1 00:00:01,468 --> 00:00:03,519 - Sometimes light seems to act as a wave, 2 00:00:03,519 --> 00:00:06,201 and sometimes light seems to act as a particle. 3 00:00:06,201 --> 00:00:07,931 And, an example of this, would be 4 00:00:07,931 --> 00:00:11,750 the Photoelectric effect, as described by Einstein. 5 00:00:11,750 --> 00:00:13,652 So let's say you had a piece of metal, 6 00:00:13,652 --> 00:00:15,563 and we know the metal has electrons. 7 00:00:15,563 --> 00:00:18,020 I'm gonna go ahead and draw one electron in here, 8 00:00:18,020 --> 00:00:20,966 and this electron is bound to the metal 9 00:00:20,966 --> 00:00:21,860 because it's attracted 10 00:00:21,860 --> 00:00:24,501 to the positive charges in the nucleus. 11 00:00:24,501 --> 00:00:27,264 If you shine a light on the metal, 12 00:00:27,264 --> 00:00:30,271 so the right kind of light with the right kind of frequency, 13 00:00:30,271 --> 00:00:32,831 you can actually knock some of those electrons loose, 14 00:00:32,831 --> 00:00:36,001 which causes a current of electrons to flow. 15 00:00:36,001 --> 00:00:37,626 So this is kind of like a collision 16 00:00:37,626 --> 00:00:39,495 between two particles, 17 00:00:39,495 --> 00:00:41,792 if we think about light as being a particle. 18 00:00:41,792 --> 00:00:44,209 So I'm gonna draw in a particle of light 19 00:00:44,209 --> 00:00:47,602 which we call a photon, so this is massless, 20 00:00:47,602 --> 00:00:51,536 and the photon is going to hit this electron, 21 00:00:51,536 --> 00:00:53,730 and if the photon has enough energy, 22 00:00:53,730 --> 00:00:55,802 it can free the electron, right? 23 00:00:55,802 --> 00:00:57,204 So we can knock it loose, 24 00:00:57,204 --> 00:00:58,911 and so let me go ahead and show that. 25 00:00:58,911 --> 00:01:01,471 So here, we're showing the electron being knocked loose 26 00:01:01,471 --> 00:01:03,259 and so the electron's moving in, 27 00:01:03,259 --> 00:01:04,742 let's just say, this direction, 28 00:01:04,742 --> 00:01:06,956 with some velocity, v, 29 00:01:06,956 --> 00:01:09,863 and if the electron has mass, m, 30 00:01:09,863 --> 00:01:12,259 we know that there's a kinetic energy. 31 00:01:12,259 --> 00:01:13,824 The kinetic energy of the electron 32 00:01:13,824 --> 00:01:17,399 would be equal to one half mv squared. 33 00:01:17,399 --> 00:01:20,650 This freed electron is usually referred to now 34 00:01:20,650 --> 00:01:22,458 as a photoelectron. 35 00:01:22,458 --> 00:01:26,400 So one photon creates one photoelectron. 36 00:01:26,400 --> 00:01:29,000 So one particle hits another particle. 37 00:01:29,000 --> 00:01:32,590 And, if you think about this in terms of classical physics, 38 00:01:32,590 --> 00:01:35,856 you could think about energy being conserved. 39 00:01:35,856 --> 00:01:38,557 So the energy of the photon, the energy that went in, 40 00:01:38,557 --> 00:01:40,084 so let me go ahead and write this here, 41 00:01:40,084 --> 00:01:41,995 so the energy of the photon, 42 00:01:41,995 --> 00:01:43,174 the energy that went in, 43 00:01:43,174 --> 00:01:45,246 what happened to that energy? 44 00:01:45,246 --> 00:01:48,923 Some of that energy was needed to free the electron. 45 00:01:48,923 --> 00:01:51,727 So the electron was bound, and some of the energy 46 00:01:51,727 --> 00:01:52,866 freed the electron. 47 00:01:52,866 --> 00:01:54,390 I'm gonna call that E naught, 48 00:01:54,390 --> 00:01:56,137 the energy that freed the electron, 49 00:01:56,137 --> 00:01:57,802 and then the rest of that energy 50 00:01:57,802 --> 00:02:01,357 must have gone into the kinetic energy of the electron, 51 00:02:01,357 --> 00:02:02,923 and so we can write here 52 00:02:02,923 --> 00:02:07,169 kinetic energy of the photoelectron that was produced. 53 00:02:07,169 --> 00:02:10,987 So, kinetic energy of the photoelectron. 54 00:02:10,987 --> 00:02:12,412 So let's say you wanted to solve 55 00:02:12,412 --> 00:02:15,603 for the kinetic energy of that photoelectron. 56 00:02:15,603 --> 00:02:17,349 So that would be very simple, it would just be 57 00:02:17,349 --> 00:02:19,442 kinetic energy would be equal to 58 00:02:19,442 --> 00:02:21,758 the energy of the photon, 59 00:02:21,758 --> 00:02:23,059 energy of the photon, 60 00:02:23,059 --> 00:02:25,293 minus the energy that was necessary 61 00:02:25,293 --> 00:02:29,153 to free the electron from the metallic surface. 62 00:02:29,153 --> 00:02:31,408 And this E naught, here I'm calling it E naught, 63 00:02:31,408 --> 00:02:34,051 you might see it written differently, 64 00:02:34,051 --> 00:02:35,411 a different symbol, 65 00:02:35,411 --> 00:02:37,139 but this is the work function. 66 00:02:37,139 --> 00:02:40,043 Let me go ahead and write work function here, 67 00:02:40,043 --> 00:02:42,279 and the work function is different 68 00:02:42,279 --> 00:02:44,208 for every kind of metal. 69 00:02:44,208 --> 00:02:47,479 So, it's the minimum amount of energy 70 00:02:47,479 --> 00:02:50,385 that's necessary to free the electron, 71 00:02:50,385 --> 00:02:51,888 and so obviously that's going to be different 72 00:02:51,888 --> 00:02:54,103 depending on what metal you're talking about. 73 00:02:54,103 --> 00:02:55,526 All right, let's do a problem. 74 00:02:55,526 --> 00:02:57,150 Now that we understand the general idea 75 00:02:57,150 --> 00:02:58,756 of the Photoelectric effect, 76 00:02:58,756 --> 00:03:01,193 let's look at what this problem asks us. 77 00:03:01,193 --> 00:03:04,180 So the problem says, "If a photon of wavelength 78 00:03:04,180 --> 00:03:08,426 "525 nm hits metallic cesium..." 79 00:03:08,426 --> 00:03:11,413 And so here's the work function for metallic cesium. 80 00:03:11,413 --> 00:03:15,496 "What is the velocity of the photoelectron produced?" 81 00:03:15,496 --> 00:03:17,013 So they want to know the velocity 82 00:03:17,013 --> 00:03:18,455 of the photoelectron produced, 83 00:03:18,455 --> 00:03:21,767 which we know is hiding in the kinetic energy right here, 84 00:03:21,767 --> 00:03:24,002 and we also know what the work function is. 85 00:03:24,002 --> 00:03:25,732 So we know what E naught is here. 86 00:03:25,732 --> 00:03:28,453 What we don't know is the energy of the photon 87 00:03:28,453 --> 00:03:30,851 so that's what we need to calculate first. 88 00:03:30,851 --> 00:03:32,984 And so the energy of the photon, 89 00:03:32,984 --> 00:03:35,728 energy of the photon, is equal to 90 00:03:35,728 --> 00:03:38,165 h, which is Planck's constant, 91 00:03:38,165 --> 00:03:42,221 times the frequency, which is usually symbolized by nu. 92 00:03:42,221 --> 00:03:45,864 So, we got the frequency, but they gave us the wavelength 93 00:03:45,864 --> 00:03:46,759 in the problem here. 94 00:03:46,759 --> 00:03:48,526 They gave us wavelength, so we need to relate 95 00:03:48,526 --> 00:03:50,315 frequency to wavelength, 96 00:03:50,315 --> 00:03:53,098 and that's related by c, which is the speed of light, 97 00:03:53,098 --> 00:03:56,044 is equal to lambda times nu. 98 00:03:56,044 --> 00:03:57,324 So, c is the speed of light, 99 00:03:57,324 --> 00:03:58,664 and that's equal to the frequency 100 00:03:58,664 --> 00:04:00,270 times the wavelength. 101 00:04:00,270 --> 00:04:03,887 So we can substitute n for the frequency, 102 00:04:03,887 --> 00:04:05,572 all right, 'cause we just use this equation 103 00:04:05,572 --> 00:04:07,320 and say that the frequency is equal 104 00:04:07,320 --> 00:04:10,957 to the speed of light divided by the wavelength. 105 00:04:12,756 --> 00:04:15,777 The frequency is equal to speed of light over lambda, 106 00:04:15,777 --> 00:04:17,708 so we can plug that into here, 107 00:04:17,708 --> 00:04:19,699 and so now we have the energy of the photon 108 00:04:19,699 --> 00:04:22,665 is equal to hc over lambda, 109 00:04:22,665 --> 00:04:23,945 and we can plug in those numbers. 110 00:04:23,945 --> 00:04:27,920 h is Planck's constant, which is 6.626 111 00:04:27,920 --> 00:04:30,623 times 10 to the negative 34. 112 00:04:30,623 --> 00:04:33,265 So, times 10 to the negative 34 here. 113 00:04:33,265 --> 00:04:34,829 c is the speed of light, 114 00:04:34,829 --> 00:04:39,687 which is 2.998 times 10 to the 8th 115 00:04:39,687 --> 00:04:44,574 meters over seconds, and all over lambda. 116 00:04:44,574 --> 00:04:46,078 Lambda is the wavelength. 117 00:04:46,078 --> 00:04:48,048 That's 525 nanometers. 118 00:04:48,048 --> 00:04:50,337 So 525 times 10 119 00:04:50,337 --> 00:04:53,282 to the negative 9th meters. 120 00:04:53,282 --> 00:04:55,212 All right, so let's get out our calculator 121 00:04:55,212 --> 00:04:57,959 and calculate the energy of the photon here. 122 00:04:57,959 --> 00:05:00,721 So, let's go ahead and do that math, 123 00:05:00,721 --> 00:05:05,247 so we have 6.626 times 124 00:05:05,247 --> 00:05:09,245 10 to the negative 34, 125 00:05:09,245 --> 00:05:11,601 and we're going to multiply that number 126 00:05:11,601 --> 00:05:14,711 by the speed of light, 2.998 127 00:05:14,711 --> 00:05:18,362 times 10 to the 8th, 128 00:05:18,362 --> 00:05:19,824 and we get that number. 129 00:05:19,824 --> 00:05:22,018 We're gonna divide it by the wavelength, 130 00:05:22,018 --> 00:05:24,097 525 times 131 00:05:24,097 --> 00:05:27,389 10 to the negative 9, 132 00:05:27,389 --> 00:05:30,101 and we get 3.78 times 133 00:05:30,101 --> 00:05:32,295 10 to the negative 19. 134 00:05:32,295 --> 00:05:33,994 So, let me go ahead and write that down here. 135 00:05:33,994 --> 00:05:38,647 3.78 times 10 to the negative 19, 136 00:05:38,647 --> 00:05:40,374 and if you did you units up here, 137 00:05:40,374 --> 00:05:42,263 you would get joules, 138 00:05:42,263 --> 00:05:44,693 and so let's think about this number for a second, 139 00:05:44,693 --> 00:05:47,536 3.78 times 10 to the negative 19 140 00:05:47,536 --> 00:05:49,264 is the energy of the photon. 141 00:05:49,264 --> 00:05:51,652 And that energy of the photon is greater 142 00:05:51,652 --> 00:05:54,254 than the work function, which means 143 00:05:54,254 --> 00:05:57,099 that that's a high-energy photon. 144 00:05:57,099 --> 00:05:59,759 It's able to knock the electron free, 145 00:05:59,759 --> 00:06:01,425 'cause remember, this number right here, 146 00:06:01,425 --> 00:06:03,680 is the minimum amount of energy needed 147 00:06:03,680 --> 00:06:05,834 to free the electron and so we've exceeded 148 00:06:05,834 --> 00:06:07,683 that minimum amount of energy, 149 00:06:07,683 --> 00:06:10,102 and so we will produce a photoelectron. 150 00:06:10,102 --> 00:06:12,782 So, this photon is high-energy enough 151 00:06:12,782 --> 00:06:14,917 to produce a photoelectron. 152 00:06:14,917 --> 00:06:18,695 So let's go ahead and find the kinetic energy 153 00:06:18,695 --> 00:06:21,112 of the photoelectron that's produced. 154 00:06:21,112 --> 00:06:24,038 So we're gonna use this equation right up here. 155 00:06:24,038 --> 00:06:25,826 So let me just go and get some more room, 156 00:06:25,826 --> 00:06:27,473 and I will rewrite that equation. 157 00:06:27,473 --> 00:06:31,210 So we have the kinetic energy of the photoelectron, 158 00:06:31,210 --> 00:06:33,141 kinetic energy of the photoelectron, 159 00:06:33,141 --> 00:06:37,833 is equal to the energy of the photon, 160 00:06:37,833 --> 00:06:42,146 energy of the photon, minus the work function. 161 00:06:42,146 --> 00:06:43,516 So let's plug in our numbers. 162 00:06:43,516 --> 00:06:44,857 The energy of the photon was 163 00:06:44,857 --> 00:06:49,407 3.78 times 10 the negative 19 joules, 164 00:06:49,407 --> 00:06:52,191 and then the work function is right up here again, 165 00:06:52,191 --> 00:06:56,369 it's 3.43, so minus 3.43 166 00:06:56,369 --> 00:07:00,353 times 10 to the negative 19 joules. 167 00:07:00,353 --> 00:07:02,384 So let's get out the calculator again. 168 00:07:02,384 --> 00:07:05,456 So, from that we're going to subtract the work function 169 00:07:06,841 --> 00:07:10,029 3.43 times 170 00:07:10,029 --> 00:07:13,492 10 to the negative 19 171 00:07:13,492 --> 00:07:16,055 and we get 3.5 172 00:07:16,055 --> 00:07:18,331 times 10 to the negative 20. 173 00:07:18,331 --> 00:07:19,368 So let's go ahead and write that. 174 00:07:19,368 --> 00:07:22,293 This is equal to 3.5 175 00:07:22,293 --> 00:07:26,421 times 10 to the negative 20 joules. 176 00:07:26,421 --> 00:07:28,585 This is equal to the kinetic energy 177 00:07:28,585 --> 00:07:30,434 of the photoelectron, and we know that 178 00:07:30,434 --> 00:07:34,694 kinetic energy is equal to one half mv squared. 179 00:07:34,694 --> 00:07:36,676 The problem asked us to solve 180 00:07:36,676 --> 00:07:39,528 for the velocity of the photoelectron. 181 00:07:39,528 --> 00:07:42,650 So all we have to do is plug in the mass of an electron, 182 00:07:42,650 --> 00:07:44,376 which is 9.11 times 183 00:07:44,376 --> 00:07:47,592 10 to the negative 31st kilograms, 184 00:07:47,592 --> 00:07:49,076 times v squared. 185 00:07:49,076 --> 00:07:50,904 This is equal to 3.5 186 00:07:50,904 --> 00:07:53,627 times 10 to the negative 20. 187 00:07:53,627 --> 00:07:55,192 So, let's do that math. 188 00:07:55,192 --> 00:07:58,747 So we take 3.5 times 10 to the negative 20, 189 00:07:58,747 --> 00:08:01,035 we multiply that by 2, 190 00:08:01,035 --> 00:08:04,387 and then we divide by the mass of an electron, 191 00:08:04,387 --> 00:08:07,108 9.11 times 192 00:08:07,108 --> 00:08:10,603 10 to the negative 31st, 193 00:08:10,603 --> 00:08:13,000 and this gives us that number, 194 00:08:13,000 --> 00:08:15,642 which we need to take the square root of. 195 00:08:15,642 --> 00:08:18,384 So, square root of our answer 196 00:08:18,384 --> 00:08:21,513 gives us the velocity of the electron, 197 00:08:23,451 --> 00:08:26,786 2.8 times 10 to the 5th. 198 00:08:26,786 --> 00:08:28,500 So if you look at your decimal place here, 199 00:08:28,500 --> 00:08:31,568 this'll be one, two, three, 200 00:08:31,568 --> 00:08:35,774 four, five, so 2.8 times 10 to the 5th 201 00:08:35,774 --> 00:08:36,993 meters per second. 202 00:08:36,993 --> 00:08:40,379 So here's the velocity of the photoelectron produced, 203 00:08:40,379 --> 00:08:43,631 2.8 times 10 to the 5th 204 00:08:43,631 --> 00:08:46,243 meters per second, 205 00:08:46,243 --> 00:08:49,066 and if you increased the intensity of this light, 206 00:08:49,066 --> 00:08:51,220 so you had more photons, 207 00:08:51,220 --> 00:08:54,299 they would produce more photoelectrons. 208 00:08:54,299 --> 00:08:57,265 So one photon knocks out one photoelectron 209 00:08:57,265 --> 00:08:59,501 if it has enough energy to do so. 210 00:08:59,501 --> 00:09:02,243 So let's think about this same problem, 211 00:09:02,243 --> 00:09:04,255 but let's change the wavelength. 212 00:09:04,255 --> 00:09:07,606 So, what if your wavelength changed 213 00:09:07,606 --> 00:09:11,771 to 625 nanometers. 214 00:09:11,771 --> 00:09:13,724 So what would happen now? 215 00:09:13,724 --> 00:09:16,243 Well, to save time, I won't do the calculation, 216 00:09:16,243 --> 00:09:17,340 but all we would have to do 217 00:09:17,340 --> 00:09:20,875 is plug in 625 up here. 218 00:09:20,875 --> 00:09:24,878 So instead of 525, just plug in 625 219 00:09:24,878 --> 00:09:26,768 to calculate your energy, 220 00:09:26,768 --> 00:09:27,925 and if you did that, 221 00:09:27,925 --> 00:09:30,181 so if you used 625 222 00:09:30,181 --> 00:09:32,923 times 10 to the negative 9 here, 223 00:09:32,923 --> 00:09:34,437 I'll go ahead and give you the answer 224 00:09:34,437 --> 00:09:35,363 just to save some time, 225 00:09:35,363 --> 00:09:38,837 you would get 3.2 times 226 00:09:38,837 --> 00:09:41,803 10 to the negative 19 joules. 227 00:09:41,803 --> 00:09:44,779 And that is lower than the work function. 228 00:09:44,779 --> 00:09:46,376 So let me go ahead and highlight that here. 229 00:09:46,376 --> 00:09:49,484 So this number is not 230 00:09:49,484 --> 00:09:51,191 as high as the work function. 231 00:09:51,191 --> 00:09:52,999 The work function was how much energy 232 00:09:52,999 --> 00:09:55,071 we needed to free that electron, 233 00:09:55,071 --> 00:09:57,103 and since this is lower than the work function 234 00:09:57,103 --> 00:10:00,334 that means we do not get a photoelectron. 235 00:10:00,334 --> 00:10:03,360 So, you have to have a high enough energy photon 236 00:10:03,360 --> 00:10:05,921 in order to produce a photoelectron. 237 00:10:05,921 --> 00:10:09,192 It wouldn't even matter if we increased the intensity. 238 00:10:09,192 --> 00:10:11,284 So if we had more and more and more 239 00:10:11,284 --> 00:10:13,519 of these photons at this wavelength, 240 00:10:13,519 --> 00:10:15,836 we still wouldn't produce any photoelectrons. 241 00:10:15,836 --> 00:10:18,375 And so, this is the idea of the Photoelectric effect, 242 00:10:18,375 --> 00:10:19,695 which is best explained 243 00:10:19,695 --> 00:00:00,000 by thinking about light as a particle.