1 00:00:00,840 --> 00:00:03,180 The following content is provided under a Creative 2 00:00:03,180 --> 00:00:04,570 Commons license. 3 00:00:04,570 --> 00:00:06,780 Your support will help MIT OpenCourseWare 4 00:00:06,780 --> 00:00:10,870 continue to offer high quality educational resources for free. 5 00:00:10,870 --> 00:00:13,440 To make a donation or to view additional materials 6 00:00:13,440 --> 00:00:17,400 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:17,400 --> 00:00:19,260 at ocw.mit.edu. 8 00:00:22,790 --> 00:00:25,490 MICHAEL SHORT: Today we launch into radioactive decay. 9 00:00:25,490 --> 00:00:28,580 And so this is kind of what makes us, us in this field, 10 00:00:28,580 --> 00:00:29,540 right? 11 00:00:29,540 --> 00:00:31,880 Now that you've learned the general cu equation 12 00:00:31,880 --> 00:00:35,813 we're going to look at some very simple, specific cases, 13 00:00:35,813 --> 00:00:37,730 and specifically all the different things that 14 00:00:37,730 --> 00:00:40,340 can come flying out of nuclei and the orbiting 15 00:00:40,340 --> 00:00:42,350 electrons around them. 16 00:00:42,350 --> 00:00:46,110 First I'd like to try and develop a generalized decay 17 00:00:46,110 --> 00:00:46,610 diagram. 18 00:00:46,610 --> 00:00:50,120 What are all the different ways that nuclei can decay? 19 00:00:50,120 --> 00:00:53,030 And I had written one of these up to show on the slides, 20 00:00:53,030 --> 00:00:57,118 and my one-year-old son fixed it with a bunch of markers 21 00:00:57,118 --> 00:00:58,910 and crayons, so I think we're going to have 22 00:00:58,910 --> 00:01:00,065 to redo this from scratch. 23 00:01:02,680 --> 00:01:09,360 So let's say you had a generalized unstable nucleus 24 00:01:09,360 --> 00:01:10,560 over here. 25 00:01:10,560 --> 00:01:14,100 And we're going to start drawing a generalized decay diagram. 26 00:01:14,100 --> 00:01:19,170 You'll see decay diagrams, well, much like these. 27 00:01:19,170 --> 00:01:21,000 I've already shown you a couple of these, 28 00:01:21,000 --> 00:01:24,150 like these decay diagrams for uranium 235, 29 00:01:24,150 --> 00:01:27,420 soon as I clone my screen so you can see it. 30 00:01:27,420 --> 00:01:30,030 There are a couple of axes that aren't 31 00:01:30,030 --> 00:01:31,600 drawn on these decay diagrams that 32 00:01:31,600 --> 00:01:33,160 will help you interpret them. 33 00:01:33,160 --> 00:01:37,110 And the first one, the imaginary y-axis, 34 00:01:37,110 --> 00:01:41,070 is in order of increasing energy. 35 00:01:41,070 --> 00:01:46,000 And the second imaginary y-axis is z, atomic number. 36 00:01:46,000 --> 00:01:48,090 So this will help you determine how we read these 37 00:01:48,090 --> 00:01:50,135 and how to actually write them. 38 00:01:50,135 --> 00:01:51,760 Now what are some of the different ways 39 00:01:51,760 --> 00:01:54,450 you've heard of things that can radioactively decay, 40 00:01:54,450 --> 00:01:57,080 or that you might have read from the reading? 41 00:01:57,080 --> 00:01:58,403 Just yell them out. 42 00:01:58,403 --> 00:01:59,320 AUDIENCE: Alpha decay. 43 00:01:59,320 --> 00:02:00,445 MICHAEL SHORT: Alpha decay. 44 00:02:00,445 --> 00:02:03,940 So in alpha decay, what actually happens? 45 00:02:03,940 --> 00:02:08,050 Let's say that we had a parent nucleus with atomic number 46 00:02:08,050 --> 00:02:12,318 z and mass number a. 47 00:02:12,318 --> 00:02:13,360 What does it change into? 48 00:02:19,370 --> 00:02:22,880 Anyone know what an alpha particle consists of? 49 00:02:22,880 --> 00:02:23,516 Yeah. 50 00:02:23,516 --> 00:02:24,641 AUDIENCE: A helium nucleus. 51 00:02:24,641 --> 00:02:26,310 MICHAEL SHORT: A helium nucleus. 52 00:02:26,310 --> 00:02:27,780 So let's just say helium. 53 00:02:27,780 --> 00:02:30,260 This will be a 4 and a 2. 54 00:02:30,260 --> 00:02:32,480 and there's going to be some daughter nucleus-- 55 00:02:32,480 --> 00:02:34,100 we don't know what-- 56 00:02:34,100 --> 00:02:40,700 with z minus 2 protons and a minus 4 total nucleons. 57 00:02:40,700 --> 00:02:45,440 So if we were to describe alpha decay on a decay diagram, 58 00:02:45,440 --> 00:02:49,850 where would we write the final state of this alpha decayed 59 00:02:49,850 --> 00:02:50,993 daughter nucleus? 60 00:02:50,993 --> 00:02:52,160 To the left or to the right? 61 00:02:58,220 --> 00:03:01,163 I know it's like 9:00 AM, but someone just shout it out. 62 00:03:01,163 --> 00:03:02,580 You don't have to raise your hand. 63 00:03:02,580 --> 00:03:03,260 AUDIENCE: To the left. 64 00:03:03,260 --> 00:03:03,860 MICHAEL SHORT: To the left. 65 00:03:03,860 --> 00:03:04,430 Yep. 66 00:03:04,430 --> 00:03:09,110 Something that's decreasing in z and also decreasing in energy, 67 00:03:09,110 --> 00:03:12,870 we would draw an alpha decay like this to the left. 68 00:03:12,870 --> 00:03:15,680 So let's say this would be something more 69 00:03:15,680 --> 00:03:19,490 stable with a z minus 2-- 70 00:03:19,490 --> 00:03:23,180 make that clear-- and an a minus 4. 71 00:03:23,180 --> 00:03:26,450 What are some other ways things can decay? 72 00:03:26,450 --> 00:03:27,200 I heard a whisper. 73 00:03:27,200 --> 00:03:28,100 AUDIENCE: Beta. 74 00:03:28,100 --> 00:03:29,550 MICHAEL SHORT: Beta decay. 75 00:03:29,550 --> 00:03:32,270 So what happens in-- 76 00:03:32,270 --> 00:03:34,100 usually by beta decay, we're referring 77 00:03:34,100 --> 00:03:36,050 to beta minus decay, which would be 78 00:03:36,050 --> 00:03:39,350 the emission of an electron from the nucleus. 79 00:03:39,350 --> 00:03:42,050 Again, what's the physical difference 80 00:03:42,050 --> 00:03:44,690 between a beta particle and an electron? 81 00:03:44,690 --> 00:03:45,560 Nothing. 82 00:03:45,560 --> 00:03:48,320 What's the nomenclature difference? 83 00:03:48,320 --> 00:03:49,977 The beta comes from the nucleus. 84 00:03:49,977 --> 00:03:51,560 Otherwise, when they come out, they're 85 00:03:51,560 --> 00:03:53,680 kind of indistinguishable. 86 00:03:53,680 --> 00:03:55,120 So what happens in beta decay? 87 00:03:55,120 --> 00:03:57,500 Let's say we have the same parent nucleus starting with 88 00:03:57,500 --> 00:04:00,070 z,a. 89 00:04:00,070 --> 00:04:06,430 We know it emits an electron with no mass. 90 00:04:06,430 --> 00:04:07,145 And what else? 91 00:04:10,640 --> 00:04:14,874 This is just a matter of conservation of things here. 92 00:04:14,874 --> 00:04:16,170 AUDIENCE: Anti-neutrino. 93 00:04:16,170 --> 00:04:19,350 MICHAEL SHORT: There is an anti-neutrino 94 00:04:19,350 --> 00:04:22,530 which has pretty close to no mass and no charge. 95 00:04:22,530 --> 00:04:24,960 And what about this daughter nucleus? 96 00:04:24,960 --> 00:04:28,040 How many protons and total nucleons would it have? 97 00:04:31,730 --> 00:04:32,317 Yeah. 98 00:04:32,317 --> 00:04:33,900 AUDIENCE: Should have one more proton. 99 00:04:33,900 --> 00:04:37,310 MICHAEL SHORT: Should have one more proton 100 00:04:37,310 --> 00:04:39,830 and how many more total nucleons? 101 00:04:39,830 --> 00:04:40,480 The same. 102 00:04:40,480 --> 00:04:42,590 Yep, like that. 103 00:04:42,590 --> 00:04:44,870 And so how would we draw beta decay 104 00:04:44,870 --> 00:04:49,603 on this generalized diagram, to the left or to the right? 105 00:04:49,603 --> 00:04:50,270 AUDIENCE: Right. 106 00:04:50,270 --> 00:04:51,437 MICHAEL SHORT: To the right. 107 00:04:51,437 --> 00:04:52,850 It's increasing in z. 108 00:04:52,850 --> 00:04:54,920 I haven't defined any scale, so let's just 109 00:04:54,920 --> 00:04:57,170 say that's a change of 0. 110 00:04:57,170 --> 00:04:59,060 That's 1. 111 00:04:59,060 --> 00:05:01,660 That's 2. 112 00:05:01,660 --> 00:05:04,460 And that's plus 1. 113 00:05:04,460 --> 00:05:06,240 That's plus 2. 114 00:05:06,240 --> 00:05:09,050 Hopefully we won't get to today. 115 00:05:09,050 --> 00:05:14,240 So a beta decay would proceed thusly. 116 00:05:14,240 --> 00:05:19,010 So you'd have some other stable nucleus with c 117 00:05:19,010 --> 00:05:22,373 plus 1 and mass number 8. 118 00:05:22,373 --> 00:05:24,790 What are some other decays you might have heard of before? 119 00:05:27,275 --> 00:05:28,400 AUDIENCE: Electron capture. 120 00:05:28,400 --> 00:05:29,960 MICHAEL SHORT: Electron capture. 121 00:05:29,960 --> 00:05:36,350 So in electron capture, what actually happens? 122 00:05:36,350 --> 00:05:39,870 Start with the same parent nucleus. 123 00:05:39,870 --> 00:05:43,350 In this case, the nucleus actually captures an electron 124 00:05:43,350 --> 00:05:46,260 from one of the inner orbitals. 125 00:05:46,260 --> 00:05:49,590 And so that, in effect, like, neutralizes a proton, right, 126 00:05:49,590 --> 00:05:50,917 in terms of charge. 127 00:05:50,917 --> 00:05:52,000 So what do we end up with? 128 00:05:59,790 --> 00:06:00,290 Yep. 129 00:06:00,290 --> 00:06:01,920 So we'd have some daughter nucleus. 130 00:06:01,920 --> 00:06:07,140 If it neutralizes a proton, we'd have one fewer protons. 131 00:06:07,140 --> 00:06:08,515 And then how many total nucleons? 132 00:06:11,470 --> 00:06:12,030 The same. 133 00:06:12,030 --> 00:06:13,920 Yep. 134 00:06:13,920 --> 00:06:15,120 There we go. 135 00:06:15,120 --> 00:06:18,270 And so if we were to draw electron capture on this map, 136 00:06:18,270 --> 00:06:21,230 we would have one fewer proton. 137 00:06:21,230 --> 00:06:26,090 So we could have some sort of decay by electron capture. 138 00:06:31,840 --> 00:06:32,810 And anything else? 139 00:06:32,810 --> 00:06:37,350 What other particles can be emitted from a nucleus? 140 00:06:37,350 --> 00:06:37,850 Yeah. 141 00:06:37,850 --> 00:06:39,030 AUDIENCE: Positrons? 142 00:06:39,030 --> 00:06:40,710 MICHAEL SHORT: Positrons. 143 00:06:40,710 --> 00:06:42,150 So let's get this list going up. 144 00:06:46,550 --> 00:06:50,940 So if we start off with a parent, z and a, 145 00:06:50,940 --> 00:06:53,850 we know we emit a positron, which 146 00:06:53,850 --> 00:06:56,220 is the anti-matter equivalent of an electron. 147 00:06:56,220 --> 00:06:59,580 So same general characteristics except opposite charge. 148 00:06:59,580 --> 00:07:04,500 In this case, we'll give it a 0 protons and 0 neutrons. 149 00:07:04,500 --> 00:07:08,415 And we end up with-- well, the same daughter nucleus. 150 00:07:11,560 --> 00:07:16,810 So we could say that this precedes by positron creation 151 00:07:16,810 --> 00:07:18,070 or electron capture. 152 00:07:18,070 --> 00:07:21,340 It's the same process, or the same ending state. 153 00:07:21,340 --> 00:07:26,560 But can you have positrons in any possible decay? 154 00:07:26,560 --> 00:07:28,150 We actually went over this once. 155 00:07:28,150 --> 00:07:30,090 Anyone remember? 156 00:07:30,090 --> 00:07:31,632 Yeah, so you're shaking your head no. 157 00:07:31,632 --> 00:07:33,465 AUDIENCE: You have to have a certain energy, 158 00:07:33,465 --> 00:07:35,520 but I can't remember what the energy is. 159 00:07:35,520 --> 00:07:37,187 MICHAEL SHORT: We'll get back into that. 160 00:07:37,187 --> 00:07:37,980 You're right. 161 00:07:37,980 --> 00:07:39,840 So I'll put a little box around this 162 00:07:39,840 --> 00:07:42,030 because you have to have a certain amount of energy 163 00:07:42,030 --> 00:07:44,520 in order to create the positron. 164 00:07:44,520 --> 00:07:45,160 And what else? 165 00:07:45,160 --> 00:07:48,758 What about the easiest one? 166 00:07:48,758 --> 00:07:50,425 What else can be emitted from a nucleus? 167 00:07:53,518 --> 00:07:54,450 AUDIENCE: [INAUDIBLE] 168 00:07:54,450 --> 00:07:55,230 MICHAEL SHORT: I heard a couple of things. 169 00:07:55,230 --> 00:07:56,410 Neutrons. 170 00:07:56,410 --> 00:07:59,830 So certainly if you emit a neutron, 171 00:07:59,830 --> 00:08:02,390 there are some very unstable nuclei, 172 00:08:02,390 --> 00:08:04,660 like helium 5, which exists for what, 173 00:08:04,660 --> 00:08:08,080 10 to the minus 26 seconds or something, 174 00:08:08,080 --> 00:08:11,090 that could omit a neutron. 175 00:08:11,090 --> 00:08:14,590 If we start off with z and a, then we'll 176 00:08:14,590 --> 00:08:18,400 start off with a neutron and a daughter 177 00:08:18,400 --> 00:08:23,183 with the same z and a minus 1 total. 178 00:08:23,183 --> 00:08:25,100 So what would that look like on a decay chain? 179 00:08:25,100 --> 00:08:28,010 You don't usually see this, but we'll draw it anyway. 180 00:08:34,030 --> 00:08:35,922 It would go straight down, right? 181 00:08:35,922 --> 00:08:37,339 So there'll be some other nucleus. 182 00:08:40,700 --> 00:08:44,649 So it'd be the same z, but an a minus 1. 183 00:08:44,649 --> 00:08:47,050 And it could decay by neutron emission. 184 00:08:47,050 --> 00:08:48,700 Yeah, that totally happens. 185 00:08:48,700 --> 00:08:52,870 If you look at the very, very right edge 186 00:08:52,870 --> 00:08:55,090 of the table of nuclides-- 187 00:08:55,090 --> 00:08:57,370 let's go back to the home page for that-- 188 00:09:00,450 --> 00:09:02,940 and look at the super neutron rich. 189 00:09:02,940 --> 00:09:03,960 Like helium 10. 190 00:09:03,960 --> 00:09:06,210 Who's ever heard of this? 191 00:09:06,210 --> 00:09:08,875 Doesn't even say, let's say, two neutrons. 192 00:09:08,875 --> 00:09:11,250 So this is so unstable that it just immediately spits out 193 00:09:11,250 --> 00:09:11,850 two neutrons. 194 00:09:11,850 --> 00:09:13,260 So yeah, these things happen. 195 00:09:13,260 --> 00:09:16,620 You won't tend to see this decay in textbooks because it only 196 00:09:16,620 --> 00:09:19,080 happens for exceptionally unstable nuclei. 197 00:09:19,080 --> 00:09:20,250 But yeah, that's true. 198 00:09:20,250 --> 00:09:21,742 It does happen. 199 00:09:21,742 --> 00:09:22,700 What else could happen? 200 00:09:26,220 --> 00:09:27,730 Remember we've been talking about-- 201 00:09:27,730 --> 00:09:28,355 yeah. 202 00:09:28,355 --> 00:09:28,840 AUDIENCE: Gammas? 203 00:09:28,840 --> 00:09:29,715 MICHAEL SHORT: Right. 204 00:09:29,715 --> 00:09:30,840 Could be gammas. 205 00:09:30,840 --> 00:09:33,030 And so I'll make one little extra piece 206 00:09:33,030 --> 00:09:36,720 here for gamma decay, which is nothing more than a photon 207 00:09:36,720 --> 00:09:38,980 emitted from the nucleus. 208 00:09:38,980 --> 00:09:42,960 We start off with a parent z and a. 209 00:09:42,960 --> 00:09:47,373 And this becomes-- well, what? 210 00:09:47,373 --> 00:09:48,915 Should I even write daughter nucleus? 211 00:09:51,700 --> 00:09:53,500 I see some people shaking their heads no. 212 00:09:53,500 --> 00:09:54,000 Why not? 213 00:09:56,550 --> 00:09:58,165 Yeah? 214 00:09:58,165 --> 00:10:00,040 AUDIENCE: You have essentially the same atom. 215 00:10:00,040 --> 00:10:01,582 It's just one of its electrons should 216 00:10:01,582 --> 00:10:04,438 be at a lower energy state. 217 00:10:04,438 --> 00:10:05,230 MICHAEL SHORT: Yep. 218 00:10:05,230 --> 00:10:05,770 Very close. 219 00:10:05,770 --> 00:10:09,340 You have the same atom, so let's say the same parent, 220 00:10:09,340 --> 00:10:11,440 with the same number of protons, the same number 221 00:10:11,440 --> 00:10:12,945 of total nucleons. 222 00:10:12,945 --> 00:10:15,070 And I'll just correct that to say one of its nuclei 223 00:10:15,070 --> 00:10:16,630 is at a lower energy state. 224 00:10:16,630 --> 00:10:19,340 But otherwise everything is completely correct. 225 00:10:19,340 --> 00:10:22,150 So why don't we put a little star here 226 00:10:22,150 --> 00:10:24,520 to say that that was at an excited state? 227 00:10:24,520 --> 00:10:27,610 Just like electrons can be promoted to outer shells, 228 00:10:27,610 --> 00:10:30,640 pick up a little bit of energy, so can nucleons. 229 00:10:30,640 --> 00:10:32,470 So can protons and neutrons. 230 00:10:32,470 --> 00:10:34,540 And this is going to be a subject of, well, 231 00:10:34,540 --> 00:10:36,730 great discussion in 22.02. 232 00:10:36,730 --> 00:10:40,570 For now all you have to know is that nucleons, like electrons, 233 00:10:40,570 --> 00:10:42,730 can occupy higher energy states. 234 00:10:42,730 --> 00:10:44,710 And when they fall down to lower energy states, 235 00:10:44,710 --> 00:10:49,150 they can release that energy in the form of a gamma ray. 236 00:10:49,150 --> 00:10:51,010 So you could also have, let's say, 237 00:10:51,010 --> 00:10:56,470 squiggly line gamma decay to something stable. 238 00:10:56,470 --> 00:11:00,685 And so this right here would be the generalized decay diagram. 239 00:11:04,140 --> 00:11:06,090 Anyone ever heard of one isotope that 240 00:11:06,090 --> 00:11:10,700 undergoes all these possible decay mechanisms? 241 00:11:10,700 --> 00:11:13,760 Glad no one's saying anything, because neither have I. 242 00:11:13,760 --> 00:11:16,040 There's one that comes close. 243 00:11:16,040 --> 00:11:17,477 Actually, if you look at-- 244 00:11:17,477 --> 00:11:19,310 no, that's not this part I want to show you. 245 00:11:19,310 --> 00:11:20,700 I want to show you the big one. 246 00:11:20,700 --> 00:11:22,880 If you look at potassium 40, the nuclide we probably 247 00:11:22,880 --> 00:11:25,310 talked about the most so far, it covers 248 00:11:25,310 --> 00:11:28,250 most of the space of this generalized decay diagram. 249 00:11:28,250 --> 00:11:30,550 And there was a question that came through-- 250 00:11:30,550 --> 00:11:33,170 at least, I think for non-anonymous email, 251 00:11:33,170 --> 00:11:36,190 what is it that makes these even, even versus odd, 252 00:11:36,190 --> 00:11:38,460 odd nuclei less or more stable? 253 00:11:38,460 --> 00:11:41,660 Anytime you have an odd, odd nucleus, both the number 254 00:11:41,660 --> 00:11:43,400 of protons and the number of neutrons, 255 00:11:43,400 --> 00:11:46,340 these nuclear shells are not fully occupied 256 00:11:46,340 --> 00:11:49,430 and they're not that stable compared to an even, even 257 00:11:49,430 --> 00:11:53,182 nucleus that has an even number of z and an even number of n. 258 00:11:53,182 --> 00:11:54,890 Just kind of like electrons, these things 259 00:11:54,890 --> 00:11:56,600 tend to travel in pairs. 260 00:11:56,600 --> 00:12:00,590 And not fully occupied energy levels will be left stable. 261 00:12:00,590 --> 00:12:05,090 Potassium 40 happens to be one of those odd, odd nuclei that 262 00:12:05,090 --> 00:12:07,550 is relatively unstable. 263 00:12:07,550 --> 00:12:08,660 And it can go either way. 264 00:12:08,660 --> 00:12:11,930 Either you can lose a proton or you can gain a proton 265 00:12:11,930 --> 00:12:15,950 by competing mechanisms like positron or electron 266 00:12:15,950 --> 00:12:20,110 capture or beta emission. 267 00:12:20,110 --> 00:12:22,020 So this one I like a lot because it gives you 268 00:12:22,020 --> 00:12:24,720 almost every possible decay with the exception 269 00:12:24,720 --> 00:12:27,750 of alpha decay and spontaneous neutron emission. 270 00:12:27,750 --> 00:12:30,260 It's not that unstable. 271 00:12:30,260 --> 00:12:33,250 Then the only one really missing from here, I found what I think 272 00:12:33,250 --> 00:12:36,220 is the simplest decay diagram ever, dysprosium-151. 273 00:12:36,220 --> 00:12:40,930 There's only one thing it can do is it can decay by alpha decay 274 00:12:40,930 --> 00:12:42,490 to its ground state. 275 00:12:42,490 --> 00:12:44,830 I want to point out a few of the features of these decay 276 00:12:44,830 --> 00:12:47,830 diagrams so you know what to look for. 277 00:12:47,830 --> 00:12:49,630 Up here is the parent nucleus. 278 00:12:49,630 --> 00:12:51,940 Down there is the daughter nucleus. 279 00:12:51,940 --> 00:12:54,930 And these energies are not absolute. 280 00:12:54,930 --> 00:12:58,060 They're relative to the ground state of whatever the daughter 281 00:12:58,060 --> 00:12:59,620 nucleus is. 282 00:12:59,620 --> 00:13:04,030 So simple example helps show you that gadolinium-147 doesn't 283 00:13:04,030 --> 00:13:05,950 have a binding energy of 0. 284 00:13:05,950 --> 00:13:09,760 This is relative to the ground state of gadolinium-147. 285 00:13:09,760 --> 00:13:12,760 And that will tell you that the Q value for this reaction 286 00:13:12,760 --> 00:13:16,720 is 4.1796 MeV. 287 00:13:16,720 --> 00:13:20,470 These things are usually listed in MeV unless said otherwise. 288 00:13:20,470 --> 00:13:24,010 You also might notice a pattern that most alpha particles 289 00:13:24,010 --> 00:13:27,340 tend to come out around 4 MeV or larger. 290 00:13:27,340 --> 00:13:30,130 The answer to why is going to be given in 22.02. 291 00:13:30,130 --> 00:13:31,000 Yep. 292 00:13:31,000 --> 00:13:32,975 AUDIENCE: Where do these percentages come from? 293 00:13:32,975 --> 00:13:35,350 MICHAEL SHORT: These percentages tell you the probability 294 00:13:35,350 --> 00:13:36,720 that each decay will happen. 295 00:13:36,720 --> 00:13:37,512 AUDIENCE: Oh, yeah. 296 00:13:37,512 --> 00:13:39,573 Like how do we derive-- 297 00:13:39,573 --> 00:13:40,615 how do we find those out? 298 00:13:40,615 --> 00:13:42,115 MICHAEL SHORT: Ah, these are usually 299 00:13:42,115 --> 00:13:44,170 measured because it can be-- let's 300 00:13:44,170 --> 00:13:46,510 say things get quantum and difficult in terms 301 00:13:46,510 --> 00:13:47,650 of calculating these. 302 00:13:47,650 --> 00:13:49,540 And our knowledge of wave functions 303 00:13:49,540 --> 00:13:53,380 of, well, higher and higher a or z nuclei 304 00:13:53,380 --> 00:13:55,810 gets a little more tenuous. 305 00:13:55,810 --> 00:13:57,310 So a lot of these would be measured. 306 00:13:57,310 --> 00:14:00,940 You can look at the number of alpha particles of each energy 307 00:14:00,940 --> 00:14:04,750 that you observe, and then you get the average probabilities. 308 00:14:04,750 --> 00:14:05,870 For this one, it's simple. 309 00:14:05,870 --> 00:14:07,420 There's 100% probability that this 310 00:14:07,420 --> 00:14:09,250 is the only thing that exists. 311 00:14:09,250 --> 00:14:11,500 The other things to note, the half life 312 00:14:11,500 --> 00:14:14,290 will be given up here, in this case, at 17.9 minutes. 313 00:14:14,290 --> 00:14:18,502 So relatively long half life compared to helium 5. 314 00:14:18,502 --> 00:14:20,210 And we'll be going over what half life is 315 00:14:20,210 --> 00:14:22,210 and what they are on Friday. 316 00:14:22,210 --> 00:14:25,150 And then the last thing are the spin states 317 00:14:25,150 --> 00:14:26,860 of the initial and final nuclei, which 318 00:14:26,860 --> 00:14:30,670 we will not cover in this class, but you will cover in 22.02. 319 00:14:30,670 --> 00:14:32,290 So don't worry about those now, but do 320 00:14:32,290 --> 00:14:34,990 know that when you need to go find the spin 321 00:14:34,990 --> 00:14:37,240 states of the initial and final nuclei 322 00:14:37,240 --> 00:14:39,880 to see if certain transitions are allowed, 323 00:14:39,880 --> 00:14:42,440 this is where you're going to go. 324 00:14:42,440 --> 00:14:45,350 Any questions on what you see here on how to read these decay 325 00:14:45,350 --> 00:14:45,850 diagrams? 326 00:14:48,565 --> 00:14:49,510 Cool. 327 00:14:49,510 --> 00:14:51,050 OK. 328 00:14:51,050 --> 00:14:53,510 Then let's move on to the simplest of them, which, 329 00:14:53,510 --> 00:14:55,763 in the table, can look the most complicated. 330 00:14:55,763 --> 00:14:57,680 So here you can see that there's a whole bunch 331 00:14:57,680 --> 00:15:00,950 of different probabilities for different alpha decay nuclei. 332 00:15:00,950 --> 00:15:03,200 This is one of those more complex examples where 333 00:15:03,200 --> 00:15:05,600 the easiest thing to do is just measure, 334 00:15:05,600 --> 00:15:07,940 see how many alphas you get at each energy, 335 00:15:07,940 --> 00:15:10,430 and this will give you the approximate probabilities 336 00:15:10,430 --> 00:15:11,987 that each decay happens. 337 00:15:11,987 --> 00:15:13,820 And you'll notice here that the final energy 338 00:15:13,820 --> 00:15:18,140 states for each of these alphas is not necessarily 0. 339 00:15:18,140 --> 00:15:20,720 This will tell you what they are relative to the ground state 340 00:15:20,720 --> 00:15:24,110 of, in this case, thorium 231. 341 00:15:24,110 --> 00:15:28,130 So you can emit an alpha from any combination 342 00:15:28,130 --> 00:15:31,530 of nuclear shell levels inside this nucleus. 343 00:15:31,530 --> 00:15:33,410 And you might end up with a new daughter 344 00:15:33,410 --> 00:15:37,648 nucleus whose protons or neutrons are in excited states. 345 00:15:37,648 --> 00:15:39,440 And the way you remove those excited states 346 00:15:39,440 --> 00:15:42,760 is gamma decay, like we talked about here. 347 00:15:42,760 --> 00:15:46,670 So a lot of alpha decays are immediately 348 00:15:46,670 --> 00:15:50,600 followed by a chain of gamma decays, 349 00:15:50,600 --> 00:15:54,560 or what we call ITs, or isometric transitions. 350 00:15:54,560 --> 00:15:56,245 So you'll see a couple bits of notation. 351 00:15:59,300 --> 00:16:01,700 For example, gamma decay, you may hear 352 00:16:01,700 --> 00:16:03,333 it called isomeric transition. 353 00:16:03,333 --> 00:16:05,750 We'll try to give them all so that in the various readings 354 00:16:05,750 --> 00:16:08,531 you have, you know what's what. 355 00:16:08,531 --> 00:16:11,730 So notice here, you can have, with a probability 356 00:16:11,730 --> 00:16:14,030 so small that they didn't bother to draw it, 357 00:16:14,030 --> 00:16:17,630 an alpha decay 2.634 MeV. 358 00:16:17,630 --> 00:16:20,210 And then any series of gammas from, let's 359 00:16:20,210 --> 00:16:22,460 say, from this state to that state, 360 00:16:22,460 --> 00:16:25,610 and then from this state to one of those 361 00:16:25,610 --> 00:16:28,130 or one of those, and then another one down there. 362 00:16:28,130 --> 00:16:29,630 So an alpha decay may be followed 363 00:16:29,630 --> 00:16:34,860 by a whole bunch of gamma transitions, or as few as none. 364 00:16:34,860 --> 00:16:36,990 If you want to see what the alpha energies are, 365 00:16:36,990 --> 00:16:39,730 well, let's head to the table of nuclides 366 00:16:39,730 --> 00:16:46,800 and look at uranium 235. 367 00:16:46,800 --> 00:16:50,210 So if we look up U 235, you can see that it alpha 368 00:16:50,210 --> 00:16:53,375 decays to thorium 231. 369 00:16:53,375 --> 00:16:55,000 And I'll show you the part of the table 370 00:16:55,000 --> 00:16:58,150 that I didn't show you in the slides, which is then 371 00:16:58,150 --> 00:17:02,140 you've got a table of alpha decay energies 372 00:17:02,140 --> 00:17:05,410 as well as relative intensities and what's called a hindrance. 373 00:17:05,410 --> 00:17:07,990 This stuff right here comes from the fact 374 00:17:07,990 --> 00:17:10,450 that different alpha decay energies 375 00:17:10,450 --> 00:17:13,150 can happen with different probabilities 376 00:17:13,150 --> 00:17:14,810 at different times. 377 00:17:14,810 --> 00:17:17,589 So the half life of a particular alpha decay 378 00:17:17,589 --> 00:17:18,819 can be slightly different. 379 00:17:18,819 --> 00:17:22,210 And this is another one of those really kooky things, where 380 00:17:22,210 --> 00:17:26,079 certain energy alpha transitions will happen a little more often 381 00:17:26,079 --> 00:17:27,910 initially then finally. 382 00:17:27,910 --> 00:17:29,700 But we don't have to worry about that yet. 383 00:17:29,700 --> 00:17:32,428 I just want you to know that's why the hindrance is there. 384 00:17:32,428 --> 00:17:33,970 And so you can look, from this table, 385 00:17:33,970 --> 00:17:37,600 what's the probability that each of these alphas will come out. 386 00:17:37,600 --> 00:17:40,070 And there's going to be some uncertainty associated 387 00:17:40,070 --> 00:17:40,570 with these. 388 00:17:40,570 --> 00:17:42,737 This is going to usually be some sort of measurement 389 00:17:42,737 --> 00:17:44,010 uncertainty. 390 00:17:44,010 --> 00:17:46,110 Then you might also ask, why is it 391 00:17:46,110 --> 00:17:48,630 that the highest energy alpha ray 392 00:17:48,630 --> 00:17:55,210 is not the same energy as the Q value? 393 00:17:55,210 --> 00:17:59,920 So for this, it's a greatly simplified application 394 00:17:59,920 --> 00:18:03,272 of the Q equation that we learned last time. 395 00:18:03,272 --> 00:18:05,230 So for here, what are the two equations that we 396 00:18:05,230 --> 00:18:09,440 need to conserve if we have a system consisting of-- 397 00:18:09,440 --> 00:18:13,535 we have our initial nuclei going into our final nuclei. 398 00:18:17,420 --> 00:18:21,170 And they go off in equal and opposite directions. 399 00:18:21,170 --> 00:18:26,630 If it's alpha decay, then we have no little initial nucleus. 400 00:18:26,630 --> 00:18:30,650 We just had a large initial nucleus at rest. 401 00:18:30,650 --> 00:18:34,070 And afterwards, you've got a small final nucleus, which 402 00:18:34,070 --> 00:18:37,580 we know is the alpha particle, and a large final nucleus, 403 00:18:37,580 --> 00:18:39,620 which we'll call the daughter product. 404 00:18:39,620 --> 00:18:43,892 And let's say this is the parent. 405 00:18:43,892 --> 00:18:46,100 It's a much, much simpler system than the general one 406 00:18:46,100 --> 00:18:47,600 we analyzed last week. 407 00:18:47,600 --> 00:18:49,100 So what are the equations that we'll 408 00:18:49,100 --> 00:18:51,592 use to serve to find out what's the energy 409 00:18:51,592 --> 00:18:52,550 of this alpha particle? 410 00:18:57,290 --> 00:18:57,790 Anyone? 411 00:18:57,790 --> 00:19:00,990 Same three answers as always. 412 00:19:00,990 --> 00:19:01,798 Yep. 413 00:19:01,798 --> 00:19:03,340 AUDIENCE: Mass, energy, and momentum. 414 00:19:03,340 --> 00:19:04,132 MICHAEL SHORT: Yep. 415 00:19:04,132 --> 00:19:07,645 Mass, energy, and momentum. 416 00:19:11,043 --> 00:19:13,210 I'm going to lump these two together because they're 417 00:19:13,210 --> 00:19:14,780 kind of the same thing. 418 00:19:14,780 --> 00:19:17,420 So let's just go with energy and momentum. 419 00:19:17,420 --> 00:19:21,342 So what is the initial kinetic energy, or let's say, 420 00:19:21,342 --> 00:19:23,050 the initial kinetic energy of this parent 421 00:19:23,050 --> 00:19:25,297 nucleus we can assume to be 0. 422 00:19:25,297 --> 00:19:27,380 What about the final kinetic energy of the system? 423 00:19:31,075 --> 00:19:32,450 Well, there's only two particles. 424 00:19:32,450 --> 00:19:36,560 There's going to be some kinetic energy of the alpha particle 425 00:19:36,560 --> 00:19:40,910 plus the recoil kinetic energy because if the alpha goes 426 00:19:40,910 --> 00:19:43,760 in one direction, the daughter nucleus has to go off 427 00:19:43,760 --> 00:19:45,020 in the other direction. 428 00:19:45,020 --> 00:19:50,090 And the total energy comes out to Q. 429 00:19:50,090 --> 00:19:52,700 This Q value you can get by conserving mass, where 430 00:19:52,700 --> 00:19:58,620 we can say that the mass of the parent 431 00:19:58,620 --> 00:20:02,640 has to equal the mass of the alpha 432 00:20:02,640 --> 00:20:08,870 plus the mass of the daughter plus Q. 433 00:20:08,870 --> 00:20:11,570 So that's where we can get Q if we don't know it already. 434 00:20:11,570 --> 00:20:14,668 Luckily, we know it already. 435 00:20:14,668 --> 00:20:15,710 So there we've used mass. 436 00:20:15,710 --> 00:20:17,180 There we've used energy. 437 00:20:17,180 --> 00:20:21,080 And now what are the momenta of the initial and final states 438 00:20:21,080 --> 00:20:21,740 here? 439 00:20:21,740 --> 00:20:22,010 Anyone? 440 00:20:22,010 --> 00:20:22,760 Just shout it out. 441 00:20:22,760 --> 00:20:24,956 What's the initial momentum of the parent nucleus? 442 00:20:24,956 --> 00:20:25,690 AUDIENCE: 0. 443 00:20:25,690 --> 00:20:28,245 MICHAEL SHORT: 0 equals-- 444 00:20:28,245 --> 00:20:29,620 what's the momentum of the alpha? 445 00:20:33,690 --> 00:20:36,340 Anyone remember that trick if we want to say p 446 00:20:36,340 --> 00:20:40,110 equals mv equals what more convenient form 447 00:20:40,110 --> 00:20:41,430 that contains the energy? 448 00:20:46,040 --> 00:20:47,540 Square root of 2 mt. 449 00:20:50,770 --> 00:20:52,180 So let's go with that. 450 00:20:52,180 --> 00:20:55,660 So there'll be the square root of 2 mass 451 00:20:55,660 --> 00:20:58,300 of the alpha, kinetic energy of the alpha, 452 00:20:58,300 --> 00:21:01,600 minus the square root of 2 times the mass 453 00:21:01,600 --> 00:21:05,020 of the daughter times the kinetic energy of the daughter 454 00:21:05,020 --> 00:21:07,840 because these have to have equal and opposite momenta. 455 00:21:07,840 --> 00:21:11,810 So all we have to do is move that one over here. 456 00:21:14,320 --> 00:21:17,140 This makes that equation easy. 457 00:21:17,140 --> 00:21:19,960 Everything's got a square root of 2. 458 00:21:19,960 --> 00:21:21,235 We can square both sides. 459 00:21:24,910 --> 00:21:27,400 And we end up with a pretty simple relation, 460 00:21:27,400 --> 00:21:30,560 mass of the alpha times the kinetic energy of the alpha 461 00:21:30,560 --> 00:21:33,230 is the mass of the daughter times the kinetic energy 462 00:21:33,230 --> 00:21:35,710 of the daughter. 463 00:21:35,710 --> 00:21:37,930 We don't usually care about the kinetic energy 464 00:21:37,930 --> 00:21:40,045 of the recoil nucleus or the daughter 465 00:21:40,045 --> 00:21:41,920 because the range is so small that we usually 466 00:21:41,920 --> 00:21:43,030 don't get to measure it. 467 00:21:43,030 --> 00:21:44,740 But we are trying to measure what 468 00:21:44,740 --> 00:21:47,650 are the actual alpha particle energies so 469 00:21:47,650 --> 00:21:55,270 that we can reconstruct this table down here. 470 00:21:55,270 --> 00:21:57,700 So we can take our energy conservation equation 471 00:21:57,700 --> 00:22:02,420 and rearrange it to isolate td, the kinetic energy 472 00:22:02,420 --> 00:22:08,360 of the daughter, and say td equals Q minus t alpha. 473 00:22:11,280 --> 00:22:13,730 Substitute that in here. 474 00:22:13,730 --> 00:22:15,900 And let's rewrite what we've got. 475 00:22:15,900 --> 00:22:19,890 Mass of the alpha, t alpha, equals mass of the daughter 476 00:22:19,890 --> 00:22:24,660 times Q minus t alpha. 477 00:22:24,660 --> 00:22:32,310 If we multiply each term in here by md, we get mdQ minus md t 478 00:22:32,310 --> 00:22:34,020 alpha. 479 00:22:34,020 --> 00:22:36,960 Then we can take all of the t alphas on one side. 480 00:22:36,960 --> 00:22:41,940 So we'll just add md t alpha to each side. 481 00:22:41,940 --> 00:22:46,710 So we have m alpha t alpha plus md t 482 00:22:46,710 --> 00:22:55,870 alpha equals md Q. We can factor out the t alpha here. 483 00:22:59,350 --> 00:23:04,480 And then we can divide each side by m alpha plus m daughter. 484 00:23:09,480 --> 00:23:12,630 Cancel out the ma plus md. 485 00:23:12,630 --> 00:23:14,830 And there we have the answer. 486 00:23:14,830 --> 00:23:17,060 The kinetic energy of the alpha is just 487 00:23:17,060 --> 00:23:20,600 the q value times the ratio of the daughter 488 00:23:20,600 --> 00:23:22,820 mass to the total mass. 489 00:23:22,820 --> 00:23:25,520 This should look awfully familiar. 490 00:23:25,520 --> 00:23:28,700 When we did this in the frame of neutron elastic scattering 491 00:23:28,700 --> 00:23:31,490 or any other reaction, we had the same equation 492 00:23:31,490 --> 00:23:33,410 with just different notation. 493 00:23:33,410 --> 00:23:35,780 So do you guys recognize this firm, 494 00:23:35,780 --> 00:23:44,780 where we had t3 equals Q times m4 over m3 plus m4. 495 00:23:44,780 --> 00:23:48,560 It's the exact same result, just different notation. 496 00:23:48,560 --> 00:23:51,320 Last time we did it in the most complex way possible. 497 00:23:51,320 --> 00:23:54,080 This time we started off with the simplest possible equations 498 00:23:54,080 --> 00:23:55,430 for alpha decay. 499 00:23:55,430 --> 00:23:57,645 In the end it's the same Q equation. 500 00:23:57,645 --> 00:24:00,020 We just didn't bother with all the other terms and angles 501 00:24:00,020 --> 00:24:01,270 and things that we don't need. 502 00:24:03,670 --> 00:24:07,660 So is everyone clear where this came from? 503 00:24:07,660 --> 00:24:08,530 Cool. 504 00:24:08,530 --> 00:24:10,570 And that's why you're never going 505 00:24:10,570 --> 00:24:13,000 to see an alpha particle that's got 506 00:24:13,000 --> 00:24:18,100 the same energy as the initial minus the final energy 507 00:24:18,100 --> 00:24:20,860 because the recoil nucleus, or the daughter nucleus, 508 00:24:20,860 --> 00:24:23,200 takes away some of that kinetic energy 509 00:24:23,200 --> 00:24:26,140 in order to conserve the momentum of the system that 510 00:24:26,140 --> 00:24:28,983 was initially at rest. 511 00:24:28,983 --> 00:24:30,400 Another way to say this, for those 512 00:24:30,400 --> 00:24:31,900 who like center of mass coordinates, 513 00:24:31,900 --> 00:24:34,420 is the center of mass of this system 514 00:24:34,420 --> 00:24:36,340 was just the parent nucleus. 515 00:24:36,340 --> 00:24:37,870 It was at rest. 516 00:24:37,870 --> 00:24:40,570 The center of mass of the final system has to remain at rest 517 00:24:40,570 --> 00:24:42,370 to conserve momentum. 518 00:24:42,370 --> 00:24:44,890 But again, I won't go much into center of mass 519 00:24:44,890 --> 00:24:47,230 because I find it a little unintuitive. 520 00:24:47,230 --> 00:24:50,240 I'll stick with a laboratory frame of reference. 521 00:24:50,240 --> 00:24:53,650 So any questions before I move on? 522 00:24:53,650 --> 00:24:56,170 Alpha, I think, is the simplest case of radioactive decay. 523 00:24:56,170 --> 00:25:01,060 And I think now you know all you need to know about it. 524 00:25:01,060 --> 00:25:02,230 Yes. 525 00:25:02,230 --> 00:25:04,390 AUDIENCE: So why do you get so many different types 526 00:25:04,390 --> 00:25:06,300 if we just calculated it? 527 00:25:06,300 --> 00:25:11,770 Like mb, in mass [INAUDIBLE] change? 528 00:25:11,770 --> 00:25:13,960 MICHAEL SHORT: Not ma and md. 529 00:25:13,960 --> 00:25:18,490 But ta and td would change. 530 00:25:18,490 --> 00:25:18,990 Yep. 531 00:25:18,990 --> 00:25:21,750 So in this case, for different alpha decays, 532 00:25:21,750 --> 00:25:23,760 they'll have different Q values. 533 00:25:23,760 --> 00:25:26,730 So the Q value of, let's say, this top alpha decay 534 00:25:26,730 --> 00:25:32,430 is this energy here, 4.676 MeV minus 0.634. 535 00:25:32,430 --> 00:25:38,245 So use a different Q and you'll get different ta's and td's. 536 00:25:38,245 --> 00:25:38,870 So don't worry. 537 00:25:38,870 --> 00:25:40,960 You'll get chances to try out these calculations 538 00:25:40,960 --> 00:25:42,460 on the homework, where I'll actually 539 00:25:42,460 --> 00:25:46,990 ask you to calculate some of these from this equation, 540 00:25:46,990 --> 00:25:50,990 make sure you get the same values as the table. 541 00:25:50,990 --> 00:25:55,060 Any other questions on alpha decay before moving on to beta? 542 00:25:55,060 --> 00:25:58,540 Just going in order of the Greek alphabet. 543 00:25:58,540 --> 00:26:00,640 So beta decay is a kind of funny one. 544 00:26:00,640 --> 00:26:03,940 You don't tend to get a beta particle out 545 00:26:03,940 --> 00:26:07,520 at the energy of this Q value. 546 00:26:07,520 --> 00:26:09,650 You actually end up getting a spectrum. 547 00:26:09,650 --> 00:26:15,020 And this measured spectrum of different beta kinetic energies 548 00:26:15,020 --> 00:26:16,940 is what led to the thoughts that there 549 00:26:16,940 --> 00:26:20,360 must be something else carrying away some of that extra mass 550 00:26:20,360 --> 00:26:21,880 or some of that extra energy. 551 00:26:21,880 --> 00:26:24,710 I say that like it's the same thing because it totally is. 552 00:26:24,710 --> 00:26:26,750 And this is what led to the thinking 553 00:26:26,750 --> 00:26:29,810 that there's got to be some other very difficult to detect 554 00:26:29,810 --> 00:26:30,320 particle. 555 00:26:30,320 --> 00:26:32,480 So the theorists here we're saying, 556 00:26:32,480 --> 00:26:37,520 if we know the initial and final energies from beta decay, 557 00:26:37,520 --> 00:26:40,430 and we know that we get a spectrum of different beta 558 00:26:40,430 --> 00:26:42,680 energies and the probability of finding 559 00:26:42,680 --> 00:26:46,640 a beta particle at energy Q drops to, like, 0, 560 00:26:46,640 --> 00:26:48,140 you'll almost never see it. 561 00:26:48,140 --> 00:26:51,300 There's got to be something else carrying away the energy. 562 00:26:51,300 --> 00:26:53,370 So this idea of the neutrino, or in this case, 563 00:26:53,370 --> 00:26:55,340 the anti-neutrino, was proposed a long time 564 00:26:55,340 --> 00:26:57,590 before it was confirmed. 565 00:26:57,590 --> 00:26:59,575 And finally we know why. 566 00:26:59,575 --> 00:27:01,700 And one of the questions I want you to think about, 567 00:27:01,700 --> 00:27:05,330 because it might be on an exam in exactly two weeks, 568 00:27:05,330 --> 00:27:09,560 is if this is the relative number of electrons 569 00:27:09,560 --> 00:27:12,270 from beta decay as a function of energy, 570 00:27:12,270 --> 00:27:14,660 what does the number of anti-neutrinos versus energy 571 00:27:14,660 --> 00:27:18,328 look like in order to maintain conservation of energy? 572 00:27:18,328 --> 00:27:20,370 So it's something I want you guys to think about, 573 00:27:20,370 --> 00:27:21,787 but I'm not going to tell you what 574 00:27:21,787 --> 00:27:24,900 it is until the solutions for an exam. 575 00:27:24,900 --> 00:27:27,180 In the meantime, another thing to note 576 00:27:27,180 --> 00:27:29,670 is that these beta decays can also 577 00:27:29,670 --> 00:27:32,410 be followed by any number of gamma transitions. 578 00:27:32,410 --> 00:27:34,170 I've given you a simple one. 579 00:27:34,170 --> 00:27:37,020 If you want to look up simple ones to test your knowledge, 580 00:27:37,020 --> 00:27:38,880 go with the light elements. 581 00:27:38,880 --> 00:27:40,530 They don't have that many nucleons 582 00:27:40,530 --> 00:27:43,110 and they won't have that many transitions. 583 00:27:43,110 --> 00:27:47,690 For example, if we pick a beta decay nucleus, 584 00:27:47,690 --> 00:27:50,150 something simple. 585 00:27:50,150 --> 00:27:53,430 Let's go with lithium, which typically has-- 586 00:27:53,430 --> 00:27:56,920 the stable isotopes are lithium 6 or lithium 7. 587 00:27:56,920 --> 00:27:59,470 So do you think that higher or lower 588 00:27:59,470 --> 00:28:03,608 mass number lithium will tend to go by beta decay 589 00:28:03,608 --> 00:28:05,275 based on this generalized decay diagram? 590 00:28:08,960 --> 00:28:10,920 It's what? 591 00:28:10,920 --> 00:28:12,245 AUDIENCE: [INAUDIBLE] 592 00:28:12,245 --> 00:28:13,120 MICHAEL SHORT: Lower. 593 00:28:13,120 --> 00:28:14,175 Lower proton number? 594 00:28:14,175 --> 00:28:16,300 Well, we've got to stick with the number of protons 595 00:28:16,300 --> 00:28:18,370 because we need to remain lithium. 596 00:28:18,370 --> 00:28:20,120 So in other words, do you expect lithium 4 597 00:28:20,120 --> 00:28:24,880 and lithium 5 or lithium 8 and lithium 9 to go by beta decay? 598 00:28:30,577 --> 00:28:31,660 AUDIENCE: The higher ones. 599 00:28:31,660 --> 00:28:32,400 MICHAEL SHORT: The higher ones. 600 00:28:32,400 --> 00:28:32,995 OK. 601 00:28:32,995 --> 00:28:34,620 If you guys remember the mass parabolas 602 00:28:34,620 --> 00:28:36,720 from a couple of weeks ago, we delineated 603 00:28:36,720 --> 00:28:43,920 where you'd expect beta decay in order 604 00:28:43,920 --> 00:28:45,808 to increase the proton number. 605 00:28:45,808 --> 00:28:47,850 So if you've got too many neutrons and not enough 606 00:28:47,850 --> 00:28:51,690 protons, chances are beta decay will help equalize you out. 607 00:28:51,690 --> 00:28:52,470 So as a guess-- 608 00:28:52,470 --> 00:28:53,550 I haven't even tried this at home. 609 00:28:53,550 --> 00:28:54,057 Let's see. 610 00:28:54,057 --> 00:28:55,640 Let's see what happens with lithium 8. 611 00:28:55,640 --> 00:28:56,860 Oh, look at that. 612 00:28:56,860 --> 00:28:58,740 Beta decay. 613 00:28:58,740 --> 00:29:01,020 It can also decay by beta plus 2 alpha, 614 00:29:01,020 --> 00:29:05,330 which is another word for the nucleus just blows apart. 615 00:29:05,330 --> 00:29:08,570 It's interesting, too, if you read Chadwick's paper again, 616 00:29:08,570 --> 00:29:12,350 the way he described a beryllium nucleus is consisting 617 00:29:12,350 --> 00:29:16,010 of a neutron plus two alpha particles. 618 00:29:16,010 --> 00:29:17,630 Interesting, huh? 619 00:29:17,630 --> 00:29:20,100 Lithium 9 could decay by--or let's say lithium 8. 620 00:29:20,100 --> 00:29:21,380 What do we have? 621 00:29:21,380 --> 00:29:22,510 Beta plus 2 alpha. 622 00:29:22,510 --> 00:29:23,240 Yeah. 623 00:29:23,240 --> 00:29:25,490 So Chadwick described any nucleus 624 00:29:25,490 --> 00:29:28,400 as consisting of these elementary-ish particles 625 00:29:28,400 --> 00:29:29,780 that you could measure. 626 00:29:29,780 --> 00:29:32,150 And in this case, you kind of see a physical example. 627 00:29:32,150 --> 00:29:33,830 When this nucleus blows apart, it just 628 00:29:33,830 --> 00:29:35,780 becomes two alphas in a beta. 629 00:29:35,780 --> 00:29:36,790 Interesting. 630 00:29:36,790 --> 00:29:40,340 But let's look at the beta decay to beryllium 8. 631 00:29:40,340 --> 00:29:42,040 Pretty simple. 632 00:29:42,040 --> 00:29:45,970 You may ask why can't you have beta decay directly 633 00:29:45,970 --> 00:29:49,530 from the highest energy to the ground state energy? 634 00:29:49,530 --> 00:29:51,700 That is a 22.02 question that I'll mention. 635 00:29:51,700 --> 00:29:56,410 There are allowed and unaligned transitions between spins 636 00:29:56,410 --> 00:29:57,650 and energy states. 637 00:29:57,650 --> 00:30:01,060 So if you're wondering why isn't every line drawn, 638 00:30:01,060 --> 00:30:02,800 in the case of really complex nuclei, 639 00:30:02,800 --> 00:30:05,350 there aren't enough pixels on the screen sometimes. 640 00:30:05,350 --> 00:30:07,690 But for the simple nuclei, there are actually 641 00:30:07,690 --> 00:30:09,580 rules of selection to decide when 642 00:30:09,580 --> 00:30:11,158 you can make this transition. 643 00:30:11,158 --> 00:30:12,700 But a lot of beta decays will usually 644 00:30:12,700 --> 00:30:17,370 be something like a beta decay followed by a gamma. 645 00:30:17,370 --> 00:30:21,160 So let's see a couple of well-known examples. 646 00:30:21,160 --> 00:30:22,450 For example, carbon-14. 647 00:30:22,450 --> 00:30:25,180 This is the basis behind carbon dating, one 648 00:30:25,180 --> 00:30:28,907 of those rare instances when you have a beta decay directly 649 00:30:28,907 --> 00:30:29,740 to the ground state. 650 00:30:29,740 --> 00:30:31,930 It's about as simple as it gets. 651 00:30:31,930 --> 00:30:35,890 And because the half life is 5,730 years, 652 00:30:35,890 --> 00:30:38,110 it's really useful for dating when 653 00:30:38,110 --> 00:30:40,270 did an organism or piece of material 654 00:30:40,270 --> 00:30:44,320 die on the timescale of, let's say, tens to tens of thousands 655 00:30:44,320 --> 00:30:45,550 of years. 656 00:30:45,550 --> 00:30:47,310 Once you've gone past a few half lives 657 00:30:47,310 --> 00:30:49,695 and there's very little carbon-14 left, 658 00:30:49,695 --> 00:30:51,070 there aren't a lot of decays left 659 00:30:51,070 --> 00:30:53,260 and your counting statistics get crappy, 660 00:30:53,260 --> 00:30:55,960 and it gets harder and harder to carbon date things. 661 00:30:55,960 --> 00:30:59,200 The basis behind this is that all living organisms that 662 00:30:59,200 --> 00:31:02,770 are intaking and exhaling carbon by some means 663 00:31:02,770 --> 00:31:06,430 remain in isotopic equilibrium with the carbon surrounding 664 00:31:06,430 --> 00:31:07,330 them. 665 00:31:07,330 --> 00:31:10,390 And while most carbon is CO2, and food and whatever 666 00:31:10,390 --> 00:31:12,490 is carbon-12, you're going to have 667 00:31:12,490 --> 00:31:15,880 a little bit of carbon-14 production 668 00:31:15,880 --> 00:31:17,110 from the upper atmosphere. 669 00:31:17,110 --> 00:31:18,850 This is usually a cosmic ray phenomenon, 670 00:31:18,850 --> 00:31:21,880 which we'll get into when we get into cosmic rays. 671 00:31:21,880 --> 00:31:25,150 The moment you die you stop intaking carbon, 672 00:31:25,150 --> 00:31:28,270 and the little bit of carbon-14 in the cloth and the food 673 00:31:28,270 --> 00:31:30,970 and your body, whatever, starts to decay naturally 674 00:31:30,970 --> 00:31:33,840 with a very regular decay curve. 675 00:31:33,840 --> 00:31:36,257 And so this is the whole basis behind carbon dating. 676 00:31:36,257 --> 00:31:37,840 And in the next p-set, you'll actually 677 00:31:37,840 --> 00:31:41,560 see how this was used to debunk the Shroud of Turin, 678 00:31:41,560 --> 00:31:44,320 or the supposed burial cloth of Jesus of Nazareth, 679 00:31:44,320 --> 00:31:47,250 because the carbon dating data just didn't check out. 680 00:31:47,250 --> 00:31:50,920 As much as people really wanted to feel like we found it, no. 681 00:31:50,920 --> 00:31:52,060 Science. 682 00:31:52,060 --> 00:31:52,900 That's the answer. 683 00:31:52,900 --> 00:31:54,970 No. 684 00:31:54,970 --> 00:31:57,640 Another well-known one we've talked about before 685 00:31:57,640 --> 00:32:02,950 is molybdenum 99 decaying to technetium 99 meta stable. 686 00:32:02,950 --> 00:32:04,660 Notice how here, any number of beta 687 00:32:04,660 --> 00:32:08,890 decays and any cascade of very fast gamma transitions, 688 00:32:08,890 --> 00:32:13,738 they almost all end right here at this state of about-- 689 00:32:13,738 --> 00:32:16,030 let's see, there's two numbers written over each other. 690 00:32:16,030 --> 00:32:20,230 But it's about 140 keV or 0.14 MeV. 691 00:32:20,230 --> 00:32:22,720 This transition from this state to the ground state 692 00:32:22,720 --> 00:32:24,390 is a slow transition. 693 00:32:24,390 --> 00:32:26,890 So you can actually build up technitum 99 694 00:32:26,890 --> 00:32:28,870 in what's called series decay, which 695 00:32:28,870 --> 00:32:30,790 we're going to cover on Friday. 696 00:32:30,790 --> 00:32:34,780 And then you can use these 140 KeV gamma 697 00:32:34,780 --> 00:32:36,878 rays to do medical imaging. 698 00:32:36,878 --> 00:32:38,920 So when you get a medical imaging procedure done, 699 00:32:38,920 --> 00:32:41,830 chances are this is how it's done. 700 00:32:41,830 --> 00:32:46,720 You get moly 99 out of a reactor or an accelerator, 701 00:32:46,720 --> 00:32:49,420 chemically isolate the technetium 99 meta 702 00:32:49,420 --> 00:32:51,970 stable, which lasts on the order of six days 703 00:32:51,970 --> 00:32:55,180 or so, very quickly get it to someone, inject it, 704 00:32:55,180 --> 00:32:57,110 and image where do the gamma rays go, 705 00:32:57,110 --> 00:33:00,840 or where do the gamma rays come from? 706 00:33:00,840 --> 00:33:04,950 One last notable one is responsible for a lot of, well, 707 00:33:04,950 --> 00:33:07,320 problems when folks go urban exploring 708 00:33:07,320 --> 00:33:09,480 in old dentist's offices. 709 00:33:09,480 --> 00:33:14,040 Nowadays they have electrostatic x-ray machines 710 00:33:14,040 --> 00:33:15,030 at dentist's offices. 711 00:33:15,030 --> 00:33:17,460 But back in the day, you could get a little button 712 00:33:17,460 --> 00:33:21,420 of cobalt 60, which would emit two very characteristic gamma 713 00:33:21,420 --> 00:33:24,460 rays in addition to its beta decays. 714 00:33:24,460 --> 00:33:28,020 So normally what happens is cobalt 60 decays quickly 715 00:33:28,020 --> 00:33:29,760 to an excited state and gives off 716 00:33:29,760 --> 00:33:32,400 two gamma rays in succession, which 717 00:33:32,400 --> 00:33:34,490 would be used for imaging. 718 00:33:34,490 --> 00:33:36,073 Problem is that's the a cobalt source. 719 00:33:36,073 --> 00:33:38,323 And if you don't know what it is, and you're like, oh, 720 00:33:38,323 --> 00:33:41,660 cool, what's this blue thing, I think I'll put it in my pocket 721 00:33:41,660 --> 00:33:42,560 and keep it-- 722 00:33:42,560 --> 00:33:45,860 that has been responsible for some injuries 723 00:33:45,860 --> 00:33:48,942 from some folks that didn't know any better. 724 00:33:48,942 --> 00:33:50,650 And then how do you detect the neutrinos? 725 00:33:50,650 --> 00:33:53,810 We talked about the theoretical reason why they exist. 726 00:33:53,810 --> 00:33:55,660 Let's actually see how they're measured. 727 00:33:55,660 --> 00:33:57,790 There is a hollowed out salt mine 728 00:33:57,790 --> 00:34:01,270 of some sort called Kamiokande in Japan. 729 00:34:01,270 --> 00:34:05,680 It's a humongous hole in the ground filled with water, 730 00:34:05,680 --> 00:34:09,820 for a reason, and lined with tens of thousands 731 00:34:09,820 --> 00:34:12,219 of highly sensitive photo tubes that can pick up 732 00:34:12,219 --> 00:34:14,500 tiny, tiny amounts of light. 733 00:34:14,500 --> 00:34:16,750 The reason for this is because neutrinos, 734 00:34:16,750 --> 00:34:19,030 as you saw in problem set 1, are always 735 00:34:19,030 --> 00:34:22,060 traveling near the speed of light in a vacuum. 736 00:34:22,060 --> 00:34:26,020 So if the speed of light in a vacuum, 737 00:34:26,020 --> 00:34:31,989 let's call that 1, and the velocity of the neutrino-- 738 00:34:31,989 --> 00:34:33,379 wasn't it something like 9. 739 00:34:33,379 --> 00:34:36,250 999c or something like that? 740 00:34:36,250 --> 00:34:37,880 It was pretty high. 741 00:34:37,880 --> 00:34:41,770 The speed of light and water is significantly less 742 00:34:41,770 --> 00:34:43,989 than the speed of light in a vacuum. 743 00:34:43,989 --> 00:34:46,780 When you have a material or a particle that goes faster 744 00:34:46,780 --> 00:34:50,693 than the speed of light in the medium that it's traveling in, 745 00:34:50,693 --> 00:34:52,110 then you can produce what's called 746 00:34:52,110 --> 00:34:53,710 Cherenkov radiation, which I think 747 00:34:53,710 --> 00:34:55,489 I've mentioned once before. 748 00:34:55,489 --> 00:34:57,850 It's kind of like a sonic boom in that you 749 00:34:57,850 --> 00:35:01,450 get a conical shockwave of energy radiated 750 00:35:01,450 --> 00:35:04,000 from that particle that tells you which direction it's 751 00:35:04,000 --> 00:35:04,990 coming from. 752 00:35:04,990 --> 00:35:07,300 But instead of a sound wave, you get light. 753 00:35:07,300 --> 00:35:08,920 And this whole detector is designed 754 00:35:08,920 --> 00:35:12,670 to look at the ellipses of Cherenkov radiation released 755 00:35:12,670 --> 00:35:15,920 by neutrinos and anti-neutrinos. 756 00:35:15,920 --> 00:35:18,550 So what happens is if a neutrino happens 757 00:35:18,550 --> 00:35:22,180 to interact with the water here, it produces Cherenkov radiation 758 00:35:22,180 --> 00:35:24,460 lighting up a ring of these detectors 759 00:35:24,460 --> 00:35:26,320 so you can tell it's energy and you 760 00:35:26,320 --> 00:35:28,460 can tell where it came from. 761 00:35:28,460 --> 00:35:30,520 So if you, let's say, can correlate 762 00:35:30,520 --> 00:35:34,930 a supernova or some sort of crazy galactic whatever 763 00:35:34,930 --> 00:35:37,510 with a slight burst of neutrinos, 764 00:35:37,510 --> 00:35:41,290 then you've got a pretty significant astronomical event. 765 00:35:41,290 --> 00:35:43,270 It also led to my favorite BBC headline 766 00:35:43,270 --> 00:35:47,760 ever, "Particle physics telescope explodes." 767 00:35:47,760 --> 00:35:49,720 You'd see this on, like, Fox News or something. 768 00:35:49,720 --> 00:35:51,450 No, this was the BBC. 769 00:35:51,450 --> 00:35:54,060 What happened here is one of these 30,000 770 00:35:54,060 --> 00:35:56,580 or so tubes was slightly defective, 771 00:35:56,580 --> 00:35:59,570 couldn't hold the pressure, and it burst. 772 00:35:59,570 --> 00:36:02,220 And the resulting sound shock wave 773 00:36:02,220 --> 00:36:06,640 from one photo tube bursting blew up about 11,000 of them. 774 00:36:06,640 --> 00:36:09,940 So yeah, the particle physics telescope kind of did explode. 775 00:36:09,940 --> 00:36:13,480 They did rebuild it and it's still going. 776 00:36:13,480 --> 00:36:16,690 It was an expensive repair because all 11,300 something 777 00:36:16,690 --> 00:36:20,830 tubes had to be rebuilt. And if you notice, 778 00:36:20,830 --> 00:36:22,270 there's a guy on a boat there. 779 00:36:22,270 --> 00:36:23,500 How do you install them? 780 00:36:23,500 --> 00:36:27,400 Well, you float on a boat quietly, 781 00:36:27,400 --> 00:36:31,060 and put the photo tubes in, and raise the water level, 782 00:36:31,060 --> 00:36:33,670 and float to another part of the detector 783 00:36:33,670 --> 00:36:36,820 quietly, and continue installing the photo tubes 784 00:36:36,820 --> 00:36:37,860 until you're done. 785 00:36:37,860 --> 00:36:38,807 AUDIENCE: [INAUDIBLE] 786 00:36:38,807 --> 00:36:39,640 MICHAEL SHORT: Yeah. 787 00:36:39,640 --> 00:36:41,070 You don't. 788 00:36:41,070 --> 00:36:42,000 Yeah. 789 00:36:42,000 --> 00:36:43,790 Don't sneeze. 790 00:36:43,790 --> 00:36:44,480 So yeah. 791 00:36:44,480 --> 00:36:46,600 Favorite BBC headline ever. 792 00:36:46,600 --> 00:36:49,140 Thanks again, science. 793 00:36:49,140 --> 00:36:50,750 For positron decay-- 794 00:36:50,750 --> 00:36:52,560 OK, we've got about 10 minutes left-- 795 00:36:52,560 --> 00:36:55,010 for positron decay, this is the energy 796 00:36:55,010 --> 00:36:56,760 that you need in order to make a positron. 797 00:36:56,760 --> 00:37:00,840 It is approximately exactly double the [INAUDIBLE] rest 798 00:37:00,840 --> 00:37:02,360 mass of an electron. 799 00:37:02,360 --> 00:37:05,010 And the question usually comes up, well, a positron 800 00:37:05,010 --> 00:37:08,370 has a rest mass energy of 0.511 MeV. 801 00:37:08,370 --> 00:37:10,660 Why do you need double that to make the positron? 802 00:37:10,660 --> 00:37:12,910 Because in order to conserve the charge of the system, 803 00:37:12,910 --> 00:37:15,180 you have to shed an orbital electron. 804 00:37:15,180 --> 00:37:18,540 So the system has got to be able to lose two electrons 805 00:37:18,540 --> 00:37:21,160 in the process, one positively charged 806 00:37:21,160 --> 00:37:22,870 and one negatively charged. 807 00:37:22,870 --> 00:37:25,740 And so that's why the Q for positron decay 808 00:37:25,740 --> 00:37:27,240 is just going to be-- 809 00:37:27,240 --> 00:37:29,640 remember, this symbol's the excess mass here, 810 00:37:29,640 --> 00:37:32,310 excess mass of the parent minus excess mass of the daughter 811 00:37:32,310 --> 00:37:36,570 minus 2 times the rest mass of the electron squared. 812 00:37:36,570 --> 00:37:41,990 To refresh your memories a bit, find some empty space. 813 00:37:41,990 --> 00:37:44,420 The excess mass is nothing more than the mass 814 00:37:44,420 --> 00:37:48,730 minus the horrible approximation of the mass. 815 00:37:48,730 --> 00:37:52,040 So the excess mass and the real mass are directly related. 816 00:37:52,040 --> 00:37:55,430 And these are things that you can look up. 817 00:37:55,430 --> 00:37:57,260 Just to remind you guys that excess mass 818 00:37:57,260 --> 00:37:59,390 and mass and binding energy and kinetic energy 819 00:37:59,390 --> 00:38:01,500 are all related, again, by the Q equation. 820 00:38:01,500 --> 00:38:03,792 It's probably the last time I'll say it because I think 821 00:38:03,792 --> 00:38:07,290 that's about 100, by my count. 822 00:38:07,290 --> 00:38:09,810 Positrons can be used for some pretty awesome things. 823 00:38:09,810 --> 00:38:12,000 And in the last five minutes or so, 824 00:38:12,000 --> 00:38:14,190 I want to show you some work done by Professor Brian 825 00:38:14,190 --> 00:38:16,360 Wirth at the University of Tennessee, 826 00:38:16,360 --> 00:38:20,010 Knoxville on positron annihilation spectroscopy, 827 00:38:20,010 --> 00:38:22,500 using anti-matter to probe matter 828 00:38:22,500 --> 00:38:25,030 and find out what sort of defects exist. 829 00:38:25,030 --> 00:38:26,970 And as a nuclear material scientist, 830 00:38:26,970 --> 00:38:30,270 I'd be, well, terrible if I didn't inject 831 00:38:30,270 --> 00:38:32,400 a little bit of materials and how 832 00:38:32,400 --> 00:38:37,040 we use nuclear stuff in 22.01 in order to probe that thing. 833 00:38:37,040 --> 00:38:40,140 So the way that positron annihilation spectroscopy works 834 00:38:40,140 --> 00:38:42,630 is that, well, matter's mostly empty space. 835 00:38:42,630 --> 00:38:45,570 And then in a regular crystal lattice, 836 00:38:45,570 --> 00:38:52,000 where the atoms are arranged in a very regular array, 837 00:38:52,000 --> 00:38:56,110 let's say these atoms have their orbital electrons. 838 00:38:56,110 --> 00:38:59,950 The empty space between is also arranged 839 00:38:59,950 --> 00:39:01,810 in a very regular array. 840 00:39:01,810 --> 00:39:05,440 And positrons annihilate with electrons to produce-- 841 00:39:05,440 --> 00:39:07,090 well, we'll find out in a second. 842 00:39:07,090 --> 00:39:09,070 But where in matter would they want to live, 843 00:39:09,070 --> 00:39:10,420 or where would they last longer? 844 00:39:10,420 --> 00:39:13,580 Not near an atom, but near the space in between. 845 00:39:13,580 --> 00:39:16,930 So you can map out the empty spaces in matter 846 00:39:16,930 --> 00:39:19,900 in a regular crystal and calculate an average positron 847 00:39:19,900 --> 00:39:20,920 lifetime. 848 00:39:20,920 --> 00:39:25,600 If you were to fire a positron into this matter, 849 00:39:25,600 --> 00:39:28,270 how long would it sit and bounce around 850 00:39:28,270 --> 00:39:31,090 before colliding with an electron 851 00:39:31,090 --> 00:39:34,840 and releasing that extra rest mass energy? 852 00:39:34,840 --> 00:39:36,930 It turns out if you have crystalline defects, 853 00:39:36,930 --> 00:39:39,810 the positrons tend to last a little longer. 854 00:39:39,810 --> 00:39:41,950 There's a little more empty space, 855 00:39:41,950 --> 00:39:44,820 which is to say there are more places with a slightly 856 00:39:44,820 --> 00:39:47,920 less probability of finding an electron. 857 00:39:47,920 --> 00:39:49,410 And so they last longer. 858 00:39:49,410 --> 00:39:52,778 And you can measure the lifetime of positrons 859 00:39:52,778 --> 00:39:55,320 before they enter the material, and then how long before they 860 00:39:55,320 --> 00:39:59,800 produce their characteristic destruction gamma rays. 861 00:39:59,800 --> 00:40:04,020 So if you think about it, you have a positron coming in 862 00:40:04,020 --> 00:40:10,800 with a rest mass 0.511 MeV. 863 00:40:10,800 --> 00:40:14,100 And it collides with an electron from some orbital nucleus that 864 00:40:14,100 --> 00:40:16,320 has the same rest mass. 865 00:40:16,320 --> 00:40:20,080 The positron and the electron annihilate sending off 866 00:40:20,080 --> 00:40:24,300 gamma rays in opposite directions, where 867 00:40:24,300 --> 00:40:31,062 the energy of this gamma is same thing, 0.511 MV. 868 00:40:31,062 --> 00:40:32,520 So you can tell when a positron was 869 00:40:32,520 --> 00:40:36,450 destroyed because you instantly get 1/2 a MeV gamma ray. 870 00:40:36,450 --> 00:40:39,420 Or actually, you get two 1/2 MeV gamma rays. 871 00:40:39,420 --> 00:40:42,560 Then the question is, how do you tell its lifetime? 872 00:40:42,560 --> 00:40:45,920 Let's go back to something that I didn't quite point out, 873 00:40:45,920 --> 00:40:50,310 but I want to show you now, is this positron decay 874 00:40:50,310 --> 00:40:54,480 is immediately followed by a 1.27 MeV gamma 875 00:40:54,480 --> 00:40:58,690 ray, which in PAS, or Positron Annihilation Spectroscopy, 876 00:40:58,690 --> 00:41:00,540 we call this the birth gamma ray. 877 00:41:00,540 --> 00:41:05,790 This gamma ray is emitted the instant this nucleus is born. 878 00:41:05,790 --> 00:41:09,727 And the positron takes a little bit of time to get destroyed. 879 00:41:09,727 --> 00:41:11,310 So you actually look at the difference 880 00:41:11,310 --> 00:41:20,080 in time between sensing the 1.27 MeV gamma ray and the 0.511 MeV 881 00:41:20,080 --> 00:41:21,952 annihilation photons. 882 00:41:21,952 --> 00:41:23,410 And that is measured in, let's say, 883 00:41:23,410 --> 00:41:25,300 hundreds of pico seconds with resolution 884 00:41:25,300 --> 00:41:27,310 of around 5 picoseconds. 885 00:41:27,310 --> 00:41:31,000 And you can then tell, from the lifetime and how many survive, 886 00:41:31,000 --> 00:41:35,595 what sort of atomic defects might exist in the material. 887 00:41:35,595 --> 00:41:37,720 So if you want to count the number of missing atoms 888 00:41:37,720 --> 00:41:40,840 or vacancies in a material, which 889 00:41:40,840 --> 00:41:43,270 is extremely important to those of us in radiation damage, 890 00:41:43,270 --> 00:41:47,300 you can do so with positron annihilation spectroscopy. 891 00:41:47,300 --> 00:41:49,550 So I think I wanted to show you a little bit about how 892 00:41:49,550 --> 00:41:51,270 this works. 893 00:41:51,270 --> 00:41:55,050 You start off by making a radioactive salt sandwich. 894 00:41:55,050 --> 00:41:58,110 You take some sodium chloride, specifically 895 00:41:58,110 --> 00:42:02,820 of the isotope sodium 22, which is giving off positrons 896 00:42:02,820 --> 00:42:03,900 all the time. 897 00:42:03,900 --> 00:42:07,230 And you sandwich that radioactive jelly 898 00:42:07,230 --> 00:42:10,320 between the two slices of bread, better known as your sample. 899 00:42:10,320 --> 00:42:12,060 That way you catch every positron 900 00:42:12,060 --> 00:42:15,710 that gets out so you don't lose half of them to one side. 901 00:42:15,710 --> 00:42:19,320 You've got two detectors on either side waiting. 902 00:42:19,320 --> 00:42:22,228 So there's some probability that the photons emitted 903 00:42:22,228 --> 00:42:24,270 are going to go in the direction of the detector. 904 00:42:24,270 --> 00:42:27,360 So you miss most of the signal, but so what? 905 00:42:27,360 --> 00:42:32,100 Whenever you actually sense a 1.27 MeV gamma ray followed 906 00:42:32,100 --> 00:42:35,580 by two 511 KeVs here, then you know 907 00:42:35,580 --> 00:42:37,860 you've had a positron annihilation event, 908 00:42:37,860 --> 00:42:41,160 and you can actually count the time between when 909 00:42:41,160 --> 00:42:42,390 those things happened. 910 00:42:42,390 --> 00:42:43,890 And you can see the number of counts 911 00:42:43,890 --> 00:42:45,930 and get the average positron lifetime 912 00:42:45,930 --> 00:42:49,170 from finding out how many counts you get every five pico 913 00:42:49,170 --> 00:42:51,280 seconds, for example. 914 00:42:51,280 --> 00:42:53,610 There's something to note about these counting spectra. 915 00:42:53,610 --> 00:42:56,610 Anybody know why they're so smooth up here 916 00:42:56,610 --> 00:43:02,540 and then they're so delineated down here? 917 00:43:02,540 --> 00:43:03,998 Anyone have an idea? 918 00:43:06,920 --> 00:43:09,550 You're going to see this a lot in 22.09, when you actually 919 00:43:09,550 --> 00:43:12,460 count theta particles or alpha particles and your counting 920 00:43:12,460 --> 00:43:14,650 statistics get a little crappier. 921 00:43:14,650 --> 00:43:16,930 This is a log scale of counts, or in this case, 922 00:43:16,930 --> 00:43:19,780 counts per five pico seconds. 923 00:43:19,780 --> 00:43:22,090 10 to the 0's better known as 1. 924 00:43:22,090 --> 00:43:25,120 So you're looking at one count or two or three. 925 00:43:25,120 --> 00:43:26,690 You're looking at the discrete event. 926 00:43:26,690 --> 00:43:28,630 You can't have one and 1/2 counts. 927 00:43:28,630 --> 00:43:30,910 So you're going to see this kind of thing 928 00:43:30,910 --> 00:43:33,700 quite a lot when you're trying to count very rare events. 929 00:43:33,700 --> 00:43:36,640 And if you're down in the weeds like this, 930 00:43:36,640 --> 00:43:39,070 let's just say your statistics aren't that good. 931 00:43:39,070 --> 00:43:41,890 But since this is a logarithmic scale, 10 to the 4th 932 00:43:41,890 --> 00:43:43,780 is better known as 10,000, that's 933 00:43:43,780 --> 00:43:45,910 enough to get good statistics and fit 934 00:43:45,910 --> 00:43:49,600 a nice curve to this positron lifetime thing. 935 00:43:49,600 --> 00:43:52,000 This is what one of them actually looks like. 936 00:43:52,000 --> 00:43:55,058 And you can kind of tell. 937 00:43:55,058 --> 00:43:57,350 Inside there is where all the positrons are coming out. 938 00:43:57,350 --> 00:43:59,410 So that's probably lead shielding. 939 00:43:59,410 --> 00:44:01,660 Here's two detectors on either side. 940 00:44:01,660 --> 00:44:05,960 And here's another detector to detect that 1.27 MeV birth 941 00:44:05,960 --> 00:44:06,813 gamma ray. 942 00:44:06,813 --> 00:44:08,730 So if you get those three events happening all 943 00:44:08,730 --> 00:44:10,480 at the right time, you've got a positive event 944 00:44:10,480 --> 00:44:11,272 that you can count. 945 00:44:13,780 --> 00:44:17,920 And last thing I'll mention is you can actually use this, 946 00:44:17,920 --> 00:44:20,380 like I said, to gut not just the number of vacancies, 947 00:44:20,380 --> 00:44:23,050 but the number of different size defects. 948 00:44:23,050 --> 00:44:24,970 You might have two or three missing atoms next 949 00:44:24,970 --> 00:44:28,140 to each other, which will have different positron lifetimes. 950 00:44:28,140 --> 00:44:31,780 And you can actually count the number of each of these 951 00:44:31,780 --> 00:44:35,322 to get the diameter or the size of these atomic defects. 952 00:44:35,322 --> 00:44:37,030 And this is one of the ways of confirming 953 00:44:37,030 --> 00:44:40,630 our models of radiation damage, which is, like, all I do. 954 00:44:40,630 --> 00:44:42,785 That's half of our group. 955 00:44:42,785 --> 00:44:44,160 If you want to read anything more 956 00:44:44,160 --> 00:44:46,800 about positron annihilation spectroscopy, 957 00:44:46,800 --> 00:44:48,665 all the stuff in these slides were 958 00:44:48,665 --> 00:44:50,790 from these references, which you can look up easily 959 00:44:50,790 --> 00:44:52,440 on the MIT libraries. 960 00:44:52,440 --> 00:44:54,750 We have access to everything because that's MIT. 961 00:44:54,750 --> 00:44:56,705 We just buy everything there is. 962 00:44:56,705 --> 00:44:58,080 So I'd encourage you to look here 963 00:44:58,080 --> 00:45:00,750 if you want to see more details on how this works 964 00:45:00,750 --> 00:45:02,450 and why it works. 965 00:45:02,450 --> 00:45:06,140 So because it's exactly five of five of, 966 00:45:06,140 --> 00:45:08,930 I want to open it up to any questions on alpha decay, 967 00:45:08,930 --> 00:45:12,065 beta decay, positron decay, or the decay diagrams 968 00:45:12,065 --> 00:45:13,190 that we've developed today. 969 00:45:18,690 --> 00:45:19,360 Yes. 970 00:45:19,360 --> 00:45:21,540 AUDIENCE: What is the most dangerous kind of decay? 971 00:45:21,540 --> 00:45:23,457 MICHAEL SHORT: What is the most dangerous kind 972 00:45:23,457 --> 00:45:25,320 of decay to be exposed to? 973 00:45:25,320 --> 00:45:28,640 So in this case, you'd want to say the energy of the particle 974 00:45:28,640 --> 00:45:31,440 is held constant, and the number of those particles 975 00:45:31,440 --> 00:45:33,150 is held constant. 976 00:45:33,150 --> 00:45:35,643 And actually, we're going to answer this question 977 00:45:35,643 --> 00:45:37,560 when we get to medical and biological effects. 978 00:45:37,560 --> 00:45:39,163 But let's do a little flash word now. 979 00:45:39,163 --> 00:45:41,580 Let's assume, if you want to see which one of these decays 980 00:45:41,580 --> 00:45:44,610 is most dangerous, we'll have to say constant-- 981 00:45:47,210 --> 00:45:54,010 constant-- energy of decay, constant activity, and what 982 00:45:54,010 --> 00:45:56,850 else can we hold constant? 983 00:45:56,850 --> 00:45:59,070 Well, constant you. 984 00:45:59,070 --> 00:46:02,360 Let's say the same number of particles end up hitting you. 985 00:46:02,360 --> 00:46:07,080 That depends on whether they're inside or outside your body. 986 00:46:07,080 --> 00:46:10,680 If you were to ingest material, then alphas 987 00:46:10,680 --> 00:46:13,200 would be your worst because alpha particles 988 00:46:13,200 --> 00:46:16,650 are massive and charged nuclei, which 989 00:46:16,650 --> 00:46:18,630 means they interact very strongly with matter 990 00:46:18,630 --> 00:46:19,210 around them. 991 00:46:19,210 --> 00:46:21,182 So if you ingest them and they end up 992 00:46:21,182 --> 00:46:23,640 incorporating into your cells, where they can just get next 993 00:46:23,640 --> 00:46:26,580 to DNA, they can just blast it apart. 994 00:46:26,580 --> 00:46:29,460 However, an alpha source of equal strength held 995 00:46:29,460 --> 00:46:31,920 in your hand would do nothing. 996 00:46:31,920 --> 00:46:35,142 The dead skin cells are enough to stop alpha particles. 997 00:46:35,142 --> 00:46:36,600 And we're going to find out exactly 998 00:46:36,600 --> 00:46:38,850 why when we look at the range and stopping 999 00:46:38,850 --> 00:46:41,540 power of different particles and matter. 1000 00:46:41,540 --> 00:46:44,950 From the outside, alphas won't really get through your skin. 1001 00:46:44,950 --> 00:46:48,110 Betas might get through a little bit of your skin, but not much. 1002 00:46:48,110 --> 00:46:50,660 Gamma rays will mostly go right through you. 1003 00:46:50,660 --> 00:46:54,650 It's neutrons that are the real killers. 1004 00:46:54,650 --> 00:46:58,190 Those neutrons are heavy but uncharged. 1005 00:46:58,190 --> 00:47:00,380 So they interact kind of strongly. 1006 00:47:00,380 --> 00:47:02,590 When they do hit, they pack a wallop 1007 00:47:02,590 --> 00:47:04,130 and they do a lot of damage. 1008 00:47:04,130 --> 00:47:05,900 And they're mean free path, and you is 1009 00:47:05,900 --> 00:47:07,920 on the order of 10 centimeters. 1010 00:47:07,920 --> 00:47:11,030 So a neutron source from the outside can do a lot of damage 1011 00:47:11,030 --> 00:47:12,112 from the outside. 1012 00:47:12,112 --> 00:47:13,820 The alphas and the betas would be stopped 1013 00:47:13,820 --> 00:47:15,530 by your skin and clothes. 1014 00:47:15,530 --> 00:47:18,072 The gamma rays, almost all of them will go right through you. 1015 00:47:18,072 --> 00:47:20,322 And you guys will actually have to do this calculation 1016 00:47:20,322 --> 00:47:22,010 to find out how many gamma rays would 1017 00:47:22,010 --> 00:47:23,803 you absorb from a gamma ray emission, 1018 00:47:23,803 --> 00:47:25,220 and how many go right through you. 1019 00:47:25,220 --> 00:47:28,760 The hint is most of them get out. 1020 00:47:28,760 --> 00:47:30,590 So there's an exam question we used 1021 00:47:30,590 --> 00:47:33,080 to ask in 22.01 that I was asked during the first exam, 1022 00:47:33,080 --> 00:47:37,340 is you've got four cookies, an alpha emitter, a beta emitter, 1023 00:47:37,340 --> 00:47:41,690 a gamma emitter, and a neutron emitter of constant energy 1024 00:47:41,690 --> 00:47:42,890 and activity. 1025 00:47:42,890 --> 00:47:44,940 You must do one of the following. 1026 00:47:44,940 --> 00:47:48,320 You have to hold one in your hand at arm's length. 1027 00:47:48,320 --> 00:47:50,270 You have to put one in your pocket. 1028 00:47:50,270 --> 00:47:55,400 You have to eat one, and you have to give one to a friend. 1029 00:47:55,400 --> 00:47:58,582 What do you do and why? 1030 00:47:58,582 --> 00:48:00,025 Anyone have an idea? 1031 00:48:03,400 --> 00:48:03,940 Pop quiz. 1032 00:48:03,940 --> 00:48:05,220 Yeah? 1033 00:48:05,220 --> 00:48:08,323 AUDIENCE: Probably give the neutron one to a friend. 1034 00:48:08,323 --> 00:48:09,490 MICHAEL SHORT: That's right. 1035 00:48:09,490 --> 00:48:11,198 I can tell this is the west, because when 1036 00:48:11,198 --> 00:48:14,680 I asked a group of Singaporean students the same question, 1037 00:48:14,680 --> 00:48:17,560 they would eat the neutron to save the friend because 1038 00:48:17,560 --> 00:48:19,150 of Confucian ethics. 1039 00:48:19,150 --> 00:48:21,190 Yeah, it doesn't fly here. 1040 00:48:21,190 --> 00:48:24,717 Your answer is correct because this is America. 1041 00:48:24,717 --> 00:48:26,342 What would you do with the other three? 1042 00:48:26,342 --> 00:48:27,580 AUDIENCE: Eat the gamma. 1043 00:48:27,580 --> 00:48:29,872 MICHAEL SHORT: Eat the gamma because most of the gammas 1044 00:48:29,872 --> 00:48:32,590 will just get to the friend, right? 1045 00:48:32,590 --> 00:48:35,560 What about the alpha and the beta? 1046 00:48:35,560 --> 00:48:41,807 AUDIENCE: [INAUDIBLE] 1047 00:48:41,807 --> 00:48:42,640 MICHAEL SHORT: Yeah. 1048 00:48:42,640 --> 00:48:44,515 Hold the beta at arm's length because there's 1049 00:48:44,515 --> 00:48:47,320 another aspect of shielding betas that we'll get into. 1050 00:48:47,320 --> 00:48:49,240 When betas stop in material, they 1051 00:48:49,240 --> 00:48:52,013 produce some low energy x-rays called bremsstrahlung. 1052 00:48:52,013 --> 00:48:53,680 So you'd want to get those far from you. 1053 00:48:53,680 --> 00:48:55,600 And the alpha in your pocket will just 1054 00:48:55,600 --> 00:48:56,920 be absorbed by the pocket. 1055 00:48:56,920 --> 00:48:58,640 Yeah, so that's the right question. 1056 00:48:58,640 --> 00:49:01,130 So you're not going to see that on the exam. 1057 00:49:01,130 --> 00:49:03,530 But good news is you pretty much got the right answer 1058 00:49:03,530 --> 00:49:06,080 because this is America. 1059 00:49:06,080 --> 00:49:08,600 Probably time for one more question if anyone has one. 1060 00:49:12,110 --> 00:49:13,010 Cool. 1061 00:49:13,010 --> 00:49:15,240 If not, then I want to remind you 1062 00:49:15,240 --> 00:49:18,770 Amelia will see you on Thursday, so do come to class Thursday. 1063 00:49:18,770 --> 00:49:21,950 I'm going to change the syllabus to reflect that. 1064 00:49:21,950 --> 00:49:24,230 And we'll have two hours of class on Friday 1065 00:49:24,230 --> 00:49:27,260 to get through decay and activity and half life, 1066 00:49:27,260 --> 00:49:30,140 followed by an hour of recitation. 1067 00:49:30,140 --> 00:49:32,373 So I will see you guys Friday, and we'll 1068 00:49:32,373 --> 00:49:34,790 see what mood I'm in depending on how the nano calorimetry 1069 00:49:34,790 --> 00:49:37,220 goes. 1070 00:49:37,220 --> 00:49:39,900 Could be a fun measurement.