a really exciting time. 00:19:57.050 --> 00:19:58.190 OK. 00:19:58.190 --> 00:20:01.610 So we're going to now move to matter. 00:20:01.610 --> 00:20:03.050 So we've been talking about light 00:20:03.050 --> 00:20:08.870 and how light has this dual, particle, wavelike properties. 00:20:08.870 --> 00:20:10.370 But what about matter? 00:20:10.370 --> 00:20:15.260 So we accept that matter has particle-like properties. 00:20:15.260 --> 00:20:17.135 But what about as a wave? 00:20:20.550 --> 00:20:25.960 So enter de Broglie into this area. 00:20:25.960 --> 00:20:31.050 And so he was following what Einstein was thinking about. 00:20:31.050 --> 00:20:34.690 And he said, OK, so that's pretty cool. 00:20:34.690 --> 00:20:38.620 If you have momentum is equal to Planck's constant divided 00:20:38.620 --> 00:20:40.210 by wavelength, if you could think 00:20:40.210 --> 00:20:43.750 of things that have wavelengths as having momentum. 00:20:43.750 --> 00:20:47.620 And he said, or I can rewrite this equation, 00:20:47.620 --> 00:20:52.150 that wavelength equals Planck's constant divided by momentum. 00:20:52.150 --> 00:20:54.760 And we know something about momentum. 00:20:54.760 --> 00:20:58.600 We know that momentum is often associated with something's 00:20:58.600 --> 00:21:01.550 mass times its velocity. 00:21:01.550 --> 00:21:06.700 So therefore, I should be able to rewrite this equation again 00:21:06.700 --> 00:21:09.250 in terms of wavelength being equal to Planck's 00:21:09.250 --> 00:21:13.240 constant divided by a mass and a velocity. 00:21:13.240 --> 00:21:18.300 And here, we are expressing wavelengths in terms of masses. 00:21:18.300 --> 00:21:19.930 So this was really something. 00:21:19.930 --> 00:21:22.420 And this was basically his PhD thesis. 00:21:22.420 --> 00:21:24.700 I think it maybe had more pages than that, 00:21:24.700 --> 00:21:26.910 but this would have probably been enough, 00:21:26.910 --> 00:21:28.870 this sort of cover page. 00:21:28.870 --> 00:21:30.940 This is my PhD thesis. 00:21:30.940 --> 00:21:34.800 And Einstein said that he had lifted 00:21:34.800 --> 00:21:38.230 the corner of a great veil with really just manipulating 00:21:38.230 --> 00:21:41.890 what was known at the time and rearranging these equations 00:21:41.890 --> 00:21:45.300 and presenting relationships that people hadn't really 00:21:45.300 --> 00:21:46.990 put together before. 00:21:46.990 --> 00:21:49.360 So he ended up winning a Nobel Prize, 00:21:49.360 --> 00:21:53.410 basically, for his PhD thesis, which is a fairly rare thing 00:21:53.410 --> 00:21:55.020 to have happen. 00:21:55.020 --> 00:21:58.070 But this was really an incredible time. 00:21:58.070 --> 00:21:58.690 OK. 00:21:58.690 --> 00:22:03.300 So if this is true, if you have equations 00:22:03.300 --> 00:22:07.510 that relate wavelengths to mass, and particles 00:22:07.510 --> 00:22:12.030 have wavelike properties, how come we don't see this? 00:22:12.030 --> 00:22:13.690 How come this isn't part-- how come 00:22:13.690 --> 00:22:16.530 no one noticed the particle going by 00:22:16.530 --> 00:22:19.800 and this wavelength associated with it? 00:22:19.800 --> 00:22:25.630 So why don't we observe this wavelike behavior 00:22:25.630 --> 00:22:29.750 if, in fact, it is associated with particles? 00:22:29.750 --> 00:22:32.140 So let's think about this a minute. 00:22:32.140 --> 00:22:37.450 And we can consider why, when you go to Fenway Park-- 00:22:37.450 --> 00:22:39.630 and you should, because it's fun-- 00:22:39.630 --> 00:22:42.060 and you watch someone throw a fastball, 00:22:42.060 --> 00:22:46.770 why you don't see a wave associated with that fastball. 00:22:46.770 --> 00:22:51.910 So we can consider a fastball and that the mass of a baseball 00:22:51.910 --> 00:22:57.020 is about 5 ounces, or 0.142 kilograms. 00:22:57.020 --> 00:23:01.290 And the velocity of a fastball is around 94 miles per hour, 00:23:01.290 --> 00:23:04.150 or 42 meters per second. 00:23:04.150 --> 00:23:05.920 And so we can do a little calculation 00:23:05.920 --> 00:23:09.460 and figure out what the wavelength associated 00:23:09.460 --> 00:23:12.610 with that ball should be. 00:23:12.610 --> 00:23:16.750 So wavelength should be Planck's constant over the mass 00:23:16.750 --> 00:23:19.450 times the velocity of the ball. 00:23:19.450 --> 00:23:21.490 And we can plug in these values. 00:23:21.490 --> 00:23:23.750 And here's Planck's constant again. 00:23:23.750 --> 00:23:27.670 And now you'll note I did something with the units. 00:23:27.670 --> 00:23:30.790 So instead of joule seconds, I substituted 00:23:30.790 --> 00:23:37.260 joules with kilograms meters squared seconds to the minus 2. 00:23:37.260 --> 00:23:39.460 And that's what's equal to a joule. 00:23:39.460 --> 00:23:42.290 And I'm going to do that so I can cancel out my units. 00:23:42.290 --> 00:23:45.190 And again, all of this will be provided on an equation sheet. 00:23:45.190 --> 00:23:48.970 You do not need to remember all of these conversions. 00:23:48.970 --> 00:23:55.006 And so over the mass of the baseball and the velocity 00:23:55.006 --> 00:23:56.380 of the baseball-- and we're going 00:23:56.380 --> 00:23:58.560 to put the velocity in meters per second 00:23:58.560 --> 00:24:00.950 so our units can cancel out. 00:24:00.950 --> 00:24:03.940 And so I'll just cancel units out. 00:24:03.940 --> 00:24:05.680 So we're canceling our kilograms. 00:24:05.680 --> 00:24:08.040 We're canceling one of the meters, 00:24:08.040 --> 00:24:10.420 and canceling all of the seconds. 00:24:10.420 --> 00:24:13.444 And we have one meter left, which 00:24:13.444 --> 00:24:15.485 is good, because we're talking about wavelengths. 00:24:15.485 --> 00:24:18.160 So that's the unit we should have. 00:24:18.160 --> 00:24:23.820 And the wavelength is 1.1 times 10 to the minus 34 meters. 00:24:23.820 --> 00:24:29.710 That is a really small number times 10 to the 34. 00:24:29.710 --> 00:24:34.480 And it is, in fact, undetectably small. 00:24:34.480 --> 00:24:35.440 OK. 00:24:35.440 --> 00:24:38.760 So now why don't you try your hand at this, 00:24:38.760 --> 00:24:40.410 and we'll try a clicker question. 00:25:22.963 --> 00:25:23.950 Yeah, it's very tiny. 00:25:39.061 --> 00:25:39.560 All right. 00:25:39.560 --> 00:25:41.588 Let's take just 10 more seconds. 00:25:49.240 --> 00:25:51.165 Oh, or five seconds. 00:25:57.370 --> 00:25:57.940 OK. 00:25:57.940 --> 00:25:58.880 Awesome. 00:26:01.790 --> 00:26:02.860 It went away. 00:26:02.860 --> 00:26:04.030 That's OK. 00:26:04.030 --> 00:26:07.230 So they're in-- 97%. 00:26:07.230 --> 00:26:08.530 I like 97%. 00:26:08.530 --> 00:26:11.110 That's a good number. 00:26:11.110 --> 00:26:13.150 So again, you want to think about this 00:26:13.150 --> 00:26:15.760 and just realize the relationship, the equation, 00:26:15.760 --> 00:26:16.690 involved. 00:26:16.690 --> 00:26:21.660 And so thinking about-- oops, I switched pointers. 00:26:21.660 --> 00:26:23.470 I like the green better. 00:26:23.470 --> 00:26:27.130 So think about the relationship between the velocity 00:26:27.130 --> 00:26:29.090 of the ball and the wavelength. 00:26:29.090 --> 00:26:32.220 And so Wakefield, who was an knuckleballer, 00:26:32.220 --> 00:26:35.830 is the winner here, with the longest wavelength. 00:26:35.830 --> 00:26:40.120 But still, the number for this is 1.4 times 10 00:26:40.120 --> 00:26:41.900 to the minus 34. 00:26:41.900 --> 00:26:45.730 And so this is still undetectably small. 00:26:45.730 --> 00:26:50.020 So of course, no one had noticed this property before. 00:26:50.020 --> 00:26:53.330 But it still, it still exists. 00:26:53.330 --> 00:26:56.260 So when you're talking about a baseball, 00:26:56.260 --> 00:26:59.530 the wavelength is really not very, relevant to you, 00:26:59.530 --> 00:27:04.130 because it is this incredibly small, undetectable number. 00:27:04.130 --> 00:27:07.000 But if you're talking about an electron, 00:27:07.000 --> 00:27:08.870 it's entirely different. 00:27:08.870 --> 00:27:12.340 So now, if we think about a gaseous electron traveling 00:27:12.340 --> 00:27:16.750 at 4 times 10 to the 6 meters per second, and so 00:27:16.750 --> 00:27:20.770 that's associated with an eV of about 54. 00:27:20.770 --> 00:27:24.310 So we have this electron traveling with this velocity. 00:27:24.310 --> 00:27:27.940 And now, if we do this calculation, 00:27:27.940 --> 00:27:31.360 so if we use Planck's constant divided 00:27:31.360 --> 00:27:33.670 by the mass of the electron-- and that's 00:27:33.670 --> 00:27:38.470 known, in another great experiment-- and its velocity, 00:27:38.470 --> 00:27:41.230 now we can calculate out the wavelength. 00:27:41.230 --> 00:27:47.090 And it's 2 times 10 to the minus 10, or about two angstroms. 00:27:47.090 --> 00:27:51.970 Now, 2 angstroms is a relevant number, 00:27:51.970 --> 00:27:54.130 when you're talking about an electron, 00:27:54.130 --> 00:27:56.570 because an electron is in an atom. 00:27:56.570 --> 00:28:01.310 And atoms tend to be-- you have diameters 0.5 to 4 angstroms. 00:28:01.310 --> 00:28:04.630 So now the wavelength is on the same scale 00:28:04.630 --> 00:28:07.750 as the size of the object you're talking about. 00:28:07.750 --> 00:28:11.090 And so when that's true, all of a sudden, the wavelength-- 00:28:11.090 --> 00:28:14.650 the wavelike property becomes super important to thinking 00:28:14.650 --> 00:28:15.760 about this. 00:28:15.760 --> 00:28:19.720 So for an electron that is a particle, 00:28:19.720 --> 00:28:24.040 it's really important to think about its wavelike properties. 00:28:24.040 --> 00:28:27.580 And so people were saying, OK, if electrons are waves, then 00:28:27.580 --> 00:28:30.370 maybe we should see other wavelike properties, 00:28:30.370 --> 00:28:32.950 such as diffraction. 00:28:32.950 --> 00:28:35.290 Diffraction, we talked about last time, 00:28:35.290 --> 00:28:37.210 is an important wavelike property 00:28:37.210 --> 00:28:40.640 of constructive interference, destructive interference. 00:28:40.640 --> 00:28:42.220 So people looked to see whether there 00:28:42.220 --> 00:28:44.150 were diffraction-like properties, 00:28:44.150 --> 00:28:46.180 and in fact, there are. 00:28:46.180 --> 00:28:49.150 So we had observed, then, the first 00:28:49.150 --> 00:28:52.570 was observing diffraction of electrons 00:28:52.570 --> 00:28:54.190 from a nickel crystal. 00:28:54.190 --> 00:28:57.790 And then JP Thomson showed that electrons 00:28:57.790 --> 00:29:00.880 that pass through gold foil again 00:29:00.880 --> 00:29:02.870 produced a diffraction pattern. 00:29:02.870 --> 00:29:06.470 So again, this was a wavelike property. 00:29:06.470 --> 00:29:09.970 So you might think Thomson, that sounds a little familiar to me. 00:29:09.970 --> 00:29:12.610 Didn't she just talk about that last week? 00:29:12.610 --> 00:29:14.980 And yes, here there are two important Thomsons 00:29:14.980 --> 00:29:15.670 in this story. 00:29:15.670 --> 00:29:18.970 And this is a father and son team. 00:29:18.970 --> 00:29:23.710 And so JJ Thomson won a Nobel Prize in 1906 00:29:23.710 --> 00:29:26.230 for showing that an electron is a particle. 00:29:26.230 --> 00:29:28.630 He discovered an electron. 00:29:28.630 --> 00:29:34.300 And then in 1937, his son wins a Nobel Prize for showing-- son 00:29:34.300 --> 00:29:38.190 just had to be like, Dad, I'm going to show you're wrong. 00:29:38.190 --> 00:29:41.415 An electron is, in fact, a wave. 00:29:41.415 --> 00:29:42.790 But I think they were both happy. 00:29:42.790 --> 00:29:45.730 I think they both got along, no father-son rivalry. 00:29:45.730 --> 00:29:49.060 I think this is one of the cooler stories in science, 00:29:49.060 --> 00:29:52.330 how this father, son both had kind 00:29:52.330 --> 00:29:55.990 of opposite discoveries, which both ended up being true, 00:29:55.990 --> 00:30:00.190 and really changed the way we thought about matter. 00:30:00.190 --> 00:30:01.300 All right. 00:30:01.300 --> 00:30:08.410 So we have light as a particle and as a wave. 00:30:08.410 --> 00:30:11.080 We have matter, particularly electrons, 00:30:11.080 --> 00:30:14.150 as particles and waves. 00:30:14.150 --> 00:30:17.110 And now we are ready for a way to think 00:30:17.110 --> 00:30:19.880 about how to put this together. 00:30:19.880 --> 00:30:22.750 So before we move on and talk about the Schrodinger equation, 00:30:22.750 --> 00:30:25.687 I just want to take a break from history for a minute, 00:30:25.687 --> 00:30:27.520 because some of you are like, OK, well, this 00:30:27.520 --> 00:30:30.400 is really cool for the father and son team, 00:30:30.400 --> 00:30:32.380 but what about today? 00:30:32.380 --> 00:30:33.740 What's happening today? 00:30:33.740 --> 00:30:36.280 So let's take a break from history for a second 00:30:36.280 --> 00:30:40.000 and talk about why you should care about small particles. 00:30:40.000 --> 00:30:42.070 Small particles of special properties, 00:30:42.070 --> 00:30:43.929 if they're on the subatomic scale, 00:30:43.929 --> 00:30:45.220 their properties are different. 00:30:45.220 --> 00:30:49.200 If you have very, very few atoms, versus many atoms, 00:30:49.200 --> 00:30:52.184 the things with very few atoms have special properties. 00:30:52.184 --> 00:30:53.600 So why should you care about that? 00:30:53.600 --> 00:30:55.930 Why should you care about the energies 00:30:55.930 --> 00:30:58.136 that we can get out of the Schrodinger equation? 00:30:58.136 --> 00:31:00.760 So why should we care about the Schrodinger equation or quantum 00:31:00.760 --> 00:31:01.780 mechanics? 00:31:01.780 --> 00:31:04.870 So there are many reasons, but I will share one with you. 00:31:04.870 --> 00:31:07.990 And this is a segment in their own words. 00:31:07.990 --> 00:31:11.640 So you're going to hear from Darcy, who was actually 00:31:11.640 --> 00:31:14.070 a former TA for 5.111. 00:31:14.070 --> 00:31:16.190 So she is associated with this class. 00:31:16.190 --> 00:31:21.330 She actually just got her PhD in the spring from MIT, 00:31:21.330 --> 00:31:25.080 and she now works at Google. 00:31:25.080 --> 00:31:26.940 But in this short, she's going to tell you 00:31:26.940 --> 00:31:29.130 about research in Moungi Bawendi's Lab, 00:31:29.130 --> 00:31:32.190 and why you should care about quantum dots, which 00:31:32.190 --> 00:31:35.590 are small collections of atoms. 00:31:35.590 --> 00:31:37.440 So I'm going to try to switch over 00:31:37.440 --> 00:31:40.750 now and hope that our demo before 00:31:40.750 --> 00:31:42.780 didn't screw up the sound. 00:31:42.780 --> 00:31:44.970 But we'll see what we can do. 00:31:44.970 --> 00:31:51.424 And I think it should be good. 00:31:51.424 --> 00:31:52.090 [VIDEO PLAYBACK] 00:31:52.090 --> 00:31:54.548 - My name is Darcy Wanger, and I work as a graduate student 00:31:54.548 --> 00:31:56.630 in the Bawendi Lab at MIT. 00:31:56.630 --> 00:31:59.740 I work with quantum dots in my research. 00:31:59.740 --> 00:32:03.130 Quantum dots are really, really tiny particles 00:32:03.130 --> 00:32:04.960 of a semiconductor. 00:32:04.960 --> 00:32:09.850 So we're talking like 4 nanometers in diameter. 00:32:09.850 --> 00:32:14.292 In a particle that small, there are only 10,000 or so atoms, 00:32:14.292 --> 00:32:16.000 which seems like a lot of atoms if you're 00:32:16.000 --> 00:32:17.500 comparing to something like water, 00:32:17.500 --> 00:32:19.510 which only has 3 atoms in it. 00:32:19.510 --> 00:32:21.910 But if you compare it to something you can actually 00:32:21.910 --> 00:32:25.180 hold in your hand, which has a lot of atoms in it, 00:32:25.180 --> 00:32:27.730 10,000 is actually a pretty small number. 00:32:27.730 --> 00:32:31.600 So a particle this small has really strange properties. 00:32:31.600 --> 00:32:34.260 Different things start to matter when you get really small. 00:32:34.260 --> 00:32:36.970 And just like an atom, a quantum dot, 00:32:36.970 --> 00:32:40.930 or semiconductor nanocrystal, has discrete energy levels. 00:32:40.930 --> 00:32:44.020 So if an electron is sitting at this energy level, 00:32:44.020 --> 00:32:46.300 and it absorbs light, an electron 00:32:46.300 --> 00:32:48.730 can get excited to a higher energy level. 00:32:48.730 --> 00:32:51.790 And then, when that electron relaxes back down to the ground 00:32:51.790 --> 00:32:54.190 state, it emits light. 00:32:54.190 --> 00:32:56.650 And the energy of that light is exactly 00:32:56.650 --> 00:32:58.625 the difference between these two energy levels. 00:33:01.450 --> 00:33:03.400 The difference between the energy levels 00:33:03.400 --> 00:33:06.460 is related to the size of the dot. 00:33:06.460 --> 00:33:08.530 So in a really small quantum dot, 00:33:08.530 --> 00:33:10.600 the energy levels are far apart. 00:33:10.600 --> 00:33:13.000 So the light it emits is higher energy, 00:33:13.000 --> 00:33:16.060 because there's a large energy difference between the energy 00:33:16.060 --> 00:33:17.740 levels. 00:33:17.740 --> 00:33:20.230 If we use a larger quantum dot, the distance 00:33:20.230 --> 00:33:23.470 between the energy levels is smaller, so the light it emits 00:33:23.470 --> 00:33:26.680 is lower energy, or redder. 00:33:26.680 --> 00:33:30.490 People in our lab are working to make quantum dots bind 00:33:30.490 --> 00:33:31.360 to a tumor. 00:33:31.360 --> 00:33:34.120 So when a doctor goes in to remove a tumor, 00:33:34.120 --> 00:33:36.880 they can see the shining of the UV light on it, 00:33:36.880 --> 00:33:38.380 and see whether it's all gone when 00:33:38.380 --> 00:33:39.640 they've taken out the tumor. 00:33:39.640 --> 00:33:42.760 They can also use quantum dots to label other things 00:33:42.760 --> 00:33:47.860 other than tumors, like pH or oxygen level or antibodies 00:33:47.860 --> 00:33:50.890 or the other drugs that are treating the cancer tumor. 00:33:50.890 --> 00:33:52.730 Each of those can be different colors. 00:33:52.730 --> 00:33:54.550 So if you shine a light on that whole area, 00:33:54.550 --> 00:33:58.270 you can see, oh, that orange spot, that's some cancer cells. 00:33:58.270 --> 00:34:02.920 Oh, and that green tells me that the pH is above 7.4. 00:34:02.920 --> 00:34:07.480 So it's pretty cool that we can use the idea of energy levels 00:34:07.480 --> 00:34:12.460 in something so applicable like surgery, where it can actually 00:34:12.460 --> 00:34:16.510 be used to track things and make it easy for doctors 00:34:16.510 --> 00:34:18.801 to see what's going on while they're doing a surgery. 00:34:18.801 --> 00:34:21.060 [END PLAYBACK] 00:34:21.060 --> 00:34:22.570 CATHERINE DRENNAN: OK. 00:34:22.570 --> 00:34:25.900 So that's an example for course 5 research. 00:34:25.900 --> 00:34:29.134 [APPLAUSE] 00:34:31.491 --> 00:34:33.199 And you can see all these credits online. 00:34:33.199 --> 00:34:36.500 I will mention that some of those nice animations 00:34:36.500 --> 00:34:41.060 were done by a former graduate student in the chemistry 00:34:41.060 --> 00:34:41.659 department. 00:34:41.659 --> 00:34:44.389 So these videos, even the art was 00:34:44.389 --> 00:34:46.940 done by chemists, which is a lot of fun. 00:34:46.940 --> 00:34:47.719 OK. 00:34:47.719 --> 00:34:50.659 So let's introduce the Schrodinger equation. 00:34:50.659 --> 00:34:54.139 And we'll spend some more time on this 00:34:54.139 --> 00:34:57.710 as we go along, on Friday. 00:34:57.710 --> 00:35:03.680 So we needed now-- we had learned a lot 00:35:03.680 --> 00:35:08.420 about wave particle duality and about 00:35:08.420 --> 00:35:10.017 these subatomic particles. 00:35:10.017 --> 00:35:11.600 And we needed a way to think about it. 00:35:11.600 --> 00:35:14.900 We needed a theory to describe their behavior. 00:35:14.900 --> 00:35:19.500 And classical mechanics had some flaws in with respect. 00:35:19.500 --> 00:35:22.610 So we needed a new kind of mechanism. 00:35:22.610 --> 00:35:24.590 We needed quantum mechanics. 00:35:24.590 --> 00:35:27.410 So here, if we're thinking about particles 00:35:27.410 --> 00:35:29.690 that are really small like electrons, 00:35:29.690 --> 00:35:32.610 we need to consider the wavelike properties. 00:35:32.610 --> 00:35:35.810 It's really important when you have a wavelength that 00:35:35.810 --> 00:35:38.630 is so similar to the size of the object 00:35:38.630 --> 00:35:40.130 that you're thinking about. 00:35:40.130 --> 00:35:42.110 So the Schrodinger equation really 00:35:42.110 --> 00:35:46.700 became to quantum mechanics like Newton's equations 00:35:46.700 --> 00:35:49.110 were to classical mechanics. 00:35:49.110 --> 00:35:50.942 So what is the Schrodinger equation? 00:35:50.942 --> 00:35:52.400 So here's a picture of Schrodinger. 00:35:52.400 --> 00:35:53.900 And he looks so happy. 00:35:53.900 --> 00:35:56.870 I would be happy, too, if I had come up with this equation, 00:35:56.870 --> 00:35:57.680 I think. 00:35:57.680 --> 00:36:00.680 So here's the simplest form of the equation 00:36:00.680 --> 00:36:03.140 that you will probably ever see. 00:36:03.140 --> 00:36:08.510 And so we'll just define some of these terms. 00:36:08.510 --> 00:36:12.710 So we have wave function, psi. 00:36:12.710 --> 00:36:16.770 And over here is the binding energy, 00:36:16.770 --> 00:36:20.820 and that's the energy of binding an electron to a nucleus. 00:36:20.820 --> 00:36:26.040 And then an H with a hat, we have our Hamiltonian operator. 00:36:26.040 --> 00:36:29.250 And in this course, you will not be solving this equation. 00:36:29.250 --> 00:36:32.310 We're just going to be talking about what sorts of things 00:36:32.310 --> 00:36:34.740 came out of this equation. 00:36:34.740 --> 00:36:38.700 So I'm going to give you a little bit longer 00:36:38.700 --> 00:36:41.640 version of the equation now. 00:36:41.640 --> 00:36:44.350 And so again, you're thinking about the electron. 00:36:44.350 --> 00:36:48.120 It has these wavelike properties. 00:36:48.120 --> 00:36:54.210 And it's somewhere in the atom, not crashing into the nucleus. 00:36:54.210 --> 00:36:57.460 And it needs to be defined in three dimensions. 00:36:57.460 --> 00:37:00.210 And it has momentum, so it's moving. 00:37:00.210 --> 00:37:04.500 So we need to think about this as an equation of motion 00:37:04.500 --> 00:37:07.860 in a three-dimensional space. 00:37:07.860 --> 00:37:10.630 And the equation is going to change. 00:37:10.630 --> 00:37:12.600 The math will change, depending on where 00:37:12.600 --> 00:37:16.650 the electron is located, which you won't know exactly. 00:37:16.650 --> 00:37:19.480 So this is a very hard problem. 00:37:19.480 --> 00:37:22.500 But it's not totally without anything 00:37:22.500 --> 00:37:24.970 to do with classical mechanics. 00:37:24.970 --> 00:37:26.700 And if we write the longest version 00:37:26.700 --> 00:37:30.570 you'll see, at least in this course, for the hydrogen atom, 00:37:30.570 --> 00:37:32.970 I just want to show this to point out 00:37:32.970 --> 00:37:37.440 that there are some terms from classical mechanics in here. 00:37:37.440 --> 00:37:40.050 This is Coulomb's energy, also sometimes called 00:37:40.050 --> 00:37:41.500 potential energy. 00:37:41.500 --> 00:37:43.440 So we saw Coulomb's force before. 00:37:43.440 --> 00:37:45.060 Here is Coulomb's energy. 00:37:45.060 --> 00:37:46.710 So some of the classical mechanics 00:37:46.710 --> 00:37:49.860 is contained within this, but it expands 00:37:49.860 --> 00:37:51.990 from classical mechanics to consider 00:37:51.990 --> 00:37:57.190 the wavelike properties of the electrons. 00:37:57.190 --> 00:38:00.930 So whenever I talk about this, I always 00:38:00.930 --> 00:38:05.310 feel like I want to have something better 00:38:05.310 --> 00:38:10.530 to say about really what this is doing and where it came from. 00:38:10.530 --> 00:38:14.160 In terms of what it's doing, how is solving this helping you? 00:38:14.160 --> 00:38:16.830 What are you learning from solving this? 00:38:16.830 --> 00:38:19.170 So one thing you're learning from solving 00:38:19.170 --> 00:38:22.110 this is you're finding E. And that's 00:38:22.110 --> 00:38:24.702 really important, the binding energy of the nucleus 00:38:24.702 --> 00:38:25.410 and the electron. 00:38:25.410 --> 00:38:27.540 And we saw before that, if you just 00:38:27.540 --> 00:38:30.510 used simple classical mechanics, you 00:38:30.510 --> 00:38:32.250 have a positive and negative charge that 00:38:32.250 --> 00:38:33.700 are close to each other. 00:38:33.700 --> 00:38:36.000 Why don't they come and crash into each other? 00:38:36.000 --> 00:38:39.360 We want to know how they are bonded to each other, what's 00:38:39.360 --> 00:38:41.820 the real energy of that association. 00:38:41.820 --> 00:38:44.100 We also saw, with the photoelectric effect, 00:38:44.100 --> 00:38:45.930 that it's not that easy to get an electron 00:38:45.930 --> 00:38:48.750 to eject from a metal surface. 00:38:48.750 --> 00:38:50.230 So it's bound in there. 00:38:50.230 --> 00:38:52.920 And what is that actual binding energy? 00:38:52.920 --> 00:38:55.570 So that comes out of the Schrodinger equation. 00:38:55.570 --> 00:38:58.650 This E here is the binding energy. 00:38:58.650 --> 00:39:02.100 And also, solving it will tell you about the wave function 00:39:02.100 --> 00:39:03.960 or, as chemists like to talk about, 00:39:03.960 --> 00:39:08.010 orbitals, where the electrons are, in what orbitals. 00:39:08.010 --> 00:39:10.980 So this is the information you get out. 00:39:10.980 --> 00:39:15.390 And importantly, it works. 00:39:15.390 --> 00:39:17.790 It matches experiment. 00:39:17.790 --> 00:39:19.980 So chemists are experimentalists. 00:39:19.980 --> 00:39:22.890 We love experiments, and we see this data, 00:39:22.890 --> 00:39:25.030 and we want to understand it. 00:39:25.030 --> 00:39:27.200 And the Schrodinger equation helps us understand it. 00:39:27.200 --> 00:39:31.650 It correctly predicts binding energies and wave functions, 00:39:31.650 --> 00:39:34.980 and it explains why the hydrogen atom is, in fact, stable, 00:39:34.980 --> 00:39:40.180 where you don't have crashing or exploding of the hydrogen atom. 00:39:40.180 --> 00:39:44.040 So where did this equation come from that works so well? 00:39:44.040 --> 00:39:46.837 How did Schrodinger come up with this? 00:39:46.837 --> 00:39:49.170 And this is always sort of the puzzle when I teach this. 00:39:49.170 --> 00:39:52.110 I feel like I should have something profound to say 00:39:52.110 --> 00:39:54.390 about where this came from. 00:39:54.390 --> 00:39:56.370 And so I've done a little reading and looked, 00:39:56.370 --> 00:39:58.980 and I thought the best explanation for this 00:39:58.980 --> 00:40:02.640 that I ever saw came from Richard Feynman. 00:40:02.640 --> 00:40:04.590 And when he was asked how Schrodinger came up 00:40:04.590 --> 00:40:07.320 with this equation, he said, "it is not 00:40:07.320 --> 00:40:10.650 possible to derive it from anything you know. 00:40:10.650 --> 00:40:14.220 It came out of the mind of Schrodinger." 00:40:14.220 --> 00:40:18.060 And I thought that pretty much summed it up. 00:40:18.060 --> 00:40:20.010 So sometimes-- after class last week, 00:40:20.010 --> 00:40:22.110 on Wednesday, someone came down and said, 00:40:22.110 --> 00:40:23.490 you know, the Thomson experiment, 00:40:23.490 --> 00:40:25.531 discovering the electron, why didn't someone else 00:40:25.531 --> 00:40:26.820 do that experiment? 00:40:26.820 --> 00:40:28.590 It seemed like it's not a cathode ray. 00:40:28.590 --> 00:40:31.650 And you have to have a little phosphorous screen. 00:40:31.650 --> 00:40:33.900 Why didn't someone else discover the electron? 00:40:33.900 --> 00:40:36.581 And some of these other-- de Broglie rearranged 00:40:36.581 --> 00:40:38.580 some equations, did it in a way that no one else 00:40:38.580 --> 00:40:40.200 was thinking, but still. 00:40:40.200 --> 00:40:43.479 Or plot solving the equation of a straight line. 00:40:43.479 --> 00:40:45.270 No one else was thinking about it some way, 00:40:45.270 --> 00:40:46.800 using other people's data. 00:40:46.800 --> 00:40:49.470 They just sort of saw things in data that other people didn't. 00:40:49.470 --> 00:40:53.160 But you think why didn't someone else see that, too? 00:40:53.160 --> 00:40:54.960 When it comes to the Schrodinger equation, 00:40:54.960 --> 00:40:57.930 the question is why didn't someone else or lots of people 00:40:57.930 --> 00:40:58.860 come up with it? 00:40:58.860 --> 00:41:01.230 I think the question really is, how did Schrodinger 00:41:01.230 --> 00:41:01.990 come up with it? 00:41:01.990 --> 00:41:03.780 At least, that's the question to me. 00:41:03.780 --> 00:41:06.770 And I have never really-- that's the best explanation I have. 00:41:06.770 --> 00:41:09.930 It just came out of his mind. 00:41:09.930 --> 00:41:10.740 OK. 00:41:10.740 --> 00:41:12.510 So we're many years later. 00:41:12.510 --> 00:41:14.890 We've had the Schrodinger equation for a while. 00:41:14.890 --> 00:41:17.490 So this is an old story, right? 00:41:17.490 --> 00:41:20.040 Well, maybe for the hydrogen atom, 00:41:20.040 --> 00:41:24.480 but this is still actually a very active area of research. 00:41:24.480 --> 00:41:26.490 Oh, my startup disk is full. 00:41:26.490 --> 00:41:27.960 Thank you. 00:41:27.960 --> 00:41:29.160 Let's go back to that. 00:41:29.160 --> 00:41:30.966 All right. 00:41:30.966 --> 00:41:32.340 So I just thought-- I always like 00:41:32.340 --> 00:41:36.250 to give you examples of current research on these areas. 00:41:36.250 --> 00:41:38.010 And so I know a number of you were 00:41:38.010 --> 00:41:41.700 interested in potential of being chemical engineering majors, 00:41:41.700 --> 00:41:42.265 undergrads. 00:41:42.265 --> 00:41:43.890 And I'll tell you about a new professor 00:41:43.890 --> 00:41:46.440 who started about a year ago, Heather Kulik. 00:41:46.440 --> 00:41:50.190 And her research group is really interested in using 00:41:50.190 --> 00:41:53.310 a quantum mechanical approach to study materials 00:41:53.310 --> 00:41:55.140 and to study proteins. 00:41:55.140 --> 00:41:56.920 But when you get to things like proteins, 00:41:56.920 --> 00:41:58.920 there's thousands and thousands of atoms around. 00:41:58.920 --> 00:42:02.520 Forget multiple electrons, we're talking about multiple atoms 00:42:02.520 --> 00:42:05.580 with multiple electrons, huge complexes. 00:42:05.580 --> 00:42:08.970 How can you give a quantum mechanical analysis 00:42:08.970 --> 00:42:10.492 of things that are so large? 00:42:10.492 --> 00:42:11.700 And this is really important. 00:42:11.700 --> 00:42:15.240 I mean, I think that one of the big problems moving forward 00:42:15.240 --> 00:42:17.085 is solving the energy problem and doing it 00:42:17.085 --> 00:42:19.440 in a way that doesn't destroy our environment, so 00:42:19.440 --> 00:42:21.900 new batteries, new electrodes, new materials. 00:42:21.900 --> 00:42:24.330 We need to understand the properties of different metals 00:42:24.330 --> 00:42:26.585 to understand what will make those good electrodes. 00:42:26.585 --> 00:42:27.960 And to really understand them, we 00:42:27.960 --> 00:42:29.700 need a quantum mechanical approach. 00:42:29.700 --> 00:42:31.470 But these are big areas. 00:42:31.470 --> 00:42:33.660 There's a lot of things to consider here. 00:42:33.660 --> 00:42:36.330 So Heather is interested in coming up 00:42:36.330 --> 00:42:40.320 with improving algorithms, improving the computation, 00:42:40.320 --> 00:42:44.010 to really give a quantum mechanical analysis to systems 00:42:44.010 --> 00:42:46.290 that have a lot of atoms in them. 00:42:46.290 --> 00:42:49.360 So if you're interested in this area, you're not too late. 00:42:49.360 --> 00:42:51.870 You don't have to go back to the early 1900s. 00:42:51.870 --> 00:42:55.620 There's still a lot to do in this area. 00:42:55.620 --> 00:42:56.490 OK. 00:42:56.490 --> 00:43:00.210 So very briefly now, let's just look 00:43:00.210 --> 00:43:03.250 at the Schrodinger equation we saw from the hydrogen atom. 00:43:03.250 --> 00:43:05.160 So we'll go back to understanding 00:43:05.160 --> 00:43:09.690 quantum mechanical analysis of photosynthesis-- amazing, 00:43:09.690 --> 00:43:11.060 don't understand how it works. 00:43:11.060 --> 00:43:12.090 That would be great if we did. 00:43:12.090 --> 00:43:14.131 That would really solve a lot of energy problems. 00:43:14.131 --> 00:43:17.890 But we'll just go to hydrogen atom, one electron back. 00:43:17.890 --> 00:43:20.046 So if you solve the Schrodinger equation for this-- 00:43:20.046 --> 00:43:22.170 and I think I did this in college, not in freshman, 00:43:22.170 --> 00:43:24.990 chemistry, but somewhere along the line-- 00:43:24.990 --> 00:43:26.550 you'll come up with this term. 00:43:26.550 --> 00:43:28.680 So again, this is the binding energy. 00:43:28.680 --> 00:43:31.530 We just want to know about how the electron is 00:43:31.530 --> 00:43:34.050 being held by the nucleus. 00:43:34.050 --> 00:43:36.330 And there are some terms in here. 00:43:36.330 --> 00:43:40.350 We have the electrons mass-- that's known, 00:43:40.350 --> 00:43:42.300 the electrons charge. 00:43:42.300 --> 00:43:46.050 We have a permittivity constant and Planck's constant. 00:43:46.050 --> 00:43:48.570 And if you look at this, you go, wait a minute. 00:43:48.570 --> 00:43:49.770 That's a constant. 00:43:49.770 --> 00:43:50.670 That's a constant. 00:43:50.670 --> 00:43:51.570 That's a constant. 00:43:51.570 --> 00:43:53.100 That's a constant. 00:43:53.100 --> 00:43:56.220 We can simplify that. 00:43:56.220 --> 00:43:58.470 And we will. 00:43:58.470 --> 00:44:03.210 And that is the Rydberg's constant, 2.18 times 00:44:03.210 --> 00:44:05.620 10 to the minus 18th joules. 00:44:05.620 --> 00:44:07.710 So now it doesn't look quite as scary. 00:44:07.710 --> 00:44:11.670 We can just substitute this RH. 00:44:11.670 --> 00:44:13.646 That makes us feel a lot better. 00:44:13.646 --> 00:44:16.020 It's one number that will be given on the equation sheet, 00:44:16.020 --> 00:44:18.210 so we don't even have to remember it. 00:44:18.210 --> 00:44:22.500 And now we can rewrite this in terms of the binding energy. 00:44:22.500 --> 00:44:25.620 So again, the binding energy, this is a constant. 00:44:25.620 --> 00:44:32.450 So now this turns into minus RH over n squared. 00:44:32.450 --> 00:44:35.430 And n, what is n? 00:44:35.430 --> 00:44:41.920 n is a positive integer 1, 2, 3, up to infinity. 00:44:41.920 --> 00:44:44.370 And what's its name? 00:44:44.370 --> 00:44:46.662 What is n? 00:44:46.662 --> 00:44:48.270 You can you yell it out. 00:44:48.270 --> 00:44:49.050 Some of you know. 00:44:49.050 --> 00:44:50.165 AUDIENCE: [INAUDIBLE] 00:44:50.165 --> 00:44:51.165 CATHERINE DRENNAN: Yeah. 00:44:51.165 --> 00:44:54.960 The principle quantum number, that's right. 00:44:54.960 --> 00:44:57.420 So the principle quantum number comes out 00:44:57.420 --> 00:44:59.280 of the Schrodinger equation. 00:44:59.280 --> 00:45:01.030 And that's how we can think about it. 00:45:01.030 --> 00:45:03.500 And again, here are these ideas. 00:45:03.500 --> 00:45:06.140 The binding energies are quantized. 00:45:06.140 --> 00:45:09.120 This is a constant over here. 00:45:09.120 --> 00:45:11.100 So the principle quantum number comes out 00:45:11.100 --> 00:45:13.020 of the Schrodinger equation. 00:45:13.020 --> 00:45:13.530 All right. 00:45:13.530 --> 00:45:16.800 So now, next time, we're going to think more 00:45:16.800 --> 00:45:18.600 about the Rydberg constant. 00:45:18.600 --> 00:45:22.050 And we're going to do a demonstration next Friday 00:45:22.050 --> 00:45:26.190 of the hydrogen atom spectrum to show that the Schrodinger 00:45:26.190 --> 00:45:30.090 equation, in fact, can explain binding energies. 00:45:30.090 --> 00:45:34.870 So that's on Friday, and that's our first clicker competition. 00:45:34.870 --> 00:45:35.610 So come. 00:45:35.610 --> 00:45:37.680 Be ready with your clickers. 00:45:37.680 --> 00:45:39.870 You can sit in recitations. 00:45:39.870 --> 00:45:42.570 You can share answers before clicking in. 00:45:42.570 --> 00:45:43.980 It's not cheating. 00:45:43.980 --> 00:45:45.190 It's teamwork. 00:45:45.190 --> 00:45:45.690 OK. 00:45:45.690 --> 00:45:47.540 See you Friday.