1 00:00:01 --> 00:00:04 The following content is provided by MIT OpenCourseWare 2 00:00:04 --> 00:00:06 under a Creative Commons license. 3 00:00:06 --> 00:00:10 Additional information about our license and MIT 4 00:00:10 --> 00:00:15 OpenCourseWare in general is available at ocw.mit.edu. 5 00:00:15 --> 00:00:17 Where were we, last time? 6 00:00:17 --> 00:00:22 Last time, we said we were setting aside the problem of the 7 00:00:22 --> 00:00:26 structure of the atom. We were setting it aside 8 00:00:26 --> 00:00:30 because we were stuck, and what we had to do was to 9 00:00:30 --> 00:00:34 look at another area of discussion. 10 00:00:34 --> 00:00:38 And that is this wave-particle duality of light and matter, 11 00:00:38 --> 00:00:43 because it is that discussion that is going to give us the 12 00:00:43 --> 00:00:48 clues about how to proceed. We are putting aside the 13 00:00:48 --> 00:00:53 discussion of the structure of the atom all the way until next 14 00:00:53 --> 00:00:57 Wednesday, because next Monday, I was reminded, 15 00:00:57 --> 00:01:10 is a student holiday. [APPLAUSE] 16 00:01:10 --> 00:01:14 And so we started. We talked about the wave-like 17 00:01:14 --> 00:01:19 properties of light. We said that the property of 18 00:01:19 --> 00:01:23 superposition, the fact that you can put waves 19 00:01:23 --> 00:01:29 at the same point in space and their amplitudes add. 20 00:01:29 --> 00:01:33 Since waves have both positive and negative amplitude, 21 00:01:33 --> 00:01:37 that means that you have constructive and destructive 22 00:01:37 --> 00:01:40 interference. And it is those interference 23 00:01:40 --> 00:01:43 phenomena, then, that are evidence for wave-like 24 00:01:43 --> 00:01:46 property. And we did the two-slit 25 00:01:46 --> 00:01:50 experiment to try to give you an example of interference 26 00:01:50 --> 00:01:53 phenomena. We were trying to understand 27 00:01:53 --> 00:01:57 those interference phenomena, and did so in terms of this 28 00:01:57 --> 00:02:02 diagram here. The interference phenomena that 29 00:02:02 --> 00:02:07 we saw was an array, actually a row of bright spots, 30 00:02:07 --> 00:02:10 dark spots, bright spots, dark spots. 31 00:02:10 --> 00:02:15 And we drew these semicircles here around each one of the 32 00:02:15 --> 00:02:18 slits. They represent a little bit of 33 00:02:18 --> 00:02:22 the wave that emanated through those slits. 34 00:02:22 --> 00:02:27 Because those slits are small, then, those waves emanated 35 00:02:27 --> 00:02:33 equally in all directions. That is why these semicircles 36 00:02:33 --> 00:02:37 represent the wave maxima. And what we discovered is that 37 00:02:37 --> 00:02:42 if we looked along this line here, this line which led to 38 00:02:42 --> 00:02:45 this bright spot, that all of the waves along 39 00:02:45 --> 00:02:48 this line were constructively interfering. 40 00:02:48 --> 00:02:53 That is, we had the maximum of the two waves at the same point 41 00:02:53 --> 00:02:58 in space, or the minimum of the two waves at the same point in 42 00:02:58 --> 00:03:02 space. And we noticed that everywhere 43 00:03:02 --> 00:03:05 along this line, where we had that constructive 44 00:03:05 --> 00:03:08 interference, the difference in the distance 45 00:03:08 --> 00:03:10 of the waves traveled was one lambda. 46 00:03:10 --> 00:03:13 We noticed, here, that everywhere along this line 47 00:03:13 --> 00:03:17 that led to a very bright spot, we had constructive 48 00:03:17 --> 00:03:20 interference. And the difference in distance 49 00:03:20 --> 00:03:23 traveled by those two waves was two lambda. 50 00:03:23 --> 00:03:25 And, likewise, up here, along this line, 51 00:03:25 --> 00:03:31 the difference in the distance traveled was zero lambda. 52 00:03:31 --> 00:03:34 And from just that, in a sense, qualitative 53 00:03:34 --> 00:03:37 observation, we drew a conclusion. 54 00:03:37 --> 00:03:41 And that conclusion was in order to get maximum 55 00:03:41 --> 00:03:46 constructive interference, a condition that had obtain, 56 00:03:46 --> 00:03:50 is that the difference in the distance traveled by the two 57 00:03:50 --> 00:03:55 waves has to be an integral multiple of the wavelength. 58 00:03:55 --> 00:03:59 N could be 0, 1, 2, 3, etc. 59 00:03:59 --> 00:04:03 And so, the very bright spot here that always bisects the two 60 00:04:03 --> 00:04:06 slits, since N is 0, we call that the zero-order 61 00:04:06 --> 00:04:10 interference feature, or the zero-order fraction 62 00:04:10 --> 00:04:13 feature. The bright spot that is either 63 00:04:13 --> 00:04:17 to the left or to the right or up or down of that center bright 64 00:04:17 --> 00:04:21 spot is the first-order diffraction feature or the 65 00:04:21 --> 00:04:23 first-order interference feature. 66 00:04:23 --> 00:04:28 And then the second bright spot up or down from the center is a 67 00:04:28 --> 00:04:32 second-order diffraction feature. 68 00:04:32 --> 00:04:35 And so on and so on. And in recitation section, 69 00:04:35 --> 00:04:40 what you also should have done, is you should have reasoned 70 00:04:40 --> 00:04:45 through what the condition was for destructive interference. 71 00:04:45 --> 00:04:50 That is in between these bright spots, you have dark spots as a 72 00:04:50 --> 00:04:53 result of destructive interference. 73 00:04:53 --> 00:04:58 And that results because, say, right here you get a dark 74 00:04:58 --> 00:05:02 spot -- Right here at that point you 75 00:05:02 --> 00:05:07 would see the maximum of one wave at the same point in space 76 00:05:07 --> 00:05:12 as the minimum of the other, and so they exactly cancel. 77 00:05:12 --> 00:05:17 And so by just analyzing what waves were destructively 78 00:05:17 --> 00:05:21 interfering, you should have come up with a general 79 00:05:21 --> 00:05:24 expression for destructive interference, 80 00:05:24 --> 00:05:27 of N plus one-half, that quanity, 81 00:05:27 --> 00:05:32 times lambda. That is your general condition 82 00:05:32 --> 00:05:37 for destructive interference, the difference in the distance 83 00:05:37 --> 00:05:41 traveled by the two waves. This kind of diagram here we 84 00:05:41 --> 00:05:45 are also going to see on Friday, because this interference 85 00:05:45 --> 00:05:49 phenomenon is the property associated with waves. 86 00:05:49 --> 00:05:54 And what we are going to do is see this diagram again when we 87 00:05:54 --> 00:06:00 scatter electrons for particles. We are going to see that 88 00:06:00 --> 00:06:04 particles, also, will destructively and 89 00:06:04 --> 00:06:09 constructively interfere. They also have wave-like 90 00:06:09 --> 00:06:13 properties. That is what we will do on 91 00:06:13 --> 00:06:15 Friday. We have established, 92 00:06:15 --> 00:06:20 now, the wave-like properties of radiation, 93 00:06:20 --> 00:06:26 so I would like to move on and talk about the evidence for the 94 00:06:26 --> 00:06:31 particle-like nature of radiation. 95 00:06:31 --> 00:06:36 96 00:06:36 --> 00:06:41 The evidence for the particle-like nature of 97 00:06:41 --> 00:06:48 radiation comes from an effect called the photoelectric effect. 98 00:06:48 --> 00:06:53 Shortly after Thompson discovered the electron, 99 00:06:53 --> 00:07:00 scientists were noticing that if you took a metal and shined 100 00:07:00 --> 00:07:06 radiation on that metal, that indeed electrons were 101 00:07:06 --> 00:07:10 emitted. Electrons came off. 102 00:07:10 --> 00:07:14 These were called photoelectrons. 103 00:07:14 --> 00:07:20 However, the radiation that you shined on the metal had to have 104 00:07:20 --> 00:07:26 a frequency nu that was greater than or equal to some threshold 105 00:07:26 --> 00:07:32 frequency, nu nought. That is, if you took radiation 106 00:07:32 --> 00:07:38 of some frequency here, nu, that was less than this 107 00:07:38 --> 00:07:43 threshold frequency, well, you did not get any 108 00:07:43 --> 00:07:48 electrons off. Well, another way to kind of 109 00:07:48 --> 00:07:54 understand that data or that effect is to just plot the 110 00:07:54 --> 00:08:01 number of the electrons that come off as a function of the 111 00:08:01 --> 00:08:08 frequency of the radiation. And so at low frequency, 112 00:08:08 --> 00:08:12 there are no electrons, but all of a sudden you get to 113 00:08:12 --> 00:08:16 nu nought, and then electrons start coming off. 114 00:08:16 --> 00:08:21 And no matter how high you increase the frequency here, 115 00:08:21 --> 00:08:25 the number of electrons that come off remains the same, 116 00:08:25 --> 00:08:30 remains constant. And it turned out that for the 117 00:08:30 --> 00:08:34 metals that were looked at, at that time, 118 00:08:34 --> 00:08:38 the threshold frequency, here, was in the UV range of 119 00:08:38 --> 00:08:43 the electromagnetic spectrum. Well, in addition to just 120 00:08:43 --> 00:08:47 measuring the number of electrons and generally 121 00:08:47 --> 00:08:52 observing this effect, scientists did not understand 122 00:08:52 --> 00:08:56 what was going on. So they just started measuring 123 00:08:56 --> 00:09:02 everything they could think about measuring. 124 00:09:02 --> 00:09:06 And one quantity that they measured was the kinetic energy 125 00:09:06 --> 00:09:10 of these electrons that were being emitted. 126 00:09:10 --> 00:09:15 And so you take kinetic energy here, KE, as a function of the 127 00:09:15 --> 00:09:18 frequency. They found that at low 128 00:09:18 --> 00:09:22 frequency, again, there is no kinetic energy, 129 00:09:22 --> 00:09:27 because there are no electrons. And then at some frequency, 130 00:09:27 --> 00:09:32 all of a sudden electrons started coming off. 131 00:09:32 --> 00:09:38 And the kinetic energy of those electrons seemed to increase 132 00:09:38 --> 00:09:43 with the frequency once past that threshold frequency, 133 00:09:43 --> 00:09:47 nu nought. Well, this was really another 134 00:09:47 --> 00:09:51 one of these conundrums, here, at that time, 135 00:09:51 --> 00:09:57 because classical physics, classical electromagnetism, 136 00:09:57 --> 00:10:04 classical physics had no way of explaining these data. 137 00:10:04 --> 00:10:06 And, in fact, what classical physics 138 00:10:06 --> 00:10:10 predicted is that the kinetic energy of these electrons, 139 00:10:10 --> 00:10:14 that that kinetic energy should have nothing to do with the 140 00:10:14 --> 00:10:18 frequency of the light. That is, the kinetic energy was 141 00:10:18 --> 00:10:21 constant. As you increased the frequency 142 00:10:21 --> 00:10:24 of the light, classical physics would tell 143 00:10:24 --> 00:10:28 you that the kinetic energy should not be affected by the 144 00:10:28 --> 00:10:33 frequency of the light. There was nothing in the 145 00:10:33 --> 00:10:38 classical way of thinking, classical electromagnetism that 146 00:10:38 --> 00:10:43 connected the frequency of the light to the kind of energy, 147 00:10:43 --> 00:10:48 to the kinetic energy. There was no way for blue light 148 00:10:48 --> 00:10:52 to make the electrons have a larger kinetic energy, 149 00:10:52 --> 00:10:57 and for blue light to have an effect on the kinetic energy, 150 00:10:57 --> 00:11:04 and red light to not have an effect on the kinetic energy. 151 00:11:04 --> 00:11:07 In addition, what classical physics 152 00:11:07 --> 00:11:13 predicted is that the kinetic energy of the electrons should 153 00:11:13 --> 00:11:17 be dependent on the intensity of the light. 154 00:11:17 --> 00:11:22 That is, the more and more intense the radiation on the 155 00:11:22 --> 00:11:28 metal, the more and more kinetic energy those electrons should 156 00:11:28 --> 00:11:31 have. Because, after all, 157 00:11:31 --> 00:11:36 if you increase the intensity of the light going into the 158 00:11:36 --> 00:11:41 metal, you are putting more and more energy into it. 159 00:11:41 --> 00:11:45 That should be reflected in just how energetic those 160 00:11:45 --> 00:11:49 electrons were picked out. The more energy in, 161 00:11:49 --> 00:11:54 the electrons ought to come out with larger and larger kinetic 162 00:11:54 --> 00:11:58 energy. Of course, the observation was 163 00:11:58 --> 00:12:03 that the kinetic energy of the electrons had nothing to do with 164 00:12:03 --> 00:12:09 the intensity of light. The kinetic energy of the 165 00:12:09 --> 00:12:14 electrons did not increase as you made the light brighter and 166 00:12:14 --> 00:12:18 brighter. As you put more and more energy 167 00:12:18 --> 00:12:21 in, the kinetic energy remained the same. 168 00:12:21 --> 00:12:26 It didn't have an effect. This was a real conundrum here. 169 00:12:26 --> 00:12:31 The known classical physics was making predictions really just 170 00:12:31 --> 00:12:36 contrary to what was being observed. 171 00:12:36 --> 00:12:41 These data, here, of the kinetic energy versus 172 00:12:41 --> 00:12:45 the frequency, were around for a few years 173 00:12:45 --> 00:12:50 before Einstein took a look at them in 1905, 174 00:12:50 --> 00:12:56 a hundred years ago. And he looked at these data for 175 00:12:56 --> 00:13:03 many different metals. Here is some data for metal A, 176 00:13:03 --> 00:13:07 for example, and here is some data for metal 177 00:13:07 --> 00:13:09 B. And, in both cases, 178 00:13:09 --> 00:13:15 it certainly looked like the kinetic energy was linearly 179 00:13:15 --> 00:13:19 dependent on the frequency of the radiation. 180 00:13:19 --> 00:13:25 But what was different for the two different metals was the 181 00:13:25 --> 00:13:30 threshold frequency here, nu nought. 182 00:13:30 --> 00:13:36 What Einstein did was, he went and fitted a straight 183 00:13:36 --> 00:13:43 line to these data, y equals mx plus b. 184 00:13:43 --> 00:13:46 And when he did that, 185 00:13:46 --> 00:13:51 and he went to calculate the slope here, m, 186 00:13:51 --> 00:13:59 of these lines, he thought "very interesting." 187 00:13:59 --> 00:14:05 Because the slope of those lines was 6.626x10^-34 joule 188 00:14:05 --> 00:14:09 seconds. The slope of those lines was 189 00:14:09 --> 00:14:14 something called Planck's constant, h. 190 00:14:14 --> 00:14:19 You say so what? Well, the reason he was so 191 00:14:19 --> 00:14:25 interested in this is because just a few years earlier, 192 00:14:25 --> 00:14:31 there was a scientist by the name of Max Planck who was 193 00:14:31 --> 00:14:38 interested in understanding what was called the black-body 194 00:14:38 --> 00:14:44 radiation data. What is a black-body? 195 00:14:44 --> 00:14:47 Well, let's just, for simplicity purposes, 196 00:14:47 --> 00:14:53 think of the black-body as the burner on an electric stove. 197 00:14:53 --> 00:14:58 What you know is that if you turn up the voltage on that 198 00:14:58 --> 00:15:04 burner, the burner gets hot. It increased in temperature. 199 00:15:04 --> 00:15:07 And you increase the temperature, and sooner or 200 00:15:07 --> 00:15:10 later, that burner is glowing bright red. 201 00:15:10 --> 00:15:13 And you increase the temperature some more, 202 00:15:13 --> 00:15:16 and the burner is glowing a brighter red. 203 00:15:16 --> 00:15:19 And you increase it some more, and it is glowing orange. 204 00:15:19 --> 00:15:23 And you increase it some more, which you shouldn't do, 205 00:15:23 --> 00:15:27 and it's glowing yellow. And then if you could increase 206 00:15:27 --> 00:15:31 it some more, it's glowing white. 207 00:15:31 --> 00:15:34 What is happening, as you increase the 208 00:15:34 --> 00:15:39 temperature, is that the radiation from that black-body, 209 00:15:39 --> 00:15:44 this is the black-body radiation, is increasing in 210 00:15:44 --> 00:15:47 intensity. But, more importantly, 211 00:15:47 --> 00:15:51 the frequency is getting larger and larger. 212 00:15:51 --> 00:15:54 Dark red, bright red, orange, yellow, 213 00:15:54 --> 00:15:57 white, those are all frequencies. 214 00:15:57 --> 00:16:04 The frequency is shifting to higher and higher values. 215 00:16:04 --> 00:16:10 And what was actually done at that time is that the intensity 216 00:16:10 --> 00:16:16 of that black-body radiation, oh, and this material is not in 217 00:16:16 --> 00:16:21 your notes, because you are not responsible for it. 218 00:16:21 --> 00:16:27 I am just trying to make this surprise that Einstein noticed 219 00:16:27 --> 00:16:32 about the slope. I am just trying to put it in 220 00:16:32 --> 00:16:35 some context, why he was so surprised and 221 00:16:35 --> 00:16:39 amazed at it. This black-body intensity here, 222 00:16:39 --> 00:16:43 people had dispersed that radiation and looked at the 223 00:16:43 --> 00:16:46 frequencies that were coming off. 224 00:16:46 --> 00:16:49 This is intensity versus frequency. 225 00:16:49 --> 00:16:54 Here is a general shape of that intensity versus frequency. 226 00:16:54 --> 00:17:00 That was observed for some temperature T one. 227 00:17:00 --> 00:17:05 That was a low temperature. And then, when the temperature 228 00:17:05 --> 00:17:10 was increased and the intensity versus frequency was observed, 229 00:17:10 --> 00:17:14 well, the frequencies generally got higher. 230 00:17:14 --> 00:17:18 This is higher temperature. Intensity goes up. 231 00:17:18 --> 00:17:22 And you increase the temperature some more, 232 00:17:22 --> 00:17:25 and you get even higher frequency. 233 00:17:25 --> 00:17:30 T three is the highest temperature. 234 00:17:30 --> 00:17:36 And that is what the data were. What Planck was trying to do 235 00:17:36 --> 00:17:43 was to understand the origin of that black-body radiation. 236 00:17:43 --> 00:17:48 What he said was that in these black-bodies, 237 00:17:48 --> 00:17:52 in these materials, what there must be are 238 00:17:52 --> 00:17:59 oscillators that are giving off this radiation. 239 00:17:59 --> 00:18:04 But he had another little kick to these oscillators. 240 00:18:04 --> 00:18:10 These oscillators were giving off radiation or energy in 241 00:18:10 --> 00:18:13 chunks, in quanta, in particles. 242 00:18:13 --> 00:18:18 And using that idea, plus some statistical 243 00:18:18 --> 00:18:23 mechanics, he was able to calculate the shapes of these 244 00:18:23 --> 00:18:26 curves. That is, he indeed got, 245 00:18:26 --> 00:18:32 for the lowest temperature here, a curve that looked like 246 00:18:32 --> 00:18:36 this. And for T two, 247 00:18:36 --> 00:18:39 he got a curve that looked like this. 248 00:18:39 --> 00:18:44 And for T three, he got a curve that looked like 249 00:18:44 --> 00:18:47 this. He got the shape right, 250 00:18:47 --> 00:18:50 but he wanted to get the intensity right, 251 00:18:50 --> 00:18:53 too. What he realized he had to do 252 00:18:53 --> 00:18:57 was he essentially needed to have a scaling factor, 253 00:18:57 --> 00:19:04 actually, in front of his frequencies of his oscillators. 254 00:19:04 --> 00:19:07 He wanted a constant. And so he said, 255 00:19:07 --> 00:19:13 what constant do I have to have in order to make all of these 256 00:19:13 --> 00:19:18 data fit the observation? That constant is Planck's 257 00:19:18 --> 00:19:22 constant, his own 6.626x10^-34 joule seconds. 258 00:19:22 --> 00:19:26 There it is. That is Planck's constant. 259 00:19:26 --> 00:19:31 That is it. There is nothing deeper here. 260 00:19:31 --> 00:19:36 It is a natural constant. It comes from our observations 261 00:19:36 --> 00:19:39 of the world, of nature. 262 00:19:39 --> 00:19:42 That is it. It is a fitting constant. 263 00:19:42 --> 00:19:47 And so that is why Einstein was so amazed, here, 264 00:19:47 --> 00:19:54 when he realized this number is the same as what comes out of 265 00:19:54 --> 00:19:57 here. There must be something very 266 00:19:57 --> 00:20:04 fundamental about this h, this Planck's constant. 267 00:20:04 --> 00:20:09 That is the story. Isn't that amazing? 268 00:20:09 --> 00:20:16 What Einstein then proceeded to do, of course, 269 00:20:16 --> 00:20:24 is to write down the equation of the straight line that he 270 00:20:24 --> 00:20:33 just put through these data. And so that equation is the 271 00:20:33 --> 00:20:38 kinetic energy equal to nu, which is our x, 272 00:20:38 --> 00:20:44 h, which is the slope. And then what he found was that 273 00:20:44 --> 00:20:50 the intercept here, of course, is minus h times nu 274 00:20:50 --> 00:20:56 nought. This is plus minus h times nu 275 00:20:56 --> 00:21:02 nought. And that is the equation of a 276 00:21:02 --> 00:21:05 straight line. Of course, he realized, 277 00:21:05 --> 00:21:11 if this is energy on this side, boy, there better be energy on 278 00:21:11 --> 00:21:14 this side. And so this h times nu 279 00:21:14 --> 00:21:18 better be an energy. And since this nu was the 280 00:21:18 --> 00:21:22 frequency of the incident radiation, therefore, 281 00:21:22 --> 00:21:27 h times nu better be the energy of the incident radiation, 282 00:21:27 --> 00:21:32 E sub i. That is where this expression, 283 00:21:32 --> 00:21:36 energy equals h times nu comes from. 284 00:21:36 --> 00:21:40 Nothing more. That is where it comes from, 285 00:21:40 --> 00:21:45 the photoelectric effect. This was the first time that 286 00:21:45 --> 00:21:50 there was any relationship between the frequency of the 287 00:21:50 --> 00:21:53 radiation and the energy of the radiation. 288 00:21:53 --> 00:21:58 In classical electromagnetism, there is no relationship 289 00:21:58 --> 00:22:03 between the frequency and the energy. 290 00:22:03 --> 00:22:08 This was the first time in which that relationship was 291 00:22:08 --> 00:22:12 observed. And what this is saying is the 292 00:22:12 --> 00:22:16 following. This is saying that you can 293 00:22:16 --> 00:22:23 have any frequency of radiation you want, but the corresponding 294 00:22:23 --> 00:22:30 energy comes in these chunks of h times nu. 295 00:22:30 --> 00:22:35 h is a quantization constant. Radiation, nu, 296 00:22:35 --> 00:22:41 is continuous, but the energy that corresponds 297 00:22:41 --> 00:22:48 to any given frequency of radiation is h times nu. 298 00:22:48 --> 00:22:56 This E equals h times nu, here, is thought of as a 299 00:22:56 --> 00:23:02 quantum of energy. A particle of energy. 300 00:23:02 --> 00:23:08 A chunk of energy. Later on, it became the photon, 301 00:23:08 --> 00:23:15 the energy of a photon. If this h times nu here 302 00:23:15 --> 00:23:20 was an energy, well, this h times nu nought 303 00:23:20 --> 00:23:25 also better be an energy. 304 00:23:25 --> 00:23:32 It is the threshold energy. Let's draw an energy level 305 00:23:32 --> 00:23:36 diagram to try to understand that. 306 00:23:36 --> 00:23:40 I am going to plot an energy here. 307 00:23:40 --> 00:23:44 Let's draw an energy level for an electron. 308 00:23:44 --> 00:23:49 This is an electron, here, bound to the metal. 309 00:23:49 --> 00:23:56 And we know that it takes some energy to rip this electron off 310 00:23:56 --> 00:24:01 of the metal. Up here, at higher energy, 311 00:24:01 --> 00:24:03 is going to be our free electron. 312 00:24:03 --> 00:24:06 I will just call it electron-free, 313 00:24:06 --> 00:24:11 not bound to the metal anymore. And the energy that is required 314 00:24:11 --> 00:24:15 to pull the electron off, from the bound state to its 315 00:24:15 --> 00:24:20 free state, is this threshold energy, h times nu nought. 316 00:24:20 --> 00:24:23 This threshold energy is like 317 00:24:23 --> 00:24:27 an ionization potential. You know what the ionization 318 00:24:27 --> 00:24:32 potential is. Just the energy required to 319 00:24:32 --> 00:24:35 pull an electron off an atom or a molecule. 320 00:24:35 --> 00:24:40 However, when we are pulling an electron off a chunk of a metal, 321 00:24:40 --> 00:24:43 we actually have another name for it. 322 00:24:43 --> 00:24:47 It is called the work function. That is just historical, 323 00:24:47 --> 00:24:51 but it is the same thing as an ionization potential. 324 00:24:51 --> 00:24:54 And we often give it the symbol phi. 325 00:24:54 --> 00:24:58 That threshold energy, ionization energy for a metal, 326 00:24:58 --> 00:25:01 is the work function, here, h times nu, 327 00:25:01 --> 00:25:06 phi. The important point here is 328 00:25:06 --> 00:25:11 this. In order to get an electron off 329 00:25:11 --> 00:25:17 of the metal, what you have to have is 330 00:25:17 --> 00:25:24 energy, E sub i. That energy E sub i has to be 331 00:25:24 --> 00:25:32 equal to at least the threshold energy, h times nu nought. 332 00:25:32 --> 00:25:37 If you come in with energy of 333 00:25:37 --> 00:25:41 this radiation, of this wavelength and that 334 00:25:41 --> 00:25:45 frequency, you pulled the electron off, 335 00:25:45 --> 00:25:50 and then the electron is off the metal and it just kind of 336 00:25:50 --> 00:25:53 stays there. It doesn't move away. 337 00:25:53 --> 00:25:57 But you can also come in with energy here, E sub i, 338 00:25:57 --> 00:26:03 that is greater than this work function, than the threshold 339 00:26:03 --> 00:26:07 energy. And you can pull the electron 340 00:26:07 --> 00:26:09 off. But then, the electron is 341 00:26:09 --> 00:26:14 actually going to move away from the metal, and the energy with 342 00:26:14 --> 00:26:18 which it moves away from the metal, its kinetic energy, 343 00:26:18 --> 00:26:23 is just the incident energy minus this threshold energy. 344 00:26:23 --> 00:26:27 It is the excess energy here. And I am going to write it as 345 00:26:27 --> 00:26:33 the kinetic energy. From that energy level diagram, 346 00:26:33 --> 00:26:37 this energy, the incident energy, 347 00:26:37 --> 00:26:43 has to be equal to the work function, h nu nought, 348 00:26:43 --> 00:26:48 plus the kinetic energy. 349 00:26:48 --> 00:26:54 Or, if I turned this around, the kinetic energy is equal to 350 00:26:54 --> 00:27:02 the incident energy minus h nu nought. 351 00:27:02 --> 00:27:06 The actual expression for the energy that Einstein found, 352 00:27:06 --> 00:27:08 I just turned that equation around. 353 00:27:08 --> 00:27:11 This is an equation that you have to know. 354 00:27:11 --> 00:27:14 I will not give this to you on an exam. 355 00:27:14 --> 00:27:17 Now, you don't have to memorize it. 356 00:27:17 --> 00:27:21 You just have to reason it. Draw yourself an energy 357 00:27:21 --> 00:27:23 diagram. You know conservation of 358 00:27:23 --> 00:27:26 energy. The sum of these two energies 359 00:27:26 --> 00:27:30 has to equal the incident energy. 360 00:27:30 --> 00:27:37 Then you will be all set. Now, what is very important 361 00:27:37 --> 00:27:44 here is the following. If I come in with radiation 362 00:27:44 --> 00:27:50 that is, say, a half of the threshold energy. 363 00:27:50 --> 00:27:58 Suppose I come in with two photons, where each photon is 364 00:27:58 --> 00:28:03 one half h nu -- 365 00:28:03 --> 00:28:08 366 00:28:08 --> 00:28:12 The bottom line is that you are not going to get an electron 367 00:28:12 --> 00:28:15 off. Even though you are coming in 368 00:28:15 --> 00:28:19 with two photons, which together are going to 369 00:28:19 --> 00:28:23 give you the threshold energy, you won't get a photon off. 370 00:28:23 --> 00:28:28 You have to come in with at least the energy of the work 371 00:28:28 --> 00:28:33 function. A photon has to have at least 372 00:28:33 --> 00:28:37 this energy to get an electron off. 373 00:28:37 --> 00:28:42 That is the particle-like nature of radiation. 374 00:28:42 --> 00:28:47 Energy comes in chunks, in particles of energy, 375 00:28:47 --> 00:28:53 in quanta of energy. Likewise, if I came in here 376 00:28:53 --> 00:29:00 with a photon that had twice the energy of the work function or 377 00:29:00 --> 00:29:05 the threshold energy, I would still only get one 378 00:29:05 --> 00:29:11 electron off. I would not get two electrons 379 00:29:11 --> 00:29:15 off, even though energetically you would be able, 380 00:29:15 --> 00:29:19 in principle, to get two electrons off. 381 00:29:19 --> 00:29:23 But you won't. You will only get one electron 382 00:29:23 --> 00:29:26 off. Whenever you send a photon in, 383 00:29:26 --> 00:29:31 if it has enough energy, that is if its energy is equal 384 00:29:31 --> 00:29:35 to or greater than the work function, you will get an 385 00:29:35 --> 00:29:40 electron off. There is one electron for every 386 00:29:40 --> 00:29:44 photon. You never get two electrons for 387 00:29:44 --> 00:29:48 every photon, or you can never get one 388 00:29:48 --> 00:29:52 electron for two photons that are lower energy. 389 00:29:52 --> 00:29:56 That is the particle quantum nature of radiation. 390 00:29:56 --> 00:30:00 That is important. Yes? 391 00:30:00 --> 00:30:08 392 00:30:08 --> 00:30:18 What is the form of the photon? What do you mean by form? 393 00:30:18 --> 00:30:25 Oh, you want a picture of the photon. 394 00:30:25 --> 00:30:33 You're looking at them. You cannot draw a picture of a 395 00:30:33 --> 00:30:39 photon because you want to relate it to something that is 396 00:30:39 --> 00:30:42 within your classical experience. 397 00:30:42 --> 00:30:48 And you cannot do that. It isn't a classical particle. 398 00:30:48 --> 00:30:53 That is what you're working with right here. 399 00:30:53 --> 00:30:59 You are trying to use your experiences, that are everyday 400 00:30:59 --> 00:31:05 experiences, to explain something that isn't within your 401 00:31:05 --> 00:31:13 everyday experiences. You don't have a frame or a 402 00:31:13 --> 00:31:18 format to do that. Yeah? 403 00:31:18 --> 00:31:30 404 00:31:30 --> 00:31:33 Yes. If you have a constant flux of 405 00:31:33 --> 00:31:39 photons onto the surface, you will have a constant flux 406 00:31:39 --> 00:31:44 of electrons. Now, there is a probability. 407 00:31:44 --> 00:31:50 It is not necessarily the case that every photon gets in, 408 00:31:50 --> 00:31:56 will eject electrons, because there are other kinds 409 00:31:56 --> 00:32:02 of competing processes. Whatever the rate with which 410 00:32:02 --> 00:32:07 the photons come in. It depends on the flux of the 411 00:32:07 --> 00:32:11 photons. And we will have some problems 412 00:32:11 --> 00:32:17 like that, where we are going to assume that the probability of 413 00:32:17 --> 00:32:23 the electron coming off is going to be one, so one electron for 414 00:32:23 --> 00:32:26 every photon. But, in reality, 415 00:32:26 --> 00:32:32 there are competing processes. Are all electrons being 416 00:32:32 --> 00:32:35 ejected? Actually, some electrons. 417 00:32:35 --> 00:32:39 Again, this goes to the probability. 418 00:32:39 --> 00:32:47 Some are actually kind of going in, too, into deeper the metal. 419 00:32:47 --> 00:32:53 420 00:32:53 --> 00:32:55 Not the probability, right. 421 00:32:55 --> 00:33:01 The rate at which the electrons come out with is dependent on 422 00:33:01 --> 00:33:06 the intensity. The more photons you send in, 423 00:33:06 --> 00:33:12 the larger the number of photons per second coming in, 424 00:33:12 --> 00:33:18 the larger the number of electrons per second coming out. 425 00:33:18 --> 00:33:23 This is a plot, here, of the energy of the 426 00:33:23 --> 00:33:26 electrons. That's all right. 427 00:33:26 --> 00:33:30 Other questions? Yeah? 428 00:33:30 --> 00:33:35 429 00:33:35 --> 00:33:36 Eventually. Yes. 430 00:33:36 --> 00:33:39 Absolutely. There are other problems that 431 00:33:39 --> 00:33:43 will come in. Usually, your light source 432 00:33:43 --> 00:33:48 isn't so energetic that you could possibly do that. 433 00:33:48 --> 00:33:53 Now, also usually what happens is that you've got your metal 434 00:33:53 --> 00:33:58 grounded, so that as you lose electrons, new electrons come in 435 00:33:58 --> 00:34:03 and fill it up to the fermi level. 436 00:34:03 --> 00:34:06 And so you don't charge up your sample. 437 00:34:06 --> 00:34:10 In an experiment, if you had your metal just not 438 00:34:10 --> 00:34:15 grounded and you did shine some radiation, what would happen is 439 00:34:15 --> 00:34:18 the metal would start to charge up. 440 00:34:18 --> 00:34:23 Then, that would make it difficult to get electrons off. 441 00:34:23 --> 00:34:25 Yes? 442 00:34:25 --> 00:34:35 443 00:34:35 --> 00:34:37 Yes. How strongly those electrons 444 00:34:37 --> 00:34:42 are bound to the metal depends on the electronic structure of 445 00:34:42 --> 00:34:44 the metal. And we are going to talk a 446 00:34:44 --> 00:34:49 little bit about what determines the strength of the interaction 447 00:34:49 --> 00:34:53 for electrons on atoms and molecules, but it is similar to 448 00:34:53 --> 00:34:57 what it is for metals. That is coming in a few days. 449 00:34:57 --> 00:34:59 Yes? 450 00:34:59 --> 00:35:04 451 00:35:04 --> 00:35:05 Yes, there is. Right. 452 00:35:05 --> 00:35:08 You don't actually have to have a metal. 453 00:35:08 --> 00:35:11 You could do it. There are usually higher 454 00:35:11 --> 00:35:14 frequencies on insulators and semiconductors, 455 00:35:14 --> 00:35:17 right. It is harder to see the effect, 456 00:35:17 --> 00:35:19 but it can be done and has been done. 457 00:35:19 --> 00:35:24 Well, what I want to do right now is to show you an experiment 458 00:35:24 --> 00:35:27 we are going to do. We are going to do a 459 00:35:27 --> 00:35:30 photoelectron experiment. 460 00:35:30 --> 00:35:45 461 00:35:45 --> 00:35:53 And the experiment is this. We have a device up here. 462 00:35:53 --> 00:36:00 What we have is an aluminum plate. 463 00:36:00 --> 00:36:05 And that aluminum plate is mounted on this blue metal rod. 464 00:36:05 --> 00:36:10 And in the middle of this rod is a needle on a pivot. 465 00:36:10 --> 00:36:14 And this is a fairly frictionless pivot. 466 00:36:14 --> 00:36:17 This black ring, here, is just a support 467 00:36:17 --> 00:36:22 structure, an insulating support structure. 468 00:36:22 --> 00:36:27 What we are going to do is put some excess charge on this 469 00:36:27 --> 00:36:32 aluminum plate. And that excess charge is going 470 00:36:32 --> 00:36:35 to run down this metal rod and then onto this needle. 471 00:36:35 --> 00:36:40 And because that excess charge, the electrons on the needle and 472 00:36:40 --> 00:36:43 the electrons on the metal rod are repulsive, 473 00:36:43 --> 00:36:45 since this is rather frictionless, 474 00:36:45 --> 00:36:49 that needle is going to move because of the repulsive 475 00:36:49 --> 00:36:52 interactions between these electrons. 476 00:36:52 --> 00:36:56 What we're then going to do is try to do the photoelectron 477 00:36:56 --> 00:37:00 experiment. We are going to take some UV 478 00:37:00 --> 00:37:07 radiation and shine it on this metal and drive the electrons 479 00:37:07 --> 00:37:09 off. And we should see, 480 00:37:09 --> 00:37:14 then, the needle swing back to its original position. 481 00:37:14 --> 00:37:20 I need a couple of volunteers in order to do this experiment 482 00:37:20 --> 00:37:22 here. Come on up. 483 00:37:22 --> 00:37:24 All right. Fantastic. 484 00:37:24 --> 00:37:27 I think that is all right. Good. 485 00:37:27 --> 00:37:32 Okay. One of you needs to be the 486 00:37:32 --> 00:37:35 charger, and the other needs to be the discharger. 487 00:37:35 --> 00:37:38 Which one? You want to discharge? 488 00:37:38 --> 00:37:41 Discharge, okay. You come over here. 489 00:37:41 --> 00:37:45 And what you are going to do is discharge the aluminum plate 490 00:37:45 --> 00:37:48 after we get some excess charge on it. 491 00:37:48 --> 00:37:52 You are going to do it just by holding it up to here. 492 00:37:52 --> 00:37:57 You have to get it kind of close because it is not a very 493 00:37:57 --> 00:38:03 intense UV source. Could you get the video cam on 494 00:38:03 --> 00:38:09 the side or on the center to get where we are putting it? 495 00:38:09 --> 00:38:13 I guess we are putting it on the side, right? 496 00:38:13 --> 00:38:15 Okay. There we go. 497 00:38:15 --> 00:38:19 There is the device. You are the charger. 498 00:38:19 --> 00:38:24 What we are going to do, to get the excess charge, 499 00:38:24 --> 00:38:30 we are taking a piece of natural fur. 500 00:38:30 --> 00:38:33 We are going to rub it on this Lucite rod. 501 00:38:33 --> 00:38:37 You have to keep your fingers on the yellow tape here. 502 00:38:37 --> 00:38:41 And we are going to transfer some of the natural oils here 503 00:38:41 --> 00:38:44 onto this rod. And there are plenty of 504 00:38:44 --> 00:38:47 negative ions around here and free electrons. 505 00:38:47 --> 00:38:52 That oil likes those negative charges, and so there are going 506 00:38:52 --> 00:38:57 to be excess negative charges on this Lucite rod. 507 00:38:57 --> 00:39:03 And then you are going to come over here and just touch the 508 00:39:03 --> 00:39:08 edge of this and let the electrons flow onto there. 509 00:39:08 --> 00:39:13 Are you right-handed? You have to rub that really, 510 00:39:13 --> 00:39:16 really hard. [LAUGHTER] Great. 511 00:39:16 --> 00:39:19 Go over there. Touch the end. 512 00:39:19 --> 00:39:23 Cool. Why don't you give it another 513 00:39:23 --> 00:39:30 jolt here and we will really move that needle over. 514 00:39:30 --> 00:39:31 Okay. Discharger. 515 00:39:31 --> 00:39:33 We have to give it another jolt. 516 00:39:33 --> 00:39:36 That is okay. You may have touched it with 517 00:39:36 --> 00:39:40 something else and discharged it a little bit. 518 00:39:40 --> 00:39:43 No, that's okay. You have to get the hang of 519 00:39:43 --> 00:39:46 this, here. You are doing fantastic. 520 00:39:46 --> 00:39:49 Take it off. That's what it is. 521 00:39:49 --> 00:39:53 You are holding it on too long. Okay, that is pretty good. 522 00:39:53 --> 00:39:57 Put it in front there. Get it a little bit closer. 523 00:39:57 --> 00:40:02 Here comes the UV radiation. We did it. 524 00:40:02 --> 00:40:06 Try it again really hard. Just touch it. 525 00:40:06 --> 00:40:09 Take it off. Do it again. 526 00:40:09 --> 00:40:14 You need to do it again. You've got to get it right 527 00:40:14 --> 00:40:16 here. Not too much, 528 00:40:16 --> 00:40:18 not too little. Okay. 529 00:40:18 --> 00:40:22 It is doing it. Discharge in front. 530 00:40:22 --> 00:40:27 Electrons off. Now we have to do a control 531 00:40:27 --> 00:40:33 experiment. That is, you have got to charge 532 00:40:33 --> 00:40:38 it up again, but now, when you put the light there, 533 00:40:38 --> 00:40:44 what I am going to do is hold up a Pyrex plate in between the 534 00:40:44 --> 00:40:49 light and the metal. It is going to block the 535 00:40:49 --> 00:40:53 radiation, and it should not discharge. 536 00:40:53 --> 00:40:57 You need to get on there. Fantastic. 537 00:40:57 --> 00:41:02 There it goes. Here is the plate. 538 00:41:02 --> 00:41:07 Get it to a little bit lower. Do a good discharge. 539 00:41:07 --> 00:41:12 [APPLAUSE] Fantastic. Thank you very much. 540 00:41:12 --> 00:41:15 Thank you for being a good sport. 541 00:41:15 --> 00:41:19 That is the photoelectron experiment. 542 00:41:19 --> 00:41:24 Hey, it works. Well, what I want to do now is 543 00:41:24 --> 00:41:32 just spend a few minutes working on a few problems. 544 00:41:32 --> 00:41:36 I think these are pretty straightforward, 545 00:41:36 --> 00:41:42 but I just want to make sure that everybody is on the same 546 00:41:42 --> 00:41:47 page here in terms of being able to do the homework. 547 00:41:47 --> 00:41:53 Here is the first problem. The first problem says, 548 00:41:53 --> 00:41:57 how many photons? And remember what we said a 549 00:41:57 --> 00:42:02 photon was? E equals h nu. 550 00:42:02 --> 00:42:07 This is the number of joules. Implied is the number of joules 551 00:42:07 --> 00:42:11 per photon, although we don't usually write this, 552 00:42:11 --> 00:42:15 but that is what that is, joules per photon. 553 00:42:15 --> 00:42:20 You may want to write it as you do these problems. 554 00:42:20 --> 00:42:28 How many photons associated with radiation of a wavelength 555 00:42:28 --> 00:42:35 lambda equals one picometer, which is 1.0x10^-12 meters, 556 00:42:35 --> 00:42:42 how many of these do you need in order to create, 557 00:42:42 --> 00:42:49 say, a laser pulse of energy that is one joule? 558 00:42:49 --> 00:42:55 Lasers are pulsed, so I am talking about a pulse 559 00:42:55 --> 00:43:02 of energy, one joule. You want to draw yourself a 560 00:43:02 --> 00:43:06 picture, here. We are drawing a picture of one 561 00:43:06 --> 00:43:08 pulse of energy, one joule. 562 00:43:08 --> 00:43:13 Now, we have not been given the frequency, here, 563 00:43:13 --> 00:43:17 of this radiation, but we know the wavelength, 564 00:43:17 --> 00:43:21 and we know the relationship between frequency and 565 00:43:21 --> 00:43:25 wavelength. It is just c over lambda. 566 00:43:25 --> 00:43:30 I know what lambda is. I can calculate nu. 567 00:43:30 --> 00:43:34 And, when I do that, I find that the energy of the 568 00:43:34 --> 00:43:40 photon, hc over lambda, that energy of the 569 00:43:40 --> 00:43:44 photon is 1.99x10^-13 joules per photon. 570 00:43:44 --> 00:43:50 And I am using one more figure than is significant since this 571 00:43:50 --> 00:43:55 an intermediate step in the calculation. 572 00:43:55 --> 00:44:02 If I want a pulse of one joule of energy and I am asked how 573 00:44:02 --> 00:44:10 many photons do I need to get that, and each photon is 574 00:44:10 --> 00:44:16 1.99x10^-13 joules, well, that means that I am 575 00:44:16 --> 00:44:24 going to need 5.0x10^12 photons. There was a question here? 576 00:44:24 --> 00:44:30 All right. Let's work another one. 577 00:44:30 --> 00:44:34 Here, we want to define what we mean by power. 578 00:44:34 --> 00:44:40 This says the power of radiation from the continuous 579 00:44:40 --> 00:44:44 laser is three milliwatts. 580 00:44:44 --> 00:44:50 We have some laser, and the power of that radiation 581 00:44:50 --> 00:44:55 coming out is three milliwatts. Well, what is power? 582 00:44:55 --> 00:45:02 Power is energy per unit time. It is the energy delivered or 583 00:45:02 --> 00:45:06 the energy expended per unit time. 584 00:45:06 --> 00:45:11 The unit of power that we are going to use is a watt. 585 00:45:11 --> 00:45:16 A watt is a joule per second. We are told that we have 586 00:45:16 --> 00:45:22 radiation of three milliwatts. That is 3.0x10^-3 joules per 587 00:45:22 --> 00:45:25 second. And the question asks, 588 00:45:25 --> 00:45:30 how long will it take for a total energy of one joule to be 589 00:45:30 --> 00:45:36 supplied? Well, one joule. 590 00:45:36 --> 00:45:47 And we have the rate of energy supply as 3x10^-3 joules per 591 00:45:47 --> 00:45:54 second. That gives us 330 seconds. 592 00:45:54 --> 00:46:04 That is straightforward. Finally, we have one more. 593 00:46:04 --> 00:46:11 It says, how many photons per second of, again, 594 00:46:11 --> 00:46:17 the same radiation, of the wavelength of one 595 00:46:17 --> 00:46:22 picometer. That means, again, 596 00:46:22 --> 00:46:29 we are dealing with photons that have an energy of 597 00:46:29 --> 00:46:39 1.99x10^-13 joules per photon. How many photons per second, 598 00:46:39 --> 00:46:45 the rate of photons at the wavelength do you have to have, 599 00:46:45 --> 00:46:49 or do you have, if the power of the radiation 600 00:46:49 --> 00:46:54 is three milliwatts? Well, the power of the 601 00:46:54 --> 00:47:00 radiation is 3.0x10^-3 joules per second, -- 602 00:47:00 --> 00:47:06 -- and we have 1.99x10^-13 joules per photon. 603 00:47:06 --> 00:47:11 604 00:47:11 --> 00:47:18 In order to have this kind of power, what we have to have 605 00:47:18 --> 00:47:25 being emitted is 1.5x10^10 photons per second. 606 00:47:25 --> 00:47:34 607 00:47:34 --> 00:47:38 All right. The photoelectric effect is one 608 00:47:38 --> 00:47:43 of the experiments that demonstrated the particle-like 609 00:47:43 --> 00:47:46 nature of light, of radiation. 610 00:47:46 --> 00:47:52 Particle-like nature because you have to have these chunks of 611 00:47:52 --> 00:47:57 energy to make some process occur. 612 00:47:57 --> 00:48:03 Next time, we are going to look at and will just talk briefly 613 00:48:03 --> 00:48:09 about the other experiments that demonstrated the particle-like 614 00:48:09 --> 00:48:14 nature of radiation. And that other experiment is 615 00:48:14 --> 00:48:18 the demonstration that a photon has momentum, 616 00:48:18 --> 00:48:22 even though it doesn't have any mass. 617 00:48:22.562 --> 48:25 See you Wednesday. See you Friday.