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