1 00:00:00 --> 00:00:00,721 2 00:00:00,721 --> 00:00:03,503 All right, you did well on the exam. 3 00:00:03,503 --> 00:00:07,954 Class average was sixty-two. I always aim for sixty-five, 4 00:00:07,954 --> 00:00:11,451 so I was very happy. Eleven students scored a 5 00:00:11,451 --> 00:00:14,392 hundred. I believe that my exam review 6 00:00:14,392 --> 00:00:18,287 was extremely fair. According to some instructors, 7 00:00:18,287 --> 00:00:20,99 perhaps even too close for comfort. 8 00:00:20,99 --> 00:00:25,203 I did a problem with parallel resistors and a battery. 9 00:00:25,203 --> 00:00:28,859 I applied Gauss's Law for cylindrical symmetry. 10 00:00:28,859 --> 00:00:34,027 I spent quite a bit of time discussing where charge 11 00:00:34,027 --> 00:00:38,413 occurs and where charge can not be located on conductors and I 12 00:00:38,413 --> 00:00:42,45 hit the idea of capacitors and dielectrics also quite hard. 13 00:00:42,45 --> 00:00:46,627 I prefer not to think about a rigid division between pass and 14 00:00:46,627 --> 00:00:50,803 fail, but I'd rather tell you that all of you who scored less 15 00:00:50,803 --> 00:00:54,075 than forty-seven, in my book, are sort of in the 16 00:00:54,075 --> 00:00:56,79 danger zone. Now, that doesn't mean that 17 00:00:56,79 --> 00:01:04,316 you're going to fail the course, nor does it mean that you will 18 00:01:04,316 --> 00:01:07,159 pass the course if you scored seventy. 19 00:01:07,159 --> 00:01:10,156 But those people are in the danger zone. 20 00:01:10,156 --> 00:01:14,843 I think you should talk to your instructor, and I would advise 21 00:01:14,843 --> 00:01:18,915 those people also to make frequent use of our tutors. 22 00:01:18,915 --> 00:01:21,297 Two exams to go, plus the final. 23 00:01:21,297 --> 00:01:25,908 Today I'm going to uncover a whole new world for you and you 24 00:01:25,908 --> 00:01:30,672 will see how eight oh two comes in there in a very natural way. 25 00:01:30,672 --> 00:01:38,049 The Lawrence force F is the charge times the cross product 26 00:01:38,049 --> 00:01:43,849 of the velocity of that charge and the B field that the charge 27 00:01:43,849 --> 00:01:47,463 experiences. If I have here a positive 28 00:01:47,463 --> 00:01:52,788 charge plus Q and it has a velocity V in this direction, 29 00:01:52,788 --> 00:01:58,589 and the magnetic fields would be uniform and coming out of the 30 00:01:58,589 --> 00:02:04,675 blackboards, there's going to be a force on this charge according 31 00:02:04,675 --> 00:02:11,807 to this relationship and the force 32 00:02:11,807 --> 00:02:14,632 is then like so. Perpendicular to V, 33 00:02:14,632 --> 00:02:18,085 perpendicular to B. In this case the charged 34 00:02:18,085 --> 00:02:21,459 particle is going to go around in a circle . 35 00:02:21,459 --> 00:02:24,833 The Lawrence force can not change the speed, 36 00:02:24,833 --> 00:02:29,07 can not change the kinetic energy, because the force is 37 00:02:29,07 --> 00:02:33,542 always perpendicular to the velocity but it can change the 38 00:02:33,542 --> 00:02:37,779 direction of the velocity. And so, what you're going to 39 00:02:37,779 --> 00:02:44,228 see is that the charged particle will 40 00:02:44,228 --> 00:02:48,943 go around into a perfect circle if the magnetic field is 41 00:02:48,943 --> 00:02:53,069 constant throughout. And the radius of this circle 42 00:02:53,069 --> 00:02:58,037 can very easily be calculated using some of our knowledge of 43 00:02:58,037 --> 00:03:01,405 eight oh two. The force is QVB because I 44 00:03:01,405 --> 00:03:06,625 chose B also perpendicular to V, and so there is no sign of the 45 00:03:06,625 --> 00:03:10,666 angle between them. This one, and this now has to 46 00:03:10,666 --> 00:03:16,639 be the centripetal force that we 47 00:03:16,639 --> 00:03:22,291 encountered in eight oh one, which is MV squared divided by 48 00:03:22,291 --> 00:03:26,19 R, M now being the mass of this particle. 49 00:03:26,19 --> 00:03:31,355 And so you'll find now that R equals MV divided by QB. 50 00:03:31,355 --> 00:03:35,448 And this, by the way, I want to remind you, 51 00:03:35,448 --> 00:03:38,566 is the momentum of that particle. 52 00:03:38,566 --> 00:03:43,537 If you look at this equation, it's sort of pleasing. 53 00:03:43,537 --> 00:03:48,272 If the charge is high then the 54 00:03:48,272 --> 00:03:52,197 Lawrence force is high so the radius is small. 55 00:03:52,197 --> 00:03:57,431 If the magnetic field is high then the Lawrence force is high 56 00:03:57,431 --> 00:04:02,054 so the radius is small. If the mass of the particle is 57 00:04:02,054 --> 00:04:07,374 high, there is a lot of inertia and so it is very difficult to 58 00:04:07,374 --> 00:04:09,991 make it go around, so to speak, 59 00:04:09,991 --> 00:04:14,353 so a very high mass, you expect a very high radius. 60 00:04:14,353 --> 00:04:18,539 And so that looks all intuitively quite pleasing. 61 00:04:18,539 --> 00:04:21,069 Let's do a numerical example. 62 00:04:21,069 --> 00:04:23,163 63 00:04:23,163 --> 00:04:26,505 I take a proton, P stands for proton, 64 00:04:26,505 --> 00:04:31,891 and I take a one MEV proton. It's the same I took during my 65 00:04:31,891 --> 00:04:35,791 test review. One MEV means that the kinetic 66 00:04:35,791 --> 00:04:41,455 energy is one MEV is the charge times the potential difference 67 00:04:41,455 --> 00:04:46,283 over which this proton was accelerated, in this case, 68 00:04:46,283 --> 00:04:49,44 delta V would be one million volts. 69 00:04:49,44 --> 00:04:53,805 And this now equals one-half times 70 00:04:53,805 --> 00:04:57,653 the mass of that proton times the velocity squared. 71 00:04:57,653 --> 00:05:00,347 In this case, if I have the one MEV, 72 00:05:00,347 --> 00:05:04,58 so it is a million volts, you will find that this is one 73 00:05:04,58 --> 00:05:08,275 point six times ten to the minus thirteen joules. 74 00:05:08,275 --> 00:05:13,047 I gave you there the charge of the proton, you multiplied it by 75 00:05:13,047 --> 00:05:15,587 a million, and this is the energy. 76 00:05:15,587 --> 00:05:19,974 And so now you can calculate the velocity because you know 77 00:05:19,974 --> 00:05:23,437 the mass of the proton. I gave 78 00:05:23,437 --> 00:05:24,948 you that too, there. 79 00:05:24,948 --> 00:05:29,481 And so you will find exactly what you found during my test 80 00:05:29,481 --> 00:05:34,014 review, one point four times ten to the seventh meters per 81 00:05:34,014 --> 00:05:38,069 second, which is five percent of the speed of light, 82 00:05:38,069 --> 00:05:42,523 comfortably low so we don't have to make any relativistic 83 00:05:42,523 --> 00:05:45,624 corrections. If this proton now enters a 84 00:05:45,624 --> 00:05:48,487 magnetic field B, which is one Tesla, 85 00:05:48,487 --> 00:05:51,906 then by using the equation I have up there, 86 00:05:51,906 --> 00:05:56,36 you know the mass of the proton, 87 00:05:56,36 --> 00:05:59,263 we just calculated the velocity. 88 00:05:59,263 --> 00:06:04,696 You know the charge of the proton and you know the B field. 89 00:06:04,696 --> 00:06:09,192 You will find that R is oh point one five meters, 90 00:06:09,192 --> 00:06:14,25 which is fifteen centimeters, just a numerical example. 91 00:06:14,25 --> 00:06:18,09 It is more common, or at least often done, 92 00:06:18,09 --> 00:06:23,242 to eliminate out of that equation there the velocity and 93 00:06:23,242 --> 00:06:28,113 replace it by the potential difference, 94 00:06:28,113 --> 00:06:32,702 capital V, over which we accelerate these particles. 95 00:06:32,702 --> 00:06:37,651 And so, what you can do, you can replace this V by using 96 00:06:37,651 --> 00:06:42,15 the equation I have there, the one half MV squared, 97 00:06:42,15 --> 00:06:47,369 so we have that one-half MV squared equals Q times delta V, 98 00:06:47,369 --> 00:06:52,678 but I will write for that just a capital V, and I substitute 99 00:06:52,678 --> 00:06:56,817 this V now in here, and so I now longer see the 100 00:06:56,817 --> 00:07:01,496 velocity but I now see this potential 101 00:07:01,496 --> 00:07:05,282 difference. In the case of that proton, 102 00:07:05,282 --> 00:07:10,961 this V would be a million and you will find then that R is 103 00:07:10,961 --> 00:07:16,939 then the square root of two M times that capital V divided by 104 00:07:16,939 --> 00:07:21,223 Q B squared. And so the two equations are of 105 00:07:21,223 --> 00:07:25,408 course the same physics, but it's different 106 00:07:25,408 --> 00:07:29,891 representation. If you put in for V now ten to 107 00:07:29,891 --> 00:07:36,012 the sixth mass of the proton, charge of the proton, 108 00:07:36,012 --> 00:07:40,385 and one Tesla field, of course you find exactly the 109 00:07:40,385 --> 00:07:45,458 same point one five meters. Now this is all nice and dandy, 110 00:07:45,458 --> 00:07:50,618 but this works as long as the speed is much smaller than the 111 00:07:50,618 --> 00:07:54,466 speed of light. If that's no longer the case, 112 00:07:54,466 --> 00:07:59,714 then we have to apply special relativity and that is not part 113 00:07:59,714 --> 00:08:04,699 of this course but I would like to briefly touch upon that 114 00:08:04,699 --> 00:08:09,83 today. I can show you how things go 115 00:08:09,83 --> 00:08:17,197 sour because suppose we have a five hundred kilo electric volt 116 00:08:17,197 --> 00:08:21,423 electron. So that means that in this 117 00:08:21,423 --> 00:08:26,858 equation here, the V is five hundred thousand, 118 00:08:26,858 --> 00:08:33,621 the Q is the charge of the electron, M is now the mass of 119 00:08:33,621 --> 00:08:38,811 the electron, and if I apply that equation I 120 00:08:38,811 --> 00:08:43,555 find that V is four point two times ten to the eighth meters 121 00:08:43,555 --> 00:08:47,816 per second and that is larger than the speed of light, 122 00:08:47,816 --> 00:08:51,676 so that's clearly not possible. The actual speed, 123 00:08:51,676 --> 00:08:55,938 if you make relativistic corrections, is two point six 124 00:08:55,938 --> 00:08:59,234 times ten to the eighth meters per second. 125 00:08:59,234 --> 00:09:03,657 And although I don't expect you to be able to make those 126 00:09:03,657 --> 00:09:08,079 relativistic corrections, I will make them today and you 127 00:09:08,079 --> 00:09:11,244 will see why I have to, 128 00:09:11,244 --> 00:09:16 and I want to show you that in fact this is not all that 129 00:09:16 --> 00:09:21,362 difficult even though I will not hold you responsible for these 130 00:09:21,362 --> 00:09:24,475 equations. So what I have here is now 131 00:09:24,475 --> 00:09:26,81 kinetic energy, is again QV, 132 00:09:26,81 --> 00:09:30,961 that's not changing, but is no longer one-half MV 133 00:09:30,961 --> 00:09:35,284 squared but it is gamma minus one times MC squared, 134 00:09:35,284 --> 00:09:41,683 and gamma is defined there -- it's called the Lorenz Factor, 135 00:09:41,683 --> 00:09:46,253 and so if you know now for the electron that capital V is five 136 00:09:46,253 --> 00:09:49,849 hundred thousand, you can calculate what gamma is 137 00:09:49,849 --> 00:09:54,418 from the first equation and then you go to the second equation 138 00:09:54,418 --> 00:09:58,988 and you find what the speed is, and you will see then that you 139 00:09:58,988 --> 00:10:02,658 never find a speed larger than the speed of light. 140 00:10:02,658 --> 00:10:07,078 And so we now have to make the correction also for the radii 141 00:10:07,078 --> 00:10:11,873 and those corrections become again relatively easy. 142 00:10:11,873 --> 00:10:15,765 This now requires a factor gamma and you see that on the 143 00:10:15,765 --> 00:10:19,233 upper blackboard there, and this too now has to be 144 00:10:19,233 --> 00:10:23,267 replaced by this gamma plus one and then everything is OK. 145 00:10:23,267 --> 00:10:27,371 So I don't expect you to know this, but I don't want you to 146 00:10:27,371 --> 00:10:30,839 think that all these relativistic corrections come 147 00:10:30,839 --> 00:10:34,166 out of the blue, nor do I want you think that it 148 00:10:34,166 --> 00:10:36,572 is very difficult. It really isn't. 149 00:10:36,572 --> 00:10:39,615 The equations are extremely straightforward. 150 00:10:39,615 --> 00:10:41,313 151 00:10:41,313 --> 00:10:46,261 So I want to show you now some of the results that we just 152 00:10:46,261 --> 00:10:49,82 discussed. The one MEV proton and the five 153 00:10:49,82 --> 00:10:53,292 hundred KEV electron, this is on the Web. 154 00:10:53,292 --> 00:10:57,805 You can click on Lecture Supplements and you can make 155 00:10:57,805 --> 00:11:01,972 yourself a hard copy. So here you see the kinetic 156 00:11:01,972 --> 00:11:06,051 energy, one MEV proton. Notice the speed that we 157 00:11:06,051 --> 00:11:09,176 calculated there is non-relativistic, 158 00:11:09,176 --> 00:11:14,5 gamma is very close to one. You don't have to make a 159 00:11:14,5 --> 00:11:17,228 correction. And in a one Tesla field you 160 00:11:17,228 --> 00:11:20,654 get a radius of fifteen centimeters, which we just 161 00:11:20,654 --> 00:11:23,102 calculated. If you go to a fifty MEV 162 00:11:23,102 --> 00:11:27,159 proton, it's sort of in the borderline between relativistic 163 00:11:27,159 --> 00:11:30,516 and non-relativistic. It's still non-relativistic 164 00:11:30,516 --> 00:11:34,152 enough, and if it is non-relativistic you can clearly 165 00:11:34,152 --> 00:11:38,349 see here that the radius goes with the square root of capital 166 00:11:38,349 --> 00:11:39,747 V. And for fifty MEV, 167 00:11:39,747 --> 00:11:44,059 capital V is fifty million, and for one MEV, 168 00:11:44,059 --> 00:11:47,771 capital V is one million. And since it goes with the 169 00:11:47,771 --> 00:11:51,12 square root of V, you expect roughly the radius 170 00:11:51,12 --> 00:11:55,341 to be the square root of fifty times larger which is seven, 171 00:11:55,341 --> 00:11:58,908 and indeed, you see that. So you see, from fifteen 172 00:11:58,908 --> 00:12:02,256 centimeters the radius goes to about one meter. 173 00:12:02,256 --> 00:12:05,24 Um, here is our five hundred KEV electron, 174 00:12:05,24 --> 00:12:08,661 and notice that I did the calculation correctly. 175 00:12:08,661 --> 00:12:13,257 This is relativistically corrected now. 176 00:12:13,257 --> 00:12:17,955 You get your two point six times ten to the eighth meters 177 00:12:17,955 --> 00:12:22,654 per second by applying the formalism that you see there. 178 00:12:22,654 --> 00:12:26,513 I will leave this here throughout this lecture, 179 00:12:26,513 --> 00:12:30,121 because I will return to this several times. 180 00:12:30,121 --> 00:12:33,644 I want to show you a a cute demonstration. 181 00:12:33,644 --> 00:12:37 I have an, er, electron gun here and the 182 00:12:37 --> 00:12:42,789 electron gun comes like so. 183 00:12:42,789 --> 00:12:45,885 This is the velocity of the electrons. 184 00:12:45,885 --> 00:12:50,153 I put a minus sign there to remind you that they are 185 00:12:50,153 --> 00:12:52,915 electrons. If electrons go in this 186 00:12:52,915 --> 00:12:56,681 direction, the current goes in that direction. 187 00:12:56,681 --> 00:13:01,703 And so if now I have a magnetic field which, let's assume the 188 00:13:01,703 --> 00:13:04,632 magnetic field is in the blackboard. 189 00:13:04,632 --> 00:13:08,063 This is B. Then I cross B is the direction 190 00:13:08,063 --> 00:13:11,076 of the force. I is in this direction, 191 00:13:11,076 --> 00:13:16,103 B is in the blackboard. So if I'm not mistaken, 192 00:13:16,103 --> 00:13:20,057 I think the force is in this direction and so you will see 193 00:13:20,057 --> 00:13:22,832 that it starts to bend in this direction. 194 00:13:22,832 --> 00:13:26,231 If you change the direction of the magnetic field, 195 00:13:26,231 --> 00:13:29,7 the magnetic field is coming out of the blackboard, 196 00:13:29,7 --> 00:13:32,683 then the electron will go in this direction, 197 00:13:32,683 --> 00:13:36,637 and I can show you that here. It is not too different from 198 00:13:36,637 --> 00:13:40,591 the distortion experiment I did when I had the television 199 00:13:40,591 --> 00:13:45,03 program there and I had the strong magnet 200 00:13:45,03 --> 00:13:50,822 and we distorted the image, but this of course is a little 201 00:13:50,822 --> 00:13:55,495 bit more controlled. So, we're going to see the 202 00:13:55,495 --> 00:14:01,287 image there and we want to make it quite dark in the room. 203 00:14:01,287 --> 00:14:04,741 Mmm. And turn on the electron gun. 204 00:14:04,741 --> 00:14:11,142 So you see, the electron gun it strikes a fluorescent screen and 205 00:14:11,142 --> 00:14:19,592 that's how you can see it, and I have here a bar magnet 206 00:14:19,592 --> 00:14:26,377 and if I hold the bar magnet behind it then I can create more 207 00:14:26,377 --> 00:14:33,048 or less situations like this. I can flip over the magnet and 208 00:14:33,048 --> 00:14:37,911 then the direction of bending should change, 209 00:14:37,911 --> 00:14:42,773 so here I come with the magnet, and you see, 210 00:14:42,773 --> 00:14:48,54 curve up the electrons. I turn the magnet over and I 211 00:14:48,54 --> 00:14:52,272 come in again and they curve down. 212 00:14:52,272 --> 00:14:56,004 Very straightforward, very simple. 213 00:14:56,004 --> 00:14:56,343 OK. 214 00:14:56,343 --> 00:14:59,961 215 00:14:59,961 --> 00:15:05,452 There is a fantastic way in physics that we can separate 216 00:15:05,452 --> 00:15:09,246 isotopes from one and the same element. 217 00:15:09,246 --> 00:15:12,541 If we, for instance, take uranium, 218 00:15:12,541 --> 00:15:15,436 now uranium, when you find it, 219 00:15:15,436 --> 00:15:20,327 is for ninety-nine point three percent uranium two 220 00:15:20,327 --> 00:15:24,421 thirty-eight. That means it had ninety-two 221 00:15:24,421 --> 00:15:29,912 protons, otherwise it wouldn't be uranium, 222 00:15:29,912 --> 00:15:32,913 and it has hundred and forty-six neutrons, 223 00:15:32,913 --> 00:15:35,182 ninety-nine point three percent. 224 00:15:35,182 --> 00:15:38,549 Point seven percent is uranium two thirty-five. 225 00:15:38,549 --> 00:15:42,209 Again, ninety-two protons, otherwise it wouldn't be 226 00:15:42,209 --> 00:15:46,016 uranium, but only a hundred and forty-three neutrons, 227 00:15:46,016 --> 00:15:50,188 and that you'll find in nature for oh point seven percent. 228 00:15:50,188 --> 00:15:54,58 So you go to a chemist and you give a chemist a little bit of 229 00:15:54,58 --> 00:15:58,533 uranium and you say would you please separate these two 230 00:15:58,533 --> 00:16:02,956 isotopes for me, and he of course would laugh at 231 00:16:02,956 --> 00:16:06,452 you and he would say go fly a kite because the chemical 232 00:16:06,452 --> 00:16:10,402 properties are exactly the same for the two because uranium is 233 00:16:10,402 --> 00:16:12,473 uranium. Neutral uranium here has 234 00:16:12,473 --> 00:16:16,293 ninety-two electrons and neutral uranium here has ninety-two 235 00:16:16,293 --> 00:16:20,114 electrons, so there's no way that they could separate those. 236 00:16:20,114 --> 00:16:23,869 And I will show you now how they can be separated with what 237 00:16:23,869 --> 00:16:27,689 we call a mass spectrometer. You heat the uranium so that it 238 00:16:27,689 --> 00:16:30,149 ionizes. Let's assume it's ionized once 239 00:16:30,149 --> 00:16:33,179 so it loses one electron, 240 00:16:33,179 --> 00:16:36,991 so it's positively charged with one unit charge, 241 00:16:36,991 --> 00:16:40,072 one of those charges that you see here. 242 00:16:40,072 --> 00:16:44,938 And we now accelerate it over certain potential difference so 243 00:16:44,938 --> 00:16:48,749 these uranium atoms, two thirty-five and the two 244 00:16:48,749 --> 00:16:53,858 thirty-eight get a certain speed and they come in here with this 245 00:16:53,858 --> 00:16:58,886 speed V, so they're positively charged and let's assume that we 246 00:16:58,886 --> 00:17:03,84 have a magnetic field that is uniform and that 247 00:17:03,84 --> 00:17:08,09 is in this direction, comes out of the blackboard. 248 00:17:08,09 --> 00:17:13,035 So what will happen is that these charged particles which 249 00:17:13,035 --> 00:17:16,765 are positively charged now, one unit charge, 250 00:17:16,765 --> 00:17:20,581 are going to go around a circle and hit here. 251 00:17:20,581 --> 00:17:24,571 It is the radius. But if you look here at these 252 00:17:24,571 --> 00:17:32,291 equations so you will see that the radius is proportional with 253 00:17:32,291 --> 00:17:36,568 the square root of the mass of the particle and the mass of two 254 00:17:36,568 --> 00:17:40,706 thirty-eight is one point two percent larger than the mass of 255 00:17:40,706 --> 00:17:43,533 two thirty-five. And so with one point two 256 00:17:43,533 --> 00:17:46,568 percent larger, since we have the square root 257 00:17:46,568 --> 00:17:50,568 there, we see here the square root, we accelerate them over 258 00:17:50,568 --> 00:17:54,499 the same potential difference, so this one doesn't change. 259 00:17:54,499 --> 00:17:56,913 This is the only thing that changes. 260 00:17:56,913 --> 00:18:01,189 So then you expect an oh point six percent change in radius and 261 00:18:01,189 --> 00:18:04,498 so the two thirty-eight will end up 262 00:18:04,498 --> 00:18:06,651 here. I exaggerate that very highly. 263 00:18:06,651 --> 00:18:09,112 And the two thirty-five will end up here. 264 00:18:09,112 --> 00:18:12,558 The two thirty-eight has a larger radius because it has a 265 00:18:12,558 --> 00:18:14,65 larger mass, and you see that here. 266 00:18:14,65 --> 00:18:17,48 There's no change in B, there's no change in Q, 267 00:18:17,48 --> 00:18:19,571 and there's no change in capital V. 268 00:18:19,571 --> 00:18:22,832 We accelerate them over the same potential difference. 269 00:18:22,832 --> 00:18:24,924 And so if the radius, for instance, 270 00:18:24,924 --> 00:18:28,554 were one meter of this mass spectrometer then the difference 271 00:18:28,554 --> 00:18:32,368 here -- remember this is two R -- the difference would come out 272 00:18:32,368 --> 00:18:35,578 to be about one point two 273 00:18:35,578 --> 00:18:40,632 centimeters, and so you have a collector here where you collect 274 00:18:40,632 --> 00:18:45,442 your two thirty-eight nuclei atoms and here you collect your 275 00:18:45,442 --> 00:18:50,578 two thirty-five and that is the idea behind a mass spectrometer. 276 00:18:50,578 --> 00:18:53,838 Why did I choose this particular example? 277 00:18:53,838 --> 00:18:58,403 Well, this example changed our world and it made history. 278 00:18:58,403 --> 00:19:03,213 Uranium two thirty-five was needed by the Americans to build 279 00:19:03,213 --> 00:19:07,859 an atomic bomb to end the Second World War. 280 00:19:07,859 --> 00:19:12,088 This is- this was done under the famous Manhattan Project. 281 00:19:12,088 --> 00:19:16,687 And Ernest Lawrence of Berkeley built mass spectrometers which 282 00:19:16,687 --> 00:19:20,619 were able to separate uranium two thirty-five from two 283 00:19:20,619 --> 00:19:22,845 thirty-eight. In the beginning, 284 00:19:22,845 --> 00:19:26,406 it went very slowly, about one hundred micrograms 285 00:19:26,406 --> 00:19:28,705 per day. But a few kilograms was 286 00:19:28,705 --> 00:19:33,008 required for an atomic bomb. They finally managed to get up 287 00:19:33,008 --> 00:19:36,643 to one gram per day and in combination with other 288 00:19:36,643 --> 00:19:41,538 separation techniques such as the gas 289 00:19:41,538 --> 00:19:45,744 diffusion techniques which I will not discuss here now they 290 00:19:45,744 --> 00:19:49,737 managed to get a few kilograms and they dropped a bomb on 291 00:19:49,737 --> 00:19:53,587 Hiroshima on August sixth nineteen forty-five and three 292 00:19:53,587 --> 00:19:56,51 days later a bomb was dropped on Nagasaki. 293 00:19:56,51 --> 00:20:00,787 The Japanese surrendered and it was the end of World War Two. 294 00:20:00,787 --> 00:20:04,922 It's a good thing that there are many peaceful applications 295 00:20:04,922 --> 00:20:09,057 nowadays of mass spectrometers, particularly in the medical 296 00:20:09,057 --> 00:20:13,018 area. People sometimes require 297 00:20:13,018 --> 00:20:17,112 radiation and they need radiation from a particular 298 00:20:17,112 --> 00:20:21,123 radioactive isotopes, but you don't want the other 299 00:20:21,123 --> 00:20:25,953 isotopes from the same element and so you separate them then 300 00:20:25,953 --> 00:20:29,801 with a mass spectrometer. It's a whole industry, 301 00:20:29,801 --> 00:20:33,976 very important industry. And I would like to address 302 00:20:33,976 --> 00:20:38,315 the issue how you accelerate protons to extremely high 303 00:20:38,315 --> 00:20:43,882 speeds, almost approaching the speed of light. 304 00:20:43,882 --> 00:20:50,448 And that is also something for which Ernest Lawrence is 305 00:20:50,448 --> 00:20:55,069 credited. In the early days it was done 306 00:20:55,069 --> 00:21:00,298 in a cyclotron, which I will describe to you 307 00:21:00,298 --> 00:21:04,068 now. The cyclotron consists of a 308 00:21:04,068 --> 00:21:10,391 chamber which is called a D. This is one D and here's 309 00:21:10,391 --> 00:21:16,914 another D. These are conducting chambers. 310 00:21:16,914 --> 00:21:21,608 If you look from the side it would look like so. 311 00:21:21,608 --> 00:21:27,3 This is the left chamber and this is the right chamber and 312 00:21:27,3 --> 00:21:32,793 all of this is in vacuum and let's assume that we have a 313 00:21:32,793 --> 00:21:37,387 magnetic field coming out of the board like so. 314 00:21:37,387 --> 00:21:40,583 Let's revisit our one MEV proton. 315 00:21:40,583 --> 00:21:45,077 Suppose I release in this chamber 316 00:21:45,077 --> 00:21:49 here a one MEV proton and I know the speed with which it 317 00:21:49 --> 00:21:52,922 comes out, because the one MEV proton had a speed -- Oh, 318 00:21:52,922 --> 00:21:56,773 you still see it there, one point four times ten to the 319 00:21:56,773 --> 00:22:00,339 seven meters per second. We also know that in a one 320 00:22:00,339 --> 00:22:04,831 Tesla field, let's make this one Tesla, that the radius is going 321 00:22:04,831 --> 00:22:08,112 to be fifteen centimeters. You see it up there. 322 00:22:08,112 --> 00:22:10,537 So what is this proton going to do? 323 00:22:10,537 --> 00:22:13,746 It's going to do this. But when it gets there, 324 00:22:13,746 --> 00:22:19,04 the potential difference is introduced between these two 325 00:22:19,04 --> 00:22:23,739 D's, so that this is low pot- high potential and this is a low 326 00:22:23,739 --> 00:22:26,743 potential. And so you're going to get an 327 00:22:26,743 --> 00:22:31,288 electric field now in this gap in this direction and so this 328 00:22:31,288 --> 00:22:35,447 proton is being accelerated. And let's suppose that the 329 00:22:35,447 --> 00:22:38,76 difference in potential is twenty kilovolts. 330 00:22:38,76 --> 00:22:43,15 Then this proton will gain in electric- in kinetic energy, 331 00:22:43,15 --> 00:22:46,924 it will gain kinetic energy, twenty 332 00:22:46,924 --> 00:22:52,339 kilo electron volts. That's the way electron volt is 333 00:22:52,339 --> 00:22:56,267 defined. And so you start off with one 334 00:22:56,267 --> 00:23:02,531 MEV, so when it has crossed this gap it is now one point oh 335 00:23:02,531 --> 00:23:05,079 two MEV. Twenty KEV more. 336 00:23:05,079 --> 00:23:07,84 The radius, now, is larger. 337 00:23:07,84 --> 00:23:13,254 If capital V is two percent higher, and I go to this 338 00:23:13,254 --> 00:23:19,585 equation, then the radius is one percent 339 00:23:19,585 --> 00:23:24,229 higher and so when it comes out here and it makes a circle, 340 00:23:24,229 --> 00:23:29,113 the radius now is one percent higher than fifteen centimeters. 341 00:23:29,113 --> 00:23:33,437 But when it gets to this part of the D, this potential 342 00:23:33,437 --> 00:23:38,161 difference is reversed and so the electric field is again in 343 00:23:38,161 --> 00:23:41,764 this direction, in the direction of the proton 344 00:23:41,764 --> 00:23:46,568 and so it is accelerated again by twenty kilo electron volts. 345 00:23:46,568 --> 00:23:51,411 Now the radius, of course, is even larger and 346 00:23:51,411 --> 00:23:55,131 so very gradually every time that it reaches the gap the 347 00:23:55,131 --> 00:23:59,255 potential difference is changed in direction to accelerate the 348 00:23:59,255 --> 00:24:02,231 proton and so it gradually spirals out, then, 349 00:24:02,231 --> 00:24:04,597 to the largest radius that you have. 350 00:24:04,597 --> 00:24:08,79 So during one full rotation it gains twenty kilo electron volts 351 00:24:08,79 --> 00:24:12,847 once, and twenty kilo electron volts twice, so it gains forty 352 00:24:12,847 --> 00:24:16,228 kilo electron volts. And so the electric fields are 353 00:24:16,228 --> 00:24:20,961 doing the work. They accelerate the particles. 354 00:24:20,961 --> 00:24:23,923 Magnetic fields can not accelerate. 355 00:24:23,923 --> 00:24:28,975 Magnetic fields can change the direction but they can do no 356 00:24:28,975 --> 00:24:33,505 work on the particles. So the magnetic fields confine 357 00:24:33,505 --> 00:24:37,164 the particles. So let's assume we go twelve 358 00:24:37,164 --> 00:24:40,474 hundred and twenty-five full rotations. 359 00:24:40,474 --> 00:24:44,916 During each rotation the kinetic energy increased by 360 00:24:44,916 --> 00:24:48,4 forty KEV. And so if you multiply the two 361 00:24:48,4 --> 00:24:52,538 then you see now that the kinetic 362 00:24:52,538 --> 00:24:57,946 energy of this proton increased by forty-nine million electron 363 00:24:57,946 --> 00:25:02,557 volts, because it went twelve-hundred and twenty-five 364 00:25:02,557 --> 00:25:07,433 times all the way around, and so now you have forty-nine 365 00:25:07,433 --> 00:25:11,157 MEV plus the one MEV that you started with, 366 00:25:11,157 --> 00:25:14,172 so now you have a fifty MEV proton. 367 00:25:14,172 --> 00:25:19,314 You see the second line there? There we have that fifty MEV 368 00:25:19,314 --> 00:25:23,449 proton that I discussed with you 369 00:25:23,449 --> 00:25:26,848 earlier. In a one Tesla field now the 370 00:25:26,848 --> 00:25:31,665 radius is one meter, so if this unit had a radius of 371 00:25:31,665 --> 00:25:37,048 one meter that would be fine. By that time it would be all 372 00:25:37,048 --> 00:25:41,109 the way near the circumference of this unit. 373 00:25:41,109 --> 00:25:46,398 What is remarkable and not intuitive, that the time to go 374 00:25:46,398 --> 00:25:51,214 around as long as we don't have to make relativistic 375 00:25:51,214 --> 00:25:57,574 corrections, that the time for a proton to 376 00:25:57,574 --> 00:26:01,592 go around is independent of its speed. 377 00:26:01,592 --> 00:26:06,152 Not so intuitive, and you can see this very 378 00:26:06,152 --> 00:26:12,558 easily because the time to go around is two pi R divided by 379 00:26:12,558 --> 00:26:16,033 its speed. You see, the radius is 380 00:26:16,033 --> 00:26:20,702 proportional to V. And so the time itself is 381 00:26:20,702 --> 00:26:27,373 independent of V, because R itself is linearly 382 00:26:27,373 --> 00:26:33,294 proportional with the speed and so that cancels and so you'll 383 00:26:33,294 --> 00:26:38,918 find now that the time to go around is simply two pi times 384 00:26:38,918 --> 00:26:42,766 the mass of that particle divided by QB. 385 00:26:42,766 --> 00:26:46,219 And if you correct relativistically, 386 00:26:46,219 --> 00:26:51,153 then you have to multiply by gamma, but if you stay 387 00:26:51,153 --> 00:26:55,593 non-relativistic, then it's independent of the 388 00:26:55,593 --> 00:27:00,991 speed of the protons. So if we stick to this 389 00:27:00,991 --> 00:27:06,296 particular case of our one MEV proton that became a fifty MEV 390 00:27:06,296 --> 00:27:11,247 proton going around twelve hundred and twenty-five times, 391 00:27:11,247 --> 00:27:16,286 this time to go around once is only sixty-six nanoseconds, 392 00:27:16,286 --> 00:27:21,679 so this is six point six times ten to the minus eight seconds. 393 00:27:21,679 --> 00:27:26,188 Give you some feeling of how fast all this is going. 394 00:27:26,188 --> 00:27:30,255 So if you go around twelve hundred 395 00:27:30,255 --> 00:27:33,606 and twenty-five times, that would take only eighty 396 00:27:33,606 --> 00:27:37,299 microseconds so in eighty microseconds does all of this 397 00:27:37,299 --> 00:27:41,539 occur and that means you have to switch this field twice before 398 00:27:41,539 --> 00:27:45,438 rotation, make sure that the e-field is in this direction, 399 00:27:45,438 --> 00:27:49,473 but when the proton comes here the e-field has to be in that 400 00:27:49,473 --> 00:27:52,209 direction. And so the switching frequency 401 00:27:52,209 --> 00:27:55,902 which easily be calculated becomes about thirty million 402 00:27:55,902 --> 00:27:58,638 times per second, about thirty megahertz. 403 00:27:58,638 --> 00:28:04,533 And all of that takes place in eighty microseconds and you 404 00:28:04,533 --> 00:28:09,597 create one MEV protons, you turn them into fifty MEV 405 00:28:09,597 --> 00:28:12,775 protons. A mind-boggling concept, 406 00:28:12,775 --> 00:28:15,753 but it works. Quite remarkable. 407 00:28:15,753 --> 00:28:21,711 Now because of the relativistic corrections that you see here 408 00:28:21,711 --> 00:28:27,668 with gamma, if you go to very high energies then the time is 409 00:28:27,668 --> 00:28:32,832 not constant for a full rotation, 410 00:28:32,832 --> 00:28:37,892 so you have to adjust now the frequency with which you switch 411 00:28:37,892 --> 00:28:40,591 the potential between these gaps. 412 00:28:40,591 --> 00:28:45,652 So if the time increases then this switching frequency has to 413 00:28:45,652 --> 00:28:49,869 go down and we call those instruments synchrotrons, 414 00:28:49,869 --> 00:28:52,99 or synchrocyclotrons. They have names. 415 00:28:52,99 --> 00:28:57,208 So you synchronize now and correct for relativistic 416 00:28:57,208 --> 00:28:59,907 effects. Modern accelerators have 417 00:28:59,907 --> 00:29:03,787 constant radii. They are rings. 418 00:29:03,787 --> 00:29:07,127 And so if you have a ring with constant radius, 419 00:29:07,127 --> 00:29:11,483 the only way that you can keep the particles in the ring when 420 00:29:11,483 --> 00:29:15,985 they have a low energy and when they have the high energy is by 421 00:29:15,985 --> 00:29:18,817 gradually increasing the magnetic field. 422 00:29:18,817 --> 00:29:21,94 So you start off with a weak magnetic field, 423 00:29:21,94 --> 00:29:25,135 you go around huge circle, very large radius, 424 00:29:25,135 --> 00:29:29,273 and you gradually increase the magnetic fields as you keep 425 00:29:29,273 --> 00:29:33,848 accelerating them and by making the magnetic field go up just in 426 00:29:33,848 --> 00:29:36,825 the right way, maybe all the way up to two 427 00:29:36,825 --> 00:29:41,236 Tesla, you can keep them in that ring. 428 00:29:41,236 --> 00:29:46,175 The first slide that I'd like to show you is the slide of an 429 00:29:46,175 --> 00:29:50,611 ancient cyclotron that is actually a synchrocyclotron, 430 00:29:50,611 --> 00:29:55,132 was built by Lawrence in Berkeley, and this was capable 431 00:29:55,132 --> 00:29:59,401 of accelerating protons to seven hundred thirty MEV. 432 00:29:59,401 --> 00:30:04,172 You see here a person to give you feeling for the size of 433 00:30:04,172 --> 00:30:07,772 this instrument. Lawrence received the Nobel 434 00:30:07,772 --> 00:30:12,292 Prize for Physics in 1939 for his 435 00:30:12,292 --> 00:30:17,713 invention of the cyclotron. The next slide is Fermilab near 436 00:30:17,713 --> 00:30:20,984 Chicago. This is one of these modern 437 00:30:20,984 --> 00:30:25,096 accelerators also called sometimes colliders, 438 00:30:25,096 --> 00:30:29,862 and this has a diameter of two point two kilometers, 439 00:30:29,862 --> 00:30:34,535 and this instrument, this here, plans to accelerate 440 00:30:34,535 --> 00:30:38,74 protons up to thousand GEV, G stands for giga, 441 00:30:38,74 --> 00:30:44,16 giga is the same as billion. A thousand giga electron volts 442 00:30:44,16 --> 00:30:48,203 would be ten to the twelfth electron 443 00:30:48,203 --> 00:30:50,377 volts. The beams of high energy 444 00:30:50,377 --> 00:30:54,652 protons are made to collide with other nuclei to uncover the 445 00:30:54,652 --> 00:30:57,043 inner workings of nuclear physics. 446 00:30:57,043 --> 00:31:00,956 The higher the energy of the protons, the larger is the 447 00:31:00,956 --> 00:31:05,159 impact when the protons collide and the more one expects to 448 00:31:05,159 --> 00:31:07,333 learn. By using ever-increasing 449 00:31:07,333 --> 00:31:10,956 energies of the protons, which are nuclear bullets, 450 00:31:10,956 --> 00:31:14,072 one explores unknown territory. In the news, 451 00:31:14,072 --> 00:31:17,694 these colliders are often called 452 00:31:17,694 --> 00:31:21,063 atom smashers. That is a flashier name which 453 00:31:21,063 --> 00:31:25,372 appeals more to the general public who pays for all this 454 00:31:25,372 --> 00:31:29,447 with their tax money. This research is a multibillion 455 00:31:29,447 --> 00:31:32,737 dollar industry. The words atom smasher are 456 00:31:32,737 --> 00:31:36,341 actually a misnomer. The colliders smash nuclei 457 00:31:36,341 --> 00:31:40,023 which are ten thousand times smaller than atoms. 458 00:31:40,023 --> 00:31:44,567 And the next slide shows you the tunnel of the largest ring 459 00:31:44,567 --> 00:31:50,443 in the world which is in Geneva, at CERN which is a European 460 00:31:50,443 --> 00:31:53,921 collaboration. This tunnel which already 461 00:31:53,921 --> 00:31:59,002 exists for many years has a confluence of seventeen miles, 462 00:31:59,002 --> 00:32:02,836 has a radius of four point three kilometers, 463 00:32:02,836 --> 00:32:08,275 and in here are these protons being accelerated [inaudible] on 464 00:32:08,275 --> 00:32:12,465 the high vacuum. And with very modern techniques 465 00:32:12,465 --> 00:32:18,082 of superconducting magnets they can even go up now to about five 466 00:32:18,082 --> 00:32:21,291 Tesla. And in this tunnel right now a 467 00:32:21,291 --> 00:32:25,179 whole new experiment is under 468 00:32:25,179 --> 00:32:30,76 development which is called the Large Hadron Collider which is 469 00:32:30,76 --> 00:32:35,975 considered the Holy Grail for particle physicists and it's 470 00:32:35,975 --> 00:32:41,282 hoped that that will go on the air in the year Two Thousand 471 00:32:41,282 --> 00:32:45,582 Seven or so and it will accelerate protons to an 472 00:32:45,582 --> 00:32:50,98 unprecedented energy that will give them kinetic energies of 473 00:32:50,98 --> 00:32:55,463 seven thousand GEV, seven times ten to the twelfth 474 00:32:55,463 --> 00:33:00,777 electron volts. So I would like to return to my 475 00:33:00,777 --> 00:33:04,382 overhead there, so that you can see some of 476 00:33:04,382 --> 00:33:09,017 that what we just discussed right there, thank you Tom. 477 00:33:09,017 --> 00:33:13,652 So here we have Fermilab. You see a radius of one point 478 00:33:13,652 --> 00:33:17,601 one kilometers. I showed you a picture from the 479 00:33:17,601 --> 00:33:21,635 air and so they went up to one point five Tesla, 480 00:33:21,635 --> 00:33:25,497 so that's the maximum magnetic field strength. 481 00:33:25,497 --> 00:33:31,163 Get very close to the speed of light 482 00:33:31,163 --> 00:33:35,862 by the way [laughter] and you see five hundred GEV protons. 483 00:33:35,862 --> 00:33:39,752 And here you see the holy grail, the large hadron 484 00:33:39,752 --> 00:33:43,803 collider, European collaboration in Geneva at CERN, 485 00:33:43,803 --> 00:33:48,017 whereby you have the circumference of seventeen miles 486 00:33:48,017 --> 00:33:52,879 and the magnetic fields that they hope to achieve going up to 487 00:33:52,879 --> 00:33:56,688 five and a half Tesla using modern techniques of 488 00:33:56,688 --> 00:34:00,415 superconductors. So if you want to go around in 489 00:34:00,415 --> 00:34:06,363 those tunnels by the way, by the way, you need a 490 00:34:06,363 --> 00:34:10,947 motorcycle, [inaudible] go seventeen miles around. 491 00:34:10,947 --> 00:34:15,999 The goal of all this physics, of all these experiments, 492 00:34:15,999 --> 00:34:21,332 is to enter new territory, to learn about these mysterious 493 00:34:21,332 --> 00:34:26,945 nuclear forces and to see what is insi- inside protons and to 494 00:34:26,945 --> 00:34:32,465 see what is inside neutrons. And with these experiments many 495 00:34:32,465 --> 00:34:36,675 nuclear particles were discovered 496 00:34:36,675 --> 00:34:40,883 whose existence was completely unknown previously. 497 00:34:40,883 --> 00:34:45,606 Now comes the issue how can you see the results of these 498 00:34:45,606 --> 00:34:50,158 collisions of these particles with very high energies. 499 00:34:50,158 --> 00:34:54,967 Well, you can make the tracks of these particles visible. 500 00:34:54,967 --> 00:34:59,346 In fact, today you will see them with your own eyes. 501 00:34:59,346 --> 00:35:04,155 And in the old days this was done with cloud chambers and 502 00:35:04,155 --> 00:35:08,986 that's the demonstration I will do today 503 00:35:08,986 --> 00:35:11,828 for you. But nowadays they do them with 504 00:35:11,828 --> 00:35:14,969 bubble chambers. Let's first understand the 505 00:35:14,969 --> 00:35:17,96 principle. If you had a charged particle, 506 00:35:17,96 --> 00:35:22,447 whether it is an electron or a proton or an alpha particle -- 507 00:35:22,447 --> 00:35:26,709 alpha particle is the nucleus of helium, it's two protons, 508 00:35:26,709 --> 00:35:29,85 two neutrons. If it goes through the air it 509 00:35:29,85 --> 00:35:33,814 makes ions and as it goes through the air and it makes 510 00:35:33,814 --> 00:35:39,048 ions it slowly loses its kinetic energy and it finally 511 00:35:39,048 --> 00:35:42,465 comes to a halt. If we take a ten MEV electron 512 00:35:42,465 --> 00:35:46,034 and one atmosphere air it could go forty meters. 513 00:35:46,034 --> 00:35:50,361 If you take a proton of ten MEV it would only go one meter 514 00:35:50,361 --> 00:35:54,917 because the density of ions is higher because it has a higher 515 00:35:54,917 --> 00:35:59,548 mass and if you take an alpha particle which has a higher mass 516 00:35:59,548 --> 00:36:03,496 than a proton and it has a double charge of a proton, 517 00:36:03,496 --> 00:36:06,305 then it would only go ten centimeters. 518 00:36:06,305 --> 00:36:10,101 It's a very high density track that 519 00:36:10,101 --> 00:36:12,613 you would get from an alpha particle. 520 00:36:12,613 --> 00:36:16,45 And so one way you could see these tracks is using cloud 521 00:36:16,45 --> 00:36:20,566 chambers, and a cloud chamber works in principle as follows. 522 00:36:20,566 --> 00:36:24,334 You can just have a chamber in air, one atmosphere air, 523 00:36:24,334 --> 00:36:28,729 which you put liquid alcohol in there, that's the way we will do 524 00:36:28,729 --> 00:36:31,938 it, and you cool the bottom. You see one there, 525 00:36:31,938 --> 00:36:35,915 which you will see a little later, and you cool the bottom 526 00:36:35,915 --> 00:36:39,682 with solid CO two and then you get inside this chamber, 527 00:36:39,682 --> 00:36:43,938 you get a temperature gradient and there's a layer there where 528 00:36:43,938 --> 00:36:47,599 the alcohol should really condense 529 00:36:47,599 --> 00:36:51,924 into little drops because it's that cold, but for reasons that 530 00:36:51,924 --> 00:36:54,902 are complicated it doesn't do it quite yet. 531 00:36:54,902 --> 00:36:57,171 We call that undercooled alcohol. 532 00:36:57,171 --> 00:37:01,07 Even rain can be undercooled. Just below freezing point, 533 00:37:01,07 --> 00:37:03,906 still liquid. When the moment it hits the 534 00:37:03,906 --> 00:37:06,671 ground it will immediately become solid, 535 00:37:06,671 --> 00:37:09,648 by the way. That's also undercooled liquid. 536 00:37:09,648 --> 00:37:13,477 Now, here we deal with an undercooled vapor and so when 537 00:37:13,477 --> 00:37:17,301 these ions are made by these charged 538 00:37:17,301 --> 00:37:20,81 particles, these ions act as seeds for the drops, 539 00:37:20,81 --> 00:37:25,342 in this case the alcohol drops, and you can literally with your 540 00:37:25,342 --> 00:37:28,486 eyes, visually see these drops being formed. 541 00:37:28,486 --> 00:37:32,653 I'd like to go through one numerical example and I want to 542 00:37:32,653 --> 00:37:36,528 go to a five hundred KEV electron which you see there. 543 00:37:36,528 --> 00:37:39,525 Um, notice that I have corrected the speed 544 00:37:39,525 --> 00:37:42,815 relativistically, otherwise you would get this 545 00:37:42,815 --> 00:37:46,617 ridiculous number that we calculated 546 00:37:46,617 --> 00:37:50,051 earlier which is larger than the speed of light. 547 00:37:50,051 --> 00:37:53,266 And suppose we have a one-tenths Tesla field. 548 00:37:53,266 --> 00:37:56,992 Then the radius would be two point nine centimeters. 549 00:37:56,992 --> 00:38:01,376 But after a while this electron will lose its energy and then 550 00:38:01,376 --> 00:38:05,906 there comes a time that it has only hundred kilo electron volts 551 00:38:05,906 --> 00:38:07,221 left. By that time, 552 00:38:07,221 --> 00:38:11,167 the radius in a one-tenths Tesla field would now be one 553 00:38:11,167 --> 00:38:15,478 point one centimeters and so when you look at cloud chambers 554 00:38:15,478 --> 00:38:19,57 at the tracks of electrons and you have 555 00:38:19,57 --> 00:38:24,193 magnets there, you will see the tracks being 556 00:38:24,193 --> 00:38:30,537 curled up which of course is the result of the fact that the 557 00:38:30,537 --> 00:38:36,773 radius gets smaller in time and since the magnetic field is 558 00:38:36,773 --> 00:38:43,332 constant you can see then large radius here and as the kinetic 559 00:38:43,332 --> 00:38:49,568 energy slowly decreases the radius gets smaller and smaller 560 00:38:49,568 --> 00:38:54,36 and smaller. So let's look at a few more 561 00:38:54,36 --> 00:38:57,176 slides. In 1932, Anderson noticed a 562 00:38:57,176 --> 00:39:01,648 track in a cloud chamber which had the appearance of an 563 00:39:01,648 --> 00:39:04,216 electron. It had the right mass, 564 00:39:04,216 --> 00:39:08,771 it had the right charge, but the curve- the direction of 565 00:39:08,771 --> 00:39:12,994 curvature was wrong. And so he concluded that it was 566 00:39:12,994 --> 00:39:18,129 an electron which was positively charged, which is now called a 567 00:39:18,129 --> 00:39:23,016 positron. And these positrons had been 568 00:39:23,016 --> 00:39:26,83 predicted on purely theoretical grounds by Dirac, 569 00:39:26,83 --> 00:39:31,518 and Anderson receives a Nobel Pri- [break in file] discovery 570 00:39:31,518 --> 00:39:35,253 in Nineteen Thirty-Six, only four years after he 571 00:39:35,253 --> 00:39:39,782 discovered the positron and Dirac had already received his 572 00:39:39,782 --> 00:39:44,629 Nobel Prize in Nineteen Thirty Three for his theoretical work. 573 00:39:44,629 --> 00:39:48,602 The bubble chamber is an advanced form of the cloud 574 00:39:48,602 --> 00:39:50,986 chamber. In the bubble chamber, 575 00:39:50,986 --> 00:39:54,88 liquid hydrogen is used and if now 576 00:39:54,88 --> 00:39:59,591 the ions go through the ions become the seeds now for little 577 00:39:59,591 --> 00:40:02,496 gas bubbles. So you have liquids which 578 00:40:02,496 --> 00:40:07,129 really should have been gas but, uh, not quite and so now it 579 00:40:07,129 --> 00:40:10,27 forms gas bubbles. So in a cloud chamber, 580 00:40:10,27 --> 00:40:14,197 you're going to see the drops. In a bubble chamber, 581 00:40:14,197 --> 00:40:17,652 you see gas bubbles but the idea is the same, 582 00:40:17,652 --> 00:40:22,363 and Glaser who invented these chambers, is also from Berkeley 583 00:40:22,363 --> 00:40:27,774 by the way, he got a Nobel Prize for that 584 00:40:27,774 --> 00:40:32,442 in Nineteen Sixty. So let's look at the discovery 585 00:40:32,442 --> 00:40:36,526 by Anderson. Here you see a positron coming 586 00:40:36,526 --> 00:40:42,165 from above, and this positron has sixty-three MEV kinetic 587 00:40:42,165 --> 00:40:47,611 energy and Anderson put some half a centimeter of lead in 588 00:40:47,611 --> 00:40:51,986 there which was very clever, think about that. 589 00:40:51,986 --> 00:40:58,711 When it comes out, the energy now is less, 590 00:40:58,711 --> 00:41:03,208 because in the lead it produces a lot of ions and so it loses a 591 00:41:03,208 --> 00:41:06,835 lot of kinetic energy and it comes out with roughly 592 00:41:06,835 --> 00:41:09,737 twenty-three MEV. And why did he do that? 593 00:41:09,737 --> 00:41:13,871 Because now he knows for sure that this particle came from 594 00:41:13,871 --> 00:41:18,006 above, because when it loses energy the radius is smaller. 595 00:41:18,006 --> 00:41:21,85 That's why he was sure that it was curved in the wrong 596 00:41:21,85 --> 00:41:24,534 direction. If he didn't have the lead, 597 00:41:24,534 --> 00:41:28,233 you never know whether the electron 598 00:41:28,233 --> 00:41:31,304 came this way, in which case the curvature 599 00:41:31,304 --> 00:41:34,825 would be perfect. But now he knows it comes from 600 00:41:34,825 --> 00:41:39,394 above and if this had been an electron it would've curved this 601 00:41:39,394 --> 00:41:41,715 way. So this is one of the early 602 00:41:41,715 --> 00:41:45,386 discovery, cloud chamber photographed by Anderson. 603 00:41:45,386 --> 00:41:49,73 And the next slide is a bubble chamber and we see here both 604 00:41:49,73 --> 00:41:54,149 positron and an electron in a constant magnetic field and it 605 00:41:54,149 --> 00:41:58,943 speaks for itself, notice that the curvatures are 606 00:41:58,943 --> 00:42:03,111 exactly in opposite directions and you see this spiral 607 00:42:03,111 --> 00:42:07,987 structure that I discussed with you as the electrons lose their 608 00:42:07,987 --> 00:42:11,211 energy and since this is a bubble chamber, 609 00:42:11,211 --> 00:42:16,008 which has an enormous density a thousand times higher density, 610 00:42:16,008 --> 00:42:19,311 say, than air, these electrons don't travel 611 00:42:19,311 --> 00:42:23,165 forty meters in these chambers. In air they would, 612 00:42:23,165 --> 00:42:27,176 but in this case it is substantially less and so you 613 00:42:27,176 --> 00:42:30,872 can roll them up nicely. And you can study them, 614 00:42:30,872 --> 00:42:34,726 their momentum and their charge. 615 00:42:34,726 --> 00:42:39,735 Using uh, accelerators and cloud chambers and bubble 616 00:42:39,735 --> 00:42:45,032 chambers, a whole new world of nuclear physics emerged. 617 00:42:45,032 --> 00:42:47,344 Wow. And between Nineteen 618 00:42:47,344 --> 00:42:52,642 Fifty-Eight and Sixty-Eight thirty new nuclear particles 619 00:42:52,642 --> 00:42:57,073 were discovered. And MIT has always been on the 620 00:42:57,073 --> 00:43:04,78 forefront of this research. Professor Sam King, 621 00:43:04,78 --> 00:43:08,488 who is still at MIT, got the Nobel Prize in Nineteen 622 00:43:08,488 --> 00:43:10,524 Seventy-Six. Steven Weinberg, 623 00:43:10,524 --> 00:43:14,741 a theoretician who did his work while he was at MIT got his 624 00:43:14,741 --> 00:43:17,359 Nobel Prize in Nineteen Seventy-Nine. 625 00:43:17,359 --> 00:43:19,395 Jerry Friedman, still at MIT, 626 00:43:19,395 --> 00:43:22,812 and Henry Kendall, got the Nobel Prize for their 627 00:43:22,812 --> 00:43:26,448 work in Nineteen Ninety. And Clifford Shull got his 628 00:43:26,448 --> 00:43:28,993 Nobel Prize in Nineteen Ninety-Four. 629 00:43:28,993 --> 00:43:33,283 If I summarize the basic idea behind it, it is very relevant 630 00:43:33,283 --> 00:43:38,081 to eight oh two, you accelerate these particles 631 00:43:38,081 --> 00:43:41,477 using electric fields. That's the only way you can 632 00:43:41,477 --> 00:43:44,456 accelerate them. Magnetic fields can only be 633 00:43:44,456 --> 00:43:48,059 used to confine them. It can not change their kinetic 634 00:43:48,059 --> 00:43:51,8 energy but kinetic electr- magnetic fields are crucial, 635 00:43:51,8 --> 00:43:55,957 because that allows you as you gradually increase their speed 636 00:43:55,957 --> 00:43:58,244 to confine them, either by a ring, 637 00:43:58,244 --> 00:44:01,708 which is done nowadays, or in the old days in these 638 00:44:01,708 --> 00:44:04,965 chambers of the cyclotrons and the synchrotrons. 639 00:44:04,965 --> 00:44:08,845 And then we have the bubble chambers, in the old days the 640 00:44:08,845 --> 00:44:13,542 cloud chambers, whereby you use magnetic fields 641 00:44:13,542 --> 00:44:18,224 to get information on the radius of these particles as they are 642 00:44:18,224 --> 00:44:21,623 being detected. And out of all these emerged a 643 00:44:21,623 --> 00:44:26,23 whole new way of looking at our world and completely new ideas 644 00:44:26,23 --> 00:44:30,61 about what makes the world tick. This is nothing short of a 645 00:44:30,61 --> 00:44:33,782 revolution. And so now I want to enjoy with 646 00:44:33,782 --> 00:44:38,012 you the last five minutes of this lecture by looking at a 647 00:44:38,012 --> 00:44:43,158 cloud chamber and by looking at some of these tracks. 648 00:44:43,158 --> 00:44:47,069 You're going to see a lot of electrons in there. 649 00:44:47,069 --> 00:44:51,978 The walls of the cloud chamber are radioactive just like you 650 00:44:51,978 --> 00:44:55,556 are radioactive. Your bones are radioactive, 651 00:44:55,556 --> 00:44:59,633 your windows are radioactive. They emit electrons. 652 00:44:59,633 --> 00:45:03,377 No protons, but they certainly emit electrons. 653 00:45:03,377 --> 00:45:06,872 And we have in there a radioactive isotope, 654 00:45:06,872 --> 00:45:11,032 a rod, which has thorium in it which 655 00:45:11,032 --> 00:45:14,582 produces alpha particles. And so you're going to see 656 00:45:14,582 --> 00:45:18,201 electrons which make beautiful spider web structures. 657 00:45:18,201 --> 00:45:21,611 Please don't clean up yet, we have plenty of time. 658 00:45:21,611 --> 00:45:24,255 To be precise, we have five minutes and 659 00:45:24,255 --> 00:45:27,108 eighteen seconds left. So these electrons, 660 00:45:27,108 --> 00:45:31,284 you will see them going like spiders through this chamber and 661 00:45:31,284 --> 00:45:35,042 sometimes they change abrupt direction because they can 662 00:45:35,042 --> 00:45:39,218 collide, particularly when they have low energy and then they 663 00:45:39,218 --> 00:45:42,237 [break in file] so to speak, 664 00:45:42,237 --> 00:45:45,937 and then occasionally we may see an alpha particle coming 665 00:45:45,937 --> 00:45:50,032 from our radioactive thorium and that makes a very thick track. 666 00:45:50,032 --> 00:45:53,534 And so let's try this. We have an expert here which is 667 00:45:53,534 --> 00:45:56,837 Marcos who has not only borrowed these instruments, 668 00:45:56,837 --> 00:45:59,545 and if you like it we may actually buy it, 669 00:45:59,545 --> 00:46:01,461 it's not cheap, we may buy it, 670 00:46:01,461 --> 00:46:05,094 but he borrowed it specially for you, for which I'm very 671 00:46:05,094 --> 00:46:08,199 grateful, Marcos, and he also did quite a bit of 672 00:46:08,199 --> 00:46:10,313 work to get the light just right. 673 00:46:10,313 --> 00:46:14,374 It's not too easy to see those tracks. 674 00:46:14,374 --> 00:46:18,963 So Marcos, you will get a chance to adjust the lights if 675 00:46:18,963 --> 00:46:20,381 you want that. Um. 676 00:46:20,381 --> 00:46:24,887 We're going to make it very dark and let's enjoy them, 677 00:46:24,887 --> 00:46:27,974 this wonderful world, invisible world, 678 00:46:27,974 --> 00:46:31,979 of nuclear physics. So here you see this th- the 679 00:46:31,979 --> 00:46:37,236 rod with thorium so Marcos feel free to adjust the light if you 680 00:46:37,236 --> 00:46:40,907 feel the need. I will go into the audience as 681 00:46:40,907 --> 00:46:46,746 well and see whether we can 682 00:46:46,746 --> 00:46:50,17 identify the electrons. Oh, there was an alpha 683 00:46:50,17 --> 00:46:53,138 particle. So this is this rod and so the 684 00:46:53,138 --> 00:46:56,942 bottom of this chamber is cooled with solid CO two. 685 00:46:56,942 --> 00:46:59,682 Ah, there was an electron, very nice. 686 00:46:59,682 --> 00:47:03,334 As I said, you know, they almost look like spider 687 00:47:03,334 --> 00:47:05,769 webs. There was an electron here. 688 00:47:05,769 --> 00:47:10,259 Also keep an eye on this rod and occasionally you will see a 689 00:47:10,259 --> 00:47:14,368 very dense track which then indicates -- there was one, 690 00:47:14,368 --> 00:47:18,017 that's an alpha particle. 691 00:47:18,017 --> 00:47:20,302 There's a beautiful alpha particle. 692 00:47:20,302 --> 00:47:23,328 Just enjoy this. You know, you're looking at a 693 00:47:23,328 --> 00:47:26,353 world which is completely new. Think about it. 694 00:47:26,353 --> 00:47:29,445 You're looking at the world of nuclear physics. 695 00:47:29,445 --> 00:47:33,076 You're seeing individual electrons and occasionally you 696 00:47:33,076 --> 00:47:36,37 see alpha particles. Here, there's one coming out. 697 00:47:36,37 --> 00:47:39,597 And think about the physics what's going on here, 698 00:47:39,597 --> 00:47:43,698 this alcohol which refuses to become drops and then these ions 699 00:47:43,698 --> 00:47:49,126 say we force you to become uh -- here's an alpha particle, 700 00:47:49,126 --> 00:47:51,937 I don't know what it's doing there. 701 00:47:51,937 --> 00:47:55,492 So these, these, um, these ions force these, 702 00:47:55,492 --> 00:47:59,129 um, these, this, this alcohol vapor to become 703 00:47:59,129 --> 00:48:01,361 drops. That's an incredible, 704 00:48:01,361 --> 00:48:04,503 complex picture that you're looking at. 705 00:48:04,503 --> 00:48:07,396 It is amazing every time I see this. 706 00:48:07,396 --> 00:48:11,612 It's absolutely fabulous. And all through these very 707 00:48:11,612 --> 00:48:14,257 simple rules, now think about it, 708 00:48:14,257 --> 00:48:20,458 we have the Lawrence force, that makes these particles go 709 00:48:20,458 --> 00:48:25,335 around, electric fields that you can use them to accelerate 710 00:48:25,335 --> 00:48:30,378 them, and then this subtle way that you can actually make them 711 00:48:30,378 --> 00:48:33,437 visible, individual particles visible. 712 00:48:33,437 --> 00:48:37,405 It is a new world. And the goal of my lecture was 713 00:48:37,405 --> 00:48:42,365 to make you peek into this world which has revolutionized our 714 00:48:42,365 --> 48:47 whole way of thinking. Thank you.