1 00:00:00,090 --> 00:00:02,430 The following content is provided under a Creative 2 00:00:02,430 --> 00:00:03,820 Commons license. 3 00:00:03,820 --> 00:00:06,060 Your support will help MIT OpenCourseWare 4 00:00:06,060 --> 00:00:10,150 continue to offer high quality educational resources for free. 5 00:00:10,150 --> 00:00:12,690 To make a donation or to view additional materials 6 00:00:12,690 --> 00:00:16,650 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:16,650 --> 00:00:17,850 at ocw.mit.edu. 8 00:00:36,414 --> 00:00:37,330 CATHERINE DRENNAN: OK. 9 00:00:37,330 --> 00:00:38,980 We're going to take 10 more seconds. 10 00:00:56,030 --> 00:00:57,350 OK. 11 00:00:57,350 --> 00:01:01,510 Does someone want to explain how they got the right answer? 12 00:01:01,510 --> 00:01:07,600 We have a Faculty of 1,000 research bag for them. 13 00:01:11,390 --> 00:01:13,570 Do you want to hand that up and the bag, too? 14 00:01:13,570 --> 00:01:14,070 We're just-- 15 00:01:18,460 --> 00:01:22,150 AUDIENCE: So the theme of light gives enough 16 00:01:22,150 --> 00:01:24,880 energy for the electrons to be ejected. 17 00:01:24,880 --> 00:01:29,770 And the amount of energy for that is 4.3 eV. 18 00:01:29,770 --> 00:01:32,890 And then it also has kinetic energy of 7.9 eV. 19 00:01:32,890 --> 00:01:34,210 So you just add the two. 20 00:01:34,210 --> 00:01:38,543 So 4.3 plus 7.9 is 12.2 eV. 21 00:01:38,543 --> 00:01:39,626 CATHERINE DRENNAN: Thanks. 22 00:01:39,626 --> 00:01:41,631 Let's bring it back. 23 00:01:41,631 --> 00:01:42,130 OK. 24 00:01:42,130 --> 00:01:42,890 Thank you. 25 00:01:42,890 --> 00:01:43,390 All right. 26 00:01:43,390 --> 00:01:48,610 We'll have lots more practice with this today, 27 00:01:48,610 --> 00:01:51,230 and we'll get the hang of doing these problems. 28 00:01:51,230 --> 00:01:53,650 So let's just jump in and get started. 29 00:01:53,650 --> 00:01:56,830 We're still continuing to think about the photoelectric effect, 30 00:01:56,830 --> 00:01:58,660 and think about light as a particle. 31 00:01:58,660 --> 00:02:01,450 So we're going to finish up with the photoelectric effect, 32 00:02:01,450 --> 00:02:04,357 and we're going to have a little demo on that in a few minutes. 33 00:02:04,357 --> 00:02:05,440 Then we're going to go on. 34 00:02:05,440 --> 00:02:11,320 If light is, in fact, quantized, and you have these photons, 35 00:02:11,320 --> 00:02:13,930 then photons should have momentum. 36 00:02:13,930 --> 00:02:15,600 And so we'll talk about that. 37 00:02:15,600 --> 00:02:19,700 Then we've talked about white as a particle. 38 00:02:19,700 --> 00:02:23,530 And most of you are probably pretty OK with matter 39 00:02:23,530 --> 00:02:24,340 being a particle. 40 00:02:24,340 --> 00:02:26,110 But what about matter being a wave? 41 00:02:26,110 --> 00:02:28,660 So we're going to talk about matter being a wave. 42 00:02:28,660 --> 00:02:30,420 And if we have time at the end, we're 43 00:02:30,420 --> 00:02:32,461 going to start on the Schrodinger equation, which 44 00:02:32,461 --> 00:02:34,390 we're going to continue with on Friday. 45 00:02:34,390 --> 00:02:39,370 So I'll just say that sometimes, I am a little overly ambitious, 46 00:02:39,370 --> 00:02:41,710 and I put things on the handout that I'm not really 47 00:02:41,710 --> 00:02:43,120 sure I'm going to get to. 48 00:02:43,120 --> 00:02:44,860 Just because I've never gotten into it 49 00:02:44,860 --> 00:02:48,100 before doesn't mean that I won't get into it this time. 50 00:02:48,100 --> 00:02:50,680 So if I don't finish everything on a handout, 51 00:02:50,680 --> 00:02:52,602 bring your handout to the next class, 52 00:02:52,602 --> 00:02:54,060 and we'll just continue from there. 53 00:02:54,060 --> 00:02:56,530 And there'll be a new handout then as well, so 54 00:02:56,530 --> 00:02:58,220 just a heads up on that. 55 00:02:58,220 --> 00:02:58,720 All right. 56 00:02:58,720 --> 00:03:02,800 So let's continue with the photoelectric effect 57 00:03:02,800 --> 00:03:05,360 and get good at doing these kinds of problems. 58 00:03:05,360 --> 00:03:09,580 So let's look at these particular examples. 59 00:03:09,580 --> 00:03:11,770 We have three different examples here. 60 00:03:11,770 --> 00:03:14,920 We have the energy of an incoming photon 61 00:03:14,920 --> 00:03:19,960 must be equal or greater to that threshold energy or that work 62 00:03:19,960 --> 00:03:23,200 function, in order for an electron to be ejected. 63 00:03:23,200 --> 00:03:28,810 So in this case, the energy is greater than the work function. 64 00:03:28,810 --> 00:03:32,350 So tell me whether an electron will be ejected 65 00:03:32,350 --> 00:03:33,470 or will not be ejected. 66 00:03:33,470 --> 00:03:34,690 And you can just yell it out. 67 00:03:34,690 --> 00:03:35,662 What do you think? 68 00:03:35,662 --> 00:03:36,640 AUDIENCE: Will. 69 00:03:36,640 --> 00:03:37,598 CATHERINE DRENNAN: Yes. 70 00:03:37,598 --> 00:03:38,950 So an electron is ejected. 71 00:03:38,950 --> 00:03:41,260 It will be ejected. 72 00:03:41,260 --> 00:03:43,780 What about this scenario over here, 73 00:03:43,780 --> 00:03:48,310 where the energy is less than that threshold energy? 74 00:03:48,310 --> 00:03:50,520 Is or is not ejected? 75 00:03:50,520 --> 00:03:51,820 AUDIENCE: Is not. 76 00:03:51,820 --> 00:03:52,900 CATHERINE DRENNAN: Yes. 77 00:03:52,900 --> 00:03:56,210 OK now we have another scenario. 78 00:03:56,210 --> 00:03:58,660 We have three photons, each of which 79 00:03:58,660 --> 00:04:02,800 have half of the energy needed, half of that threshold energy. 80 00:04:02,800 --> 00:04:05,090 But you have three of them. 81 00:04:05,090 --> 00:04:10,864 So will an electron is or is not ejected? 82 00:04:10,864 --> 00:04:11,572 AUDIENCE: Is not. 83 00:04:14,350 --> 00:04:16,000 CATHERINE DRENNAN: Is not. 84 00:04:16,000 --> 00:04:16,959 OK. 85 00:04:16,959 --> 00:04:21,160 So three photons each that have half the energy 86 00:04:21,160 --> 00:04:22,660 does not add up. 87 00:04:22,660 --> 00:04:23,490 You cannot add it. 88 00:04:23,490 --> 00:04:25,420 It will not eject an electron. 89 00:04:25,420 --> 00:04:27,170 So let's just think about it for a minute. 90 00:04:27,170 --> 00:04:29,920 Suppose the threshold knowledge for passing 91 00:04:29,920 --> 00:04:34,180 an exam is answering three specific questions correctly. 92 00:04:34,180 --> 00:04:38,440 Suppose over here, we have the answer to one of the questions, 93 00:04:38,440 --> 00:04:40,360 but not to the other two. 94 00:04:40,360 --> 00:04:42,580 Over here, we have an answer to the middle one, 95 00:04:42,580 --> 00:04:44,252 but not the first or the second. 96 00:04:44,252 --> 00:04:46,210 And over here, we have the answer to the third, 97 00:04:46,210 --> 00:04:47,740 but not the first or the second. 98 00:04:47,740 --> 00:04:51,910 So everyone knows the answer to a different question. 99 00:04:51,910 --> 00:04:55,930 Will there be the threshold energy, a threshold knowledge, 100 00:04:55,930 --> 00:04:58,010 to pass this test? 101 00:04:58,010 --> 00:04:59,490 No. 102 00:04:59,490 --> 00:05:02,730 Everyone needs to have the threshold knowledge 103 00:05:02,730 --> 00:05:05,580 themselves to be able to pass. 104 00:05:05,580 --> 00:05:09,240 Everyone has to overcome that critical amount of knowledge 105 00:05:09,240 --> 00:05:11,250 to be able to pass the test. 106 00:05:11,250 --> 00:05:13,440 So that's the same thing here. 107 00:05:13,440 --> 00:05:15,140 You can't add it up. 108 00:05:15,140 --> 00:05:19,230 Now, with the test here at MIT, if everyone has that threshold 109 00:05:19,230 --> 00:05:21,420 knowledge, and a really high level of the threshold 110 00:05:21,420 --> 00:05:25,470 knowledge, everyone can get an A. So the more people 111 00:05:25,470 --> 00:05:29,550 with the threshold knowledge, the more tests that are passed, 112 00:05:29,550 --> 00:05:32,350 and the more the course is passed by people. 113 00:05:32,350 --> 00:05:36,030 So the more photons coming in with that threshold 114 00:05:36,030 --> 00:05:39,270 energy, the more electrons being ejected. 115 00:05:39,270 --> 00:05:41,940 But you can't add up if you have photons 116 00:05:41,940 --> 00:05:44,310 that don't have enough, if they're not greater 117 00:05:44,310 --> 00:05:45,720 than, the threshold energy. 118 00:05:45,720 --> 00:05:47,250 You won't eject an electron. 119 00:05:47,250 --> 00:05:51,000 So everyone needs to meet that threshold criteria. 120 00:05:51,000 --> 00:05:53,800 You can't add things up. 121 00:05:53,800 --> 00:05:55,800 OK. 122 00:05:55,800 --> 00:05:58,830 So here's just some useful terminology 123 00:05:58,830 --> 00:06:01,410 for solving problems on this problem set. 124 00:06:01,410 --> 00:06:04,050 And there will also be problems on problems set two 125 00:06:04,050 --> 00:06:06,990 related to this topic. 126 00:06:06,990 --> 00:06:09,390 So photons-- also called light, also 127 00:06:09,390 --> 00:06:12,270 called electric magnetic radiation-- 128 00:06:12,270 --> 00:06:17,070 may be described by their energy, by their wavelength, 129 00:06:17,070 --> 00:06:20,430 or by their frequency. 130 00:06:20,430 --> 00:06:23,880 Whereas electrons, which are sometimes also called 131 00:06:23,880 --> 00:06:28,590 photoelectrons, may be described by their kinetic energy, 132 00:06:28,590 --> 00:06:34,150 their velocity, and, as you'll see later, by their wavelength. 133 00:06:34,150 --> 00:06:36,480 So you'll be given problems where, 134 00:06:36,480 --> 00:06:38,399 given different pieces of information, 135 00:06:38,399 --> 00:06:40,690 you have to think about how you're going to convert it. 136 00:06:40,690 --> 00:06:42,940 You've got to think about am I talking about a photon? 137 00:06:42,940 --> 00:06:44,940 Am I talking about an electron? 138 00:06:44,940 --> 00:06:47,800 And you also want to think about units. 139 00:06:47,800 --> 00:06:51,780 You'll sometimes be told about energy in eVs 140 00:06:51,780 --> 00:06:54,660 and sometimes be told about energies in joules. 141 00:06:54,660 --> 00:06:56,520 So this is a conversion factor. 142 00:06:56,520 --> 00:06:59,085 All conversion factors are given to you on the exam. 143 00:06:59,085 --> 00:07:03,160 You do not need to memorize any kind of conversion factor. 144 00:07:03,160 --> 00:07:05,250 But you need to be aware, when someone 145 00:07:05,250 --> 00:07:09,090 said joules, what's that a unit for, or eV, what's that a unit 146 00:07:09,090 --> 00:07:10,990 for. 147 00:07:10,990 --> 00:07:11,490 All right. 148 00:07:11,490 --> 00:07:14,730 So now we're going to do and in-class demonstration 149 00:07:14,730 --> 00:07:16,430 of the photoelectric effect. 150 00:07:16,430 --> 00:07:19,200 But before we actually do the experiment, 151 00:07:19,200 --> 00:07:23,160 we're going to predict what the experiment will show. 152 00:07:23,160 --> 00:07:25,050 Always dangerous to do that, so we'll 153 00:07:25,050 --> 00:07:27,461 hope it works after we do the prediction. 154 00:07:27,461 --> 00:07:27,960 All right. 155 00:07:27,960 --> 00:07:31,020 So we're going to be looking at whether we're 156 00:07:31,020 --> 00:07:36,750 going to get an injection of an electron from a zinc surface. 157 00:07:36,750 --> 00:07:42,510 And we're given the threshold energy, or the work function, 158 00:07:42,510 --> 00:07:44,520 of zinc. 159 00:07:44,520 --> 00:07:47,490 Every metal-- this is a property of metals. 160 00:07:47,490 --> 00:07:49,620 They're different, as we saw last time. 161 00:07:49,620 --> 00:07:54,390 So this is 6.9 times 10 to the minus 19th joules. 162 00:07:54,390 --> 00:07:56,400 And we're going to use two different light 163 00:07:56,400 --> 00:08:00,420 sources that are going to have different wavelengths. 164 00:08:00,420 --> 00:08:04,440 And we'll predict whether they have enough energy 165 00:08:04,440 --> 00:08:07,660 to meet this threshold to go over the threshold 166 00:08:07,660 --> 00:08:09,270 and inject an electron. 167 00:08:09,270 --> 00:08:12,660 So the two different sources, we have a UV lamp 168 00:08:12,660 --> 00:08:16,480 with a wavelength of 254 nanometers 169 00:08:16,480 --> 00:08:19,650 and a red laser pointer with a wavelength 170 00:08:19,650 --> 00:08:22,631 of about 700 nanometers. 171 00:08:22,631 --> 00:08:23,130 OK. 172 00:08:23,130 --> 00:08:25,650 So before we do the experiment, let's 173 00:08:25,650 --> 00:08:29,250 do some calculations to see what we expect. 174 00:08:29,250 --> 00:08:31,860 So first, we want to see what the energy, 175 00:08:31,860 --> 00:08:34,470 or calculate what the energy, of the photon 176 00:08:34,470 --> 00:08:38,909 will be that's a emitted by the UV lamp. 177 00:08:38,909 --> 00:08:43,049 And I will write this down. 178 00:08:43,049 --> 00:08:44,190 So what do we know? 179 00:08:44,190 --> 00:08:46,230 We know a bunch of things already. 180 00:08:46,230 --> 00:08:51,420 We know that energy is equal to Planck's constant times 181 00:08:51,420 --> 00:08:52,980 the frequency. 182 00:08:52,980 --> 00:08:57,720 We also know that the frequency is related to wavelength 183 00:08:57,720 --> 00:09:00,360 by c, the speed of light. 184 00:09:00,360 --> 00:09:03,120 And then we can put those two things together 185 00:09:03,120 --> 00:09:08,070 to say the energy, then, is also the Planck's constant times 186 00:09:08,070 --> 00:09:12,750 the speed of light divided by the wavelength. 187 00:09:12,750 --> 00:09:16,710 So we can use that last equation to do a calculation, 188 00:09:16,710 --> 00:09:19,620 and figure out the energy that's associated 189 00:09:19,620 --> 00:09:22,710 with that particular wavelength of light. 190 00:09:22,710 --> 00:09:24,810 So here we have energy. 191 00:09:24,810 --> 00:09:32,910 We're going to write in Planck's constant, 6.626 times 10 192 00:09:32,910 --> 00:09:35,530 to the minus 34. 193 00:09:35,530 --> 00:09:39,000 And the units are joules times seconds 194 00:09:39,000 --> 00:09:46,200 and the speed of light, 2.998 times 10 195 00:09:46,200 --> 00:09:51,130 to the 8 meters per second. 196 00:09:51,130 --> 00:09:56,770 And we want to divide this, then, by the wavelength. 197 00:09:56,770 --> 00:09:59,580 So we have the wavelength here that we're 198 00:09:59,580 --> 00:10:11,130 using first is a 254 times 10 to the minus 19 meters. 199 00:10:13,690 --> 00:10:17,200 Oh sorry-- 9 meters. 200 00:10:17,200 --> 00:10:19,720 Thank you. 201 00:10:19,720 --> 00:10:20,630 I wrote down 19. 202 00:10:20,630 --> 00:10:21,630 I'm like, wait a minute. 203 00:10:21,630 --> 00:10:23,250 That's not right. 204 00:10:23,250 --> 00:10:24,850 OK. 205 00:10:24,850 --> 00:10:26,170 OK. 206 00:10:26,170 --> 00:10:28,410 So then we can do the calculation out. 207 00:10:28,410 --> 00:10:31,720 And here is where I got excited about 19. 208 00:10:31,720 --> 00:10:41,130 We have 7.82 times 10 to the minus 19 joules. 209 00:10:41,130 --> 00:10:42,940 And if we look at the equation, we'll 210 00:10:42,940 --> 00:10:44,890 see that the meters are going to cancel. 211 00:10:44,890 --> 00:10:46,540 The seconds cancel, and we're left 212 00:10:46,540 --> 00:10:48,990 with joules, which is good, because we want an energy. 213 00:10:48,990 --> 00:10:52,030 So joules is a good thing to have. 214 00:10:52,030 --> 00:10:54,940 So there, we can do a simple calculation. 215 00:10:54,940 --> 00:11:00,100 And we can look and say, OK, if the energy, then, associated 216 00:11:00,100 --> 00:11:03,430 with that wavelength is 7.82 times 10 217 00:11:03,430 --> 00:11:08,410 to the minus 19th joules, then we ask, is this greater or less 218 00:11:08,410 --> 00:11:11,560 than the threshold energy? 219 00:11:11,560 --> 00:11:13,720 And it's greater than that. 220 00:11:13,720 --> 00:11:16,420 So it does have enough energy. 221 00:11:16,420 --> 00:11:18,100 It should eject an electron. 222 00:11:18,100 --> 00:11:20,800 So we can try that out and see. 223 00:11:20,800 --> 00:11:24,580 Now we can look at what happens with the red laser pointer 224 00:11:24,580 --> 00:11:27,870 and see whether that should have the energy that's needed. 225 00:11:27,870 --> 00:11:32,540 And so I will just write these things down here 226 00:11:32,540 --> 00:11:33,990 instead of writing it again. 227 00:11:33,990 --> 00:11:36,220 So that was our UV. 228 00:11:36,220 --> 00:11:42,520 So now our red light, we have 700 times 10 to the minus 9 229 00:11:42,520 --> 00:11:45,520 meters, or 700 nanometers. 230 00:11:45,520 --> 00:11:48,490 And so here is our answer for the UV. 231 00:11:48,490 --> 00:11:57,160 And our answer for the red light should be 2.84 times 10 232 00:11:57,160 --> 00:12:00,340 to the minus 19 joules. 233 00:12:00,340 --> 00:12:04,820 And I'll move this up a little so people can see that. 234 00:12:04,820 --> 00:12:09,700 So does that have enough energy to eject an electron? 235 00:12:09,700 --> 00:12:12,437 AUDIENCE: [INAUDIBLE] 236 00:12:12,437 --> 00:12:14,020 CATHERINE DRENNAN: No, that should not 237 00:12:14,020 --> 00:12:17,530 work, because that's less than the threshold energy that's 238 00:12:17,530 --> 00:12:18,790 needed. 239 00:12:18,790 --> 00:12:19,530 All right. 240 00:12:19,530 --> 00:12:22,530 So we'll do one more calculation just for fun. 241 00:12:22,530 --> 00:12:24,400 And then we'll do the experiment. 242 00:12:24,400 --> 00:12:26,740 So the last calculation we'll do is 243 00:12:26,740 --> 00:12:28,900 we'll think about the number of photons 244 00:12:28,900 --> 00:12:32,410 that are emitted by a laser in 60 seconds 245 00:12:32,410 --> 00:12:38,860 if you have an intensity of one milliwatt. 246 00:12:38,860 --> 00:12:43,720 And a milliwatt is equal to 10 to the minus 3 joules 247 00:12:43,720 --> 00:12:45,160 per second. 248 00:12:45,160 --> 00:12:49,370 So we can just do that calculation over here. 249 00:12:49,370 --> 00:13:00,730 So we have 1.00 times 10 to the minus 3 joules per second, 250 00:13:00,730 --> 00:13:07,410 1 photon, and here, this is for the red laser. 251 00:13:07,410 --> 00:13:11,480 So we'll use the number that we just calculated over here. 252 00:13:11,480 --> 00:13:17,650 So we have 2.84 times 10 to the minus 19th joules 253 00:13:17,650 --> 00:13:24,400 for the red laser and times 60 seconds. 254 00:13:24,400 --> 00:13:32,200 And we should get 2.1 times 10 to the 17 photons. 255 00:13:32,200 --> 00:13:35,080 So that's how much photons, if we hold it 256 00:13:35,080 --> 00:13:40,900 for 60 seconds, that were going to be shooting at our metal's 257 00:13:40,900 --> 00:13:42,030 surface. 258 00:13:42,030 --> 00:13:43,720 So these are the kind of calculations 259 00:13:43,720 --> 00:13:46,270 that you'll be doing on these kind of problems. 260 00:13:46,270 --> 00:13:49,139 And now let's see how well the experiment works. 261 00:13:49,139 --> 00:13:51,430 So we're going to bring out our demo TAs, who are going 262 00:13:51,430 --> 00:13:53,186 to tell you about this demo. 263 00:13:53,186 --> 00:13:55,060 And we're going to try to do some fancy stuff 264 00:13:55,060 --> 00:13:57,660 with this document camera to project it on the screen. 265 00:13:57,660 --> 00:13:59,580 So this is all very exciting. 266 00:13:59,580 --> 00:14:01,310 Oh, I guess I should put that down, 267 00:14:01,310 --> 00:14:02,810 the number, in case you couldn't see 268 00:14:02,810 --> 00:14:06,260 it-- 2.1 times 10 to the 17. 269 00:14:06,260 --> 00:14:06,760 All right. 270 00:14:06,760 --> 00:14:08,385 So let's bring-- you've got the mic. 271 00:14:12,607 --> 00:14:13,440 GUEST SPEAKER 1: OK. 272 00:14:13,440 --> 00:14:15,784 So we've got our metal plate here 273 00:14:15,784 --> 00:14:16,950 that Eric's got in his hand. 274 00:14:16,950 --> 00:14:19,020 And what he's doing right now is he's 275 00:14:19,020 --> 00:14:21,722 rubbing it with a little bit of-- what is that, actually? 276 00:14:21,722 --> 00:14:23,320 ERIC: It's just steel wool. 277 00:14:23,320 --> 00:14:24,570 CATHERINE DRENNAN: Steel wool. 278 00:14:24,570 --> 00:14:24,810 GUEST SPEAKER 1: OK. 279 00:14:24,810 --> 00:14:26,476 So that's just going to get the aluminum 280 00:14:26,476 --> 00:14:28,780 oxide, because sometimes-- you guys will get to it. 281 00:14:28,780 --> 00:14:32,100 But sometimes you can get a reaction of aluminum 282 00:14:32,100 --> 00:14:36,250 with the moisture in the air, and that's 283 00:14:36,250 --> 00:14:37,500 going to cause aluminum oxide. 284 00:14:37,500 --> 00:14:39,230 So he's getting get rid of that. 285 00:14:39,230 --> 00:14:43,704 And now we've put this on a-- what is this? 286 00:14:43,704 --> 00:14:44,580 ERIC: [INAUDIBLE]. 287 00:14:44,580 --> 00:14:45,470 GUEST SPEAKER 1: What do you call it? 288 00:14:45,470 --> 00:14:46,570 A detector of some kind. 289 00:14:46,570 --> 00:14:49,620 So basically, when he charges this, what's going to happen 290 00:14:49,620 --> 00:14:54,660 is that you have this plate, and you have this joint. 291 00:14:54,660 --> 00:14:58,290 And they're both going to be electrically negative, 292 00:14:58,290 --> 00:15:00,230 because you've introduced some electrons. 293 00:15:00,230 --> 00:15:02,160 And they're going to repel each other, 294 00:15:02,160 --> 00:15:03,000 because they're both negative. 295 00:15:03,000 --> 00:15:04,583 Two negative charges repel each other. 296 00:15:04,583 --> 00:15:08,190 So you're going to see some space develop as Eric's done. 297 00:15:08,190 --> 00:15:10,760 Now, what he's doing is he's got a plastic rod here 298 00:15:10,760 --> 00:15:13,440 that he's charging with the fur. 299 00:15:13,440 --> 00:15:16,637 And he's introducing those electrons onto the plate. 300 00:15:16,637 --> 00:15:18,470 So now we've got a negatively charged plate, 301 00:15:18,470 --> 00:15:20,460 and you can see that by the fact that you 302 00:15:20,460 --> 00:15:23,220 see some repulsion between that rod and the rest 303 00:15:23,220 --> 00:15:25,670 of the detector, which is actually working out 304 00:15:25,670 --> 00:15:27,860 pretty nicely. 305 00:15:27,860 --> 00:15:28,360 So once-- 306 00:15:28,360 --> 00:15:30,068 CATHERINE DRENNAN: So say this experiment 307 00:15:30,068 --> 00:15:31,340 is very weather-dependent. 308 00:15:31,340 --> 00:15:36,410 If it's really humid or too dry, it doesn't work nearly as well. 309 00:15:36,410 --> 00:15:37,910 But today, today's good weather. 310 00:15:37,910 --> 00:15:39,618 Today's good weather for this experiment, 311 00:15:39,618 --> 00:15:42,320 not so much good for sunbathing outside, but good 312 00:15:42,320 --> 00:15:43,885 weather for this experiment. 313 00:15:43,885 --> 00:15:47,810 GUEST SPEAKER 1: Although we have UV lamps, so maybe. 314 00:15:47,810 --> 00:15:49,217 CATHERINE DRENNAN: That's true. 315 00:15:49,217 --> 00:15:50,050 GUEST SPEAKER 1: OK. 316 00:15:50,050 --> 00:15:51,487 So now we've got a charge. 317 00:15:51,487 --> 00:15:53,570 CATHERINE DRENNAN: That's the green laser pointer. 318 00:15:53,570 --> 00:15:54,992 Let's get the red. 319 00:15:54,992 --> 00:15:56,950 GUEST SPEAKER 1: It's underneath here, I think. 320 00:15:56,950 --> 00:15:58,317 CATHERINE DRENNAN: Oh, yeah. 321 00:15:58,317 --> 00:15:59,150 GUEST SPEAKER 1: OK. 322 00:15:59,150 --> 00:15:59,960 So now-- 323 00:15:59,960 --> 00:16:01,340 CATHERINE DRENNAN: We could do the calculation for the green. 324 00:16:01,340 --> 00:16:03,770 If you want to do the calculation for the green, 325 00:16:03,770 --> 00:16:04,740 we can try it later. 326 00:16:04,740 --> 00:16:06,200 GUEST SPEAKER 1: Eric's got a red laser pointer in his hand. 327 00:16:06,200 --> 00:16:07,158 He's going to shine it. 328 00:16:07,158 --> 00:16:11,450 And we're going to see that nothing happens, 329 00:16:11,450 --> 00:16:15,170 because as we calculated, the energy of these photons 330 00:16:15,170 --> 00:16:17,069 is not enough to get over the threshold 331 00:16:17,069 --> 00:16:18,110 of this particular metal. 332 00:16:18,110 --> 00:16:20,600 CATHERINE DRENNAN: So if electrons were being ejected, 333 00:16:20,600 --> 00:16:23,599 you should see it move. 334 00:16:23,599 --> 00:16:25,640 GUEST SPEAKER 1: And we'll do that one more time. 335 00:16:25,640 --> 00:16:26,889 Maybe the green one will work. 336 00:16:26,889 --> 00:16:28,242 It doesn't. 337 00:16:28,242 --> 00:16:29,450 CATHERINE DRENNAN: All right. 338 00:16:29,450 --> 00:16:31,310 Well, now we have to see if the UV-- we built it up. 339 00:16:31,310 --> 00:16:31,970 The UV should-- 340 00:16:31,970 --> 00:16:32,440 GUEST SPEAKER 1: So hopefully this works. 341 00:16:32,440 --> 00:16:32,900 CATHERINE DRENNAN: --work. 342 00:16:32,900 --> 00:16:33,637 Let's see. 343 00:16:33,637 --> 00:16:36,167 GUEST SPEAKER 2: [INAUDIBLE] 344 00:16:36,167 --> 00:16:37,000 GUEST SPEAKER 1: OK. 345 00:16:37,000 --> 00:16:38,877 So oh-- maybe-- 346 00:16:38,877 --> 00:16:39,752 AUDIENCE: [INAUDIBLE] 347 00:16:39,752 --> 00:16:40,668 CATHERINE DRENNAN: Oh. 348 00:16:40,668 --> 00:16:42,740 GUEST SPEAKER 1: Oh, well, I guess it worked. 349 00:16:42,740 --> 00:16:44,410 CATHERINE DRENNAN: It did work. 350 00:16:44,410 --> 00:16:45,580 You could sort of see that. 351 00:16:45,580 --> 00:16:47,330 GUEST SPEAKER 1: So maybe we can charge it 352 00:16:47,330 --> 00:16:48,690 up again while I talk about it. 353 00:16:48,690 --> 00:16:48,995 CATHERINE DRENNAN: Yeah, sometimes 354 00:16:48,995 --> 00:16:49,953 the charge [INAUDIBLE]. 355 00:16:49,953 --> 00:16:51,710 GUEST SPEAKER 1: The UV lamp, obviously, 356 00:16:51,710 --> 00:16:54,050 has enough energy in each of these photons. 357 00:16:54,050 --> 00:16:58,250 So when you shine that light at the metal, 358 00:16:58,250 --> 00:16:59,900 you have the electrons on the surface, 359 00:16:59,900 --> 00:17:01,850 which are being ejected. 360 00:17:01,850 --> 00:17:03,650 And if those electrons get ejected, 361 00:17:03,650 --> 00:17:06,010 then the whole system becomes neutral. 362 00:17:06,010 --> 00:17:09,050 If the systems become neutral, then that rod can go back 363 00:17:09,050 --> 00:17:13,060 and is no longer feels a repulsion, 364 00:17:13,060 --> 00:17:15,410 because the two parts are no longer negative. 365 00:17:15,410 --> 00:17:17,450 So once we charge this up again, maybe we 366 00:17:17,450 --> 00:17:19,859 can go to the other side and-- I think it's good. 367 00:17:19,859 --> 00:17:20,359 It's good. 368 00:17:20,359 --> 00:17:21,096 CATHERINE DRENNAN: Yeah, that's good. 369 00:17:21,096 --> 00:17:21,869 Oh-- 370 00:17:21,869 --> 00:17:23,801 GUEST SPEAKER 1: It will be fine. 371 00:17:23,801 --> 00:17:25,292 GUEST SPEAKER 2: Wavering. 372 00:17:25,292 --> 00:17:26,750 CATHERINE DRENNAN: OK. 373 00:17:26,750 --> 00:17:27,960 GUEST SPEAKER 1: OK. 374 00:17:27,960 --> 00:17:29,720 Now we're just going to try it again. 375 00:17:29,720 --> 00:17:34,182 And yay. 376 00:17:34,182 --> 00:17:35,140 CATHERINE DRENNAN: Yay. 377 00:17:35,140 --> 00:17:36,265 GUEST SPEAKER 1: We got it. 378 00:17:36,265 --> 00:17:39,550 [APPLAUSE] 379 00:17:39,550 --> 00:17:40,990 CATHERINE DRENNAN: OK. 380 00:17:40,990 --> 00:17:41,490 Great. 381 00:17:41,490 --> 00:17:43,520 We can just leave this here. 382 00:17:43,520 --> 00:17:45,070 All right. 383 00:17:45,070 --> 00:17:47,360 And I think he held it for 60 seconds, so you 384 00:17:47,360 --> 00:17:49,400 know how many photons were coming off, 385 00:17:49,400 --> 00:17:51,860 too, if you want to do that calculation. 386 00:17:51,860 --> 00:17:55,220 So again, the photoelectric effect 387 00:17:55,220 --> 00:17:58,850 was really important at this time 388 00:17:58,850 --> 00:18:03,140 in understanding the properties that were being observed, 389 00:18:03,140 --> 00:18:07,370 to help us understand about this quantized energy of particles, 390 00:18:07,370 --> 00:18:10,290 that light had this particle-like property. 391 00:18:10,290 --> 00:18:12,290 It had this quantized energy. 392 00:18:12,290 --> 00:18:15,110 And you needed a certain amount of it 393 00:18:15,110 --> 00:18:17,900 to eject an electron from a metal surface. 394 00:18:17,900 --> 00:18:21,530 So we all know that light is a wave. 395 00:18:21,530 --> 00:18:23,240 But now there's this evidence that, 396 00:18:23,240 --> 00:18:27,590 even though it's pretty much this massless particle, 397 00:18:27,590 --> 00:18:31,070 that it still has particle-like properties. 398 00:18:31,070 --> 00:18:34,887 So light is a really amazing thing. 399 00:18:34,887 --> 00:18:36,470 This doesn't really show up very well. 400 00:18:36,470 --> 00:18:37,803 It's a view of the Stata Center. 401 00:18:37,803 --> 00:18:41,360 Stata Center always has some really spectacular sunlight 402 00:18:41,360 --> 00:18:43,200 coming around it sometimes. 403 00:18:43,200 --> 00:18:43,700 All right. 404 00:18:43,700 --> 00:18:47,900 So now, if this is true, that means 405 00:18:47,900 --> 00:18:51,530 that photons that have this quantized energy 406 00:18:51,530 --> 00:18:53,980 should have momentum as well. 407 00:18:53,980 --> 00:18:56,390 And so Einstein was thinking about that. 408 00:18:56,390 --> 00:18:59,450 And so he reasoned that this had to be true. 409 00:18:59,450 --> 00:19:03,650 There had to be some kind of momentum associated with them. 410 00:19:03,650 --> 00:19:07,490 And so momentum, or p, here is equal to Planck's 411 00:19:07,490 --> 00:19:11,840 constant times the frequency divided by the speed of light, 412 00:19:11,840 --> 00:19:12,740 c. 413 00:19:12,740 --> 00:19:16,250 And since the speed of light is equal to the frequency 414 00:19:16,250 --> 00:19:18,770 times the wavelength of the light, 415 00:19:18,770 --> 00:19:22,280 then the momentum should be equal to Planck's constant 416 00:19:22,280 --> 00:19:24,530 divided by the wavelength. 417 00:19:24,530 --> 00:19:27,050 So this is really-- we're talking about momentum 418 00:19:27,050 --> 00:19:31,470 in terms of wavelength, this inverse relationship here. 419 00:19:31,470 --> 00:19:33,590 This was just a kind of a crazy idea 420 00:19:33,590 --> 00:19:35,570 to be thinking about momentum, when 421 00:19:35,570 --> 00:19:37,560 you're talking about light. 422 00:19:37,560 --> 00:19:41,120 And this really came out of the photoelectric effect. 423 00:19:41,120 --> 00:19:43,700 And also, there were some experiments 424 00:19:43,700 --> 00:19:48,560 done by Arthur Compton that also showed that you could 425 00:19:48,560 --> 00:19:51,110 sort of transfer this momentum. 426 00:19:51,110 --> 00:19:54,170 And so that's again the particle-like property. 427 00:19:54,170 --> 00:19:57,050 So it's a really exciting time. 428 00:19:57,050 --> 00:19:58,190 OK. 429 00:19:58,190 --> 00:20:01,610 So we're going to now move to matter. 430 00:20:01,610 --> 00:20:03,050 So we've been talking about light 431 00:20:03,050 --> 00:20:08,870 and how light has this dual, particle, wavelike properties. 432 00:20:08,870 --> 00:20:10,370 But what about matter? 433 00:20:10,370 --> 00:20:15,260 So we accept that matter has particle-like properties. 434 00:20:15,260 --> 00:20:17,135 But what about as a wave? 435 00:20:20,550 --> 00:20:25,960 So enter de Broglie into this area. 436 00:20:25,960 --> 00:20:31,050 And so he was following what Einstein was thinking about. 437 00:20:31,050 --> 00:20:34,690 And he said, OK, so that's pretty cool. 438 00:20:34,690 --> 00:20:38,620 If you have momentum is equal to Planck's constant divided 439 00:20:38,620 --> 00:20:40,210 by wavelength, if you could think 440 00:20:40,210 --> 00:20:43,750 of things that have wavelengths as having momentum. 441 00:20:43,750 --> 00:20:47,620 And he said, or I can rewrite this equation, 442 00:20:47,620 --> 00:20:52,150 that wavelength equals Planck's constant divided by momentum. 443 00:20:52,150 --> 00:20:54,760 And we know something about momentum. 444 00:20:54,760 --> 00:20:58,600 We know that momentum is often associated with something's 445 00:20:58,600 --> 00:21:01,550 mass times its velocity. 446 00:21:01,550 --> 00:21:06,700 So therefore, I should be able to rewrite this equation again 447 00:21:06,700 --> 00:21:09,250 in terms of wavelength being equal to Planck's 448 00:21:09,250 --> 00:21:13,240 constant divided by a mass and a velocity. 449 00:21:13,240 --> 00:21:18,300 And here, we are expressing wavelengths in terms of masses. 450 00:21:18,300 --> 00:21:19,930 So this was really something. 451 00:21:19,930 --> 00:21:22,420 And this was basically his PhD thesis. 452 00:21:22,420 --> 00:21:24,700 I think it maybe had more pages than that, 453 00:21:24,700 --> 00:21:26,910 but this would have probably been enough, 454 00:21:26,910 --> 00:21:28,870 this sort of cover page. 455 00:21:28,870 --> 00:21:30,940 This is my PhD thesis. 456 00:21:30,940 --> 00:21:34,800 And Einstein said that he had lifted 457 00:21:34,800 --> 00:21:38,230 the corner of a great veil with really just manipulating 458 00:21:38,230 --> 00:21:41,890 what was known at the time and rearranging these equations 459 00:21:41,890 --> 00:21:45,300 and presenting relationships that people hadn't really 460 00:21:45,300 --> 00:21:46,990 put together before. 461 00:21:46,990 --> 00:21:49,360 So he ended up winning a Nobel Prize, 462 00:21:49,360 --> 00:21:53,410 basically, for his PhD thesis, which is a fairly rare thing 463 00:21:53,410 --> 00:21:55,020 to have happen. 464 00:21:55,020 --> 00:21:58,070 But this was really an incredible time. 465 00:21:58,070 --> 00:21:58,690 OK. 466 00:21:58,690 --> 00:22:03,300 So if this is true, if you have equations 467 00:22:03,300 --> 00:22:07,510 that relate wavelengths to mass, and particles 468 00:22:07,510 --> 00:22:12,030 have wavelike properties, how come we don't see this? 469 00:22:12,030 --> 00:22:13,690 How come this isn't part-- how come 470 00:22:13,690 --> 00:22:16,530 no one noticed the particle going by 471 00:22:16,530 --> 00:22:19,800 and this wavelength associated with it? 472 00:22:19,800 --> 00:22:25,630 So why don't we observe this wavelike behavior 473 00:22:25,630 --> 00:22:29,750 if, in fact, it is associated with particles? 474 00:22:29,750 --> 00:22:32,140 So let's think about this a minute. 475 00:22:32,140 --> 00:22:37,450 And we can consider why, when you go to Fenway Park-- 476 00:22:37,450 --> 00:22:39,630 and you should, because it's fun-- 477 00:22:39,630 --> 00:22:42,060 and you watch someone throw a fastball, 478 00:22:42,060 --> 00:22:46,770 why you don't see a wave associated with that fastball. 479 00:22:46,770 --> 00:22:51,910 So we can consider a fastball and that the mass of a baseball 480 00:22:51,910 --> 00:22:57,020 is about 5 ounces, or 0.142 kilograms. 481 00:22:57,020 --> 00:23:01,290 And the velocity of a fastball is around 94 miles per hour, 482 00:23:01,290 --> 00:23:04,150 or 42 meters per second. 483 00:23:04,150 --> 00:23:05,920 And so we can do a little calculation 484 00:23:05,920 --> 00:23:09,460 and figure out what the wavelength associated 485 00:23:09,460 --> 00:23:12,610 with that ball should be. 486 00:23:12,610 --> 00:23:16,750 So wavelength should be Planck's constant over the mass 487 00:23:16,750 --> 00:23:19,450 times the velocity of the ball. 488 00:23:19,450 --> 00:23:21,490 And we can plug in these values. 489 00:23:21,490 --> 00:23:23,750 And here's Planck's constant again. 490 00:23:23,750 --> 00:23:27,670 And now you'll note I did something with the units. 491 00:23:27,670 --> 00:23:30,790 So instead of joule seconds, I substituted 492 00:23:30,790 --> 00:23:37,260 joules with kilograms meters squared seconds to the minus 2. 493 00:23:37,260 --> 00:23:39,460 And that's what's equal to a joule. 494 00:23:39,460 --> 00:23:42,290 And I'm going to do that so I can cancel out my units. 495 00:23:42,290 --> 00:23:45,190 And again, all of this will be provided on an equation sheet. 496 00:23:45,190 --> 00:23:48,970 You do not need to remember all of these conversions. 497 00:23:48,970 --> 00:23:55,006 And so over the mass of the baseball and the velocity 498 00:23:55,006 --> 00:23:56,380 of the baseball-- and we're going 499 00:23:56,380 --> 00:23:58,560 to put the velocity in meters per second 500 00:23:58,560 --> 00:24:00,950 so our units can cancel out. 501 00:24:00,950 --> 00:24:03,940 And so I'll just cancel units out. 502 00:24:03,940 --> 00:24:05,680 So we're canceling our kilograms. 503 00:24:05,680 --> 00:24:08,040 We're canceling one of the meters, 504 00:24:08,040 --> 00:24:10,420 and canceling all of the seconds. 505 00:24:10,420 --> 00:24:13,444 And we have one meter left, which 506 00:24:13,444 --> 00:24:15,485 is good, because we're talking about wavelengths. 507 00:24:15,485 --> 00:24:18,160 So that's the unit we should have. 508 00:24:18,160 --> 00:24:23,820 And the wavelength is 1.1 times 10 to the minus 34 meters. 509 00:24:23,820 --> 00:24:29,710 That is a really small number times 10 to the 34. 510 00:24:29,710 --> 00:24:34,480 And it is, in fact, undetectably small. 511 00:24:34,480 --> 00:24:35,440 OK. 512 00:24:35,440 --> 00:24:38,760 So now why don't you try your hand at this, 513 00:24:38,760 --> 00:24:40,410 and we'll try a clicker question. 514 00:25:22,963 --> 00:25:23,950 Yeah, it's very tiny. 515 00:25:39,061 --> 00:25:39,560 All right. 516 00:25:39,560 --> 00:25:41,588 Let's take just 10 more seconds. 517 00:25:49,240 --> 00:25:51,165 Oh, or five seconds. 518 00:25:57,370 --> 00:25:57,940 OK. 519 00:25:57,940 --> 00:25:58,880 Awesome. 520 00:26:01,790 --> 00:26:02,860 It went away. 521 00:26:02,860 --> 00:26:04,030 That's OK. 522 00:26:04,030 --> 00:26:07,230 So they're in-- 97%. 523 00:26:07,230 --> 00:26:08,530 I like 97%. 524 00:26:08,530 --> 00:26:11,110 That's a good number. 525 00:26:11,110 --> 00:26:13,150 So again, you want to think about this 526 00:26:13,150 --> 00:26:15,760 and just realize the relationship, the equation, 527 00:26:15,760 --> 00:26:16,690 involved. 528 00:26:16,690 --> 00:26:21,660 And so thinking about-- oops, I switched pointers. 529 00:26:21,660 --> 00:26:23,470 I like the green better. 530 00:26:23,470 --> 00:26:27,130 So think about the relationship between the velocity 531 00:26:27,130 --> 00:26:29,090 of the ball and the wavelength. 532 00:26:29,090 --> 00:26:32,220 And so Wakefield, who was an knuckleballer, 533 00:26:32,220 --> 00:26:35,830 is the winner here, with the longest wavelength. 534 00:26:35,830 --> 00:26:40,120 But still, the number for this is 1.4 times 10 535 00:26:40,120 --> 00:26:41,900 to the minus 34. 536 00:26:41,900 --> 00:26:45,730 And so this is still undetectably small. 537 00:26:45,730 --> 00:26:50,020 So of course, no one had noticed this property before. 538 00:26:50,020 --> 00:26:53,330 But it still, it still exists. 539 00:26:53,330 --> 00:26:56,260 So when you're talking about a baseball, 540 00:26:56,260 --> 00:26:59,530 the wavelength is really not very, relevant to you, 541 00:26:59,530 --> 00:27:04,130 because it is this incredibly small, undetectable number. 542 00:27:04,130 --> 00:27:07,000 But if you're talking about an electron, 543 00:27:07,000 --> 00:27:08,870 it's entirely different. 544 00:27:08,870 --> 00:27:12,340 So now, if we think about a gaseous electron traveling 545 00:27:12,340 --> 00:27:16,750 at 4 times 10 to the 6 meters per second, and so 546 00:27:16,750 --> 00:27:20,770 that's associated with an eV of about 54. 547 00:27:20,770 --> 00:27:24,310 So we have this electron traveling with this velocity. 548 00:27:24,310 --> 00:27:27,940 And now, if we do this calculation, 549 00:27:27,940 --> 00:27:31,360 so if we use Planck's constant divided 550 00:27:31,360 --> 00:27:33,670 by the mass of the electron-- and that's 551 00:27:33,670 --> 00:27:38,470 known, in another great experiment-- and its velocity, 552 00:27:38,470 --> 00:27:41,230 now we can calculate out the wavelength. 553 00:27:41,230 --> 00:27:47,090 And it's 2 times 10 to the minus 10, or about two angstroms. 554 00:27:47,090 --> 00:27:51,970 Now, 2 angstroms is a relevant number, 555 00:27:51,970 --> 00:27:54,130 when you're talking about an electron, 556 00:27:54,130 --> 00:27:56,570 because an electron is in an atom. 557 00:27:56,570 --> 00:28:01,310 And atoms tend to be-- you have diameters 0.5 to 4 angstroms. 558 00:28:01,310 --> 00:28:04,630 So now the wavelength is on the same scale 559 00:28:04,630 --> 00:28:07,750 as the size of the object you're talking about. 560 00:28:07,750 --> 00:28:11,090 And so when that's true, all of a sudden, the wavelength-- 561 00:28:11,090 --> 00:28:14,650 the wavelike property becomes super important to thinking 562 00:28:14,650 --> 00:28:15,760 about this. 563 00:28:15,760 --> 00:28:19,720 So for an electron that is a particle, 564 00:28:19,720 --> 00:28:24,040 it's really important to think about its wavelike properties. 565 00:28:24,040 --> 00:28:27,580 And so people were saying, OK, if electrons are waves, then 566 00:28:27,580 --> 00:28:30,370 maybe we should see other wavelike properties, 567 00:28:30,370 --> 00:28:32,950 such as diffraction. 568 00:28:32,950 --> 00:28:35,290 Diffraction, we talked about last time, 569 00:28:35,290 --> 00:28:37,210 is an important wavelike property 570 00:28:37,210 --> 00:28:40,640 of constructive interference, destructive interference. 571 00:28:40,640 --> 00:28:42,220 So people looked to see whether there 572 00:28:42,220 --> 00:28:44,150 were diffraction-like properties, 573 00:28:44,150 --> 00:28:46,180 and in fact, there are. 574 00:28:46,180 --> 00:28:49,150 So we had observed, then, the first 575 00:28:49,150 --> 00:28:52,570 was observing diffraction of electrons 576 00:28:52,570 --> 00:28:54,190 from a nickel crystal. 577 00:28:54,190 --> 00:28:57,790 And then JP Thomson showed that electrons 578 00:28:57,790 --> 00:29:00,880 that pass through gold foil again 579 00:29:00,880 --> 00:29:02,870 produced a diffraction pattern. 580 00:29:02,870 --> 00:29:06,470 So again, this was a wavelike property. 581 00:29:06,470 --> 00:29:09,970 So you might think Thomson, that sounds a little familiar to me. 582 00:29:09,970 --> 00:29:12,610 Didn't she just talk about that last week? 583 00:29:12,610 --> 00:29:14,980 And yes, here there are two important Thomsons 584 00:29:14,980 --> 00:29:15,670 in this story. 585 00:29:15,670 --> 00:29:18,970 And this is a father and son team. 586 00:29:18,970 --> 00:29:23,710 And so JJ Thomson won a Nobel Prize in 1906 587 00:29:23,710 --> 00:29:26,230 for showing that an electron is a particle. 588 00:29:26,230 --> 00:29:28,630 He discovered an electron. 589 00:29:28,630 --> 00:29:34,300 And then in 1937, his son wins a Nobel Prize for showing-- son 590 00:29:34,300 --> 00:29:38,190 just had to be like, Dad, I'm going to show you're wrong. 591 00:29:38,190 --> 00:29:41,415 An electron is, in fact, a wave. 592 00:29:41,415 --> 00:29:42,790 But I think they were both happy. 593 00:29:42,790 --> 00:29:45,730 I think they both got along, no father-son rivalry. 594 00:29:45,730 --> 00:29:49,060 I think this is one of the cooler stories in science, 595 00:29:49,060 --> 00:29:52,330 how this father, son both had kind 596 00:29:52,330 --> 00:29:55,990 of opposite discoveries, which both ended up being true, 597 00:29:55,990 --> 00:30:00,190 and really changed the way we thought about matter. 598 00:30:00,190 --> 00:30:01,300 All right. 599 00:30:01,300 --> 00:30:08,410 So we have light as a particle and as a wave. 600 00:30:08,410 --> 00:30:11,080 We have matter, particularly electrons, 601 00:30:11,080 --> 00:30:14,150 as particles and waves. 602 00:30:14,150 --> 00:30:17,110 And now we are ready for a way to think 603 00:30:17,110 --> 00:30:19,880 about how to put this together. 604 00:30:19,880 --> 00:30:22,750 So before we move on and talk about the Schrodinger equation, 605 00:30:22,750 --> 00:30:25,687 I just want to take a break from history for a minute, 606 00:30:25,687 --> 00:30:27,520 because some of you are like, OK, well, this 607 00:30:27,520 --> 00:30:30,400 is really cool for the father and son team, 608 00:30:30,400 --> 00:30:32,380 but what about today? 609 00:30:32,380 --> 00:30:33,740 What's happening today? 610 00:30:33,740 --> 00:30:36,280 So let's take a break from history for a second 611 00:30:36,280 --> 00:30:40,000 and talk about why you should care about small particles. 612 00:30:40,000 --> 00:30:42,070 Small particles of special properties, 613 00:30:42,070 --> 00:30:43,929 if they're on the subatomic scale, 614 00:30:43,929 --> 00:30:45,220 their properties are different. 615 00:30:45,220 --> 00:30:49,200 If you have very, very few atoms, versus many atoms, 616 00:30:49,200 --> 00:30:52,184 the things with very few atoms have special properties. 617 00:30:52,184 --> 00:30:53,600 So why should you care about that? 618 00:30:53,600 --> 00:30:55,930 Why should you care about the energies 619 00:30:55,930 --> 00:30:58,136 that we can get out of the Schrodinger equation? 620 00:30:58,136 --> 00:31:00,760 So why should we care about the Schrodinger equation or quantum 621 00:31:00,760 --> 00:31:01,780 mechanics? 622 00:31:01,780 --> 00:31:04,870 So there are many reasons, but I will share one with you. 623 00:31:04,870 --> 00:31:07,990 And this is a segment in their own words. 624 00:31:07,990 --> 00:31:11,640 So you're going to hear from Darcy, who was actually 625 00:31:11,640 --> 00:31:14,070 a former TA for 5.111. 626 00:31:14,070 --> 00:31:16,190 So she is associated with this class. 627 00:31:16,190 --> 00:31:21,330 She actually just got her PhD in the spring from MIT, 628 00:31:21,330 --> 00:31:25,080 and she now works at Google. 629 00:31:25,080 --> 00:31:26,940 But in this short, she's going to tell you 630 00:31:26,940 --> 00:31:29,130 about research in Moungi Bawendi's Lab, 631 00:31:29,130 --> 00:31:32,190 and why you should care about quantum dots, which 632 00:31:32,190 --> 00:31:35,590 are small collections of atoms. 633 00:31:35,590 --> 00:31:37,440 So I'm going to try to switch over 634 00:31:37,440 --> 00:31:40,750 now and hope that our demo before 635 00:31:40,750 --> 00:31:42,780 didn't screw up the sound. 636 00:31:42,780 --> 00:31:44,970 But we'll see what we can do. 637 00:31:44,970 --> 00:31:51,424 And I think it should be good. 638 00:31:51,424 --> 00:31:52,090 [VIDEO PLAYBACK] 639 00:31:52,090 --> 00:31:54,548 - My name is Darcy Wanger, and I work as a graduate student 640 00:31:54,548 --> 00:31:56,630 in the Bawendi Lab at MIT. 641 00:31:56,630 --> 00:31:59,740 I work with quantum dots in my research. 642 00:31:59,740 --> 00:32:03,130 Quantum dots are really, really tiny particles 643 00:32:03,130 --> 00:32:04,960 of a semiconductor. 644 00:32:04,960 --> 00:32:09,850 So we're talking like 4 nanometers in diameter. 645 00:32:09,850 --> 00:32:14,292 In a particle that small, there are only 10,000 or so atoms, 646 00:32:14,292 --> 00:32:16,000 which seems like a lot of atoms if you're 647 00:32:16,000 --> 00:32:17,500 comparing to something like water, 648 00:32:17,500 --> 00:32:19,510 which only has 3 atoms in it. 649 00:32:19,510 --> 00:32:21,910 But if you compare it to something you can actually 650 00:32:21,910 --> 00:32:25,180 hold in your hand, which has a lot of atoms in it, 651 00:32:25,180 --> 00:32:27,730 10,000 is actually a pretty small number. 652 00:32:27,730 --> 00:32:31,600 So a particle this small has really strange properties. 653 00:32:31,600 --> 00:32:34,260 Different things start to matter when you get really small. 654 00:32:34,260 --> 00:32:36,970 And just like an atom, a quantum dot, 655 00:32:36,970 --> 00:32:40,930 or semiconductor nanocrystal, has discrete energy levels. 656 00:32:40,930 --> 00:32:44,020 So if an electron is sitting at this energy level, 657 00:32:44,020 --> 00:32:46,300 and it absorbs light, an electron 658 00:32:46,300 --> 00:32:48,730 can get excited to a higher energy level. 659 00:32:48,730 --> 00:32:51,790 And then, when that electron relaxes back down to the ground 660 00:32:51,790 --> 00:32:54,190 state, it emits light. 661 00:32:54,190 --> 00:32:56,650 And the energy of that light is exactly 662 00:32:56,650 --> 00:32:58,625 the difference between these two energy levels. 663 00:33:01,450 --> 00:33:03,400 The difference between the energy levels 664 00:33:03,400 --> 00:33:06,460 is related to the size of the dot. 665 00:33:06,460 --> 00:33:08,530 So in a really small quantum dot, 666 00:33:08,530 --> 00:33:10,600 the energy levels are far apart. 667 00:33:10,600 --> 00:33:13,000 So the light it emits is higher energy, 668 00:33:13,000 --> 00:33:16,060 because there's a large energy difference between the energy 669 00:33:16,060 --> 00:33:17,740 levels. 670 00:33:17,740 --> 00:33:20,230 If we use a larger quantum dot, the distance 671 00:33:20,230 --> 00:33:23,470 between the energy levels is smaller, so the light it emits 672 00:33:23,470 --> 00:33:26,680 is lower energy, or redder. 673 00:33:26,680 --> 00:33:30,490 People in our lab are working to make quantum dots bind 674 00:33:30,490 --> 00:33:31,360 to a tumor. 675 00:33:31,360 --> 00:33:34,120 So when a doctor goes in to remove a tumor, 676 00:33:34,120 --> 00:33:36,880 they can see the shining of the UV light on it, 677 00:33:36,880 --> 00:33:38,380 and see whether it's all gone when 678 00:33:38,380 --> 00:33:39,640 they've taken out the tumor. 679 00:33:39,640 --> 00:33:42,760 They can also use quantum dots to label other things 680 00:33:42,760 --> 00:33:47,860 other than tumors, like pH or oxygen level or antibodies 681 00:33:47,860 --> 00:33:50,890 or the other drugs that are treating the cancer tumor. 682 00:33:50,890 --> 00:33:52,730 Each of those can be different colors. 683 00:33:52,730 --> 00:33:54,550 So if you shine a light on that whole area, 684 00:33:54,550 --> 00:33:58,270 you can see, oh, that orange spot, that's some cancer cells. 685 00:33:58,270 --> 00:34:02,920 Oh, and that green tells me that the pH is above 7.4. 686 00:34:02,920 --> 00:34:07,480 So it's pretty cool that we can use the idea of energy levels 687 00:34:07,480 --> 00:34:12,460 in something so applicable like surgery, where it can actually 688 00:34:12,460 --> 00:34:16,510 be used to track things and make it easy for doctors 689 00:34:16,510 --> 00:34:18,801 to see what's going on while they're doing a surgery. 690 00:34:18,801 --> 00:34:21,060 [END PLAYBACK] 691 00:34:21,060 --> 00:34:22,570 CATHERINE DRENNAN: OK. 692 00:34:22,570 --> 00:34:25,900 So that's an example for course 5 research. 693 00:34:25,900 --> 00:34:29,134 [APPLAUSE] 694 00:34:31,491 --> 00:34:33,199 And you can see all these credits online. 695 00:34:33,199 --> 00:34:36,500 I will mention that some of those nice animations 696 00:34:36,500 --> 00:34:41,060 were done by a former graduate student in the chemistry 697 00:34:41,060 --> 00:34:41,659 department. 698 00:34:41,659 --> 00:34:44,389 So these videos, even the art was 699 00:34:44,389 --> 00:34:46,940 done by chemists, which is a lot of fun. 700 00:34:46,940 --> 00:34:47,719 OK. 701 00:34:47,719 --> 00:34:50,659 So let's introduce the Schrodinger equation. 702 00:34:50,659 --> 00:34:54,139 And we'll spend some more time on this 703 00:34:54,139 --> 00:34:57,710 as we go along, on Friday. 704 00:34:57,710 --> 00:35:03,680 So we needed now-- we had learned a lot 705 00:35:03,680 --> 00:35:08,420 about wave particle duality and about 706 00:35:08,420 --> 00:35:10,017 these subatomic particles. 707 00:35:10,017 --> 00:35:11,600 And we needed a way to think about it. 708 00:35:11,600 --> 00:35:14,900 We needed a theory to describe their behavior. 709 00:35:14,900 --> 00:35:19,500 And classical mechanics had some flaws in with respect. 710 00:35:19,500 --> 00:35:22,610 So we needed a new kind of mechanism. 711 00:35:22,610 --> 00:35:24,590 We needed quantum mechanics. 712 00:35:24,590 --> 00:35:27,410 So here, if we're thinking about particles 713 00:35:27,410 --> 00:35:29,690 that are really small like electrons, 714 00:35:29,690 --> 00:35:32,610 we need to consider the wavelike properties. 715 00:35:32,610 --> 00:35:35,810 It's really important when you have a wavelength that 716 00:35:35,810 --> 00:35:38,630 is so similar to the size of the object 717 00:35:38,630 --> 00:35:40,130 that you're thinking about. 718 00:35:40,130 --> 00:35:42,110 So the Schrodinger equation really 719 00:35:42,110 --> 00:35:46,700 became to quantum mechanics like Newton's equations 720 00:35:46,700 --> 00:35:49,110 were to classical mechanics. 721 00:35:49,110 --> 00:35:50,942 So what is the Schrodinger equation? 722 00:35:50,942 --> 00:35:52,400 So here's a picture of Schrodinger. 723 00:35:52,400 --> 00:35:53,900 And he looks so happy. 724 00:35:53,900 --> 00:35:56,870 I would be happy, too, if I had come up with this equation, 725 00:35:56,870 --> 00:35:57,680 I think. 726 00:35:57,680 --> 00:36:00,680 So here's the simplest form of the equation 727 00:36:00,680 --> 00:36:03,140 that you will probably ever see. 728 00:36:03,140 --> 00:36:08,510 And so we'll just define some of these terms. 729 00:36:08,510 --> 00:36:12,710 So we have wave function, psi. 730 00:36:12,710 --> 00:36:16,770 And over here is the binding energy, 731 00:36:16,770 --> 00:36:20,820 and that's the energy of binding an electron to a nucleus. 732 00:36:20,820 --> 00:36:26,040 And then an H with a hat, we have our Hamiltonian operator. 733 00:36:26,040 --> 00:36:29,250 And in this course, you will not be solving this equation. 734 00:36:29,250 --> 00:36:32,310 We're just going to be talking about what sorts of things 735 00:36:32,310 --> 00:36:34,740 came out of this equation. 736 00:36:34,740 --> 00:36:38,700 So I'm going to give you a little bit longer 737 00:36:38,700 --> 00:36:41,640 version of the equation now. 738 00:36:41,640 --> 00:36:44,350 And so again, you're thinking about the electron. 739 00:36:44,350 --> 00:36:48,120 It has these wavelike properties. 740 00:36:48,120 --> 00:36:54,210 And it's somewhere in the atom, not crashing into the nucleus. 741 00:36:54,210 --> 00:36:57,460 And it needs to be defined in three dimensions. 742 00:36:57,460 --> 00:37:00,210 And it has momentum, so it's moving. 743 00:37:00,210 --> 00:37:04,500 So we need to think about this as an equation of motion 744 00:37:04,500 --> 00:37:07,860 in a three-dimensional space. 745 00:37:07,860 --> 00:37:10,630 And the equation is going to change. 746 00:37:10,630 --> 00:37:12,600 The math will change, depending on where 747 00:37:12,600 --> 00:37:16,650 the electron is located, which you won't know exactly. 748 00:37:16,650 --> 00:37:19,480 So this is a very hard problem. 749 00:37:19,480 --> 00:37:22,500 But it's not totally without anything 750 00:37:22,500 --> 00:37:24,970 to do with classical mechanics. 751 00:37:24,970 --> 00:37:26,700 And if we write the longest version 752 00:37:26,700 --> 00:37:30,570 you'll see, at least in this course, for the hydrogen atom, 753 00:37:30,570 --> 00:37:32,970 I just want to show this to point out 754 00:37:32,970 --> 00:37:37,440 that there are some terms from classical mechanics in here. 755 00:37:37,440 --> 00:37:40,050 This is Coulomb's energy, also sometimes called 756 00:37:40,050 --> 00:37:41,500 potential energy. 757 00:37:41,500 --> 00:37:43,440 So we saw Coulomb's force before. 758 00:37:43,440 --> 00:37:45,060 Here is Coulomb's energy. 759 00:37:45,060 --> 00:37:46,710 So some of the classical mechanics 760 00:37:46,710 --> 00:37:49,860 is contained within this, but it expands 761 00:37:49,860 --> 00:37:51,990 from classical mechanics to consider 762 00:37:51,990 --> 00:37:57,190 the wavelike properties of the electrons. 763 00:37:57,190 --> 00:38:00,930 So whenever I talk about this, I always 764 00:38:00,930 --> 00:38:05,310 feel like I want to have something better 765 00:38:05,310 --> 00:38:10,530 to say about really what this is doing and where it came from. 766 00:38:10,530 --> 00:38:14,160 In terms of what it's doing, how is solving this helping you? 767 00:38:14,160 --> 00:38:16,830 What are you learning from solving this? 768 00:38:16,830 --> 00:38:19,170 So one thing you're learning from solving 769 00:38:19,170 --> 00:38:22,110 this is you're finding E. And that's 770 00:38:22,110 --> 00:38:24,702 really important, the binding energy of the nucleus 771 00:38:24,702 --> 00:38:25,410 and the electron. 772 00:38:25,410 --> 00:38:27,540 And we saw before that, if you just 773 00:38:27,540 --> 00:38:30,510 used simple classical mechanics, you 774 00:38:30,510 --> 00:38:32,250 have a positive and negative charge that 775 00:38:32,250 --> 00:38:33,700 are close to each other. 776 00:38:33,700 --> 00:38:36,000 Why don't they come and crash into each other? 777 00:38:36,000 --> 00:38:39,360 We want to know how they are bonded to each other, what's 778 00:38:39,360 --> 00:38:41,820 the real energy of that association. 779 00:38:41,820 --> 00:38:44,100 We also saw, with the photoelectric effect, 780 00:38:44,100 --> 00:38:45,930 that it's not that easy to get an electron 781 00:38:45,930 --> 00:38:48,750 to eject from a metal surface. 782 00:38:48,750 --> 00:38:50,230 So it's bound in there. 783 00:38:50,230 --> 00:38:52,920 And what is that actual binding energy? 784 00:38:52,920 --> 00:38:55,570 So that comes out of the Schrodinger equation. 785 00:38:55,570 --> 00:38:58,650 This E here is the binding energy. 786 00:38:58,650 --> 00:39:02,100 And also, solving it will tell you about the wave function 787 00:39:02,100 --> 00:39:03,960 or, as chemists like to talk about, 788 00:39:03,960 --> 00:39:08,010 orbitals, where the electrons are, in what orbitals. 789 00:39:08,010 --> 00:39:10,980 So this is the information you get out. 790 00:39:10,980 --> 00:39:15,390 And importantly, it works. 791 00:39:15,390 --> 00:39:17,790 It matches experiment. 792 00:39:17,790 --> 00:39:19,980 So chemists are experimentalists. 793 00:39:19,980 --> 00:39:22,890 We love experiments, and we see this data, 794 00:39:22,890 --> 00:39:25,030 and we want to understand it. 795 00:39:25,030 --> 00:39:27,200 And the Schrodinger equation helps us understand it. 796 00:39:27,200 --> 00:39:31,650 It correctly predicts binding energies and wave functions, 797 00:39:31,650 --> 00:39:34,980 and it explains why the hydrogen atom is, in fact, stable, 798 00:39:34,980 --> 00:39:40,180 where you don't have crashing or exploding of the hydrogen atom. 799 00:39:40,180 --> 00:39:44,040 So where did this equation come from that works so well? 800 00:39:44,040 --> 00:39:46,837 How did Schrodinger come up with this? 801 00:39:46,837 --> 00:39:49,170 And this is always sort of the puzzle when I teach this. 802 00:39:49,170 --> 00:39:52,110 I feel like I should have something profound to say 803 00:39:52,110 --> 00:39:54,390 about where this came from. 804 00:39:54,390 --> 00:39:56,370 And so I've done a little reading and looked, 805 00:39:56,370 --> 00:39:58,980 and I thought the best explanation for this 806 00:39:58,980 --> 00:40:02,640 that I ever saw came from Richard Feynman. 807 00:40:02,640 --> 00:40:04,590 And when he was asked how Schrodinger came up 808 00:40:04,590 --> 00:40:07,320 with this equation, he said, "it is not 809 00:40:07,320 --> 00:40:10,650 possible to derive it from anything you know. 810 00:40:10,650 --> 00:40:14,220 It came out of the mind of Schrodinger." 811 00:40:14,220 --> 00:40:18,060 And I thought that pretty much summed it up. 812 00:40:18,060 --> 00:40:20,010 So sometimes-- after class last week, 813 00:40:20,010 --> 00:40:22,110 on Wednesday, someone came down and said, 814 00:40:22,110 --> 00:40:23,490 you know, the Thomson experiment, 815 00:40:23,490 --> 00:40:25,531 discovering the electron, why didn't someone else 816 00:40:25,531 --> 00:40:26,820 do that experiment? 817 00:40:26,820 --> 00:40:28,590 It seemed like it's not a cathode ray. 818 00:40:28,590 --> 00:40:31,650 And you have to have a little phosphorous screen. 819 00:40:31,650 --> 00:40:33,900 Why didn't someone else discover the electron? 820 00:40:33,900 --> 00:40:36,581 And some of these other-- de Broglie rearranged 821 00:40:36,581 --> 00:40:38,580 some equations, did it in a way that no one else 822 00:40:38,580 --> 00:40:40,200 was thinking, but still. 823 00:40:40,200 --> 00:40:43,479 Or plot solving the equation of a straight line. 824 00:40:43,479 --> 00:40:45,270 No one else was thinking about it some way, 825 00:40:45,270 --> 00:40:46,800 using other people's data. 826 00:40:46,800 --> 00:40:49,470 They just sort of saw things in data that other people didn't. 827 00:40:49,470 --> 00:40:53,160 But you think why didn't someone else see that, too? 828 00:40:53,160 --> 00:40:54,960 When it comes to the Schrodinger equation, 829 00:40:54,960 --> 00:40:57,930 the question is why didn't someone else or lots of people 830 00:40:57,930 --> 00:40:58,860 come up with it? 831 00:40:58,860 --> 00:41:01,230 I think the question really is, how did Schrodinger 832 00:41:01,230 --> 00:41:01,990 come up with it? 833 00:41:01,990 --> 00:41:03,780 At least, that's the question to me. 834 00:41:03,780 --> 00:41:06,770 And I have never really-- that's the best explanation I have. 835 00:41:06,770 --> 00:41:09,930 It just came out of his mind. 836 00:41:09,930 --> 00:41:10,740 OK. 837 00:41:10,740 --> 00:41:12,510 So we're many years later. 838 00:41:12,510 --> 00:41:14,890 We've had the Schrodinger equation for a while. 839 00:41:14,890 --> 00:41:17,490 So this is an old story, right? 840 00:41:17,490 --> 00:41:20,040 Well, maybe for the hydrogen atom, 841 00:41:20,040 --> 00:41:24,480 but this is still actually a very active area of research. 842 00:41:24,480 --> 00:41:26,490 Oh, my startup disk is full. 843 00:41:26,490 --> 00:41:27,960 Thank you. 844 00:41:27,960 --> 00:41:29,160 Let's go back to that. 845 00:41:29,160 --> 00:41:30,966 All right. 846 00:41:30,966 --> 00:41:32,340 So I just thought-- I always like 847 00:41:32,340 --> 00:41:36,250 to give you examples of current research on these areas. 848 00:41:36,250 --> 00:41:38,010 And so I know a number of you were 849 00:41:38,010 --> 00:41:41,700 interested in potential of being chemical engineering majors, 850 00:41:41,700 --> 00:41:42,265 undergrads. 851 00:41:42,265 --> 00:41:43,890 And I'll tell you about a new professor 852 00:41:43,890 --> 00:41:46,440 who started about a year ago, Heather Kulik. 853 00:41:46,440 --> 00:41:50,190 And her research group is really interested in using 854 00:41:50,190 --> 00:41:53,310 a quantum mechanical approach to study materials 855 00:41:53,310 --> 00:41:55,140 and to study proteins. 856 00:41:55,140 --> 00:41:56,920 But when you get to things like proteins, 857 00:41:56,920 --> 00:41:58,920 there's thousands and thousands of atoms around. 858 00:41:58,920 --> 00:42:02,520 Forget multiple electrons, we're talking about multiple atoms 859 00:42:02,520 --> 00:42:05,580 with multiple electrons, huge complexes. 860 00:42:05,580 --> 00:42:08,970 How can you give a quantum mechanical analysis 861 00:42:08,970 --> 00:42:10,492 of things that are so large? 862 00:42:10,492 --> 00:42:11,700 And this is really important. 863 00:42:11,700 --> 00:42:15,240 I mean, I think that one of the big problems moving forward 864 00:42:15,240 --> 00:42:17,085 is solving the energy problem and doing it 865 00:42:17,085 --> 00:42:19,440 in a way that doesn't destroy our environment, so 866 00:42:19,440 --> 00:42:21,900 new batteries, new electrodes, new materials. 867 00:42:21,900 --> 00:42:24,330 We need to understand the properties of different metals 868 00:42:24,330 --> 00:42:26,585 to understand what will make those good electrodes. 869 00:42:26,585 --> 00:42:27,960 And to really understand them, we 870 00:42:27,960 --> 00:42:29,700 need a quantum mechanical approach. 871 00:42:29,700 --> 00:42:31,470 But these are big areas. 872 00:42:31,470 --> 00:42:33,660 There's a lot of things to consider here. 873 00:42:33,660 --> 00:42:36,330 So Heather is interested in coming up 874 00:42:36,330 --> 00:42:40,320 with improving algorithms, improving the computation, 875 00:42:40,320 --> 00:42:44,010 to really give a quantum mechanical analysis to systems 876 00:42:44,010 --> 00:42:46,290 that have a lot of atoms in them. 877 00:42:46,290 --> 00:42:49,360 So if you're interested in this area, you're not too late. 878 00:42:49,360 --> 00:42:51,870 You don't have to go back to the early 1900s. 879 00:42:51,870 --> 00:42:55,620 There's still a lot to do in this area. 880 00:42:55,620 --> 00:42:56,490 OK. 881 00:42:56,490 --> 00:43:00,210 So very briefly now, let's just look 882 00:43:00,210 --> 00:43:03,250 at the Schrodinger equation we saw from the hydrogen atom. 883 00:43:03,250 --> 00:43:05,160 So we'll go back to understanding 884 00:43:05,160 --> 00:43:09,690 quantum mechanical analysis of photosynthesis-- amazing, 885 00:43:09,690 --> 00:43:11,060 don't understand how it works. 886 00:43:11,060 --> 00:43:12,090 That would be great if we did. 887 00:43:12,090 --> 00:43:14,131 That would really solve a lot of energy problems. 888 00:43:14,131 --> 00:43:17,890 But we'll just go to hydrogen atom, one electron back. 889 00:43:17,890 --> 00:43:20,046 So if you solve the Schrodinger equation for this-- 890 00:43:20,046 --> 00:43:22,170 and I think I did this in college, not in freshman, 891 00:43:22,170 --> 00:43:24,990 chemistry, but somewhere along the line-- 892 00:43:24,990 --> 00:43:26,550 you'll come up with this term. 893 00:43:26,550 --> 00:43:28,680 So again, this is the binding energy. 894 00:43:28,680 --> 00:43:31,530 We just want to know about how the electron is 895 00:43:31,530 --> 00:43:34,050 being held by the nucleus. 896 00:43:34,050 --> 00:43:36,330 And there are some terms in here. 897 00:43:36,330 --> 00:43:40,350 We have the electrons mass-- that's known, 898 00:43:40,350 --> 00:43:42,300 the electrons charge. 899 00:43:42,300 --> 00:43:46,050 We have a permittivity constant and Planck's constant. 900 00:43:46,050 --> 00:43:48,570 And if you look at this, you go, wait a minute. 901 00:43:48,570 --> 00:43:49,770 That's a constant. 902 00:43:49,770 --> 00:43:50,670 That's a constant. 903 00:43:50,670 --> 00:43:51,570 That's a constant. 904 00:43:51,570 --> 00:43:53,100 That's a constant. 905 00:43:53,100 --> 00:43:56,220 We can simplify that. 906 00:43:56,220 --> 00:43:58,470 And we will. 907 00:43:58,470 --> 00:44:03,210 And that is the Rydberg's constant, 2.18 times 908 00:44:03,210 --> 00:44:05,620 10 to the minus 18th joules. 909 00:44:05,620 --> 00:44:07,710 So now it doesn't look quite as scary. 910 00:44:07,710 --> 00:44:11,670 We can just substitute this RH. 911 00:44:11,670 --> 00:44:13,646 That makes us feel a lot better. 912 00:44:13,646 --> 00:44:16,020 It's one number that will be given on the equation sheet, 913 00:44:16,020 --> 00:44:18,210 so we don't even have to remember it. 914 00:44:18,210 --> 00:44:22,500 And now we can rewrite this in terms of the binding energy. 915 00:44:22,500 --> 00:44:25,620 So again, the binding energy, this is a constant. 916 00:44:25,620 --> 00:44:32,450 So now this turns into minus RH over n squared. 917 00:44:32,450 --> 00:44:35,430 And n, what is n? 918 00:44:35,430 --> 00:44:41,920 n is a positive integer 1, 2, 3, up to infinity. 919 00:44:41,920 --> 00:44:44,370 And what's its name? 920 00:44:44,370 --> 00:44:46,662 What is n? 921 00:44:46,662 --> 00:44:48,270 You can you yell it out. 922 00:44:48,270 --> 00:44:49,050 Some of you know. 923 00:44:49,050 --> 00:44:50,165 AUDIENCE: [INAUDIBLE] 924 00:44:50,165 --> 00:44:51,165 CATHERINE DRENNAN: Yeah. 925 00:44:51,165 --> 00:44:54,960 The principle quantum number, that's right. 926 00:44:54,960 --> 00:44:57,420 So the principle quantum number comes out 927 00:44:57,420 --> 00:44:59,280 of the Schrodinger equation. 928 00:44:59,280 --> 00:45:01,030 And that's how we can think about it. 929 00:45:01,030 --> 00:45:03,500 And again, here are these ideas. 930 00:45:03,500 --> 00:45:06,140 The binding energies are quantized. 931 00:45:06,140 --> 00:45:09,120 This is a constant over here. 932 00:45:09,120 --> 00:45:11,100 So the principle quantum number comes out 933 00:45:11,100 --> 00:45:13,020 of the Schrodinger equation. 934 00:45:13,020 --> 00:45:13,530 All right. 935 00:45:13,530 --> 00:45:16,800 So now, next time, we're going to think more 936 00:45:16,800 --> 00:45:18,600 about the Rydberg constant. 937 00:45:18,600 --> 00:45:22,050 And we're going to do a demonstration next Friday 938 00:45:22,050 --> 00:45:26,190 of the hydrogen atom spectrum to show that the Schrodinger 939 00:45:26,190 --> 00:45:30,090 equation, in fact, can explain binding energies. 940 00:45:30,090 --> 00:45:34,870 So that's on Friday, and that's our first clicker competition. 941 00:45:34,870 --> 00:45:35,610 So come. 942 00:45:35,610 --> 00:45:37,680 Be ready with your clickers. 943 00:45:37,680 --> 00:45:39,870 You can sit in recitations. 944 00:45:39,870 --> 00:45:42,570 You can share answers before clicking in. 945 00:45:42,570 --> 00:45:43,980 It's not cheating. 946 00:45:43,980 --> 00:45:45,190 It's teamwork. 947 00:45:45,190 --> 00:45:45,690 OK. 948 00:45:45,690 --> 00:45:47,540 See you Friday.