1 00:00:00,000 --> 00:00:00,016 The following content is provided under a Creative 2 00:00:00,016 --> 00:00:00,022 Commons license. 3 00:00:00,022 --> 00:00:00,038 Your support will help MIT OpenCourseWare continue to 4 00:00:00,038 --> 00:00:00,054 offer high quality educational resources for free. 5 00:00:00,054 --> 00:00:00,072 To make a donation or view additional materials from 6 00:00:00,072 --> 00:00:00,088 hundreds of MIT courses, visit MIT OpenCourseWare at 7 00:00:00,088 --> 00:00:00,110 ocw.mit.edu. 8 00:00:00,110 --> 00:00:22,110 PROFESSOR: All right. 9 00:00:22,110 --> 00:00:23,160 Let's get started. 10 00:00:23,160 --> 00:00:25,700 Why doesn't everyone go ahead and take ten more seconds on 11 00:00:25,700 --> 00:00:37,260 the clicker question. 12 00:00:37,260 --> 00:00:38,580 All right, and let's see how we did. 13 00:00:38,580 --> 00:00:41,970 Alright, excellent job, 86% of you, that's right. 14 00:00:41,970 --> 00:00:44,890 What we had just done a clicker question on is 15 00:00:44,890 --> 00:00:48,080 discussing light as a particle and the photoelectric effect, 16 00:00:48,080 --> 00:00:50,250 so we're going to finish up with a few points about the 17 00:00:50,250 --> 00:00:52,550 photoelectric effect today. 18 00:00:52,550 --> 00:00:55,940 And then we're going to try a demo to see if we can convince 19 00:00:55,940 --> 00:00:58,790 ourselves that the kind of calculations we make work out 20 00:00:58,790 --> 00:01:02,060 perfectly, and we'll do a test up here about 21 00:01:02,060 --> 00:01:03,510 half way through class. 22 00:01:03,510 --> 00:01:06,640 And we'll also talk about photon momentum as another 23 00:01:06,640 --> 00:01:09,010 example of light behaving up as a particle. 24 00:01:09,010 --> 00:01:12,850 After that, we'll move on to matter as a wave, and then the 25 00:01:12,850 --> 00:01:16,580 Schrodinger equation, which is actually a wave equation that 26 00:01:16,580 --> 00:01:19,280 describes the behavior of particles by taking into 27 00:01:19,280 --> 00:01:22,490 account the fact that matter also has these wave-like 28 00:01:22,490 --> 00:01:25,490 properties. 29 00:01:25,490 --> 00:01:27,440 So, starting back with the photoelectric effect -- yes. 30 00:01:27,440 --> 00:01:33,070 STUDENT: [INAUDIBLE] class last time [INAUDIBLE] notes. 31 00:01:33,070 --> 00:01:34,130 PROFESSOR: Oh, sure. 32 00:01:34,130 --> 00:01:37,018 Can one of the TAs maybe come up and hand around anyone that 33 00:01:37,018 --> 00:01:37,660 didn't get notes? 34 00:01:37,660 --> 00:01:40,650 We have not yet perfected the art of entering and exiting 35 00:01:40,650 --> 00:01:42,490 this classroom yet, we're still working on that. 36 00:01:42,490 --> 00:01:44,380 Raise your hand if you need notes and we'll make sure we 37 00:01:44,380 --> 00:01:46,650 get those to you. 38 00:01:46,650 --> 00:01:48,470 All right, so where we left off with the photoelectric 39 00:01:48,470 --> 00:01:52,090 effect was when we first introduced the effect, we were 40 00:01:52,090 --> 00:01:54,190 talking about it in terms of frequencies. 41 00:01:54,190 --> 00:01:56,870 So, for example, we were talking about a threshold 42 00:01:56,870 --> 00:01:59,780 frequency as in a minimum frequency of light that you 43 00:01:59,780 --> 00:02:03,120 need in order to eject an electron from a metal surface. 44 00:02:03,120 --> 00:02:06,160 What Einstein then clarified for us was that we could also 45 00:02:06,160 --> 00:02:10,320 be talking about energies, and he described the relationship 46 00:02:10,320 --> 00:02:13,810 between frequency and energy that they're proportional, if 47 00:02:13,810 --> 00:02:16,440 you want to know the energy, you just multiply the 48 00:02:16,440 --> 00:02:18,470 frequency by Planck's constant. 49 00:02:18,470 --> 00:02:20,650 So, now we can talk about it in different terms, for 50 00:02:20,650 --> 00:02:24,340 example, talking about e sub i, which is the incident 51 00:02:24,340 --> 00:02:27,310 energy or the energy of the light that comes in, or 52 00:02:27,310 --> 00:02:31,100 talking about work function here, and that's just another 53 00:02:31,100 --> 00:02:32,910 way to say threshold energy. 54 00:02:32,910 --> 00:02:35,510 So, the work function's the minimum amount of energy 55 00:02:35,510 --> 00:02:39,300 that's required in order to eject an electron, and most of 56 00:02:39,300 --> 00:02:41,280 you understand this relationship here, which is a 57 00:02:41,280 --> 00:02:44,260 little bit cut off, but it is all the way on in your notes, 58 00:02:44,260 --> 00:02:47,470 and that is what you saw the clicker question on -- how you 59 00:02:47,470 --> 00:02:49,890 can figure out, for example, the kinetic energy of the 60 00:02:49,890 --> 00:02:52,950 ejected electron by looking at the difference between how 61 00:02:52,950 --> 00:02:55,890 much energy you put in and how much energy is required to 62 00:02:55,890 --> 00:02:59,210 eject that electron in the first place. 63 00:02:59,210 --> 00:03:02,720 So, in this class we'll be talking about energy a lot, 64 00:03:02,720 --> 00:03:07,433 and it's often useful to draw some sort of energy diagram to 65 00:03:07,433 --> 00:03:09,940 visualize the differences in energy that we're discussing. 66 00:03:09,940 --> 00:03:13,360 So, we do this here for the photoelectric effect, and in 67 00:03:13,360 --> 00:03:15,600 terms of the photoelectric effect, what we know the 68 00:03:15,600 --> 00:03:19,290 important point is that the incoming photon has to be 69 00:03:19,290 --> 00:03:22,230 equal or greater in energy then the work 70 00:03:22,230 --> 00:03:23,660 function of the metal. 71 00:03:23,660 --> 00:03:27,810 So here we have energy increasing on the y-axis, and 72 00:03:27,810 --> 00:03:31,710 you see this straight line at the bottom here is lower down 73 00:03:31,710 --> 00:03:34,854 on the graph, and that's the energy of a bound electron, so 74 00:03:34,854 --> 00:03:37,110 that's going to be a low stable energy. 75 00:03:37,110 --> 00:03:40,510 But we see if we have a free electron, as we do in this 76 00:03:40,510 --> 00:03:43,910 dotted line here, that's going to be a higher energy that's 77 00:03:43,910 --> 00:03:44,860 less stable. 78 00:03:44,860 --> 00:03:47,930 So, if we want to go from that stable state to that less 79 00:03:47,930 --> 00:03:50,630 stable state, we need to put in a certain amount of energy 80 00:03:50,630 --> 00:03:54,090 to our system, and that's what we define as the work function 81 00:03:54,090 --> 00:03:56,930 here -- that difference between the free electron and 82 00:03:56,930 --> 00:03:59,150 the electron bound to the metal. 83 00:03:59,150 --> 00:04:02,140 So, the most basic case to understand, which is what we 84 00:04:02,140 --> 00:04:05,740 just saw is a case where we have the incident energy 85 00:04:05,740 --> 00:04:08,880 coming in, and that incident energy is greater than the 86 00:04:08,880 --> 00:04:11,230 work function, and in that case what we see is that we 87 00:04:11,230 --> 00:04:13,680 have an electron that is ejected. 88 00:04:13,680 --> 00:04:16,200 That makes sense and it also makes sense that this little 89 00:04:16,200 --> 00:04:19,130 extra bit here, that's the amount of energy that we have 90 00:04:19,130 --> 00:04:21,410 that goes into the kinetic energy of the electrons. 91 00:04:21,410 --> 00:04:23,370 So, that's how we could also graph figuring 92 00:04:23,370 --> 00:04:25,410 out the kinetic energy. 93 00:04:25,410 --> 00:04:29,120 So, in the second case what we have is what happens if we 94 00:04:29,120 --> 00:04:32,800 have the incident energy at some amount that's less than 95 00:04:32,800 --> 00:04:36,550 the work function, and in this case we're showing 1/2 of the 96 00:04:36,550 --> 00:04:37,810 work function. 97 00:04:37,810 --> 00:04:40,610 So in this case, we don't have enough energy to eject an 98 00:04:40,610 --> 00:04:44,590 electron, so, an electron is not ejected. 99 00:04:44,590 --> 00:04:47,120 And that's pretty clear, too, and the question I want to 100 00:04:47,120 --> 00:04:50,250 pose to you is instead the third case here. 101 00:04:50,250 --> 00:04:53,620 So in the third case what I'm showing is that we have -- now 102 00:04:53,620 --> 00:04:56,630 we're not just talking about 1 photon, we're talking about 3 103 00:04:56,630 --> 00:04:59,380 photons -- let's say we shoot them all at the same time at 104 00:04:59,380 --> 00:05:03,200 our metal, each of them having some energy that's let's say 105 00:05:03,200 --> 00:05:05,170 1/2 the work function. 106 00:05:05,170 --> 00:05:08,570 So, just to take a little bit of an informal survey, who 107 00:05:08,570 --> 00:05:11,320 thinks here that we will have an electron that is 108 00:05:11,320 --> 00:05:13,890 ejected in this case? 109 00:05:13,890 --> 00:05:17,230 So a couple hands, all right. 110 00:05:17,230 --> 00:05:19,950 And what about who thinks that we will not have 111 00:05:19,950 --> 00:05:21,710 enough energy here? 112 00:05:21,710 --> 00:05:22,230 All right. 113 00:05:22,230 --> 00:05:25,760 We've got a big majority, and both are logical ways of 114 00:05:25,760 --> 00:05:28,450 thinking, but it turns out that the majority is correct, 115 00:05:28,450 --> 00:05:32,220 which is not always the case, but the electron is not 116 00:05:32,220 --> 00:05:33,610 ejected in this case. 117 00:05:33,610 --> 00:05:36,510 And the reason for this, and this is a very important point 118 00:05:36,510 --> 00:05:40,000 about the photoelectric effect, and the point here is 119 00:05:40,000 --> 00:05:43,660 that the electrons here are acting as particles, you can't 120 00:05:43,660 --> 00:05:45,640 just add those energies together. 121 00:05:45,640 --> 00:05:48,975 One individual particle is being absorbed by the metal 122 00:05:48,975 --> 00:05:50,680 and exciting an electron. 123 00:05:50,680 --> 00:05:54,000 So, having other particles around that have the same 124 00:05:54,000 --> 00:05:56,900 energy that you could technically add up if you were 125 00:05:56,900 --> 00:05:59,160 adding them up like a wave, you can't do the same thing 126 00:05:59,160 --> 00:06:01,020 with particles, they're all separate. 127 00:06:01,020 --> 00:06:03,340 So, the take-home message is whether you have three photons 128 00:06:03,340 --> 00:06:06,560 or 3,000,000 photons that you're shooting at your metal, 129 00:06:06,560 --> 00:06:09,880 if you're not at that minimum frequency or that minimum 130 00:06:09,880 --> 00:06:14,450 energy that you need, nothing is going to happen. 131 00:06:14,450 --> 00:06:17,960 So, you might ask then well what is the significance of 132 00:06:17,960 --> 00:06:21,260 shooting different amounts of photons at a metal? 133 00:06:21,260 --> 00:06:24,130 Is there any significance at all, for example, in the 134 00:06:24,130 --> 00:06:28,220 number of photons that are hitting the metal or being 135 00:06:28,220 --> 00:06:29,160 absorbed by the metal. 136 00:06:29,160 --> 00:06:32,170 And there is a relationship here, and that is that the 137 00:06:32,170 --> 00:06:35,970 number of photons absorbed by the metal are related to the 138 00:06:35,970 --> 00:06:39,320 number of electrons ejected from the metal. 139 00:06:39,320 --> 00:06:42,530 So, in this figure here what I'm actually showing is these 140 00:06:42,530 --> 00:06:44,800 little sunshines, which let's say are each 141 00:06:44,800 --> 00:06:46,430 one individual photon. 142 00:06:46,430 --> 00:06:50,220 So we had six photons going in, so the maximum number of 143 00:06:50,220 --> 00:06:53,280 electrons that we're going to have coming out is also six 144 00:06:53,280 --> 00:06:57,810 because the maximum scenario that we could have that would 145 00:06:57,810 --> 00:07:00,160 maximize the number of electrons is that each one of 146 00:07:00,160 --> 00:07:03,800 those photons comes in, excites an electron, ejects it 147 00:07:03,800 --> 00:07:05,530 from the surface of the metal. 148 00:07:05,530 --> 00:07:09,160 It's important to note, of course though, it's not just 149 00:07:09,160 --> 00:07:12,250 the number, it's really important that the energy of 150 00:07:12,250 --> 00:07:15,710 each one of these individual photons is, of course, greater 151 00:07:15,710 --> 00:07:19,390 than the work function of the metal. 152 00:07:19,390 --> 00:07:22,850 So, that's, in fact, it's that number of photons that we're 153 00:07:22,850 --> 00:07:26,380 talking about when we refer to the intensity of light, and 154 00:07:26,380 --> 00:07:29,160 the intensity of light is proportional to that number, 155 00:07:29,160 --> 00:07:31,120 because when we talk about intensity, really we're 156 00:07:31,120 --> 00:07:35,520 talking about the amount of energy that a stream of 157 00:07:35,520 --> 00:07:39,550 particles, a stream of photons, has per second. 158 00:07:39,550 --> 00:07:42,470 So, if we have a high intensity, we're talking about 159 00:07:42,470 --> 00:07:45,740 having more photons per second, and it's important to 160 00:07:45,740 --> 00:07:48,370 know also what that does not mean. 161 00:07:48,370 --> 00:07:52,950 So it does not mean that we have more energy per photon. 162 00:07:52,950 --> 00:07:54,690 This is a really important difference. 163 00:07:54,690 --> 00:07:58,220 Intensity, if we increase the intensity, we're not 164 00:07:58,220 --> 00:08:01,500 increasing the energy in each photon, we're just increasing 165 00:08:01,500 --> 00:08:03,480 the number of photons that we're shooting out of our 166 00:08:03,480 --> 00:08:06,910 laser, whatever our light source is. 167 00:08:06,910 --> 00:08:09,280 And when we talk about intensity in terms of units, 168 00:08:09,280 --> 00:08:11,700 we usually talk about watts, so if you change your 169 00:08:11,700 --> 00:08:15,450 lightbulb, usually you see the intensity in terms of watts. 170 00:08:15,450 --> 00:08:18,560 But in terms of SI units, which become much more useful 171 00:08:18,560 --> 00:08:21,230 if you're actually trying to use intensity in a problem and 172 00:08:21,230 --> 00:08:23,690 cancel out your units, we're just talking about joules per 173 00:08:23,690 --> 00:08:27,230 second is what intensity is. 174 00:08:27,230 --> 00:08:29,950 So at this point, you should be able to have all the 175 00:08:29,950 --> 00:08:32,900 background you need on the photoelectric effect to solve 176 00:08:32,900 --> 00:08:36,380 any type of problem that we throw at you, and you see 177 00:08:36,380 --> 00:08:38,950 three on this problem set, and we'll probably give you one 178 00:08:38,950 --> 00:08:42,560 more on your next problem set, and the reason we ask you so 179 00:08:42,560 --> 00:08:44,900 many questions about the photoelectric effect is 180 00:08:44,900 --> 00:08:48,870 because it actually is very similar to ionization energy 181 00:08:48,870 --> 00:08:52,030 that we'll talk about later, also problems dealing with 182 00:08:52,030 --> 00:08:52,600 photoelectron spectroscopy. 183 00:08:52,600 --> 00:08:57,340 So, we want to make sure that this is something the entire 184 00:08:57,340 --> 00:08:59,590 class is 100% solid on. 185 00:08:59,590 --> 00:09:02,200 Sometimes the questions are worded quite differently, so I 186 00:09:02,200 --> 00:09:04,000 just want to sum up here the different ways 187 00:09:04,000 --> 00:09:05,220 they could be worded. 188 00:09:05,220 --> 00:09:08,270 For example, if we talk about photons, of course, we also 189 00:09:08,270 --> 00:09:11,950 just mean light, sometimes we refer to this as 190 00:09:11,950 --> 00:09:15,410 electromagnetic radiation, and there's several ways that you 191 00:09:15,410 --> 00:09:17,830 might be asked this in a problem or that you might be 192 00:09:17,830 --> 00:09:19,180 asked to answer. 193 00:09:19,180 --> 00:09:22,210 Sometimes we might just directly tell you the energy 194 00:09:22,210 --> 00:09:25,670 of the photon -- that's probably the easiest scenario, 195 00:09:25,670 --> 00:09:27,860 because when we think about work functions those are 196 00:09:27,860 --> 00:09:30,830 usually reported in energy. 197 00:09:30,830 --> 00:09:33,780 So since that's the easiest scenario, you can probably be 198 00:09:33,780 --> 00:09:36,170 sure it's not going to be too frequently that you're just 199 00:09:36,170 --> 00:09:38,710 given the energy, right, that might be too easy. 200 00:09:38,710 --> 00:09:42,740 So really what we'll probably do is instead either give you 201 00:09:42,740 --> 00:09:45,590 the wavelength or the frequency and you'll go ahead 202 00:09:45,590 --> 00:09:48,640 and calculate the energy from there. 203 00:09:48,640 --> 00:09:51,760 In terms of talking about the electrons, I wanted to point 204 00:09:51,760 --> 00:09:54,500 out that in the book and other places you might see electrons 205 00:09:54,500 --> 00:09:57,190 referred to as photoelectrons. 206 00:09:57,190 --> 00:10:00,030 That's sometimes confusing for people, because it seems like 207 00:10:00,030 --> 00:10:02,260 okay, is it a photon or is it an electron. 208 00:10:02,260 --> 00:10:04,820 I just want to clarify that it is an electron. 209 00:10:04,820 --> 00:10:07,520 It's called this just because it's an electron that results 210 00:10:07,520 --> 00:10:10,510 when an electron absorbs a photon's worth of energy, so 211 00:10:10,510 --> 00:10:12,460 thus it's a photoelectron. 212 00:10:12,460 --> 00:10:16,650 And if we talk about electrons or photoelectrons, again we 213 00:10:16,650 --> 00:10:19,650 can describe it in terms of energy, we can talk about 214 00:10:19,650 --> 00:10:22,740 velocity, and from there, of course, you can figure out the 215 00:10:22,740 --> 00:10:26,580 energy from 1/2 m v squared, and actually we can also 216 00:10:26,580 --> 00:10:29,380 describe the electron in terms of wavelength. 217 00:10:29,380 --> 00:10:32,610 So you don't actually know this yet from this class, 218 00:10:32,610 --> 00:10:35,350 you'll know it by the end of the class that electrons can, 219 00:10:35,350 --> 00:10:36,700 in fact, have a wavelength. 220 00:10:36,700 --> 00:10:39,870 So once we cover it, it will then be fair game to ask these 221 00:10:39,870 --> 00:10:43,920 photoelectron spectroscopy or these photoelectric effect 222 00:10:43,920 --> 00:10:48,250 questions using the wavelength of the electron. 223 00:10:48,250 --> 00:10:50,460 Also to point out, a lot of times you'll see electron 224 00:10:50,460 --> 00:10:54,560 volts instead of joules, this is the conversion factor here 225 00:10:54,560 --> 00:10:58,210 just so you all have it in your notes. 226 00:10:58,210 --> 00:10:58,460 All right. 227 00:10:58,460 --> 00:11:01,590 So let's test what we, in fact, know about the 228 00:11:01,590 --> 00:11:04,050 photoelectric effect, and before we do that actually, 229 00:11:04,050 --> 00:11:07,630 we're going to calculate what we would predict, so when we 230 00:11:07,630 --> 00:11:09,770 do the demo it will be meaningful and we can tell 231 00:11:09,770 --> 00:11:11,290 whether we're successful or not. 232 00:11:11,290 --> 00:11:13,860 So hopefully we will be successful. 233 00:11:13,860 --> 00:11:17,590 And as I point this out, we now know how to do any kind of 234 00:11:17,590 --> 00:11:20,450 photoelectric effect problem, also this means you should be 235 00:11:20,450 --> 00:11:23,450 able to go back to Monday's notes where we filled in all 236 00:11:23,450 --> 00:11:26,600 those graphs, which were what different scientists were 237 00:11:26,600 --> 00:11:29,750 observing when they were measuring either the frequency 238 00:11:29,750 --> 00:11:35,450 or the intensity of light that was irradiating different 239 00:11:35,450 --> 00:11:38,940 types of metals, and also the number of electrons ejected, 240 00:11:38,940 --> 00:11:41,400 and the kinetic energy of those electrons ejected. 241 00:11:41,400 --> 00:11:43,980 You should be able to maybe print out a blank copy of 242 00:11:43,980 --> 00:11:46,435 those notes from the website and fill in all those graphs 243 00:11:46,435 --> 00:11:49,440 -- not for memorizing them, but now just understanding how 244 00:11:49,440 --> 00:11:51,620 the photoelectric effect works. 245 00:11:51,620 --> 00:11:51,820 All right. 246 00:11:51,820 --> 00:11:54,910 So let's do an in-class problem, and this will be done 247 00:11:54,910 --> 00:11:57,980 with zinc. We have a zinc plate up here, and we're going 248 00:11:57,980 --> 00:12:00,760 to -- in a minute I'll describe how we can probe if 249 00:12:00,760 --> 00:12:02,580 electrons are coming off of it. 250 00:12:02,580 --> 00:12:04,210 But we're going to irradiate it with two 251 00:12:04,210 --> 00:12:05,290 different light sources. 252 00:12:05,290 --> 00:12:09,490 We have a UV lamp right here, which is centered at a 253 00:12:09,490 --> 00:12:11,580 wavelength of 254 nanometers. 254 00:12:11,580 --> 00:12:15,860 And then since we have my red laser pointer, we will also 255 00:12:15,860 --> 00:12:19,310 try with the red laser pointer, which is centered at 256 00:12:19,310 --> 00:12:22,330 wavelength of 700 nanometers. 257 00:12:22,330 --> 00:12:25,320 So, there are a few questions that we need to answer first. 258 00:12:25,320 --> 00:12:30,010 So we want to see, do we expect to eject electrons off 259 00:12:30,010 --> 00:12:32,400 of this metal surface, or do we expect that we don't have 260 00:12:32,400 --> 00:12:33,450 enough energy? 261 00:12:33,450 --> 00:12:35,980 So that means we're going to need to figure out what is the 262 00:12:35,980 --> 00:12:38,840 energy per photon that's emitted by that UV light. 263 00:12:38,840 --> 00:12:41,750 Also, what's the energy per photon of this red laser 264 00:12:41,750 --> 00:12:45,010 pointer, and then it's also worth trying a calculation 265 00:12:45,010 --> 00:12:46,420 dealing with intensity. 266 00:12:46,420 --> 00:12:49,480 So let's also try calculating the numbers of photons that 267 00:12:49,480 --> 00:12:53,430 would be emitted by this laser pointer, if, for example, we 268 00:12:53,430 --> 00:12:56,310 were to use it for 60 seconds and this were a 269 00:12:56,310 --> 00:12:58,380 one milliwatt laser. 270 00:12:58,380 --> 00:13:03,130 So, let's do some of these calculations starting first 271 00:13:03,130 --> 00:13:06,330 with what is the energy per photon, and let's start with 272 00:13:06,330 --> 00:13:10,480 the UV lamp. 273 00:13:10,480 --> 00:13:14,370 So we know that energy is equal to Planck's constant 274 00:13:14,370 --> 00:13:17,490 times nu, but what we know about the lamp is its 275 00:13:17,490 --> 00:13:21,100 wavelength, or the light that's emitted. 276 00:13:21,100 --> 00:13:25,120 We know that nu is equal to c over wavelength. 277 00:13:25,120 --> 00:13:30,130 So we can figure out the energy of each photon emitted 278 00:13:30,130 --> 00:13:39,250 by our UV lamp by saying e is equal to h c over wavelength. 279 00:13:39,250 --> 00:13:41,870 So let's just plug in these numbers here. 280 00:13:41,870 --> 00:13:50,160 That means our energy is equal to 6.626 times 10 to the -34 281 00:13:50,160 --> 00:13:52,810 joules times seconds. 282 00:13:52,810 --> 00:13:59,970 And then we have c, the speed of light, 2.998 times 10 to 283 00:13:59,970 --> 00:14:02,660 the 8 meters per second. 284 00:14:02,660 --> 00:14:06,270 And we want to divide all of that by our wavelength, and to 285 00:14:06,270 --> 00:14:08,750 keep our units the same we'll do meters. 286 00:14:08,750 --> 00:14:18,740 So that's 254 times 10 to the -9 meters. 287 00:14:18,740 --> 00:14:21,420 So hopefully if some of you have your calculators with 288 00:14:21,420 --> 00:14:25,250 you, you can confirm the answer that I got, which is 289 00:14:25,250 --> 00:14:31,410 that the energy is 7.82 times 10 to the -19 joules. 290 00:14:31,410 --> 00:14:33,940 So, remember what we're talking about here is the 291 00:14:33,940 --> 00:14:37,120 amount of energy that's in each photon. 292 00:14:37,120 --> 00:14:41,400 So if we think about the work function for zinc, and the 293 00:14:41,400 --> 00:14:46,180 work function for zinc is 6.9 times 10 to the -19 joules, do 294 00:14:46,180 --> 00:14:49,250 we expect that when we shine our UV light on the zinc, 295 00:14:49,250 --> 00:14:52,050 we'll be able to eject electrons? 296 00:14:52,050 --> 00:14:54,760 What do you think? 297 00:14:54,760 --> 00:14:55,100 Yes. 298 00:14:55,100 --> 00:14:55,790 Good. 299 00:14:55,790 --> 00:15:00,210 OK, anyone disagree? 300 00:15:00,210 --> 00:15:04,700 No, OK and that's correct, because each photon of light 301 00:15:04,700 --> 00:15:07,020 actually has more energy than is 302 00:15:07,020 --> 00:15:08,860 needed to eject an electron. 303 00:15:08,860 --> 00:15:12,380 So, we would expect to see electrons ejected with the UV 304 00:15:12,380 --> 00:15:17,450 light source. 305 00:15:17,450 --> 00:15:25,890 So let's now think about using instead the amount of energy 306 00:15:25,890 --> 00:15:28,580 per photon in that red laser pointer. 307 00:15:28,580 --> 00:15:32,510 So again, we know that energy is equal to h c divided by 308 00:15:32,510 --> 00:15:37,160 wavelength, and energy is equal to -- you have written 309 00:15:37,160 --> 00:15:40,440 out in your notes what the actual value for h c is, but 310 00:15:40,440 --> 00:15:48,610 now our wavelength is 700 times 10 to the -9 meters. 311 00:15:48,610 --> 00:15:54,640 And what we end up with for the energy then is 2.84 times 312 00:15:54,640 --> 00:15:58,880 10 to the -19 joules. 313 00:15:58,880 --> 00:15:59,140 All right. 314 00:15:59,140 --> 00:16:01,460 So please raise your hand now if you think there'll be 315 00:16:01,460 --> 00:16:05,220 sufficient energy to eject electrons 316 00:16:05,220 --> 00:16:08,480 from the metal surface? 317 00:16:08,480 --> 00:16:11,130 And raise your hands if you think there won't be. 318 00:16:11,130 --> 00:16:11,770 OK. 319 00:16:11,770 --> 00:16:13,740 Good hand raising technique. 320 00:16:13,740 --> 00:16:14,380 Yes. 321 00:16:14,380 --> 00:16:18,090 In fact, there is not enough energy in a single photon to 322 00:16:18,090 --> 00:16:23,780 go ahead and eject an electron from this zinc surface. 323 00:16:23,780 --> 00:16:31,260 So our last question we ask is what's the total number of 324 00:16:31,260 --> 00:16:34,330 photons emitted if we give this given 325 00:16:34,330 --> 00:16:36,770 intensity for 60 seconds? 326 00:16:36,770 --> 00:16:39,750 So, keep in mind that one milliwatt is just the same as 327 00:16:39,750 --> 00:16:44,660 saying 1 times 10 to the -3 joules per second. 328 00:16:44,660 --> 00:16:52,250 So we have 1 times 10 to the -3 joules per second, and we 329 00:16:52,250 --> 00:16:57,300 want to multiply that by -- or cancel out how much energy we 330 00:16:57,300 --> 00:17:01,020 have per photon, first of all, so how much energy do we have 331 00:17:01,020 --> 00:17:03,360 per photon if we're talking about the red laser pointer? 332 00:17:03,360 --> 00:17:06,720 Right. 333 00:17:06,720 --> 00:17:08,910 So this value right here. 334 00:17:08,910 --> 00:17:15,860 So for every photon we have 2.84 times 335 00:17:15,860 --> 00:17:18,440 10 to the -19 joules. 336 00:17:18,440 --> 00:17:23,130 We're saying let's do this for 60 seconds. 337 00:17:23,130 --> 00:17:26,780 So what we end up with for the number of photons in this 338 00:17:26,780 --> 00:17:34,980 laser beam of light is 2.1 times 10 to the 17 photons. 339 00:17:34,980 --> 00:17:37,900 So this gives you a little bit of an idea of just how many 340 00:17:37,900 --> 00:17:41,390 individual photons there are in a laser beam of light. 341 00:17:41,390 --> 00:17:44,200 This is a huge number of photons. 342 00:17:44,200 --> 00:17:47,290 So the question is does this matter? 343 00:17:47,290 --> 00:17:48,990 How about if we shoot this many photons? 344 00:17:48,990 --> 00:17:51,190 Does it make any difference at all in terms of whether we can 345 00:17:51,190 --> 00:17:53,220 eject an electron? 346 00:17:53,220 --> 00:17:54,720 No, it actually doesn't. 347 00:17:54,720 --> 00:17:57,610 It is an impressive number, it is very, very large, but it 348 00:17:57,610 --> 00:17:58,990 doesn't make a difference. 349 00:17:58,990 --> 00:18:02,810 So we see that we do not eject electrons in the case of the 350 00:18:02,810 --> 00:18:07,050 laser pointer, even if we have this intensity, even for 60 351 00:18:07,050 --> 00:18:10,090 seconds -- it is still not related to the energy of an 352 00:18:10,090 --> 00:18:12,930 individual photon, so we won't see an effect. 353 00:18:12,930 --> 00:18:14,670 All right. 354 00:18:14,670 --> 00:18:18,780 So let's hope that we can confirm our predictions here 355 00:18:18,780 --> 00:18:22,100 by actually doing it, and Professor Drennen well help me 356 00:18:22,100 --> 00:18:26,370 out by loading up our device with electrons, and I'll 357 00:18:26,370 --> 00:18:32,580 explain exactly what our set up here is as she does that. 358 00:18:32,580 --> 00:18:35,880 So basically what we have is this zinc plate here. 359 00:18:35,880 --> 00:18:38,570 So that's what we want to load up with electrons, and then 360 00:18:38,570 --> 00:18:40,960 see if we can remove some. 361 00:18:40,960 --> 00:18:44,020 But that's a little bit hard, we aren't all that good at 362 00:18:44,020 --> 00:18:46,520 seeing electrons with our eyes, so we need to think of a 363 00:18:46,520 --> 00:18:47,920 way to do this. 364 00:18:47,920 --> 00:18:49,790 So what she's going to do is start loading up the 365 00:18:49,790 --> 00:18:53,320 electrons, and you see this wand here move slowly, and it 366 00:18:53,320 --> 00:18:57,850 takes a while to do it, start become perpendicular. 367 00:18:57,850 --> 00:19:01,600 The reason for that is because all of this is connected, so 368 00:19:01,600 --> 00:19:04,610 we're moving electrons everywhere in the system. 369 00:19:04,610 --> 00:19:08,450 And since we have two bars that are together like this, 370 00:19:08,450 --> 00:19:11,160 once they're both loaded up with electrons there's going 371 00:19:11,160 --> 00:19:14,260 to be negative charges that repel, so the electrons will 372 00:19:14,260 --> 00:19:17,120 want to get as far away as possible, and they're on their 373 00:19:17,120 --> 00:19:21,950 slow way to doing that, to getting as far away from each 374 00:19:21,950 --> 00:19:22,700 other as possible. 375 00:19:22,700 --> 00:19:26,590 And if we do, in fact, hit it with light to get the 376 00:19:26,590 --> 00:19:30,120 electrons off, it will go back to the straight up in 377 00:19:30,120 --> 00:19:32,370 position, or if it gets knocked hard enough 378 00:19:32,370 --> 00:19:34,240 it does that, too. 379 00:19:34,240 --> 00:19:41,280 Sometimes it's easier actually not touch it to the metal, I 380 00:19:41,280 --> 00:19:42,030 should have-- 381 00:19:42,030 --> 00:19:48,470 TA: It's hard to see if it's moving or not. 382 00:19:48,470 --> 00:19:53,130 PROFESSOR: So, our technology TA is also our paper TA. 383 00:19:53,130 --> 00:19:53,340 Darcy will hold up the yellow paper. 384 00:19:53,340 --> 00:19:55,170 Right, there we go, now we're making a little progress. 385 00:19:55,170 --> 00:20:00,760 TA: It was moving before, you just couldn't see it. 386 00:20:00,760 --> 00:20:01,170 PROFESSOR: So, does anyone have any questions about the 387 00:20:01,170 --> 00:20:03,860 set up here, does it make sense what we're looking for 388 00:20:03,860 --> 00:20:08,250 the bar to go back once we make some progress. 389 00:20:08,250 --> 00:20:11,520 This demo works wonderfully in the winter months in Boston 390 00:20:11,520 --> 00:20:15,340 when we will all be full of static at all times. 391 00:20:15,340 --> 00:20:18,370 We're still close enough to the summer that the air is not 392 00:20:18,370 --> 00:20:22,110 just filling us up with extra static electricity, so it's a 393 00:20:22,110 --> 00:20:23,600 little more challenging here. 394 00:20:23,600 --> 00:20:25,270 We'll try to make this happen only once. 395 00:20:25,270 --> 00:20:50,760 I think that's probably, if we can get one more. 396 00:20:50,760 --> 00:20:52,410 So, it works, I think it's just getting too much 397 00:20:52,410 --> 00:20:52,680 [INAUDIBLE]. 398 00:20:52,680 --> 00:21:09,430 Sometimes it helps to not actually hit the metal, just 399 00:21:09,430 --> 00:21:11,970 put it next to the -- there we go. 400 00:21:11,970 --> 00:21:13,090 I wonder if there's some UV light out of this new lighting 401 00:21:13,090 --> 00:21:16,510 set up in our classroom here. 402 00:21:16,510 --> 00:21:29,020 That would be a little tricky. 403 00:21:29,020 --> 00:21:29,290 All right. 404 00:21:29,290 --> 00:21:32,830 I think this -- if this sticks. 405 00:21:32,830 --> 00:21:33,750 Yeah, it's the pressure of the paper. 406 00:21:33,750 --> 00:21:36,250 I think that's good enough, we'll be able to see. 407 00:21:36,250 --> 00:21:38,560 If you can keep showing that, though, Darcy, we'll try 408 00:21:38,560 --> 00:21:39,980 different scenarios and I'll try not to put 409 00:21:39,980 --> 00:21:42,970 laser in your eye. 410 00:21:42,970 --> 00:21:47,050 Actually you can look down as well as an added precaution. 411 00:21:47,050 --> 00:21:48,190 OK, let's try it with that. 412 00:21:48,190 --> 00:21:49,930 That's enough then. 413 00:21:49,930 --> 00:21:51,970 So, the first thing we're going to try is with the red 414 00:21:51,970 --> 00:21:54,440 laser pointer, because that we are expecting not to have an 415 00:21:54,440 --> 00:21:56,930 effect, and that will prevent Professor Drennen from having 416 00:21:56,930 --> 00:22:00,220 to charge up our apparatus again. 417 00:22:00,220 --> 00:22:03,180 So, Darcy will look down at this moment and we will hit 418 00:22:03,180 --> 00:22:06,930 this with the laser pointer, and what we see is nothing is 419 00:22:06,930 --> 00:22:08,570 happening at all. 420 00:22:08,570 --> 00:22:10,130 OK, good. 421 00:22:10,130 --> 00:22:12,220 Control one working. 422 00:22:12,220 --> 00:22:15,410 So now very carefully take our UV light source -- 423 00:22:15,410 --> 00:22:20,550 Darcy again will divert her eyes and her skin. 424 00:22:20,550 --> 00:22:37,230 Let me make sure this is actually on. 425 00:22:37,230 --> 00:22:42,660 OK, so we've got UV light here, and let's see what we 426 00:22:42,660 --> 00:22:45,140 can see, and we lose electrons, if 427 00:22:45,140 --> 00:22:47,340 that's what's happening. 428 00:22:47,340 --> 00:22:50,310 And it often doesn't go all the way, because actually this 429 00:22:50,310 --> 00:22:52,190 device gets stuck right there. 430 00:22:52,190 --> 00:22:55,830 So let's charge it up again and see if we can check again. 431 00:22:55,830 --> 00:22:57,170 But did you see movement? 432 00:22:57,170 --> 00:23:08,510 Are you buying our story here? 433 00:23:08,510 --> 00:23:10,560 This is actually very representative of when you do 434 00:23:10,560 --> 00:23:14,420 research in the laboratory, you will find often things do 435 00:23:14,420 --> 00:23:17,550 not work quite exactly as they worked 20 minutes ago when you 436 00:23:17,550 --> 00:23:20,610 just checked it in your office, for example. 437 00:23:20,610 --> 00:23:23,100 And sometimes it's a matter of factors that you need to 438 00:23:23,100 --> 00:23:26,860 figure out what it is, and maybe it's that there's extra 439 00:23:26,860 --> 00:23:31,980 light in the room we don't know about. 440 00:23:31,980 --> 00:23:32,460 It might just be -- so, we did get it back to 441 00:23:32,460 --> 00:23:33,540 the starting position. 442 00:23:33,540 --> 00:23:40,510 Next time maybe we'll charge it up before class. 443 00:23:40,510 --> 00:23:41,120 All right. 444 00:23:41,120 --> 00:23:44,460 So we kind of saw what was happening here, you saw it 445 00:23:44,460 --> 00:23:45,710 move a little bit. 446 00:23:45,710 --> 00:23:48,920 They'll keep trying to get it going, but maybe we should 447 00:23:48,920 --> 00:23:52,860 move on with our lives here while this is happening, and 448 00:23:52,860 --> 00:23:55,220 we'll click it back at the end, and if we have a nice set 449 00:23:55,220 --> 00:23:58,280 up at any point, I'll just stop and we'll go back and 450 00:23:58,280 --> 00:24:01,100 we'll look at it again. 451 00:24:01,100 --> 00:24:05,480 Since, I think that's just not going to happen right now. 452 00:24:05,480 --> 00:24:16,070 So let's switch, actually, back to our notes. 453 00:24:16,070 --> 00:24:20,170 So, ideally what we did see was, in fact, it does have 454 00:24:20,170 --> 00:24:22,490 enough energy with the UV lamp, it wasn't a dramatic 455 00:24:22,490 --> 00:24:24,690 shift you saw because we didn't start very high and 456 00:24:24,690 --> 00:24:26,270 then it went to that stuck point. 457 00:24:26,270 --> 00:24:29,310 But luckily we had the control of the red laser pointer where 458 00:24:29,310 --> 00:24:30,750 nothing moved at all. 459 00:24:30,750 --> 00:24:33,800 So hopefully you're convinced that your predictions worked 460 00:24:33,800 --> 00:24:38,600 well and you are able to predict what's going on when 461 00:24:38,600 --> 00:24:43,890 you're looking at the photoelectric effect. 462 00:24:43,890 --> 00:24:46,850 So, it turns out that the photoelectric effect is not 463 00:24:46,850 --> 00:24:49,850 the only evidence for the fact that light has these 464 00:24:49,850 --> 00:24:51,740 particle-like characteristics. 465 00:24:51,740 --> 00:24:56,810 And one thing that Einstein put forth is he figured if 466 00:24:56,810 --> 00:24:59,450 well, what we're saying is that light is, in fact, a 467 00:24:59,450 --> 00:25:03,330 stream of particles, each one of those particles or photons 468 00:25:03,330 --> 00:25:05,410 must, therefore, have a momentum. 469 00:25:05,410 --> 00:25:08,520 And that's really neat to think about, because photons, 470 00:25:08,520 --> 00:25:11,080 of course, are massless particles, they have no mass, 471 00:25:11,080 --> 00:25:13,240 so it's neat to think about something that has no mass, 472 00:25:13,240 --> 00:25:15,080 but that actually does have a momentum. 473 00:25:15,080 --> 00:25:19,080 And the relationship that he put forth is that the momentum 474 00:25:19,080 --> 00:25:22,530 is equal to Planck's constant times nu divided by the speed 475 00:25:22,530 --> 00:25:25,790 of light, or it's often more useful for us to think about 476 00:25:25,790 --> 00:25:27,300 it in terms of wavelength. 477 00:25:27,300 --> 00:25:30,190 So, since the speed of light equals lambda nu, we can say 478 00:25:30,190 --> 00:25:34,210 that momentum is equal to h divided by lambda. 479 00:25:34,210 --> 00:25:36,940 And there was experimental evidence that came along that 480 00:25:36,940 --> 00:25:39,410 supported this, and this is called the Compton scattering 481 00:25:39,410 --> 00:25:42,470 experiment, and this was done by Arthur Compton, and 482 00:25:42,470 --> 00:25:47,450 basically what he did was he took x-ray light, which had 483 00:25:47,450 --> 00:25:49,990 some frequency, which was a very high frequency because it 484 00:25:49,990 --> 00:25:53,450 was x-rays, and he shot it at a stationary electron. 485 00:25:53,450 --> 00:25:56,880 And what he was able to observe was that the electrons 486 00:25:56,880 --> 00:25:59,960 scattered and now had some momentum, and that both the 487 00:25:59,960 --> 00:26:06,420 frequency, and therefore, the momentum of the light that he 488 00:26:06,420 --> 00:26:09,090 shot in, went down once it was scattered. 489 00:26:09,090 --> 00:26:13,500 So what he's showing here is, first of all, that the light 490 00:26:13,500 --> 00:26:16,402 has some momentum and when it hits an electron it can 491 00:26:16,402 --> 00:26:20,050 actually transfer some of that momentum to the electron. 492 00:26:20,050 --> 00:26:24,170 So the transfer of momentum from a photon to an electron 493 00:26:24,170 --> 00:26:27,740 is what was being observed, and it was seen as completely 494 00:26:27,740 --> 00:26:30,590 separate evidence to the photoelectric effect that, 495 00:26:30,590 --> 00:26:33,780 yes, in fact, light is behaving in these 496 00:26:33,780 --> 00:26:37,090 particle-like ways. 497 00:26:37,090 --> 00:26:40,940 So up to this point, before it was really established that 498 00:26:40,940 --> 00:26:44,950 yes, light is like a particle sometimes, there was this very 499 00:26:44,950 --> 00:26:48,090 strong distinction between what is 500 00:26:48,090 --> 00:26:49,620 light and what is matter. 501 00:26:49,620 --> 00:26:52,450 And the distinction was when we're talking about light, 502 00:26:52,450 --> 00:26:54,560 light is a wave, and when we're talking about matter, 503 00:26:54,560 --> 00:26:56,100 well, matter is a particle. 504 00:26:56,100 --> 00:26:59,120 And these behave completely separate, they don't overlap 505 00:26:59,120 --> 00:27:02,370 at all in terms of behavior, but then, of course, with the 506 00:27:02,370 --> 00:27:05,260 photoelectric effect with Compton's scattering, what we 507 00:27:05,260 --> 00:27:10,270 see is that, oh actually, sometimes photons behave as if 508 00:27:10,270 --> 00:27:11,410 they're particles. 509 00:27:11,410 --> 00:27:14,150 So now this relationship's beginning to get a little bit 510 00:27:14,150 --> 00:27:17,640 fuzzy in terms of what is the difference between how we 511 00:27:17,640 --> 00:27:19,650 treat light and matter. 512 00:27:19,650 --> 00:27:23,905 And actually, this was taken a step further by Louis de 513 00:27:23,905 --> 00:27:28,410 Broglie who in his PhD thesis, as part of his work as a 514 00:27:28,410 --> 00:27:32,970 graduate student, put forth the idea that, OK, Einstein 515 00:27:32,970 --> 00:27:36,620 says, and everyone agrees that, in fact, light is 516 00:27:36,620 --> 00:27:40,960 particle-like at times, and light, in fact, of course has 517 00:27:40,960 --> 00:27:44,170 a wavelength, and if it has a wavelength we're saying that 518 00:27:44,170 --> 00:27:45,920 it can have momentum. 519 00:27:45,920 --> 00:27:49,290 And what de Broglie said is well, if it's true that light, 520 00:27:49,290 --> 00:27:52,590 which has a wavelength can have momentum, then it must 521 00:27:52,590 --> 00:27:56,650 also be true that matter, which has momentum, also has a 522 00:27:56,650 --> 00:27:58,090 wavelength. 523 00:27:58,090 --> 00:28:01,460 And you can look at this in two different ways. 524 00:28:01,460 --> 00:28:04,370 One is that he's just re-arranged an equation here 525 00:28:04,370 --> 00:28:09,600 and gotten both his PhD thesis and a Nobel Prize, but I think 526 00:28:09,600 --> 00:28:12,170 the more representative way to think about this is the real 527 00:28:12,170 --> 00:28:15,510 revolutionary idea that he put forth, which is that matter 528 00:28:15,510 --> 00:28:19,840 can actually behave as a wave. And in terms of equations that 529 00:28:19,840 --> 00:28:23,670 we use, it's sometimes easier to plug in the fact, since 530 00:28:23,670 --> 00:28:26,050 momentum is equal to mass times velocity. 531 00:28:26,050 --> 00:28:29,610 We can know the wavelength of any matter -- and he's not 532 00:28:29,610 --> 00:28:31,720 limiting this, for example, to electrons. 533 00:28:31,720 --> 00:28:34,140 What de Broglie is saying we can know the wavelength of any 534 00:28:34,140 --> 00:28:36,560 matter at all, as long as we know its 535 00:28:36,560 --> 00:28:38,690 mass and it's velocity. 536 00:28:38,690 --> 00:28:41,670 And Einstein credited de Broglie, which is a fair 537 00:28:41,670 --> 00:28:44,350 statement of lifting a corner of the great veil, because 538 00:28:44,350 --> 00:28:47,540 really there was this fundamental misunderstanding 539 00:28:47,540 --> 00:28:50,490 about what the difference was between matter and light, and 540 00:28:50,490 --> 00:28:54,170 the reality is that they can both be like-particles and 541 00:28:54,170 --> 00:28:57,420 they can both show characteristics of waves. 542 00:28:57,420 --> 00:29:01,900 So I mentioned, however, that in terms of de Broglie's work. 543 00:29:01,900 --> 00:29:05,400 This was Nobel Prize worthy, absolutely, but it was also 544 00:29:05,400 --> 00:29:07,000 his PhD thesis. 545 00:29:07,000 --> 00:29:09,600 So, we can think about what would happen if we're on his 546 00:29:09,600 --> 00:29:12,710 thesis defense, we're on his thesis committee, we would 547 00:29:12,710 --> 00:29:15,970 need to think of some pretty mean, hard, nasty questions to 548 00:29:15,970 --> 00:29:18,190 be asking de Broglie about this theory -- that's what 549 00:29:18,190 --> 00:29:19,540 happens when you defend your thesis. 550 00:29:19,540 --> 00:29:23,620 This is necessary, it's hard to find holes in a Nobel Prize 551 00:29:23,620 --> 00:29:24,580 worthy idea. 552 00:29:24,580 --> 00:29:27,330 But let's just try maybe one of the basic questions they 553 00:29:27,330 --> 00:29:29,980 could ask, and they can say, all right, de Broglie, so you 554 00:29:29,980 --> 00:29:33,180 say that all matter, absolutely all matter has 555 00:29:33,180 --> 00:29:34,350 wave-like behavior. 556 00:29:34,350 --> 00:29:36,920 Why is it that we're never observing this, for example, 557 00:29:36,920 --> 00:29:39,820 why is it the table doesn't defract as we bring 558 00:29:39,820 --> 00:29:40,740 it through the door? 559 00:29:40,740 --> 00:29:45,230 Why don't we see the influence of the wave-like behavior on 560 00:29:45,230 --> 00:29:47,510 every day matter? 561 00:29:47,510 --> 00:29:51,280 So it turns out that he could have picked anything to 562 00:29:51,280 --> 00:29:53,705 explain this, and hopefully done out the calculation, and 563 00:29:53,705 --> 00:29:55,050 we'll do this ourselves. 564 00:29:55,050 --> 00:29:58,830 And the example we'll pick is considering, for example, a 565 00:29:58,830 --> 00:29:59,170 Matsuzaka fastball. 566 00:29:59,170 --> 00:30:05,670 So, many of you are new to the Boston area, now I still 567 00:30:05,670 --> 00:30:08,800 realize, and I want to let you know it's not required that 568 00:30:08,800 --> 00:30:12,180 you be a Red Sox fan to be at MIT. 569 00:30:12,180 --> 00:30:18,020 We do encourage it, however, and in general, I find you 570 00:30:18,020 --> 00:30:21,160 don't have to give up that old team, you can keep your old 571 00:30:21,160 --> 00:30:23,950 team, even if it's teams I won't name, just 572 00:30:23,950 --> 00:30:25,670 keep them to the side. 573 00:30:25,670 --> 00:30:28,690 And you can join on to the Red Sox nation on top of that, and 574 00:30:28,690 --> 00:30:31,210 part of being a good Red Sox fan is knowing the statistics 575 00:30:31,210 --> 00:30:32,300 of your team. 576 00:30:32,300 --> 00:30:34,410 For example, if we're talking about a pitcher, like 577 00:30:34,410 --> 00:30:37,090 Matsuzaka, we might want to know the speed 578 00:30:37,090 --> 00:30:38,950 of his average fastball. 579 00:30:38,950 --> 00:30:39,960 We might want to know his ERA. 580 00:30:39,960 --> 00:30:43,758 If you're really into it and you're at MIT, maybe you want 581 00:30:43,758 --> 00:30:47,490 to know the wavelength of these average fastballs. 582 00:30:47,490 --> 00:30:50,780 So, let's go ahead and look at that. 583 00:30:50,780 --> 00:30:52,920 So, if we're trying to figure out the wavelength of a 584 00:30:52,920 --> 00:30:56,790 Matsuzaka fastball, we need to consider the velocity first, 585 00:30:56,790 --> 00:30:58,890 which is 42 miles per hour. 586 00:30:58,890 --> 00:31:01,510 We don't usually do our chemistry calculations in 587 00:31:01,510 --> 00:31:05,220 miles per hour, so let's switch that to 42 meters per 588 00:31:05,220 --> 00:31:08,330 second, so it's -- sorry, it's 94 miles per hour. 589 00:31:08,330 --> 00:31:11,580 And we can use the de Broglie relationship that wavelength 590 00:31:11,580 --> 00:31:15,210 should be equal to h over mass times volume. 591 00:31:15,210 --> 00:31:19,120 And we can put up here Planck's constant -- and I 592 00:31:19,120 --> 00:31:21,870 want to make note that instead of writing joules per second, 593 00:31:21,870 --> 00:31:24,400 I actually wrote out with a joule is. 594 00:31:24,400 --> 00:31:28,640 A joule is a kilogram meter squared per second squared. 595 00:31:28,640 --> 00:31:31,360 Occasionally, you'll find you need to cancel out units, 596 00:31:31,360 --> 00:31:33,970 because, of course, you're always doing unit analysis as 597 00:31:33,970 --> 00:31:36,550 you solve your problems, and sometimes you'll need to 598 00:31:36,550 --> 00:31:38,130 convert joules to kilogram meters 599 00:31:38,130 --> 00:31:40,950 square per second squared. 600 00:31:40,950 --> 00:31:45,220 We divide that by the mass, so 0.12 kilograms, that's the 601 00:31:45,220 --> 00:31:49,450 mass of a regulation baseball for the major leagues, and the 602 00:31:49,450 --> 00:31:53,780 velocity of the baseball is 42 meters per second. 603 00:31:53,780 --> 00:31:55,860 So, we can cross out our units doing our unit analysis. 604 00:31:55,860 --> 00:32:00,500 The seconds cross out, the kilograms cross out, one of 605 00:32:00,500 --> 00:32:03,000 the meters crosses out from the top, so we're left with an 606 00:32:03,000 --> 00:32:04,480 answer in meters. 607 00:32:04,480 --> 00:32:06,650 It's always good when we're looking for a wavelength that 608 00:32:06,650 --> 00:32:08,970 our answer is in a unit of length, 609 00:32:08,970 --> 00:32:10,510 that's a good sign already. 610 00:32:10,510 --> 00:32:12,860 And what we find out is the wavelength of a Matsuzaka 611 00:32:12,860 --> 00:32:20,230 fastball is 1.1 times 10 to the -31 meters. 612 00:32:20,230 --> 00:32:24,640 So, this is really small, this is undetectably small. 613 00:32:24,640 --> 00:32:27,750 And especially when we consider it, what tends to be 614 00:32:27,750 --> 00:32:31,150 important is the size of wavelength in relationship to 615 00:32:31,150 --> 00:32:32,500 its environment. 616 00:32:32,500 --> 00:32:37,240 So 1.1 times 10 to the -31 meters is not, in fact, a 617 00:32:37,240 --> 00:32:40,380 significant number when we're comparing it, for example, to 618 00:32:40,380 --> 00:32:43,790 the length of a ball, or the size of the baseball field. 619 00:32:43,790 --> 00:32:46,940 So that would probably be de Broglie's answer for why, in 620 00:32:46,940 --> 00:32:51,000 fact, we're not observing the wavelength behavior of 621 00:32:51,000 --> 00:32:54,880 material on a day-to-day life. 622 00:32:54,880 --> 00:32:59,920 So, that's for Matsuzaka, and even if you don't memorize all 623 00:32:59,920 --> 00:33:01,690 the wavelengths for all the pitchers. 624 00:33:01,690 --> 00:33:04,360 I would expect, whether you're a Red Sox fan or not, you to 625 00:33:04,360 --> 00:33:07,810 be able to look at a list of different pitchers and their 626 00:33:07,810 --> 00:33:11,370 average velocity for their fastball, and tell me who has 627 00:33:11,370 --> 00:33:13,160 the longest or the shortest wavelength. 628 00:33:13,160 --> 00:33:15,290 You should all be able to know that relationship. 629 00:33:15,290 --> 00:33:19,050 So why don't we go to a clicker question here, and see 630 00:33:19,050 --> 00:33:22,360 if you can tell us this. 631 00:33:22,360 --> 00:33:25,850 So we have 4 different pitchers we're showing here -- 632 00:33:25,850 --> 00:33:27,740 they all have different strengths. 633 00:33:27,740 --> 00:33:30,430 It's not always how fast you throw the fastball, sometimes 634 00:33:30,430 --> 00:33:35,060 it's your different styles or the different ways that you 635 00:33:35,060 --> 00:33:36,510 decide when to throw what. 636 00:33:36,510 --> 00:33:41,020 So, first we have Matsuzaka at 94 miles per hour. 637 00:33:41,020 --> 00:33:43,830 So, click one if you think that he's going to have the 638 00:33:43,830 --> 00:33:44,770 longest wavelength. 639 00:33:44,770 --> 00:33:48,790 Tim Wakefield on the DL right now throws a lot slower, 640 00:33:48,790 --> 00:33:51,460 because he has that tricky knuckle ball, he doesn't need 641 00:33:51,460 --> 00:33:56,220 to throw as fast. Then we have Beckett who can get up 96 just 642 00:33:56,220 --> 00:33:57,690 on a regular old day. 643 00:33:57,690 --> 00:34:01,460 And Timlin who is about 91 miles per 644 00:34:01,460 --> 00:34:03,050 hour, one of our relievers. 645 00:34:03,050 --> 00:34:05,700 So, why don't you take ten seconds to do that. 646 00:34:05,700 --> 00:34:10,040 If you can't decide, Timlin is my favorite ever, so that 647 00:34:10,040 --> 00:34:14,750 would be a good back up choice if you forgot the relationship 648 00:34:14,750 --> 00:34:23,540 between wavelength and the relationship between speed. 649 00:34:23,540 --> 00:34:25,920 It looks like, in fact, people did not forget that 650 00:34:25,920 --> 00:34:29,910 relationship, and only 1% of you humored me. 651 00:34:29,910 --> 00:34:33,730 So, let's see what the correct answer is, and it is, in fact, 652 00:34:33,730 --> 00:34:36,380 Wakefield, right, because there's an inverse 653 00:34:36,380 --> 00:34:40,160 relationship between how fast a particle is going and what 654 00:34:40,160 --> 00:34:41,110 its wavelength is. 655 00:34:41,110 --> 00:34:46,420 So, in terms of wavelength, Wakefield has the largest 656 00:34:46,420 --> 00:34:49,770 wavelength, but in terms of being significant, we're still 657 00:34:49,770 --> 00:34:51,030 not even close. 658 00:34:51,030 --> 00:34:52,550 It's still undetectably small. 659 00:34:52,550 --> 00:34:52,830 Yes. 660 00:34:52,830 --> 00:34:59,890 STUDENT: Why doesn't wavelength go to infinity as 661 00:34:59,890 --> 00:35:05,740 it stops, like a standing [INAUDIBLE]. 662 00:35:05,740 --> 00:35:06,610 PROFESSOR: As it stops. 663 00:35:06,610 --> 00:35:07,670 So, let's think. 664 00:35:07,670 --> 00:35:11,320 I would think that it would approach inifinity, and I 665 00:35:11,320 --> 00:35:12,720 would need to think about it and get back to you in terms 666 00:35:12,720 --> 00:35:15,990 of why we don't actually hit it and see something with an 667 00:35:15,990 --> 00:35:18,230 infinite wavelength. 668 00:35:18,230 --> 00:35:20,660 I'm sure there's some upper limit as there are to most 669 00:35:20,660 --> 00:35:22,470 things, like if we think of wavelengths and different 670 00:35:22,470 --> 00:35:27,700 types of light, there is so large that you can get, but 671 00:35:27,700 --> 00:35:31,870 you would be approaching that level. 672 00:35:31,870 --> 00:35:32,220 All right. 673 00:35:32,220 --> 00:35:36,300 So we can switch back actually to our notes here -- 674 00:35:36,300 --> 00:35:37,910 oh, do we have--? 675 00:35:37,910 --> 00:35:38,390 OK. 676 00:35:38,390 --> 00:35:40,496 We're going to just try this one more time just 677 00:35:40,496 --> 00:35:41,850 so you can see it. 678 00:35:41,850 --> 00:35:44,260 It'll still likely get stuck in that spot, but we'll just 679 00:35:44,260 --> 00:35:51,400 show you one more time the effects of the UV light, and 680 00:35:51,400 --> 00:35:53,970 actually we'll throw in an extra trick here, too. 681 00:35:53,970 --> 00:35:57,080 We know that UV light gets absorbed by glass, so it 682 00:35:57,080 --> 00:35:58,620 shouldn't be able to go through the glass. 683 00:35:58,620 --> 00:36:03,130 So first if Professor Drennen can try it through the glass, 684 00:36:03,130 --> 00:36:05,180 and we see nothing's happening. 685 00:36:05,180 --> 00:36:11,320 Let's move the glass away. 686 00:36:11,320 --> 00:36:12,450 All right. 687 00:36:12,450 --> 00:36:13,650 [APPLAUSE] 688 00:36:13,650 --> 00:36:20,910 PROFESSOR: All right. 689 00:36:20,910 --> 00:36:21,210 Good. 690 00:36:21,210 --> 00:36:24,120 So we can fully believe what our calculations were now, 691 00:36:24,120 --> 00:36:26,600 which is a nice thing to do. 692 00:36:26,600 --> 00:36:28,650 Let's go back to considering the wavelengths 693 00:36:28,650 --> 00:36:30,300 of different objects. 694 00:36:30,300 --> 00:36:33,500 We considered a baseball, but let's also think 695 00:36:33,500 --> 00:36:35,590 about now an electron. 696 00:36:35,590 --> 00:36:39,470 And an electron is something where, in fact, we might be 697 00:36:39,470 --> 00:36:43,100 able to, if we calculate it and see how that works out, 698 00:36:43,100 --> 00:36:46,560 actually observe some of its wave-like properties. 699 00:36:46,560 --> 00:36:50,450 So, if we do this calculation for an electron, saying it 700 00:36:50,450 --> 00:36:53,910 moves at 10 to the 5 meters per second, then what we end 701 00:36:53,910 --> 00:36:59,170 up with for a wavelength is 7 times 10 to the -9 meters. 702 00:36:59,170 --> 00:37:02,700 A lot of times we talk about these kind of distances either 703 00:37:02,700 --> 00:37:05,820 in nanometers or in angstroms so we can say this is 70 704 00:37:05,820 --> 00:37:09,060 angstroms. So this is, first of all, even just on an 705 00:37:09,060 --> 00:37:12,290 absolute scale, this is way, way larger than the 706 00:37:12,290 --> 00:37:15,310 wavelengths we're talking about for baseball. 707 00:37:15,310 --> 00:37:18,560 In addition, if we compare this to the diameter of an 708 00:37:18,560 --> 00:37:21,720 atom, which is on the order of somewhere between one and ten 709 00:37:21,720 --> 00:37:25,230 angstroms, now we're seeing that, in fact, this wavelength 710 00:37:25,230 --> 00:37:28,850 is significantly larger than its environment. 711 00:37:28,850 --> 00:37:34,150 So certainly we would expect to see that it has an effect 712 00:37:34,150 --> 00:37:38,050 in terms of seeing its wave-like properties. 713 00:37:38,050 --> 00:37:42,140 And this was experimentally validated, hopefully, even 714 00:37:42,140 --> 00:37:44,380 more clearly than our experiment here. 715 00:37:44,380 --> 00:37:47,740 And at first this was done by Davidson and Germer, and they 716 00:37:47,740 --> 00:37:53,050 were American scientists who tried defracting electrons 717 00:37:53,050 --> 00:37:54,290 from a nickel crystal. 718 00:37:54,290 --> 00:37:57,570 They did this in Bell Laboratories, and they found 719 00:37:57,570 --> 00:37:59,930 that, in fact, the electronis did defract. 720 00:37:59,930 --> 00:38:02,390 And G.P. Thompson showed a similar thing. 721 00:38:02,390 --> 00:38:05,740 What he did was he defracted electrons through a very thin 722 00:38:05,740 --> 00:38:14,210 gold foil, and this is a picture -- oops, that is not. 723 00:38:14,210 --> 00:38:14,700 OK. 724 00:38:14,700 --> 00:38:19,890 It is a picture from your book here showing the defraction 725 00:38:19,890 --> 00:38:22,780 pattern of an electron going through that gold foil. 726 00:38:22,780 --> 00:38:27,090 So, you can see that, in fact, it's confirmed that an 727 00:38:27,090 --> 00:38:30,010 electron can have both wavelength and 728 00:38:30,010 --> 00:38:31,740 particle-like behavior. 729 00:38:31,740 --> 00:38:35,360 And it turns out that Davidson and Thompson shared a Nobel 730 00:38:35,360 --> 00:38:39,470 Prize for this discovery of seeing the wave-like behavior 731 00:38:39,470 --> 00:38:41,560 of electrons. 732 00:38:41,560 --> 00:38:44,110 So, this is actually kind of neat to point out, because we 733 00:38:44,110 --> 00:38:48,100 all remember J.J. Thomson from our second lecture, and J.J. 734 00:38:48,100 --> 00:38:52,200 Thomson got a Nobel Prize in 1906 for showing that 735 00:38:52,200 --> 00:38:54,480 electrons exist in that they are particles. 736 00:38:54,480 --> 00:38:57,180 And it turns out that G.P. Thompson, well, that's his 737 00:38:57,180 --> 00:39:00,330 son, so we can actually think of this -- and I'm sure this 738 00:39:00,330 --> 00:39:02,670 wasn't the case, but I like to think of it as a little bit of 739 00:39:02,670 --> 00:39:05,450 child rebelling against the father. 740 00:39:05,450 --> 00:39:08,190 So, the father gets a Nobel Prize for showing that an 741 00:39:08,190 --> 00:39:11,430 electron is a particle, and the son says, well, what can I 742 00:39:11,430 --> 00:39:12,570 do to top that? 743 00:39:12,570 --> 00:39:14,870 I'm going to show the exact opposite. 744 00:39:14,870 --> 00:39:17,420 I'm going to say that an electron's a wave no matter 745 00:39:17,420 --> 00:39:19,710 how much my father says differently, and I'm going to 746 00:39:19,710 --> 00:39:22,530 get a Nobel Prize for that, and he does. 747 00:39:22,530 --> 00:39:25,380 But the nice part of the story is, it turns out 748 00:39:25,380 --> 00:39:26,110 they're both right. 749 00:39:26,110 --> 00:39:30,390 An electron is a particle, but an electron's also a wave. So, 750 00:39:30,390 --> 00:39:32,410 father and son, happy ending, they both 751 00:39:32,410 --> 00:39:33,380 have their Noble prizes. 752 00:39:33,380 --> 00:39:38,870 So, what happens now that we, in fact, know 753 00:39:38,870 --> 00:39:40,270 that matter is a wave? 754 00:39:40,270 --> 00:39:43,940 Well, this allows us to try to go back and explain some 755 00:39:43,940 --> 00:39:46,830 phenomena that over the years, mounting evidence was building 756 00:39:46,830 --> 00:39:48,740 that couldn't be explained. 757 00:39:48,740 --> 00:39:51,720 So, for example, when people, and we'll talk about this next 758 00:39:51,720 --> 00:39:54,570 class, were looking at different characteristics 759 00:39:54,570 --> 00:39:57,890 spectra of different atoms, what they were seeing is that 760 00:39:57,890 --> 00:40:00,740 it appeared to be these very discreet lines that were 761 00:40:00,740 --> 00:40:05,430 allowed or not allowed for the different atoms to emit, but 762 00:40:05,430 --> 00:40:07,790 they had no way to explain this using classical physics. 763 00:40:07,790 --> 00:40:13,330 And it turns out that the Schrodinger equation is an 764 00:40:13,330 --> 00:40:17,870 equation of motion in which you're describing a particle 765 00:40:17,870 --> 00:40:21,930 by describing it as a wave. So you're basically having a wave 766 00:40:21,930 --> 00:40:25,180 equation for a particle, and for our purposes we're talking 767 00:40:25,180 --> 00:40:26,890 about a very particular particle. 768 00:40:26,890 --> 00:40:29,390 What we're interested in is the electron. 769 00:40:29,390 --> 00:40:32,310 So basically describing electrons by their wave-like 770 00:40:32,310 --> 00:40:35,050 properties. 771 00:40:35,050 --> 00:40:38,540 And this is Erwin Schrodinger, and this is the equation that 772 00:40:38,540 --> 00:40:43,750 he put forth where we have h hat psi being equal to e psi. 773 00:40:43,750 --> 00:40:47,370 So, let's explain what these are. 774 00:40:47,370 --> 00:40:49,820 So this symbol here is actually what 775 00:40:49,820 --> 00:40:52,080 we call a wave function. 776 00:40:52,080 --> 00:40:55,050 That doesn't mean a whole lot in itself, it will mean more 777 00:40:55,050 --> 00:40:57,120 in about two lectures from now. 778 00:40:57,120 --> 00:40:59,910 But right now, what I want you to be thinking of a wave 779 00:40:59,910 --> 00:41:03,290 function as is just some representation of an electron. 780 00:41:03,290 --> 00:41:06,140 So, it's some way of describing an electron. 781 00:41:06,140 --> 00:41:09,180 Specifically, we'll talk more about this, it's talking about 782 00:41:09,180 --> 00:41:12,350 different orbitals, it's the spatial part of an orbital. 783 00:41:12,350 --> 00:41:15,100 But before we get to that, in terms of thinking just think, 784 00:41:15,100 --> 00:41:17,690 OK, this is representing my particle, this is representing 785 00:41:17,690 --> 00:41:20,580 my electron that's what the wave function is. 786 00:41:20,580 --> 00:41:24,400 This e term here is the energy, or in our case when we 787 00:41:24,400 --> 00:41:27,660 talk about an electron in a hydrogen atom, for example, 788 00:41:27,660 --> 00:41:32,000 the binding energy of that electron to the nucleus. 789 00:41:32,000 --> 00:41:35,110 So, e is binding energy. 790 00:41:35,110 --> 00:41:38,980 And h with the carrot or the hat here, well, that carrot or 791 00:41:38,980 --> 00:41:42,580 hat tell us it must be an operator, and this is called 792 00:41:42,580 --> 00:41:44,300 the Hamiltonian operator. 793 00:41:44,300 --> 00:41:48,140 So when you operate on the wave function, what you end up 794 00:41:48,140 --> 00:41:51,870 with is getting the binding energy of the electron, and 795 00:41:51,870 --> 00:41:55,780 the wave function back out. 796 00:41:55,780 --> 00:41:59,270 When we need to describe the wave function term a little 797 00:41:59,270 --> 00:42:02,620 bit more specifically so we can describe, for example, the 798 00:42:02,620 --> 00:42:06,680 position of the electron, and I just want to mention that we 799 00:42:06,680 --> 00:42:09,230 do have two choices if we're trying to describe this, we 800 00:42:09,230 --> 00:42:11,460 could use cartesian coordinates, or we could use 801 00:42:11,460 --> 00:42:15,870 polar coordinates where we're either talking about x y z or 802 00:42:15,870 --> 00:42:17,950 r theta and phi. 803 00:42:17,950 --> 00:42:20,310 So, I just want to point out that when you look at wave 804 00:42:20,310 --> 00:42:23,270 functions, we are going to be using those spherical polar 805 00:42:23,270 --> 00:42:26,390 coordinates, and the reason is because a very important 806 00:42:26,390 --> 00:42:28,750 interaction here is the interaction between the 807 00:42:28,750 --> 00:42:31,250 electron and the nucleus, which we want to describe the 808 00:42:31,250 --> 00:42:33,800 distance of in terms of r. 809 00:42:33,800 --> 00:42:36,580 So, you can see, it's much easier to describe that as one 810 00:42:36,580 --> 00:42:40,180 term, r here, instead of using both y and z. 811 00:42:40,180 --> 00:42:43,660 Another reason I wanted to point this out in terms of the 812 00:42:43,660 --> 00:42:46,450 polar coordinates that we're using, is I think they're 813 00:42:46,450 --> 00:42:48,170 actually flipped from what you're used 814 00:42:48,170 --> 00:42:49,530 to seeing in physics. 815 00:42:49,530 --> 00:42:52,990 Sometimes different disciplines have different 816 00:42:52,990 --> 00:42:55,410 conventions, which can be very confusing because the whole 817 00:42:55,410 --> 00:42:58,190 point of what's happening now is there's so much interplay 818 00:42:58,190 --> 00:43:01,090 between different disciplines, but still I think this might 819 00:43:01,090 --> 00:43:04,980 be one remaining one where in our case theta is that 820 00:43:04,980 --> 00:43:09,530 distance from z, that angle there, where phi is this 821 00:43:09,530 --> 00:43:11,880 distance or angle from the x-axis. 822 00:43:11,880 --> 00:43:13,930 So just keep it in mind that it's flipped. 823 00:43:13,930 --> 00:43:17,890 It turns out we won't really using it, needing to identify 824 00:43:17,890 --> 00:43:20,080 it on the graph so much in chemistry. 825 00:43:20,080 --> 00:43:22,510 We'll be using the solutions, so you shouldn't have a 826 00:43:22,510 --> 00:43:25,390 problem, but I wanted to point it out so it does not look too 827 00:43:25,390 --> 00:43:27,130 strange to you. 828 00:43:27,130 --> 00:43:30,640 In terms of the Schrodinger equation, we now can write it 829 00:43:30,640 --> 00:43:33,570 in terms of our polar coordinates here. 830 00:43:33,570 --> 00:43:37,830 So we have the operation on the wave function in terms of 831 00:43:37,830 --> 00:43:41,880 r, theta, and phi and remember this e is just our binding 832 00:43:41,880 --> 00:43:44,080 energy for the electron, and we get back 833 00:43:44,080 --> 00:43:46,730 out this wave function. 834 00:43:46,730 --> 00:43:50,470 So, you might ask, this looks pretty simple up here, right, 835 00:43:50,470 --> 00:43:52,060 just with that h hat. 836 00:43:52,060 --> 00:43:54,300 It turns out, we can write it out fully. 837 00:43:54,300 --> 00:43:57,510 It's three different second derivatives in terms of the 838 00:43:57,510 --> 00:44:00,100 three different parameters. 839 00:44:00,100 --> 00:44:02,800 It's a little bit complicated. 840 00:44:02,800 --> 00:44:05,440 You won't have to solve it in this class, you can wait till 841 00:44:05,440 --> 00:44:07,850 you get to 18.03 to start solving these types of 842 00:44:07,850 --> 00:44:10,450 differential equations, and hopefully, you'll all want the 843 00:44:10,450 --> 00:44:14,260 pleasure of actually solving the Schrodinger equation at 844 00:44:14,260 --> 00:44:15,170 some point. 845 00:44:15,170 --> 00:44:18,380 So, just keep taking chemistry, you'll already have 846 00:44:18,380 --> 00:44:20,650 had 18.03 by that point and you'll have the 847 00:44:20,650 --> 00:44:22,500 opportunity to do that. 848 00:44:22,500 --> 00:44:26,170 What I want to point out also is that this h hat, the 849 00:44:26,170 --> 00:44:29,630 Hamiltonian operator written out for the simplest case we 850 00:44:29,630 --> 00:44:32,760 can even imagine, which is a hydrogen atom where we only 851 00:44:32,760 --> 00:44:35,720 have one electron that we're dealing with, and of course, 852 00:44:35,720 --> 00:44:36,480 one nucleus. 853 00:44:36,480 --> 00:44:38,520 So you can imagine it's just going to get more and more 854 00:44:38,520 --> 00:44:43,100 complicated as we get to other types of atoms, and of course, 855 00:44:43,100 --> 00:44:44,620 molecules from there. 856 00:44:44,620 --> 00:44:46,830 So, we just want to appreciate that what we'll be using in 857 00:44:46,830 --> 00:44:49,520 this class is, in fact, the solutions to the Schrodinger 858 00:44:49,520 --> 00:44:53,580 equation, and just so you can be fully thankful for not 859 00:44:53,580 --> 00:44:56,210 having to necessarily solve these as we jump into the 860 00:44:56,210 --> 00:44:59,300 solutions and just knowing that they're out there and 861 00:44:59,300 --> 00:45:00,860 you'll get to solve it at some point, 862 00:45:00,860 --> 00:45:02,260 hopefully, in your careers. 863 00:45:02,260 --> 00:45:04,860 So, we'll pick up with that, with some of the solutions and 864 00:45:04,860 --> 00:45:07,730 starting to talk about energies on Friday.