1 00:00:00,550 --> 00:00:02,920 The following content is provided under a Creative 2 00:00:02,920 --> 00:00:04,310 Commons license. 3 00:00:04,310 --> 00:00:06,520 Your support will help MIT OpenCourseWare 4 00:00:06,520 --> 00:00:10,610 continue to offer high quality educational resources for free. 5 00:00:10,610 --> 00:00:13,180 To make a donation or to view additional materials 6 00:00:13,180 --> 00:00:17,140 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:17,140 --> 00:00:18,013 at ocw.mit.edu. 8 00:00:22,195 --> 00:00:24,130 MICHAEL SHORT: I got an interesting question 9 00:00:24,130 --> 00:00:25,960 in the anonymous comment box, and I 10 00:00:25,960 --> 00:00:28,090 want to see how many other people agree 11 00:00:28,090 --> 00:00:30,130 with it the comment when something like, 12 00:00:30,130 --> 00:00:32,710 is everything in this field of nuclear science engineering 13 00:00:32,710 --> 00:00:34,067 computational in nature? 14 00:00:34,067 --> 00:00:35,650 Because so far, we've pretty much just 15 00:00:35,650 --> 00:00:38,277 thrown theory and simulations at you, 16 00:00:38,277 --> 00:00:39,610 we haven't done any experiments. 17 00:00:39,610 --> 00:00:43,465 So who shares this concern or wonder? 18 00:00:43,465 --> 00:00:45,375 So 1, 2, 3, 4-- 19 00:00:45,375 --> 00:00:46,670 OK, 5, yeah. 20 00:00:46,670 --> 00:00:48,950 So getting towards roughly half of you. 21 00:00:48,950 --> 00:00:52,280 So I can confidently answer, no, this is not 22 00:00:52,280 --> 00:00:54,320 a purely computational field. 23 00:00:54,320 --> 00:00:57,680 We just had to get you just enough science and physics 24 00:00:57,680 --> 00:01:00,050 so that you'd be able to understand some of the lab 25 00:01:00,050 --> 00:01:03,910 activities that we've got in store for you, one of whom, 26 00:01:03,910 --> 00:01:06,130 Mike Ames here from the Nuclear Reactor Lab 27 00:01:06,130 --> 00:01:07,490 is going to be helping you with-- actually, two 28 00:01:07,490 --> 00:01:08,760 of them he'll be helping with. 29 00:01:08,760 --> 00:01:09,320 MICHAEL AMES: Two? 30 00:01:09,320 --> 00:01:09,650 MICHAEL SHORT: Yeah. 31 00:01:09,650 --> 00:01:10,000 Well-- 32 00:01:10,000 --> 00:01:10,610 MICHAEL AMES: --your bananas. 33 00:01:10,610 --> 00:01:12,290 MICHAEL SHORT: The bananas and the thing 34 00:01:12,290 --> 00:01:13,540 that we dreamed up today, so-- 35 00:01:13,540 --> 00:01:14,665 MICHAEL AMES: This morning? 36 00:01:14,665 --> 00:01:15,270 OK. 37 00:01:15,270 --> 00:01:16,580 So you want an intro those-- 38 00:01:16,580 --> 00:01:17,030 MICHAEL SHORT: Sure. 39 00:01:17,030 --> 00:01:18,680 MICHAEL AMES: --and I'll, I don't know-- 40 00:01:18,680 --> 00:01:19,820 MICHAEL SHORT: Fill in what I get wrong. 41 00:01:19,820 --> 00:01:21,362 Also, Mike's going to talk about what 42 00:01:21,362 --> 00:01:23,780 we're going to do together, which is called NAA, 43 00:01:23,780 --> 00:01:25,940 or Nuclear Activation Analysis. 44 00:01:25,940 --> 00:01:28,370 There are many, many ways of measuring 45 00:01:28,370 --> 00:01:30,500 what sort of impurities may exist in materials, 46 00:01:30,500 --> 00:01:32,450 and this is among the most sensitive. 47 00:01:32,450 --> 00:01:34,903 We happen to have a nuclear reactor. 48 00:01:34,903 --> 00:01:36,320 So what we will be doing, what I'm 49 00:01:36,320 --> 00:01:38,892 going to ask each of you guys to do for a special assignment 50 00:01:38,892 --> 00:01:41,350 that not graded, except you'll need it for the problem set, 51 00:01:41,350 --> 00:01:44,180 so it kind of is, is I want each of you 52 00:01:44,180 --> 00:01:47,810 to bring something into me that weighs about 50 milligrams 53 00:01:47,810 --> 00:01:51,110 in one piece, fits in here, is not fissionable-- 54 00:01:51,110 --> 00:01:54,185 so if you have uranium at home, I shouldn't know about it. 55 00:01:54,185 --> 00:01:56,060 And we also ask that you don't bring anything 56 00:01:56,060 --> 00:01:59,750 in that is too salty, because sodium activates like crazy. 57 00:01:59,750 --> 00:02:02,360 And each of you, using your knowledge of radioactive decay 58 00:02:02,360 --> 00:02:05,060 that we learned Tuesday and today, and the Bateman 59 00:02:05,060 --> 00:02:08,120 equations in serious radioactive decay next Tuesday 60 00:02:08,120 --> 00:02:10,610 and Thursday are going to calculate what impurities 61 00:02:10,610 --> 00:02:12,540 exist in your sample. 62 00:02:12,540 --> 00:02:13,730 What is your sample? 63 00:02:13,730 --> 00:02:14,560 It's-- 64 00:02:14,560 --> 00:02:15,085 MICHAEL AMES: You're not going to be 65 00:02:15,085 --> 00:02:16,080 able to do the calculations. 66 00:02:16,080 --> 00:02:17,630 MICHAEL SHORT: We're going to make some estimates of-- 67 00:02:17,630 --> 00:02:18,140 MICHAEL AMES: Oh, OK. 68 00:02:18,140 --> 00:02:20,265 MICHAEL SHORT: The isotopes that you'll let us see. 69 00:02:20,265 --> 00:02:22,340 The shorts, yeah. 70 00:02:22,340 --> 00:02:24,507 I know we're not going to get every impurity, right? 71 00:02:24,507 --> 00:02:26,298 MICHAEL AMES: Well, we're not going to able 72 00:02:26,298 --> 00:02:27,478 to run it next week. 73 00:02:27,478 --> 00:02:30,020 MICHAEL SHORT: Yes, but I will want your materials next week. 74 00:02:30,020 --> 00:02:31,190 OK. 75 00:02:31,190 --> 00:02:32,810 So by Tuesday, I'd like each of you 76 00:02:32,810 --> 00:02:35,240 to come bring something in for what you'd 77 00:02:35,240 --> 00:02:38,750 like to know the elemental composition consisting 78 00:02:38,750 --> 00:02:40,880 of the following elements. 79 00:02:40,880 --> 00:02:42,470 Let's see. 80 00:02:42,470 --> 00:02:46,310 Problem sets, I think I've got it right up here. 81 00:02:46,310 --> 00:02:49,210 Let me just clone the screen. 82 00:02:49,210 --> 00:02:50,710 So you can see what we can look for. 83 00:02:50,710 --> 00:02:52,823 So this is provided to me by Mike. 84 00:02:52,823 --> 00:02:55,240 We're going to do what's called a short nuclear activation 85 00:02:55,240 --> 00:02:59,640 analysis run looking for any of the elements up on this list. 86 00:02:59,640 --> 00:03:03,040 Shorts 1 with extremely short half-lives, and shorts 2 87 00:03:03,040 --> 00:03:05,560 with elements in the half-lives of hours. 88 00:03:05,560 --> 00:03:08,810 And Mike, I had a question for you now that we're live. 89 00:03:08,810 --> 00:03:10,570 Can we count arsenic in that list? 90 00:03:10,570 --> 00:03:13,045 Because it's 24-point-something hours. 91 00:03:13,045 --> 00:03:14,980 MICHAEL AMES: Yeah, we could do arsenic. 92 00:03:14,980 --> 00:03:15,730 MICHAEL SHORT: OK. 93 00:03:15,730 --> 00:03:19,608 MICHAEL AMES: It's not a great shorts element. 94 00:03:19,608 --> 00:03:21,150 You'd probably have to have something 95 00:03:21,150 --> 00:03:22,710 with a bunch of arsenic in it. 96 00:03:22,710 --> 00:03:24,210 MICHAEL SHORT: So if any of you guys 97 00:03:24,210 --> 00:03:26,010 have some food that you bought online 98 00:03:26,010 --> 00:03:28,020 and you don't know what sort of contaminants there are, 99 00:03:28,020 --> 00:03:29,812 or if you've got a piece of your fingernail 100 00:03:29,812 --> 00:03:32,850 and want to see if you are what you eat, or-- 101 00:03:32,850 --> 00:03:34,980 MICHAEL AMES: After telling you why fingernails 102 00:03:34,980 --> 00:03:38,670 would be a great sample, we might 103 00:03:38,670 --> 00:03:42,720 run afoul of the human subjects in research issue 104 00:03:42,720 --> 00:03:43,435 with fingernails. 105 00:03:43,435 --> 00:03:45,185 MICHAEL SHORT: What about dog fingernails? 106 00:03:45,185 --> 00:03:46,295 MICHAEL AMES: --believe it or don't. 107 00:03:46,295 --> 00:03:47,837 Ah, yes, your dogs are probably not-- 108 00:03:47,837 --> 00:03:48,630 MICHAEL SHORT: OK. 109 00:03:48,630 --> 00:03:50,370 So clip your pets' claws if you want 110 00:03:50,370 --> 00:03:52,260 to see if they are what they eat, 111 00:03:52,260 --> 00:03:57,720 or don't tell me what nail the thing came from, or get a-- 112 00:03:57,720 --> 00:04:00,450 slice up a piece of a peanut or whatever your favorite food is. 113 00:04:00,450 --> 00:04:02,980 Or if you want to see if there are any metal dyes used 114 00:04:02,980 --> 00:04:05,285 in your clothing, cut out a little 50 milligram square, 115 00:04:05,285 --> 00:04:07,410 it'll be like a fashion statement and an experiment 116 00:04:07,410 --> 00:04:09,390 at the same time, right? 117 00:04:09,390 --> 00:04:11,110 So we ask that it's about 50 milligrams, 118 00:04:11,110 --> 00:04:14,490 it's gotta fit in here, it's gotta be not that salty and not 119 00:04:14,490 --> 00:04:18,899 fissionable, and we're going to pack a couple of these in one 120 00:04:18,899 --> 00:04:20,940 of these rabbits, these polyethylene rabbits. 121 00:04:20,940 --> 00:04:23,340 We call it those, one, because everything in nuclear 122 00:04:23,340 --> 00:04:26,137 is named after animals and farm implements for some reason. 123 00:04:26,137 --> 00:04:28,470 Did I go over that with you guys the first day of class? 124 00:04:28,470 --> 00:04:31,690 Barns, shakes, pigs, rabbits? 125 00:04:31,690 --> 00:04:32,190 OK. 126 00:04:32,190 --> 00:04:35,720 So a rabbit is a little capsule. 127 00:04:35,720 --> 00:04:37,830 Do you pop open or you screw it open? 128 00:04:37,830 --> 00:04:40,075 Oh yeah, there's like a square nut at the top. 129 00:04:40,075 --> 00:04:42,450 Just a little capsule that goes through a pneumatic tube, 130 00:04:42,450 --> 00:04:44,580 kind of like the old bank machines, 131 00:04:44,580 --> 00:04:47,520 and it'll go firing into the reactor, sit there for a while, 132 00:04:47,520 --> 00:04:49,590 and get pneumatically sucked back out so that we 133 00:04:49,590 --> 00:04:53,680 can calculate the activation and decay of the isotopes within. 134 00:04:53,680 --> 00:04:56,070 And a pig is just a big heavy thing of lead 135 00:04:56,070 --> 00:04:58,240 where you keep pieces of things that you 136 00:04:58,240 --> 00:04:59,880 irradiated for shielding. 137 00:04:59,880 --> 00:05:02,430 So if you notice the sort of methodology theme here, 138 00:05:02,430 --> 00:05:05,700 farms, pigs, rabbits, barns, shakes. 139 00:05:05,700 --> 00:05:08,370 Anyone else you know any other farmy nuclear units? 140 00:05:08,370 --> 00:05:09,012 Yeah? 141 00:05:09,012 --> 00:05:09,953 AUDIENCE: [INAUDIBLE] 142 00:05:09,953 --> 00:05:11,370 MICHAEL SHORT: Or farmy anythings? 143 00:05:11,370 --> 00:05:14,590 AUDIENCE: They follow the [INAUDIBLE] detectors 144 00:05:14,590 --> 00:05:15,857 toads and bullfrogs. 145 00:05:15,857 --> 00:05:17,690 MICHAEL SHORT: So the detectors in [? nif ?] 146 00:05:17,690 --> 00:05:19,070 are called toads and bullfrogs. 147 00:05:19,070 --> 00:05:20,933 Why is that? 148 00:05:20,933 --> 00:05:22,475 AUDIENCE: Because the people who made 149 00:05:22,475 --> 00:05:23,933 the acronym [? like making their ?] 150 00:05:23,933 --> 00:05:26,315 acronyms, and [INAUDIBLE] bullfrog was not [INAUDIBLE].. 151 00:05:26,315 --> 00:05:28,690 MICHAEL SHORT: So actually bullfrog stands for something. 152 00:05:28,690 --> 00:05:29,050 AUDIENCE: Yeah. 153 00:05:29,050 --> 00:05:30,340 MICHAEL SHORT: That's pretty cool. 154 00:05:30,340 --> 00:05:30,840 OK. 155 00:05:30,840 --> 00:05:34,460 AUDIENCE: [INAUDIBLE] acronyms are [INAUDIBLE] 156 00:05:34,460 --> 00:05:35,885 MICHAEL SHORT: Yeah. 157 00:05:35,885 --> 00:05:39,062 AUDIENCE: [INAUDIBLE] acronym for acronym. 158 00:05:39,062 --> 00:05:41,020 MICHAEL SHORT: Oh yes, the acronym for acronym. 159 00:05:41,020 --> 00:05:43,228 As well as what I study, which is CRUD or Chock River 160 00:05:43,228 --> 00:05:44,380 Unidentified Deposits. 161 00:05:44,380 --> 00:05:46,758 It's the gunk that builds up on fuel rods. 162 00:05:46,758 --> 00:05:48,550 Well, I talked to a fellow from Chock River 163 00:05:48,550 --> 00:05:51,140 who took extreme offense to this detriment 164 00:05:51,140 --> 00:05:52,900 to nuclear power plants being attributed 165 00:05:52,900 --> 00:05:54,668 to his fine laboratory. 166 00:05:54,668 --> 00:05:56,710 MICHAEL AMES: Oh, I thought it was chromium-rich. 167 00:05:56,710 --> 00:05:58,377 MICHAEL SHORT: Oh, see, that would work, 168 00:05:58,377 --> 00:06:00,310 but they're not actually chromium-rich. 169 00:06:00,310 --> 00:06:00,950 Yeah. 170 00:06:00,950 --> 00:06:01,450 Cool. 171 00:06:01,450 --> 00:06:02,710 So Mike, do you want to say anything else? 172 00:06:02,710 --> 00:06:03,502 MICHAEL AMES: Yeah. 173 00:06:03,502 --> 00:06:07,240 I think I want to say-- so yeah. 174 00:06:07,240 --> 00:06:07,930 So-- 175 00:06:07,930 --> 00:06:09,080 MICHAEL SHORT: You want to introduce yourself, too? 176 00:06:09,080 --> 00:06:10,247 MICHAEL AMES: Oh yes, sorry. 177 00:06:10,247 --> 00:06:10,980 I'm Mike Ames. 178 00:06:10,980 --> 00:06:14,330 I work over at the Nuclear Reactor Lab mostly 179 00:06:14,330 --> 00:06:19,320 doing nuclear experiments, but I also run the NAA lab there. 180 00:06:19,320 --> 00:06:21,200 And I've been doing it for a while. 181 00:06:21,200 --> 00:06:25,620 So the idea-- the reason we've got these guys, 182 00:06:25,620 --> 00:06:29,060 it'll irradiate the samples in this. 183 00:06:29,060 --> 00:06:32,270 The easiest thing for me to do without losing 184 00:06:32,270 --> 00:06:34,460 any of your samples is [INAUDIBLE] [? there, ?] 185 00:06:34,460 --> 00:06:37,730 something gets radiated in this, I slip the top off, 186 00:06:37,730 --> 00:06:40,620 and you probably can't see that, but it's for a little poly bag. 187 00:06:40,620 --> 00:06:43,790 I'll dump your sample into the poly bag. 188 00:06:43,790 --> 00:06:47,320 So it's something that's like one piece that works the best. 189 00:06:47,320 --> 00:06:49,070 What I usually tell people, it's something 190 00:06:49,070 --> 00:06:51,920 that you could pick up reasonably 191 00:06:51,920 --> 00:06:53,913 easily with a pair of tweezers. 192 00:06:53,913 --> 00:06:55,580 That way if they drop it, I can actually 193 00:06:55,580 --> 00:06:56,990 pick it up with tweeers. 194 00:06:56,990 --> 00:06:59,970 But that kind of gives you a good size. 195 00:06:59,970 --> 00:07:02,510 No-- nothing to powdery, because the powder 196 00:07:02,510 --> 00:07:07,090 is going to spread around and then get contaminations. 197 00:07:07,090 --> 00:07:10,358 Yeah, and that list there, I guess you said you posted it. 198 00:07:10,358 --> 00:07:11,150 MICHAEL SHORT: Yep. 199 00:07:11,150 --> 00:07:13,280 The list has posted on the Stellar site. 200 00:07:13,280 --> 00:07:14,322 MICHAEL AMES: Yeah, yeah. 201 00:07:14,322 --> 00:07:16,940 So yeah, we'll see mostly these light elements, 202 00:07:16,940 --> 00:07:20,000 the guys with the astericies. 203 00:07:20,000 --> 00:07:22,270 I don't see that well. 204 00:07:22,270 --> 00:07:24,410 Yeah, gallium I'm probably not going to see that. 205 00:07:24,410 --> 00:07:24,910 So-- 206 00:07:24,910 --> 00:07:26,140 MICHAEL SHORT: Interesting, we found gallium 207 00:07:26,140 --> 00:07:27,550 in your dog claws or something. 208 00:07:27,550 --> 00:07:30,370 MICHAEL AMES: Yeah, magnesium, aluminum, titanium, vanadium, 209 00:07:30,370 --> 00:07:31,752 those are easy. 210 00:07:31,752 --> 00:07:33,460 Sodium, chloride, and potassium are easy. 211 00:07:33,460 --> 00:07:36,580 The manganese will come out nicely. 212 00:07:36,580 --> 00:07:39,370 Some of the elements of-- 213 00:07:39,370 --> 00:07:41,840 generally more interest down-- further down-- 214 00:07:41,840 --> 00:07:43,600 MICHAEL SHORT: Even further-- 215 00:07:43,600 --> 00:07:46,390 MICHAEL AMES: --chromium, those have longer half-lives, 216 00:07:46,390 --> 00:07:47,880 so I'm going to see those. 217 00:07:47,880 --> 00:07:48,990 MICHAEL SHORT: Yeah. 218 00:07:48,990 --> 00:07:52,340 MICHAEL AMES: Probably do like a five or 10-minute irradiation, 219 00:07:52,340 --> 00:07:54,910 let it decay for a little while, and then we'll 220 00:07:54,910 --> 00:07:56,540 do a couple of counts. 221 00:07:56,540 --> 00:07:58,318 Have you ever get over to the reactor? 222 00:07:58,318 --> 00:08:00,110 MICHAEL SHORT: We will be there a fair bit. 223 00:08:00,110 --> 00:08:01,040 MICHAEL AMES: OK, you guys are going to be there next week. 224 00:08:01,040 --> 00:08:01,873 MICHAEL SHORT: Yeah. 225 00:08:01,873 --> 00:08:04,573 So what do you usually use NAA for? 226 00:08:04,573 --> 00:08:05,990 MICHAEL AMES: NAA, well, the thing 227 00:08:05,990 --> 00:08:09,560 we've been using it for lately a lot is anything that's 228 00:08:09,560 --> 00:08:11,660 going to go in the core of the reactor, 229 00:08:11,660 --> 00:08:16,880 we want to analyze to see if there's any surprise elements-- 230 00:08:16,880 --> 00:08:19,732 to see how much cobalt is in a piece of steel 231 00:08:19,732 --> 00:08:21,440 that we're going to put in because people 232 00:08:21,440 --> 00:08:22,820 don't usually measure the cobalt, 233 00:08:22,820 --> 00:08:25,400 but it activates really well. 234 00:08:25,400 --> 00:08:26,870 And so that causes problems later 235 00:08:26,870 --> 00:08:28,640 on when we have to take some compartments 236 00:08:28,640 --> 00:08:31,910 for cobalt-60 or half the M that shows up 237 00:08:31,910 --> 00:08:34,047 and things that you don't expect it. 238 00:08:34,047 --> 00:08:35,450 MICHAEL SHORT: Mm-hmm. 239 00:08:35,450 --> 00:08:38,360 MICHAEL AMES: My past in doing NAA was all 240 00:08:38,360 --> 00:08:40,039 environmental samples. 241 00:08:40,039 --> 00:08:42,559 So we did a lot of trace element, 242 00:08:42,559 --> 00:08:46,930 heavy metal chemistry on atmospheric particulates, 243 00:08:46,930 --> 00:08:55,340 rain water, ice cores, lake sediments, crude oil, coal, 244 00:08:55,340 --> 00:08:56,670 fly ash. 245 00:08:56,670 --> 00:08:58,940 And so we would measure that whole stack 246 00:08:58,940 --> 00:09:01,617 of elements and those guys for environmental studies. 247 00:09:01,617 --> 00:09:02,450 MICHAEL SHORT: Cool. 248 00:09:02,450 --> 00:09:04,550 MICHAEL AMES: That was my time doing NAA. 249 00:09:04,550 --> 00:09:06,050 I don't know, I think that's enough. 250 00:09:06,050 --> 00:09:08,400 You want me back here next Tuesday or Thursday-- 251 00:09:08,400 --> 00:09:09,540 MICHAEL SHORT: Yeah, to explain a little bit more 252 00:09:09,540 --> 00:09:10,820 of the specifics of the process. 253 00:09:10,820 --> 00:09:12,737 MICHAEL AMES: --give you the five, 10 minutes. 254 00:09:12,737 --> 00:09:14,420 And if you guys could-- 255 00:09:14,420 --> 00:09:16,770 I mean, are you guys can be able to come to the lab 256 00:09:16,770 --> 00:09:17,788 when we do the shorts? 257 00:09:17,788 --> 00:09:19,580 MICHAEL SHORT: Depends on when you do them. 258 00:09:19,580 --> 00:09:21,640 If it's early November, then yes. 259 00:09:21,640 --> 00:09:22,850 MICHAEL AMES: Yeah, OK. 260 00:09:22,850 --> 00:09:26,483 So when I do shorts, I put two samples in one of these guys, 261 00:09:26,483 --> 00:09:28,150 they'll shlink into the reactor and out. 262 00:09:28,150 --> 00:09:29,220 MICHAEL SHORT: Which you guys should see. 263 00:09:29,220 --> 00:09:30,270 It's pretty cool. 264 00:09:30,270 --> 00:09:33,080 MICHAEL AMES: Yeah, you can watch that part. 265 00:09:33,080 --> 00:09:34,550 And then I run it down the hallway 266 00:09:34,550 --> 00:09:37,250 and throw each sample on a detector. 267 00:09:37,250 --> 00:09:40,580 And while those samples are counting, I run another rabbit. 268 00:09:40,580 --> 00:09:43,490 So it's kind of an all-day thing running up and down the hall 269 00:09:43,490 --> 00:09:45,470 every half hour. 270 00:09:45,470 --> 00:09:47,570 So you could almost come anytime during the day 271 00:09:47,570 --> 00:09:51,799 while I'm running these and get one full round in half an hour. 272 00:09:51,799 --> 00:09:52,632 MICHAEL SHORT: Cool. 273 00:09:52,632 --> 00:09:54,090 MICHAEL AMES: I think that's the whole story. 274 00:09:54,090 --> 00:09:55,050 You can hang on to that if you want. 275 00:09:55,050 --> 00:09:55,430 MICHAEL SHORT: Yeah. 276 00:09:55,430 --> 00:09:55,940 Thanks, Mike. 277 00:09:55,940 --> 00:09:56,960 So you heard the charge. 278 00:09:56,960 --> 00:10:00,710 Bring me your dog claws, your eyebrows, your skin flakes, 279 00:10:00,710 --> 00:10:01,610 your scabs, your-- 280 00:10:01,610 --> 00:10:01,990 MICHAEL AMES: Oh yeah, can we-- 281 00:10:01,990 --> 00:10:02,710 MICHAEL SHORT: --food pieces-- 282 00:10:02,710 --> 00:10:03,860 MICHAEL AMES: --from hair? 283 00:10:03,860 --> 00:10:05,420 MICHAEL SHORT: Oh Yeah, so no hair. 284 00:10:05,420 --> 00:10:07,730 MICHAEL AMES: We used to do a bunch of hair analysis. 285 00:10:07,730 --> 00:10:10,810 Hair is a pain in the neck because it-- 286 00:10:10,810 --> 00:10:11,810 MICHAEL SHORT: Staticky? 287 00:10:11,810 --> 00:10:13,310 MICHAEL AMES: --clings to everything 288 00:10:13,310 --> 00:10:15,890 and it gets stuck to parts. 289 00:10:15,890 --> 00:10:18,520 Yeah, we did some hair analysis for the superfund site 290 00:10:18,520 --> 00:10:21,750 in Woburn, and it was a big success, 291 00:10:21,750 --> 00:10:23,730 but it was not pleasant to do the work. 292 00:10:23,730 --> 00:10:24,680 MICHAEL SHORT: So don't bring us your hair, 293 00:10:24,680 --> 00:10:27,230 but bring us your skin flakes, your scabs, your dog claws, 294 00:10:27,230 --> 00:10:28,310 your food scraps, your-- 295 00:10:28,310 --> 00:10:29,270 MICHAEL AMES: No skin flakes. 296 00:10:29,270 --> 00:10:30,590 MICHAEL SHORT: Just don't tell him. 297 00:10:30,590 --> 00:10:32,007 MICHAEL AMES: Stuff that you can-- 298 00:10:32,007 --> 00:10:34,365 like I said, something that's like one good piece 299 00:10:34,365 --> 00:10:35,600 that you can pick it up-- 300 00:10:35,600 --> 00:10:36,185 MICHAEL SHORT: Yeah, get creative. 301 00:10:36,185 --> 00:10:37,227 MICHAEL AMES: --be great. 302 00:10:37,227 --> 00:10:39,920 MICHAEL SHORT: It doesn't have to be something that I said. 303 00:10:39,920 --> 00:10:41,628 As long as it's not fissionable or salty. 304 00:10:41,628 --> 00:10:43,430 MICHAEL AMES: And we might veto samples-- 305 00:10:43,430 --> 00:10:47,240 I do need to know what they are roughly before we throw it 306 00:10:47,240 --> 00:10:50,427 in the reactor, and we might end up vetoing some samples. 307 00:10:50,427 --> 00:10:51,260 MICHAEL SHORT: Yeah. 308 00:10:51,260 --> 00:10:52,760 So let's figure it out by Tuesday. 309 00:10:52,760 --> 00:10:55,135 That way if we have to veto, we have a while for you guys 310 00:10:55,135 --> 00:10:56,290 to find another sample. 311 00:10:56,290 --> 00:10:57,290 MICHAEL AMES: Or-- yeah. 312 00:10:57,290 --> 00:11:00,708 I don't know if I'll be able to run a sample from everybody. 313 00:11:00,708 --> 00:11:01,750 MICHAEL SHORT: We'll see. 314 00:11:01,750 --> 00:11:02,470 MICHAEL AMES: We'll see. 315 00:11:02,470 --> 00:11:03,130 MICHAEL SHORT: We'll see what we can do. 316 00:11:03,130 --> 00:11:04,040 MICHAEL AMES: Anyway, I'll see you all next week. 317 00:11:04,040 --> 00:11:05,687 MICHAEL SHORT: Thanks, Mike. 318 00:11:05,687 --> 00:11:07,270 So yeah, so Mike's going to be helping 319 00:11:07,270 --> 00:11:10,150 us do some nuclear activation analysis, and in addition, 320 00:11:10,150 --> 00:11:11,650 next week we're going to be counting 321 00:11:11,650 --> 00:11:14,230 our big bag of burnt bananas, because now that you're 322 00:11:14,230 --> 00:11:16,480 learning about radioactivity, and this-- when 323 00:11:16,480 --> 00:11:18,340 we go over activity and series decay, 324 00:11:18,340 --> 00:11:19,900 you'll have enough of the science 325 00:11:19,900 --> 00:11:21,670 to understand to calculate how to what 326 00:11:21,670 --> 00:11:23,350 is the radioactivity of one banana. 327 00:11:23,350 --> 00:11:25,630 And to do so, we need like 500 bananas 328 00:11:25,630 --> 00:11:27,670 to get enough statistics. 329 00:11:27,670 --> 00:11:29,420 So we'll be going to the reactor for that. 330 00:11:29,420 --> 00:11:31,360 We've also set it up so that next week and the week 331 00:11:31,360 --> 00:11:33,490 afterwards you guys are going to be manipulating the power 332 00:11:33,490 --> 00:11:34,550 levels of the reactor. 333 00:11:34,550 --> 00:11:36,730 So you'll actually get to sit in the control seat, 334 00:11:36,730 --> 00:11:38,590 raise and lower the control rods, 335 00:11:38,590 --> 00:11:40,390 and watch the power of the reactor change 336 00:11:40,390 --> 00:11:42,490 in ways you probably won't expect unless you're 337 00:11:42,490 --> 00:11:44,240 getting operator training. 338 00:11:44,240 --> 00:11:46,750 And all of that stuff is going to be used in the lab 339 00:11:46,750 --> 00:11:48,640 components of the problem sets. 340 00:11:48,640 --> 00:11:50,140 So you guys might have noticed there 341 00:11:50,140 --> 00:11:52,960 was some spinthariscope scope thing on problem set 3. 342 00:11:52,960 --> 00:11:54,430 Radiation protection did not want 343 00:11:54,430 --> 00:11:57,370 me taking smoke detectors apart and giving them all to you 344 00:11:57,370 --> 00:12:00,070 because that's distributing open radiation sources 345 00:12:00,070 --> 00:12:02,025 and I probably shouldn't do that, 346 00:12:02,025 --> 00:12:03,400 but we've got plenty of lab stuff 347 00:12:03,400 --> 00:12:05,770 for you to do to see what is actually 348 00:12:05,770 --> 00:12:07,570 hands-on in this field. 349 00:12:07,570 --> 00:12:09,760 And if you do want to know what else is hands-on, 350 00:12:09,760 --> 00:12:11,677 I have an experimental group and you're always 351 00:12:11,677 --> 00:12:13,870 welcome to come see what we do at the lab. 352 00:12:13,870 --> 00:12:16,690 There usually isn't an explosion happening, 353 00:12:16,690 --> 00:12:19,660 but there's usually something that 1,000 to 1500 354 00:12:19,660 --> 00:12:22,750 Celsius temperature, blue uranium fluoride 355 00:12:22,750 --> 00:12:27,550 salts, nanonewton forces, extreme pressures, or what 356 00:12:27,550 --> 00:12:30,700 have you, we do a lot of it. 357 00:12:30,700 --> 00:12:33,520 So I wanted to give a quick review of where we were 358 00:12:33,520 --> 00:12:36,460 in radioactive decay last time. 359 00:12:36,460 --> 00:12:39,100 I think we left off somewhere around "Particle Physics 360 00:12:39,100 --> 00:12:43,620 Telescope Explodes" was my favorite BBC headline ever 361 00:12:43,620 --> 00:12:45,370 when we were talking about-- we've already 362 00:12:45,370 --> 00:12:50,260 gone over alpha decay, we've gone over beta decay, 363 00:12:50,260 --> 00:12:52,960 we started talking about positron decay 364 00:12:52,960 --> 00:12:57,100 and the neutrinos that come out of that, 365 00:12:57,100 --> 00:12:58,840 and this Kamiokande detector that 366 00:12:58,840 --> 00:13:01,480 is set up with lots of expensive phototubes 367 00:13:01,480 --> 00:13:03,130 to detect the cones of light left 368 00:13:03,130 --> 00:13:07,240 as neutrinos pass faster than the speed of light in water 369 00:13:07,240 --> 00:13:09,320 through water. 370 00:13:09,320 --> 00:13:12,340 And then there is my favorite headline. 371 00:13:12,340 --> 00:13:17,030 I believe we made it up to the end of positron annihilation 372 00:13:17,030 --> 00:13:19,430 spectroscopy or ways that you can actually 373 00:13:19,430 --> 00:13:22,160 use positron emission to look at the number 374 00:13:22,160 --> 00:13:26,230 and types of atomic defects in crystalline materials. 375 00:13:26,230 --> 00:13:29,770 And yep, that's where we left off, interested in PAS? 376 00:13:29,770 --> 00:13:31,730 Lots of papers to check out. 377 00:13:31,730 --> 00:13:33,760 In the meantime, let's look at one 378 00:13:33,760 --> 00:13:37,090 of the competing mechanisms for positron emission, which 379 00:13:37,090 --> 00:13:39,880 is electron capture. 380 00:13:39,880 --> 00:13:41,980 In this case-- so I will warn you, 381 00:13:41,980 --> 00:13:43,840 it's sometimes a little easy to get mixed up 382 00:13:43,840 --> 00:13:46,570 between electron capture, internal conversion, 383 00:13:46,570 --> 00:13:49,480 isometric transition, so I've left these slides on here, 384 00:13:49,480 --> 00:13:52,030 and I also took pictures of the board from last time 385 00:13:52,030 --> 00:13:53,577 and posted them on the Stellar site. 386 00:13:53,577 --> 00:13:55,660 So all the blackboards where we filled the boards, 387 00:13:55,660 --> 00:13:57,020 there's pictures of those. 388 00:13:57,020 --> 00:13:58,100 And I'm going to keep doing that. 389 00:13:58,100 --> 00:14:00,767 So if you've learned better just by looking and listening rather 390 00:14:00,767 --> 00:14:02,680 than writing everything, feel free. 391 00:14:02,680 --> 00:14:05,660 If you want to write stuff down, also feel free. 392 00:14:05,660 --> 00:14:08,480 So an electron capture, another way of, 393 00:14:08,480 --> 00:14:12,140 well, destroying positive charge would be for the nucleus 394 00:14:12,140 --> 00:14:13,520 to capture an electron. 395 00:14:13,520 --> 00:14:15,620 So either it can emit a positron, 396 00:14:15,620 --> 00:14:17,600 giving away some positive charge, 397 00:14:17,600 --> 00:14:20,243 or it can capture an electron, destroying 398 00:14:20,243 --> 00:14:21,410 one of the positive charges. 399 00:14:21,410 --> 00:14:25,160 And in each case here, we've got a proton that becomes a neutron 400 00:14:25,160 --> 00:14:26,090 and something. 401 00:14:26,090 --> 00:14:29,210 I'm won't be specific as to which one because positron 402 00:14:29,210 --> 00:14:32,600 and electron capture, well, two different but similar kind 403 00:14:32,600 --> 00:14:34,100 of decaying mechanisms. 404 00:14:34,100 --> 00:14:36,740 And then what you get is this hole 405 00:14:36,740 --> 00:14:38,910 where the electron used to be. 406 00:14:38,910 --> 00:14:40,670 And that's not a very stable configuration 407 00:14:40,670 --> 00:14:44,390 for an atom to have, let's say, one fewer electron then protons 408 00:14:44,390 --> 00:14:46,730 and especially to have a hole in the inner shell. 409 00:14:46,730 --> 00:14:49,490 So you get this cascade from straight-up from high school 410 00:14:49,490 --> 00:14:53,330 chemistry of electrons falling from one shell to the next 411 00:14:53,330 --> 00:14:55,730 and giving off characteristic X-rays-- 412 00:14:55,730 --> 00:14:57,650 that's me that cross that out there-- 413 00:14:57,650 --> 00:14:59,240 because you will find misinformation 414 00:14:59,240 --> 00:15:01,430 all over the place online, and someone 415 00:15:01,430 --> 00:15:03,980 might make a great figure and mislabel 416 00:15:03,980 --> 00:15:07,040 an electron-emitted photon as a gamma ray, and remember, 417 00:15:07,040 --> 00:15:09,320 we said gammas come from the nucleus, 418 00:15:09,320 --> 00:15:12,098 otherwise they're indistinguishable photons. 419 00:15:12,098 --> 00:15:13,640 And so in electron capture, you don't 420 00:15:13,640 --> 00:15:16,347 need much of an energy difference 421 00:15:16,347 --> 00:15:17,930 between the parents and the daughters, 422 00:15:17,930 --> 00:15:23,090 unlike positron decay where for positron decay to happen, 423 00:15:23,090 --> 00:15:25,550 you have to have Q at least equal 424 00:15:25,550 --> 00:15:31,660 to 1.022 MeV, which is the same as 2 times the rest 425 00:15:31,660 --> 00:15:34,220 mass of the electron. 426 00:15:34,220 --> 00:15:36,850 For electron capture, you don't. 427 00:15:36,850 --> 00:15:39,220 This can happen at just about any energy. 428 00:15:39,220 --> 00:15:41,350 As long as you can overcome just the binding energy 429 00:15:41,350 --> 00:15:43,450 of the electron, which is negligible 430 00:15:43,450 --> 00:15:46,090 compared to these sort of nuclear energy levels. 431 00:15:46,090 --> 00:15:48,110 And so this is the Q equation. 432 00:15:48,110 --> 00:15:51,820 Keep in mind, these deltas here are excess masses. 433 00:15:51,820 --> 00:15:54,310 So I'll put this up again, the excess mass 434 00:15:54,310 --> 00:15:58,270 is the real mass minus the terrible approximation 435 00:15:58,270 --> 00:16:00,220 of a nucleide's mass. 436 00:16:00,220 --> 00:16:03,610 And this way, excess mass and real mass are directly related, 437 00:16:03,610 --> 00:16:06,340 so you could plug in masses here, 438 00:16:06,340 --> 00:16:07,900 you could plug in binding energies 439 00:16:07,900 --> 00:16:12,040 by making everything with a minus sign, and so on. 440 00:16:12,040 --> 00:16:14,950 I think I've repeated myself enough for the Q equation 441 00:16:14,950 --> 00:16:16,860 stuff, would you guys agree? 442 00:16:16,860 --> 00:16:19,590 Yeah, OK. 443 00:16:19,590 --> 00:16:21,980 And so these are actually two competing mechanisms. 444 00:16:21,980 --> 00:16:24,710 So shown here is the decay of sodium-22 445 00:16:24,710 --> 00:16:28,340 which we don't want to happen in our nuclear activation analysis 446 00:16:28,340 --> 00:16:30,320 because it gets pretty toasty. 447 00:16:30,320 --> 00:16:32,300 It can either proceed-- 448 00:16:32,300 --> 00:16:34,430 there's a kind of hidden part of the diagram 449 00:16:34,430 --> 00:16:36,710 that I drew in to make a little more sense. 450 00:16:36,710 --> 00:16:41,150 You start off with the nucleus at 2.8 MeV above the neon 451 00:16:41,150 --> 00:16:42,980 nucleus' energy level. 452 00:16:42,980 --> 00:16:48,020 You need 1.022 MeV to create the positron-electron pair, 453 00:16:48,020 --> 00:16:51,340 at which point you can emit the positron with a certain energy. 454 00:16:51,340 --> 00:16:53,630 You're left in an excited state, and the next thing 455 00:16:53,630 --> 00:16:58,130 we'll go over is gamma decay or Isometric Transitions or IT. 456 00:16:58,130 --> 00:17:00,380 That's the next method of decay we'll talk about. 457 00:17:00,380 --> 00:17:03,560 Or the nucleus can just capture an electron, 458 00:17:03,560 --> 00:17:05,900 getting to that same energy level 459 00:17:05,900 --> 00:17:08,579 and emitting the same gamma ray. 460 00:17:08,579 --> 00:17:12,210 So these are two competing mechanisms of decay. 461 00:17:12,210 --> 00:17:13,839 And then you might ask, well, when 462 00:17:13,839 --> 00:17:16,750 is one going to happen and not the other? 463 00:17:16,750 --> 00:17:18,520 Well chances are, the lower energy 464 00:17:18,520 --> 00:17:22,240 that transition is, the more likely electron 465 00:17:22,240 --> 00:17:23,510 capture is going to happen. 466 00:17:23,510 --> 00:17:25,990 So when you look at these energy diagrams, 467 00:17:25,990 --> 00:17:28,690 you can see that as the transitions get bigger, 468 00:17:28,690 --> 00:17:33,300 the probability of positron decay goes up and up and up. 469 00:17:33,300 --> 00:17:37,250 So you need 1.022 MeV to make the positron an electron, 470 00:17:37,250 --> 00:17:42,030 but the probability of positron decay very close to this 471 00:17:42,030 --> 00:17:43,310 is fairly low. 472 00:17:43,310 --> 00:17:46,620 Possible, but unlikely. 473 00:17:46,620 --> 00:17:49,620 Is everyone clear on these two competing mechanisms? 474 00:17:49,620 --> 00:17:51,720 So one way of reducing the number of protons 475 00:17:51,720 --> 00:17:55,578 is emit a positron, another is gobble up an electron. 476 00:17:55,578 --> 00:17:57,620 In the end, they make the same daughter products, 477 00:17:57,620 --> 00:17:59,690 but they go by different mechanisms. 478 00:17:59,690 --> 00:18:02,490 And they give off different bits of radiation 479 00:18:02,490 --> 00:18:06,075 which we can actually sense and measure. 480 00:18:06,075 --> 00:18:07,970 Cool. 481 00:18:07,970 --> 00:18:10,690 So on to gamma decay or isometric transition. 482 00:18:10,690 --> 00:18:12,850 These range from the dead simple, 483 00:18:12,850 --> 00:18:16,120 like technetium-99 metastable giving off 484 00:18:16,120 --> 00:18:19,630 a characteristic 140 keV gamma ray for technetium, 485 00:18:19,630 --> 00:18:21,130 that's the medical imaging procedure 486 00:18:21,130 --> 00:18:22,345 we've talked a lot about. 487 00:18:22,345 --> 00:18:26,710 To the ridiculously complex, like americium-241, 488 00:18:26,710 --> 00:18:29,980 which has a lot, a lot, a lot of different nuclear energy 489 00:18:29,980 --> 00:18:34,030 states, all of which release anywhere between 1 490 00:18:34,030 --> 00:18:36,500 and a lot of gamma rays. 491 00:18:36,500 --> 00:18:38,920 And this is what's referred to as isometric transition. 492 00:18:38,920 --> 00:18:42,700 So we'll say gamma or isometric transition 493 00:18:42,700 --> 00:18:46,810 is like the same thing, they're just different words for it. 494 00:18:46,810 --> 00:18:47,950 These are called isomers. 495 00:18:47,950 --> 00:18:50,300 They've got the same number of protons and neutrons, 496 00:18:50,300 --> 00:18:53,770 so it's the same nuclide, but at an excited state. 497 00:18:53,770 --> 00:18:55,660 And we call it gamma decay because we 498 00:18:55,660 --> 00:18:59,170 emit gamma rays or photons. 499 00:18:59,170 --> 00:19:01,810 I think this one is the easiest one to understand, 500 00:19:01,810 --> 00:19:04,990 because the reaction goes something like-- 501 00:19:04,990 --> 00:19:06,490 let's say we have a parent nucleus 502 00:19:06,490 --> 00:19:09,310 with Z protons and A neutrons. 503 00:19:12,380 --> 00:19:13,950 Nothing happens. 504 00:19:13,950 --> 00:19:16,640 It's about the easiest nuclear reaction there is. 505 00:19:16,640 --> 00:19:19,820 Except you do give off a gamma ray. 506 00:19:19,820 --> 00:19:22,280 And we'll usually put a star or something 507 00:19:22,280 --> 00:19:24,680 to denote an excited state. 508 00:19:28,170 --> 00:19:31,640 So when you see a star in the reading over there 509 00:19:31,640 --> 00:19:33,920 on a nuclide where the charge would be, 510 00:19:33,920 --> 00:19:35,990 that's an excited energy state that will likely 511 00:19:35,990 --> 00:19:41,220 decay by IT or gamma decay. 512 00:19:41,220 --> 00:19:44,490 There is also a competing mechanism 513 00:19:44,490 --> 00:19:47,640 for isometric transition or gamma decay, 514 00:19:47,640 --> 00:19:50,700 and that's what's called internal conversion. 515 00:19:50,700 --> 00:19:52,293 In this case you can kind of think 516 00:19:52,293 --> 00:19:54,460 of it-- this isn't the correct physical explanation, 517 00:19:54,460 --> 00:19:57,150 but it's a perfectly good mental model, 518 00:19:57,150 --> 00:19:58,980 that the gamma ray would either just 519 00:19:58,980 --> 00:20:02,130 be emitted from the nucleus, at which point you would see it, 520 00:20:02,130 --> 00:20:04,680 and the energy of the gamma is the same as that Q, 521 00:20:04,680 --> 00:20:08,010 or it kind of hits an electron on its way out, 522 00:20:08,010 --> 00:20:09,990 ejecting that electron. 523 00:20:09,990 --> 00:20:12,180 So instead of finding a gamma ray, 524 00:20:12,180 --> 00:20:15,900 you may just get an electron emitted at an energy very, very 525 00:20:15,900 --> 00:20:17,880 close to that gamma ray. 526 00:20:17,880 --> 00:20:20,850 The difference between the gamma ray energy and the electron 527 00:20:20,850 --> 00:20:22,970 energy is its binding energy. 528 00:20:22,970 --> 00:20:25,530 Because if a gamma hits an electron on the way out, 529 00:20:25,530 --> 00:20:29,010 it has to overcome the binding energy of that electron, 530 00:20:29,010 --> 00:20:30,600 at which point the rest of the energy 531 00:20:30,600 --> 00:20:33,460 is just its kinetic energy. 532 00:20:33,460 --> 00:20:36,970 So again, I don't think that's the precise physical mechanism, 533 00:20:36,970 --> 00:20:39,880 but it's a perfectly good mental model to remember what this is. 534 00:20:39,880 --> 00:20:42,370 A gamma can either just get out on its own 535 00:20:42,370 --> 00:20:45,650 or it can hit an electron on its way out. 536 00:20:45,650 --> 00:20:47,690 If you hit the electron on your way out, 537 00:20:47,690 --> 00:20:50,030 just like in electron capture, then 538 00:20:50,030 --> 00:20:56,020 you get a larger shell electron falling down to the inner shell 539 00:20:56,020 --> 00:20:57,530 emitting an X-ray just like before. 540 00:21:00,033 --> 00:21:01,450 And then there's one other process 541 00:21:01,450 --> 00:21:02,860 I want you guys to be aware of. 542 00:21:02,860 --> 00:21:07,380 Has anyone here ever heard of Auger electron emission? 543 00:21:07,380 --> 00:21:09,680 Er, yeah. 544 00:21:09,680 --> 00:21:13,710 So in this case, instead of sending out an X-ray, 545 00:21:13,710 --> 00:21:16,400 you can think of it like the X-ray kind of hits 546 00:21:16,400 --> 00:21:19,010 the-- another electron on its way out. 547 00:21:19,010 --> 00:21:20,810 That's not the actual process that happens, 548 00:21:20,810 --> 00:21:22,640 but let's just think of it like that. 549 00:21:22,640 --> 00:21:24,800 And then that electron is ejected usually 550 00:21:24,800 --> 00:21:27,580 from a much outer shell. 551 00:21:27,580 --> 00:21:29,770 And we can actually use these Auger electrons 552 00:21:29,770 --> 00:21:32,770 because they have specific but very low binding 553 00:21:32,770 --> 00:21:35,140 energies to do imaging and elemental 554 00:21:35,140 --> 00:21:36,410 analysis of materials. 555 00:21:36,410 --> 00:21:38,243 So this is another one of those things where 556 00:21:38,243 --> 00:21:41,290 the stuff you're learning today is used in an Auger electron 557 00:21:41,290 --> 00:21:44,650 microscope up and Building 13 to do combined imaging 558 00:21:44,650 --> 00:21:47,970 and elemental analysis of materials. 559 00:21:47,970 --> 00:21:51,570 I want to skip back a sec, because let's say 560 00:21:51,570 --> 00:21:54,540 we have this decay diagram right here, a pretty simple one. 561 00:21:54,540 --> 00:21:57,480 Cesium-137, that isotope that everyone 562 00:21:57,480 --> 00:22:01,050 was worried about from the release from Fukushima. 563 00:22:01,050 --> 00:22:05,010 Can either proceed by just beta decay, 564 00:22:05,010 --> 00:22:08,460 or beta decay followed by an isometric transition. 565 00:22:08,460 --> 00:22:11,310 And shown here is a spectrum of all the different electron 566 00:22:11,310 --> 00:22:14,200 energies that you'll get out. 567 00:22:14,200 --> 00:22:18,960 If you remember from last time when we talked about, 568 00:22:18,960 --> 00:22:23,270 let's see, the energy of a beta particle emitted versus let's 569 00:22:23,270 --> 00:22:26,150 say the number of those particles emitted, 570 00:22:26,150 --> 00:22:30,080 if this is the Q value for that reaction, 571 00:22:30,080 --> 00:22:33,110 you don't always get a beta particle out 572 00:22:33,110 --> 00:22:35,870 at the Q value-- in fact, you never do. 573 00:22:35,870 --> 00:22:40,270 It looks something like this, where 574 00:22:40,270 --> 00:22:44,290 they'll be some, let's say, average 575 00:22:44,290 --> 00:22:49,510 or some most likely beta energy, which is about one-third Q. 576 00:22:49,510 --> 00:22:53,000 Depends on the reaction, but that's a good rule of thumb. 577 00:22:53,000 --> 00:22:57,910 So if you've got a 1.174 MeV beta particle, 578 00:22:57,910 --> 00:23:00,970 you're going to see a spectrum of electron energies ranging 579 00:23:00,970 --> 00:23:04,450 from 0 to 1.174. 580 00:23:04,450 --> 00:23:06,700 And you've got this other beta transition 581 00:23:06,700 --> 00:23:08,950 possible at about half an MeV, so you're 582 00:23:08,950 --> 00:23:11,927 going to see that same spectrum right there. 583 00:23:11,927 --> 00:23:14,260 And then there's these two, what's called the conversion 584 00:23:14,260 --> 00:23:15,460 electrons. 585 00:23:15,460 --> 00:23:19,117 That's evidence of the competing process with gamma decay. 586 00:23:19,117 --> 00:23:21,700 Which is to say that this gamma decay can either just get out, 587 00:23:21,700 --> 00:23:24,460 at which point you see a gamma ray of that energy, 588 00:23:24,460 --> 00:23:27,310 or that gamma hits an electron on its way 589 00:23:27,310 --> 00:23:30,402 out, knocking those electrons out. 590 00:23:30,402 --> 00:23:33,180 Does anyone know here what it means by K-shell or L-shell? 591 00:23:36,462 --> 00:23:37,670 If you do, just shout it out. 592 00:23:41,340 --> 00:23:43,120 So that there depends on the-- 593 00:23:43,120 --> 00:23:44,220 oh, that's correct. 594 00:23:44,220 --> 00:23:45,390 It's the energy level. 595 00:23:45,390 --> 00:23:49,450 So let's say we'll draw kind of a bore model of a nucleus, 596 00:23:49,450 --> 00:23:55,710 we'll call it N. And let's give it three electron energy 597 00:23:55,710 --> 00:23:56,750 levels. 598 00:23:56,750 --> 00:24:00,750 And let's say there's a couple electrons in the first shell 599 00:24:00,750 --> 00:24:03,690 and some electrons in the outer shells. 600 00:24:06,850 --> 00:24:11,020 And let's say this electron was struck on its way 601 00:24:11,020 --> 00:24:13,330 out by a gamma ray. 602 00:24:13,330 --> 00:24:14,770 So it's gone. 603 00:24:14,770 --> 00:24:17,320 At this point, you might have an electron fall 604 00:24:17,320 --> 00:24:22,480 from let's call this level 2 to level 1. 605 00:24:22,480 --> 00:24:28,980 And so this 2-to-1 transition is called the K-transition. 606 00:24:28,980 --> 00:24:31,530 Don't ask me why the letters are the way they are. 607 00:24:31,530 --> 00:24:33,690 I probably have read it and have forgotten it 608 00:24:33,690 --> 00:24:35,310 because it wasn't that intuitive, 609 00:24:35,310 --> 00:24:37,922 but this is referred to as a K-transition. 610 00:24:37,922 --> 00:24:39,630 So you may have what's called the K-alpha 611 00:24:39,630 --> 00:24:41,310 or a K-beta line, that depends on 612 00:24:41,310 --> 00:24:43,830 if you have an even higher energy shell, 613 00:24:43,830 --> 00:24:47,670 but whatever this letter is, it tells you what an energy level 614 00:24:47,670 --> 00:24:50,070 the electron is going to. 615 00:24:50,070 --> 00:24:52,880 So the K lines would be here. 616 00:24:52,880 --> 00:24:54,530 The L-line-- yeah, I'm sorry. 617 00:24:54,530 --> 00:24:56,990 Let me back up and say that again. 618 00:24:56,990 --> 00:25:01,340 So the idea here is that if this the-- 619 00:25:01,340 --> 00:25:02,760 but let's see. 620 00:25:02,760 --> 00:25:03,510 Which one is this? 621 00:25:03,510 --> 00:25:05,130 0.662. 622 00:25:05,130 --> 00:25:08,040 So if the gamma ray is at 0.662 MeV, which 623 00:25:08,040 --> 00:25:11,970 would be about there, notice that these K-shell and L-shell 624 00:25:11,970 --> 00:25:15,378 lines aren't quite 0.662. 625 00:25:15,378 --> 00:25:17,670 That's because they have to overcome the binding energy 626 00:25:17,670 --> 00:25:20,530 of the electron to get out. 627 00:25:20,530 --> 00:25:23,700 So to jump back to this diagram right here, 628 00:25:23,700 --> 00:25:26,550 the gamma ray loses a little bit of energy 629 00:25:26,550 --> 00:25:28,890 in freeing the electron, the rest of which 630 00:25:28,890 --> 00:25:31,050 can become kinetic energy, which is 631 00:25:31,050 --> 00:25:32,940 why you can see that the electron, let's say, 632 00:25:32,940 --> 00:25:35,570 was ejected from the K-shell here. 633 00:25:35,570 --> 00:25:36,645 And-- yeah? 634 00:25:36,645 --> 00:25:38,895 AUDIENCE: So internal conversion is the actual process 635 00:25:38,895 --> 00:25:40,978 of-- when we figure out the process of a gamma ray 636 00:25:40,978 --> 00:25:42,815 hitting the electron? 637 00:25:42,815 --> 00:25:44,940 MICHAEL SHORT: I will say that internal conversion, 638 00:25:44,940 --> 00:25:47,100 you can imagine a mental model of the gamma ray 639 00:25:47,100 --> 00:25:48,530 hits an electron on its way out. 640 00:25:48,530 --> 00:25:49,570 AUDIENCE: But it's not the actual-- that's 641 00:25:49,570 --> 00:25:50,850 not physically happening? 642 00:25:50,850 --> 00:25:52,330 MICHAEL SHORT: Physically it's more complicated. 643 00:25:52,330 --> 00:25:52,930 AUDIENCE: OK. 644 00:25:52,930 --> 00:25:53,290 MICHAEL SHORT: Yes. 645 00:25:53,290 --> 00:25:54,570 AUDIENCE: Looks like a [INAUDIBLE].. 646 00:25:54,570 --> 00:25:55,036 MICHAEL SHORT: Yeah. 647 00:25:55,036 --> 00:25:55,536 Yep. 648 00:25:55,536 --> 00:25:57,320 So if you want remember like what's what, 649 00:25:57,320 --> 00:26:00,510 I would say, just remember this diagram right here. 650 00:26:00,510 --> 00:26:01,140 Yeah, Kristen? 651 00:26:01,140 --> 00:26:02,932 AUDIENCE: You get a gamma ray and an electron or just 652 00:26:02,932 --> 00:26:03,380 the one-- 653 00:26:03,380 --> 00:26:04,430 MICHAEL SHORT: Just the-- you get just 654 00:26:04,430 --> 00:26:06,080 the electron, good question. 655 00:26:06,080 --> 00:26:08,390 Is the gamma ray is effectively absorbed 656 00:26:08,390 --> 00:26:11,180 in freeing the electron from its bound shell 657 00:26:11,180 --> 00:26:13,300 and then imparting kinetic energy. 658 00:26:13,300 --> 00:26:13,900 Yep? 659 00:26:13,900 --> 00:26:16,420 AUDIENCE: Is the Auger emission is 660 00:26:16,420 --> 00:26:18,975 when another electron hops down an energy level 661 00:26:18,975 --> 00:26:20,263 and that [INAUDIBLE] electron? 662 00:26:20,263 --> 00:26:21,430 MICHAEL SHORT: That's right. 663 00:26:21,430 --> 00:26:23,800 So that's correct. 664 00:26:23,800 --> 00:26:25,540 So I'll spend the next couple of slides 665 00:26:25,540 --> 00:26:28,300 going over what Auger electron emission is, 666 00:26:28,300 --> 00:26:31,120 but not till we finish the easier stuff, because Auger 667 00:26:31,120 --> 00:26:32,530 is a little complicated. 668 00:26:32,530 --> 00:26:36,040 Did I see another question out here? 669 00:26:36,040 --> 00:26:36,540 Cool. 670 00:26:36,540 --> 00:26:39,510 So again, all the competing methods for gamma decay, 671 00:26:39,510 --> 00:26:42,510 one, the gamma can just get out; two, the gamma 672 00:26:42,510 --> 00:26:45,240 can knock out an electron from, let's say, 673 00:26:45,240 --> 00:26:49,410 the K-shell or the L-shell or the M-shell and so on and so on 674 00:26:49,410 --> 00:26:51,878 depending on what elements you have. 675 00:26:51,878 --> 00:26:52,920 So I'll just label these. 676 00:26:52,920 --> 00:26:55,016 Like this would be like the K-shell, 677 00:26:55,016 --> 00:26:57,810 this would be the L-shell, this would be the M-shell. 678 00:27:01,150 --> 00:27:03,390 Now I want you to notice something, too. 679 00:27:03,390 --> 00:27:07,820 The K-shell electron ejected from the innermost electron 680 00:27:07,820 --> 00:27:10,560 is slightly lower than the L-shell electron. 681 00:27:10,560 --> 00:27:11,850 Why do you guys think that is? 682 00:27:18,890 --> 00:27:22,010 Let's look at the energetics for this process, right? 683 00:27:22,010 --> 00:27:24,920 The electron energy level is whatever the gamma ray level 684 00:27:24,920 --> 00:27:28,560 is minus the binding energy. 685 00:27:28,560 --> 00:27:31,140 Which of these two electrons, the K-shell or the L-shell, 686 00:27:31,140 --> 00:27:34,090 do you think is going to be more tightly-bound? 687 00:27:34,090 --> 00:27:34,720 The K-shell. 688 00:27:34,720 --> 00:27:37,370 The innermost electron is more bound, 689 00:27:37,370 --> 00:27:39,730 so it takes away more energy from that gamma ray. 690 00:27:39,730 --> 00:27:41,380 Let's say this is the gamma. 691 00:27:41,380 --> 00:27:44,800 It takes more energy to eject an electron from the K-shell 692 00:27:44,800 --> 00:27:46,230 than the L-shell. 693 00:27:46,230 --> 00:27:48,190 Or in other words, the gamma loses less energy 694 00:27:48,190 --> 00:27:51,103 ejecting a less-bound electron. 695 00:27:51,103 --> 00:27:52,270 So that's why you see these. 696 00:27:52,270 --> 00:27:54,730 If there were an M-shell, there-- 697 00:27:54,730 --> 00:27:57,370 I don't know what element this was drawn for, 698 00:27:57,370 --> 00:27:59,110 but let's say-- oh, for cesium. 699 00:27:59,110 --> 00:28:01,060 So there probably is an M-shell. 700 00:28:01,060 --> 00:28:03,700 It's just that as you get down in energy levels, 701 00:28:03,700 --> 00:28:05,770 the probability of finding an electron 702 00:28:05,770 --> 00:28:07,750 from these outer and outer energy levels 703 00:28:07,750 --> 00:28:10,090 gets way and way less likely. 704 00:28:10,090 --> 00:28:12,882 So you'll usually just see a K or an L-shell electron. 705 00:28:12,882 --> 00:28:15,090 And if I asked you to draw one of these on a problems 706 00:28:15,090 --> 00:28:17,680 set or an exam, just drawing the K and the L-shells 707 00:28:17,680 --> 00:28:19,487 is perfectly sufficient. 708 00:28:19,487 --> 00:28:21,570 Because that way at least you'll know that there's 709 00:28:21,570 --> 00:28:22,640 a couple of possibilities. 710 00:28:22,640 --> 00:28:23,140 Yeah? 711 00:28:23,140 --> 00:28:25,310 AUDIENCE: What are the two curves on the right graph 712 00:28:25,310 --> 00:28:25,810 there? 713 00:28:25,810 --> 00:28:26,330 MICHAEL SHORT: On this one? 714 00:28:26,330 --> 00:28:26,980 AUDIENCE: Yeah. 715 00:28:26,980 --> 00:28:28,397 MICHAEL SHORT: So these two curves 716 00:28:28,397 --> 00:28:31,360 represent the probability of finding an electron emitted 717 00:28:31,360 --> 00:28:32,660 at that energy. 718 00:28:32,660 --> 00:28:34,870 So this curve right here where you 719 00:28:34,870 --> 00:28:40,780 get a maximum beta energy of 512 keV comes from that beta decay. 720 00:28:40,780 --> 00:28:46,660 And the maximum for the 1.174 comes from this beta decay. 721 00:28:46,660 --> 00:28:49,030 So the total curve would be the sum 722 00:28:49,030 --> 00:28:51,610 of each of these four things. 723 00:28:51,610 --> 00:28:53,560 If I just said draw the total probability 724 00:28:53,560 --> 00:28:55,810 of detecting an electron at that temperature, 725 00:28:55,810 --> 00:28:57,660 you just add those up. 726 00:28:57,660 --> 00:28:59,910 I saw two other questions or were they the same thing? 727 00:28:59,910 --> 00:29:00,690 Yeah? 728 00:29:00,690 --> 00:29:01,428 AUDIENCE: Yeah, I was going to ask 729 00:29:01,428 --> 00:29:02,604 what the [? lower ?] [INAUDIBLE],, 730 00:29:02,604 --> 00:29:03,930 but his question made me think. 731 00:29:03,930 --> 00:29:06,680 So is it kind of like the area under both those curves 732 00:29:06,680 --> 00:29:08,054 sums to 1? 733 00:29:08,054 --> 00:29:13,280 Because the probability given that like 0.512 max is 95% of-- 734 00:29:13,280 --> 00:29:14,280 MICHAEL SHORT: Ah. 735 00:29:14,280 --> 00:29:18,510 So the question was is the area under each of these curves 1? 736 00:29:18,510 --> 00:29:20,028 Not with this scale. 737 00:29:20,028 --> 00:29:22,320 Here we're just showing a relative number of electrons. 738 00:29:22,320 --> 00:29:25,440 So if you want to find what's the total probability 739 00:29:25,440 --> 00:29:28,950 that cesium will emit an electron of each energy, 740 00:29:28,950 --> 00:29:31,680 if you integrate under all of these curves, 741 00:29:31,680 --> 00:29:33,510 that will sum to 1. 742 00:29:33,510 --> 00:29:35,580 If you're looking at just one of these decays 743 00:29:35,580 --> 00:29:38,880 and you're saying, if cesium undergoes this decay, 744 00:29:38,880 --> 00:29:41,640 what's the probability of each of these energy levels? 745 00:29:41,640 --> 00:29:44,820 Then you only integrate under the relevant curve. 746 00:29:44,820 --> 00:29:47,040 What's more practical is usually what's 747 00:29:47,040 --> 00:29:48,960 the probability of finding any electron 748 00:29:48,960 --> 00:29:50,730 at any energy from cesium? 749 00:29:50,730 --> 00:29:53,730 Then you take into account all the possible decays, 750 00:29:53,730 --> 00:29:56,640 draw all the curves independently, add them up, 751 00:29:56,640 --> 00:29:58,080 and you get the total probability 752 00:29:58,080 --> 00:30:01,960 function whose area will be 1? 753 00:30:01,960 --> 00:30:02,460 Yes? 754 00:30:02,460 --> 00:30:05,362 AUDIENCE: So maybe you could say that all L-shell electrons 755 00:30:05,362 --> 00:30:08,110 would be ejected if [INAUDIBLE] in the K-shell due to the fact 756 00:30:08,110 --> 00:30:09,620 that it's less tightly-bound? 757 00:30:09,620 --> 00:30:11,200 MICHAEL SHORT: Wait, can you say the last part again? 758 00:30:11,200 --> 00:30:12,710 AUDIENCE: Shouldn't we say the L-shell electron will 759 00:30:12,710 --> 00:30:15,335 be ejected if [INAUDIBLE] energy in the K-shell due to the fact 760 00:30:15,335 --> 00:30:16,680 that it's not as tightly-bound? 761 00:30:16,680 --> 00:30:17,930 MICHAEL SHORT: That's correct. 762 00:30:17,930 --> 00:30:21,030 So the L-shell electron in the second shell 763 00:30:21,030 --> 00:30:24,030 is less tightly-bound than the first one, which is why 764 00:30:24,030 --> 00:30:25,830 it's ejected with more energy. 765 00:30:25,830 --> 00:30:29,290 It doesn't take as much of the gamma's energy to get it out. 766 00:30:29,290 --> 00:30:33,110 If you were to get, let's say, the outermost electron ejected, 767 00:30:33,110 --> 00:30:36,610 which happens and Auger, which we'll go over next, 768 00:30:36,610 --> 00:30:40,057 it can take up anywhere from 1 to 7 eV. 769 00:30:40,057 --> 00:30:41,140 Really, really low energy. 770 00:30:41,140 --> 00:30:44,680 That's what we call the work function or the energy required 771 00:30:44,680 --> 00:30:48,190 to make the outermost electron out. 772 00:30:48,190 --> 00:30:51,040 So any other questions on this before I go Auger and show you 773 00:30:51,040 --> 00:30:53,640 that process? 774 00:30:53,640 --> 00:30:54,640 Cool. 775 00:30:54,640 --> 00:30:58,860 So then let's get into what is Auger electron emission? 776 00:30:58,860 --> 00:31:01,650 It's exactly-- Luke, is that what you said? 777 00:31:01,650 --> 00:31:02,825 Were you asking about it? 778 00:31:02,825 --> 00:31:03,450 AUDIENCE: Yeah. 779 00:31:03,450 --> 00:31:06,060 MICHAEL SHORT: Yeah So it's exactly like what Luke said. 780 00:31:06,060 --> 00:31:10,110 Normally if you have a hole in a lower-level energy shell, 781 00:31:10,110 --> 00:31:13,350 an electron from a higher shell will fall down to fill it, 782 00:31:13,350 --> 00:31:14,730 emitting an X-ray. 783 00:31:14,730 --> 00:31:18,900 A competing process for this is another electron 784 00:31:18,900 --> 00:31:23,460 from a very similar energy shell will get ejected instead. 785 00:31:23,460 --> 00:31:25,393 The mental model for this, which again, is not 786 00:31:25,393 --> 00:31:27,810 the true physical picture but it's perfectly fine to think 787 00:31:27,810 --> 00:31:31,050 of it like this, the X-ray hits another electron on its way 788 00:31:31,050 --> 00:31:32,130 out. 789 00:31:32,130 --> 00:31:35,750 And you can look at the energetics accordingly. 790 00:31:35,750 --> 00:31:39,540 Where for Auger emission, let's say the kinetic energy 791 00:31:39,540 --> 00:31:41,550 the Auger electron is the difference 792 00:31:41,550 --> 00:31:45,480 in the final and initial electron energy states 793 00:31:45,480 --> 00:31:48,670 minus the binding energy of the Auger electron, 794 00:31:48,670 --> 00:31:51,210 which will usually be very low, because the Auger 795 00:31:51,210 --> 00:31:53,310 electron that's emitted is usually one 796 00:31:53,310 --> 00:31:55,900 of the outer shell electrons. 797 00:31:55,900 --> 00:31:57,990 So to help make this a little more concrete, 798 00:31:57,990 --> 00:31:58,740 I wanted to show-- 799 00:31:58,740 --> 00:32:01,470 I will do a little calculation example-- it's just addition, 800 00:32:01,470 --> 00:32:03,760 so it's not that hard. 801 00:32:03,760 --> 00:32:05,200 So let's say we were measuring-- 802 00:32:05,200 --> 00:32:06,910 I don't even know what this is. 803 00:32:06,910 --> 00:32:10,270 And we started to see some characteristic Auger electrons 804 00:32:10,270 --> 00:32:13,310 for copper, platinum, carbon, and oxygen. 805 00:32:13,310 --> 00:32:16,510 And the question is, why do we see oxygen coming out 806 00:32:16,510 --> 00:32:20,087 right there at about 501 eV? 807 00:32:20,087 --> 00:32:21,670 Very, very low energy compared to what 808 00:32:21,670 --> 00:32:23,720 we've been talking about. 809 00:32:23,720 --> 00:32:26,390 We can actually look at the binding energies of some 810 00:32:26,390 --> 00:32:29,690 of the different electrons in oxygen. Luckily 811 00:32:29,690 --> 00:32:33,567 there aren't that many electrons in oxygen. The first-- 812 00:32:33,567 --> 00:32:35,150 the only-- well, the only K electrons, 813 00:32:35,150 --> 00:32:38,180 let's say, have a binding energy of 532 eV, 814 00:32:38,180 --> 00:32:41,820 the L1 is 24, and then the L3's something else, 815 00:32:41,820 --> 00:32:44,300 and one of the other p orbitals is 7 eV. 816 00:32:44,300 --> 00:32:46,550 And so the formula is pretty simple. 817 00:32:46,550 --> 00:32:50,510 It's just 532 minus 24-- 818 00:32:50,510 --> 00:32:53,660 that's the difference between the final and initial energy 819 00:32:53,660 --> 00:32:54,650 levels-- 820 00:32:54,650 --> 00:32:58,340 minus the seven to free that outer electron-- 821 00:32:58,340 --> 00:33:01,940 comes to 501 eV, which is exactly where you 822 00:33:01,940 --> 00:33:05,620 see the Auger line for oxygen. 823 00:33:05,620 --> 00:33:08,220 So when I ask you what are all the possible things that you 824 00:33:08,220 --> 00:33:11,610 could see during the decay of something, something, 825 00:33:11,610 --> 00:33:15,100 something, if I were to show you this curve 826 00:33:15,100 --> 00:33:18,120 and ask what's missing, what would you do? 827 00:33:24,670 --> 00:33:27,510 Where would you draw the Auger electrons on this curve? 828 00:33:27,510 --> 00:33:28,510 Yep? 829 00:33:28,510 --> 00:33:31,468 AUDIENCE: Like almost on the vertical axis 830 00:33:31,468 --> 00:33:32,510 because it's [INAUDIBLE]. 831 00:33:32,510 --> 00:33:33,302 MICHAEL SHORT: Yep. 832 00:33:33,302 --> 00:33:36,250 500 eV would be like, I don't know, one pixel away 833 00:33:36,250 --> 00:33:37,455 on this graph. 834 00:33:37,455 --> 00:33:39,580 But if you want a complete answer to this question, 835 00:33:39,580 --> 00:33:43,390 you've got to take into account all the possible beta energies 836 00:33:43,390 --> 00:33:46,240 for all the possible beta decay mechanisms; 837 00:33:46,240 --> 00:33:50,470 all of the possible conversion electrons for whatever gamma 838 00:33:50,470 --> 00:33:53,050 come out-- in this case, there's only one gamma; 839 00:33:53,050 --> 00:33:59,600 and Auger electrons which could compete with X-ray emission. 840 00:33:59,600 --> 00:34:02,187 So everyone clear on that? 841 00:34:02,187 --> 00:34:02,687 Yeah? 842 00:34:16,380 --> 00:34:18,960 So the question is if you eject an electron 843 00:34:18,960 --> 00:34:21,420 from one of the inner shells, does that eventually 844 00:34:21,420 --> 00:34:23,489 create an Auger electron, right? 845 00:34:23,489 --> 00:34:24,449 It can. 846 00:34:24,449 --> 00:34:25,889 These are competing processes. 847 00:34:25,889 --> 00:34:31,170 So to the X-ray can just escape during that transition, 848 00:34:31,170 --> 00:34:33,659 or we'll assume that it hits another electron on its way 849 00:34:33,659 --> 00:34:35,760 out and emits an Auger electron. 850 00:34:35,760 --> 00:34:38,340 So these are also competing processes. 851 00:34:38,340 --> 00:34:40,560 So you'll see one or the other-- in reality, 852 00:34:40,560 --> 00:34:43,462 you'll see a lot of both with different probabilities. 853 00:34:43,462 --> 00:34:45,420 Because you're usually not looking at one atom, 854 00:34:45,420 --> 00:34:48,760 it's usually looking at a lot. 855 00:34:48,760 --> 00:34:49,260 Cool. 856 00:34:49,260 --> 00:34:54,570 Any other questions on IT as an isomeric transition 857 00:34:54,570 --> 00:34:58,760 or internal conversion or Auger, what this is all about? 858 00:35:01,960 --> 00:35:02,980 Cool. 859 00:35:02,980 --> 00:35:04,960 Wanted to give you one note, too. 860 00:35:04,960 --> 00:35:06,950 That these Auger electrons are really, 861 00:35:06,950 --> 00:35:09,790 really low energy, which means the only ones that get out 862 00:35:09,790 --> 00:35:13,720 of the material are in the top, like, tens or so 863 00:35:13,720 --> 00:35:15,520 nanometers of the material. 864 00:35:15,520 --> 00:35:18,070 So it's a very surface-sensitive technique. 865 00:35:18,070 --> 00:35:20,020 So if you want to do a really detailed surface 866 00:35:20,020 --> 00:35:24,040 analysis or profiling, you can scan an electron beam 867 00:35:24,040 --> 00:35:27,220 across the sample and then collect the Auger electrons 868 00:35:27,220 --> 00:35:28,660 that come out-- 869 00:35:28,660 --> 00:35:30,310 skipping ahead to our calculation-- 870 00:35:30,310 --> 00:35:33,400 and get an elemental profile that'll 871 00:35:33,400 --> 00:35:35,002 tell you how much of each element 872 00:35:35,002 --> 00:35:37,210 is where depending on how many of its Auger electrons 873 00:35:37,210 --> 00:35:38,560 you can count. 874 00:35:38,560 --> 00:35:40,580 And it's pretty-- it's a pretty cool technique. 875 00:35:40,580 --> 00:35:43,300 There are just machines that do this now. 876 00:35:43,300 --> 00:35:45,797 Any interest in seeing one of these at the Center 877 00:35:45,797 --> 00:35:47,380 for Materials Science and Engineering, 878 00:35:47,380 --> 00:35:50,530 because we could try to arrange that, too? 879 00:35:50,530 --> 00:35:51,990 Cool, OK. 880 00:35:51,990 --> 00:35:53,110 I'll see what I can do. 881 00:35:53,110 --> 00:35:55,640 That'll be fun. 882 00:35:55,640 --> 00:35:59,180 And the last decay that we haven't talked about 883 00:35:59,180 --> 00:36:01,700 and did not show up in our generalized decay 884 00:36:01,700 --> 00:36:03,963 diagram from last time. 885 00:36:03,963 --> 00:36:05,630 We did talk about neutron decay, there's 886 00:36:05,630 --> 00:36:09,080 one other one that probably wouldn't fit on this diagram. 887 00:36:09,080 --> 00:36:12,220 Does anyone know what it is? 888 00:36:12,220 --> 00:36:14,140 Spontaneous fission. 889 00:36:14,140 --> 00:36:15,700 So this can happen-- that's right. 890 00:36:15,700 --> 00:36:18,610 This happens with very heavy elements. 891 00:36:18,610 --> 00:36:20,620 Then usually the heavier it is, the less stable 892 00:36:20,620 --> 00:36:22,060 it is, the higher probability this 893 00:36:22,060 --> 00:36:25,510 is at which the nucleus can once in a while, it-- nuclei just 894 00:36:25,510 --> 00:36:27,430 explode sometimes. 895 00:36:27,430 --> 00:36:30,550 Giving off two fission products, any number of neutrons-- 896 00:36:30,550 --> 00:36:33,040 usually between 1 and 3, a couple 897 00:36:33,040 --> 00:36:34,900 of gamma rays, some anti-neutrinos, 898 00:36:34,900 --> 00:36:36,645 and a whole bunch of other crazies. 899 00:36:36,645 --> 00:36:38,770 And so that, of course, doesn't fit on the diagram, 900 00:36:38,770 --> 00:36:41,140 but it is another type of decay that I'll 901 00:36:41,140 --> 00:36:43,195 ask you guys to analyze on the homework. 902 00:36:43,195 --> 00:36:45,320 And here's a hint-- you already analyzed part of it 903 00:36:45,320 --> 00:36:46,660 in problems set 1. 904 00:36:46,660 --> 00:36:50,242 I'll ask you to go a little deeper in problem set 3. 905 00:36:50,242 --> 00:36:54,180 So anyone have a question for myself? 906 00:36:54,180 --> 00:36:54,680 Cool. 907 00:36:54,680 --> 00:36:56,930 OK. 908 00:36:56,930 --> 00:36:58,580 Bear with me because I skipped back 909 00:36:58,580 --> 00:37:02,860 to like slide really far away. 910 00:37:02,860 --> 00:37:03,410 Oh cool. 911 00:37:03,410 --> 00:37:04,680 That thing actually works. 912 00:37:04,680 --> 00:37:05,590 Right to the summary. 913 00:37:05,590 --> 00:37:09,780 So in summary, the radioactive decay processes are more-- 914 00:37:09,780 --> 00:37:11,730 I think the energetics are pretty easy. 915 00:37:11,730 --> 00:37:14,400 The formulas aren't that hard to remember because most of them 916 00:37:14,400 --> 00:37:16,973 are just parents minus daughters minus something. 917 00:37:16,973 --> 00:37:18,390 But what I do want you to remember 918 00:37:18,390 --> 00:37:21,930 is which mechanisms compete with which other ones and why. 919 00:37:21,930 --> 00:37:26,040 And if I were to tell you, draw me a spectrum of photons 920 00:37:26,040 --> 00:37:29,550 that you may see from the decay of caesium-137, 921 00:37:29,550 --> 00:37:31,790 or draw me a spectrum of electrons, 922 00:37:31,790 --> 00:37:33,960 you'd be able to draw what that is 923 00:37:33,960 --> 00:37:36,540 so that when you go do lab number 4 924 00:37:36,540 --> 00:37:38,950 and we count our big bag of burnt bananas 925 00:37:38,950 --> 00:37:40,950 and you know that there's potassium-40 in there, 926 00:37:40,950 --> 00:37:43,380 you know what peaks to start looking for. 927 00:37:43,380 --> 00:37:45,990 Because you're not just going to see-- 928 00:37:45,990 --> 00:37:49,410 let's do a little flash-forward to detectors now. 929 00:37:49,410 --> 00:37:51,660 And some other stuff that nuclear engineers actually 930 00:37:51,660 --> 00:37:53,860 do on a daily basis. 931 00:37:53,860 --> 00:37:58,970 Let's say you're counting the energy of photons 932 00:37:58,970 --> 00:38:01,370 as a function of, let's say, the number of photons 933 00:38:01,370 --> 00:38:02,750 that you count. 934 00:38:02,750 --> 00:38:04,910 You're never-- you're almost never just 935 00:38:04,910 --> 00:38:11,473 going to see a lone potassium-40 peak like that. 936 00:38:11,473 --> 00:38:13,140 It's very, very rare that you would just 937 00:38:13,140 --> 00:38:14,582 capture the gamma ray as is. 938 00:38:14,582 --> 00:38:16,290 There's going to be a lot of other things 939 00:38:16,290 --> 00:38:18,738 that will go into it, which I'm not going to give away yet 940 00:38:18,738 --> 00:38:20,280 because we're going to go over photon 941 00:38:20,280 --> 00:38:22,640 interactions in like a week or two, 942 00:38:22,640 --> 00:38:24,390 but you do have to think about, well, what 943 00:38:24,390 --> 00:38:26,160 other X-rays might you see? 944 00:38:26,160 --> 00:38:29,310 What if the gamma-- what if this gamma ray hits an electron 945 00:38:29,310 --> 00:38:33,780 on the way out, and then you end up with some X-rays? 946 00:38:33,780 --> 00:38:36,120 Let's say you might have some K-level X-rays 947 00:38:36,120 --> 00:38:38,820 and some L-level X-rays and maybe some Ms? 948 00:38:38,820 --> 00:38:42,255 These could all be possible as well. 949 00:38:42,255 --> 00:38:43,630 I'll just label those real quick. 950 00:38:46,420 --> 00:38:49,390 Does anyone know how to find these energies? 951 00:38:49,390 --> 00:38:51,962 What those X-ray levels are? 952 00:38:56,030 --> 00:38:58,520 Anyone ever heard of the Lyman series? 953 00:38:58,520 --> 00:39:03,240 The emission lines from ionized hydrogen or anything like that? 954 00:39:03,240 --> 00:39:05,790 That's kind of the simpler case of it. 955 00:39:05,790 --> 00:39:09,920 The idea here is if you want to figure out 956 00:39:09,920 --> 00:39:13,958 what's the wavelength of light that's going to be emitted, 957 00:39:13,958 --> 00:39:16,250 it'll be that's this thing called the Rydberg constant, 958 00:39:16,250 --> 00:39:21,020 a more complex formula for which I have in the notes, times 1 959 00:39:21,020 --> 00:39:24,800 over your final shell squared minus 1 960 00:39:24,800 --> 00:39:27,980 over your initial shell squared. 961 00:39:27,980 --> 00:39:30,680 So the idea here is that you can look up these-- 962 00:39:30,680 --> 00:39:32,630 this Rydberg constant for any element 963 00:39:32,630 --> 00:39:35,800 that you have, and there's actually-- 964 00:39:35,800 --> 00:39:38,370 there's what's called an R infinity constant 965 00:39:38,370 --> 00:39:40,340 and I think you just multiply by Z-- 966 00:39:40,340 --> 00:39:43,690 I forget what power it is, but I will get it for you next time. 967 00:39:43,690 --> 00:39:45,440 And then it's just a matter of the squares 968 00:39:45,440 --> 00:39:48,110 between the final and the initial shell levels 969 00:39:48,110 --> 00:39:55,730 where n can vary from 1 to theoretically infinity. 970 00:39:55,730 --> 00:39:59,300 Realistically I've never heard of anything beyond a g orbital, 971 00:39:59,300 --> 00:40:00,832 so let's just say it's that. 972 00:40:00,832 --> 00:40:01,790 Or something like that. 973 00:40:04,400 --> 00:40:06,640 I'll leave the infinity there. 974 00:40:06,640 --> 00:40:08,380 That's technically correct. 975 00:40:08,380 --> 00:40:09,450 OK. 976 00:40:09,450 --> 00:40:11,380 And so all you need to do is either look up 977 00:40:11,380 --> 00:40:13,990 or calculate this constant for your element, 978 00:40:13,990 --> 00:40:16,180 and then plug-in the numbers of the shells, 979 00:40:16,180 --> 00:40:19,150 and you know what sort of photon energy you're going to get out. 980 00:40:19,150 --> 00:40:21,850 And to make that easier for you, I think now 981 00:40:21,850 --> 00:40:25,450 is a good time to introduce the NIST X-ray tables. 982 00:40:25,450 --> 00:40:27,502 So I want to make sure you can see my screen. 983 00:40:27,502 --> 00:40:28,960 And I'm going to show you something 984 00:40:28,960 --> 00:40:30,970 that's on the Stellar site which will 985 00:40:30,970 --> 00:40:32,890 help you figure this stuff out. 986 00:40:36,466 --> 00:40:38,960 20.2.0.0.1. 987 00:40:38,960 --> 00:40:40,040 Good, you can see. 988 00:40:44,930 --> 00:40:46,065 Probably will make log in. 989 00:40:53,000 --> 00:40:56,150 And all the way at the bottom of the material section, 990 00:40:56,150 --> 00:40:59,580 there's the NIST X-ray Transition Energy Database. 991 00:40:59,580 --> 00:41:01,250 So for example, you can look at-- 992 00:41:01,250 --> 00:41:03,560 I don't know, we were looking at caesium, right? 993 00:41:03,560 --> 00:41:07,400 Let's find caesium. 994 00:41:07,400 --> 00:41:10,400 And you can start to look at all transitions-- 995 00:41:10,400 --> 00:41:12,090 let's look at the simplest one. 996 00:41:12,090 --> 00:41:13,130 KL1. 997 00:41:13,130 --> 00:41:17,400 An electron going from shell number 2 to shell number 1. 998 00:41:17,400 --> 00:41:23,900 Get transitions, and you end up with a table of these energies 999 00:41:23,900 --> 00:41:25,550 in electron volts. 1000 00:41:25,550 --> 00:41:28,460 So if I were to ask you, let's say, 1001 00:41:28,460 --> 00:41:32,000 what sort of gamma rays might you see coming off of caesium, 1002 00:41:32,000 --> 00:41:35,090 that would be the most likely one where you're more likely 1003 00:41:35,090 --> 00:41:38,760 to eject an inner-shell electron, 1004 00:41:38,760 --> 00:41:41,690 and it's most likely that a number 2 shell electron will 1005 00:41:41,690 --> 00:41:45,110 fall down to a number 1 or from the L-shell to the K-shell, 1006 00:41:45,110 --> 00:41:47,750 whatever you want to call it, or the-- 1007 00:41:47,750 --> 00:41:49,520 some level orbital to some other-- 1008 00:41:49,520 --> 00:41:50,960 there seems to me like eight different letters 1009 00:41:50,960 --> 00:41:52,265 that describe the same thing. 1010 00:41:52,265 --> 00:41:54,630 I hope you guys get the idea. 1011 00:41:54,630 --> 00:41:57,840 If you want to look at all the possible transitions, 1012 00:41:57,840 --> 00:41:59,905 I have to zoom back out again. 1013 00:42:03,160 --> 00:42:04,900 Yeah. 1014 00:42:04,900 --> 00:42:06,610 Let's just scroll through it. 1015 00:42:06,610 --> 00:42:11,410 But what I want you to notice is that all of the KL transitions 1016 00:42:11,410 --> 00:42:14,210 are within like a couple hundred eV from each other. 1017 00:42:14,210 --> 00:42:17,500 So this is like the first or second or third L-shell 1018 00:42:17,500 --> 00:42:20,200 electron falling to the K-level. 1019 00:42:20,200 --> 00:42:23,560 So they call it the KL1, KL2, KL3. 1020 00:42:23,560 --> 00:42:24,682 They're all from L-shell. 1021 00:42:24,682 --> 00:42:26,890 They all just might be one of the different electrons 1022 00:42:26,890 --> 00:42:30,080 occupying that shell, which is why they're not that different. 1023 00:42:30,080 --> 00:42:34,720 So if I asked you, draw all of all of the X-rays 1024 00:42:34,720 --> 00:42:36,310 and gammas coming out, I don't want 1025 00:42:36,310 --> 00:42:38,620 to see a line for every single level. 1026 00:42:38,620 --> 00:42:41,890 I'm very happy for you just to say, this line represents 1027 00:42:41,890 --> 00:42:44,230 the KL series, this line represents 1028 00:42:44,230 --> 00:42:48,420 the KM series, all the things from shell 3 to shell 1. 1029 00:42:48,420 --> 00:42:50,970 Notice also that because it's final 1030 00:42:50,970 --> 00:42:55,310 minus initial squared, which I covered up, 1031 00:42:55,310 --> 00:42:58,340 falling from an even further outer shell 1032 00:42:58,340 --> 00:43:00,980 to the same inner shell should give you a higher energy, 1033 00:43:00,980 --> 00:43:05,430 which it does, by like 5 keV. 1034 00:43:05,430 --> 00:43:09,860 And then the KN levels, another 500 eV up. 1035 00:43:09,860 --> 00:43:11,610 They don't have KO's. 1036 00:43:11,610 --> 00:43:12,110 Interesting. 1037 00:43:12,110 --> 00:43:13,803 But they have the K-edge. 1038 00:43:13,803 --> 00:43:15,095 Anyone know what the K-edge is? 1039 00:43:19,440 --> 00:43:19,980 Exactly. 1040 00:43:19,980 --> 00:43:23,520 It's level infinity, which would mean an electron 1041 00:43:23,520 --> 00:43:25,290 from somewhere else, right? 1042 00:43:25,290 --> 00:43:27,870 So this in effect is like the energy 1043 00:43:27,870 --> 00:43:30,780 it takes to ionize a K-electron or the X-ray 1044 00:43:30,780 --> 00:43:33,150 that you would get from an electron falling 1045 00:43:33,150 --> 00:43:35,040 all the way into the K-shell. 1046 00:43:35,040 --> 00:43:37,230 So this is your kind of level infinity. 1047 00:43:37,230 --> 00:43:40,450 Notice, it's not that different from level 5. 1048 00:43:40,450 --> 00:43:44,710 That's why I wrote 6, I erased it for theoretical correctness, 1049 00:43:44,710 --> 00:43:48,660 but in all practicality, you won't see much else. 1050 00:43:48,660 --> 00:43:50,200 Does anyone have a question? 1051 00:43:50,200 --> 00:43:52,310 Thought I saw a hand. 1052 00:43:52,310 --> 00:43:52,810 OK. 1053 00:43:52,810 --> 00:43:54,550 Let's look at the L-series-- oh yes? 1054 00:43:54,550 --> 00:43:57,019 AUDIENCE: Sometimes you see L-alpha, L-beta. 1055 00:43:57,019 --> 00:43:57,811 MICHAEL SHORT: Yep. 1056 00:43:57,811 --> 00:44:01,033 AUDIENCE: Is that the same as the subscript 1, 2, 3, and 4? 1057 00:44:01,033 --> 00:44:02,575 MICHAEL SHORT: Yeah, that's another-- 1058 00:44:02,575 --> 00:44:04,660 AUDIENCE: --corresponding-- it's just a notation. 1059 00:44:04,660 --> 00:44:05,750 MICHAEL SHORT: Exactly. 1060 00:44:05,750 --> 00:44:07,630 Yeah, there's the L-alphas, the L-betas, 1061 00:44:07,630 --> 00:44:11,290 or you may see L-alpha 1 and 2 in L-beta 1 and 2. 1062 00:44:11,290 --> 00:44:14,530 So L designates that it's going to shell level 2. 1063 00:44:14,530 --> 00:44:18,250 Alpha or beta is like LM or LN. 1064 00:44:18,250 --> 00:44:22,300 Again, I think I've ranted about notations before. 1065 00:44:22,300 --> 00:44:24,363 Physics is notorious, because whoever-- 1066 00:44:24,363 --> 00:44:25,780 to describe something, and it gets 1067 00:44:25,780 --> 00:44:28,990 enough people to infect with the notation 1068 00:44:28,990 --> 00:44:31,060 that you decide it sticks. 1069 00:44:31,060 --> 00:44:33,270 But the main patterns to look at, then, 1070 00:44:33,270 --> 00:44:36,040 let's say the L1 M whatever. 1071 00:44:36,040 --> 00:44:38,380 This is from level 3 to level 2, and notice how 1072 00:44:38,380 --> 00:44:40,650 much lower an energy these are. 1073 00:44:40,650 --> 00:44:42,490 And the L-edge. 1074 00:44:42,490 --> 00:44:46,513 5 keV compared to like 36 keV. 1075 00:44:46,513 --> 00:44:48,430 And all of these sort of different transitions 1076 00:44:48,430 --> 00:44:49,930 you can calculate with this formula. 1077 00:44:49,930 --> 00:44:52,932 And this has just kind of tabulated this formula for you. 1078 00:44:52,932 --> 00:44:54,640 So whatever you're more comfortable doing 1079 00:44:54,640 --> 00:44:58,560 is putting this in Excel, look it up on NIST, your choice. 1080 00:44:58,560 --> 00:44:59,060 Yeah? 1081 00:44:59,060 --> 00:45:01,643 AUDIENCE: If we were to calculate that by hand-- 1082 00:45:01,643 --> 00:45:02,560 MICHAEL SHORT: Mm-hmm. 1083 00:45:02,560 --> 00:45:04,560 AUDIENCE: --what would you use for like NF? 1084 00:45:04,560 --> 00:45:08,443 Say, like, 5? 1085 00:45:08,443 --> 00:45:10,610 MICHAEL SHORT: Oh, what is the largest NF, you mean? 1086 00:45:10,610 --> 00:45:11,235 AUDIENCE: Yeah. 1087 00:45:11,235 --> 00:45:14,400 What numbers actually go in NF [INAUDIBLE]?? 1088 00:45:14,400 --> 00:45:19,190 MICHAEL SHORT: For that I'll put my practical thing back there. 1089 00:45:19,190 --> 00:45:20,840 You'll never see it much higher than 6 1090 00:45:20,840 --> 00:45:22,460 unless you're talking about actinides 1091 00:45:22,460 --> 00:45:26,570 and super heavy elements with even crazier shell levels. 1092 00:45:26,570 --> 00:45:29,840 But you'll put the integer shell number, 1093 00:45:29,840 --> 00:45:34,240 regardless of whether they call it L or S or whatever. 1094 00:45:34,240 --> 00:45:36,200 Just put the number here, and that 1095 00:45:36,200 --> 00:45:38,690 will give you the-- a pretty good approximation 1096 00:45:38,690 --> 00:45:42,178 of the energy transition. 1097 00:45:42,178 --> 00:45:43,970 Does anyone remember this from high school? 1098 00:45:43,970 --> 00:45:45,442 I hope they're teaching this now. 1099 00:45:45,442 --> 00:45:47,130 AUDIENCE: We learned this in [INAUDIBLE] 1100 00:45:47,130 --> 00:45:49,260 MICHAEL SHORT: Oh, they did in 5-111? 1101 00:45:49,260 --> 00:45:50,260 Oh, that's good to hear. 1102 00:45:50,260 --> 00:45:52,520 What about 3-091? 1103 00:45:52,520 --> 00:45:54,800 Anyone take that? 1104 00:45:54,800 --> 00:45:55,550 No one took 3-091? 1105 00:45:55,550 --> 00:45:57,660 Wow, OK. 1106 00:45:57,660 --> 00:45:59,900 Usually it's like half and half or so. 1107 00:45:59,900 --> 00:46:00,770 Cool. 1108 00:46:00,770 --> 00:46:02,190 And let's see, how far does it go? 1109 00:46:02,190 --> 00:46:05,000 All the way to the L3 N's in the L3 edge. 1110 00:46:05,000 --> 00:46:10,290 So that's the biggest element they have talking 1111 00:46:10,290 --> 00:46:12,690 about ridiculous transitions. 1112 00:46:15,270 --> 00:46:16,990 Yeah. 1113 00:46:16,990 --> 00:46:20,860 So notice also, as you go up in-- 1114 00:46:20,860 --> 00:46:22,987 that's number 100. 1115 00:46:22,987 --> 00:46:24,570 So this is the heaviest one they have, 1116 00:46:24,570 --> 00:46:27,600 so most likely to have the largest number of levels. 1117 00:46:27,600 --> 00:46:30,710 So here, the KL1 is like 114 keV, 1118 00:46:30,710 --> 00:46:32,480 sometimes indistinguishable from some 1119 00:46:32,480 --> 00:46:35,930 of these smaller nuclear energy level transitions. 1120 00:46:35,930 --> 00:46:38,720 So remember I said before, chemistry and nuclear differ 1121 00:46:38,720 --> 00:46:40,520 by about a factor of a million. 1122 00:46:40,520 --> 00:46:43,430 Well, not so if you're talking about weak gammas 1123 00:46:43,430 --> 00:46:47,990 versus heavy elements K-shell transitions or their K-edges. 1124 00:46:47,990 --> 00:46:50,060 Let's see, the largest X-ray you'd expect 1125 00:46:50,060 --> 00:46:55,110 would be the K-edge at 142 keV. 1126 00:46:55,110 --> 00:47:00,060 And the technetium-99 gamma ray comes out of 140 keV. 1127 00:47:00,060 --> 00:47:02,160 How do you know if it's a gamma or an X-ray? 1128 00:47:02,160 --> 00:47:03,778 You don't. 1129 00:47:03,778 --> 00:47:06,320 Unless you have really, really good energy resolution and you 1130 00:47:06,320 --> 00:47:07,460 can tell them apart. 1131 00:47:07,460 --> 00:47:07,960 Yeah? 1132 00:47:07,960 --> 00:47:09,460 AUDIENCE: This formula in this chart 1133 00:47:09,460 --> 00:47:11,922 is only for caluclating energy of X-rays, right? 1134 00:47:11,922 --> 00:47:12,880 MICHAEL SHORT: Correct. 1135 00:47:12,880 --> 00:47:13,380 This-- 1136 00:47:13,380 --> 00:47:15,873 AUDIENCE: [INAUDIBLE] for gammas. 1137 00:47:15,873 --> 00:47:17,290 MICHAEL SHORT: Things get quantum. 1138 00:47:17,290 --> 00:47:19,870 So the question was, this formula and this chart, 1139 00:47:19,870 --> 00:47:22,930 yes, this is only for X-rays and electron shells. 1140 00:47:22,930 --> 00:47:25,750 There are probably equivalent calculations 1141 00:47:25,750 --> 00:47:27,700 for nuclear energy levels. 1142 00:47:27,700 --> 00:47:31,930 I will say that's a 22.02 and far beyond topic. 1143 00:47:31,930 --> 00:47:34,420 For the nuclear energy levels, just 1144 00:47:34,420 --> 00:47:38,006 use the decay diagrams to find those. 1145 00:47:38,006 --> 00:47:39,370 Yeah. 1146 00:47:39,370 --> 00:47:43,800 The table of nuclides and all their different diagrams. 1147 00:47:43,800 --> 00:47:44,300 Cool. 1148 00:47:44,300 --> 00:47:45,500 How far do we go here? 1149 00:47:45,500 --> 00:47:48,580 LN-- yep, there's no O's. 1150 00:47:48,580 --> 00:47:51,910 So they never talk about anything beyond shell level 4, 1151 00:47:51,910 --> 00:47:52,810 even for fermium. 1152 00:47:52,810 --> 00:47:54,658 So ha, I stand corrected. 1153 00:47:57,730 --> 00:47:59,314 OK. 1154 00:47:59,314 --> 00:48:01,340 Cool. 1155 00:48:01,340 --> 00:48:02,840 So what I wanted to show you quickly 1156 00:48:02,840 --> 00:48:05,090 is is that series of hydrogen emission lines. 1157 00:48:05,090 --> 00:48:08,070 So how familiar does this look to folks? 1158 00:48:08,070 --> 00:48:10,950 Where you can have a transition from level 3 1159 00:48:10,950 --> 00:48:14,460 to level 2, level 4 to level 2, and you can actually-- 1160 00:48:14,460 --> 00:48:16,180 this is a kind of neat thing to verify. 1161 00:48:16,180 --> 00:48:17,460 I don't it as a problem set question 1162 00:48:17,460 --> 00:48:19,110 because it's not very nuclear, but you 1163 00:48:19,110 --> 00:48:22,110 can try this on your own and verify that you can actually 1164 00:48:22,110 --> 00:48:26,250 calculate the expected wavelength of these photons 1165 00:48:26,250 --> 00:48:28,290 coming off of excited hydrogen. 1166 00:48:28,290 --> 00:48:30,330 Also notice here, it goes all the way 1167 00:48:30,330 --> 00:48:33,030 out to 9 and out to infinity, because this 1168 00:48:33,030 --> 00:48:35,070 is electronic excitation. 1169 00:48:35,070 --> 00:48:37,080 You won't usually get the ejection of anything 1170 00:48:37,080 --> 00:48:41,550 beyond an M or an N electron even in the largest elements 1171 00:48:41,550 --> 00:48:45,080 from, let's say, from IC-- what is it? 1172 00:48:45,080 --> 00:48:46,735 From internal conversion. 1173 00:48:46,735 --> 00:48:48,110 But you can electronically excite 1174 00:48:48,110 --> 00:48:50,930 them to whatever energy level to the point of even ionizing 1175 00:48:50,930 --> 00:48:51,830 them. 1176 00:48:51,830 --> 00:48:54,990 That's where the infinity comes in. 1177 00:48:54,990 --> 00:48:55,490 Cool. 1178 00:48:55,490 --> 00:48:57,910 So it's like two of five of. 1179 00:48:57,910 --> 00:49:01,340 So I want to open this up to any questions about decay before we 1180 00:49:01,340 --> 00:49:04,760 move upstairs to talk about activity, half-life, and series 1181 00:49:04,760 --> 00:49:08,210 radioactive decay, which is what nuclear activation analysis is 1182 00:49:08,210 --> 00:49:09,722 all about. 1183 00:49:09,722 --> 00:49:10,430 So anything here? 1184 00:49:13,830 --> 00:49:14,506 Yep? 1185 00:49:14,506 --> 00:49:16,381 AUDIENCE: Just making sure I understand this. 1186 00:49:16,381 --> 00:49:18,841 So the H-alpha lines transition from N equals to 3 to N 1187 00:49:18,841 --> 00:49:19,400 equals 2. 1188 00:49:19,400 --> 00:49:19,755 MICHAEL SHORT: Mm-hmm. 1189 00:49:19,755 --> 00:49:21,210 AUDIENCE: Would you call that-- 1190 00:49:21,210 --> 00:49:25,072 in our previous notation, would you call that LM transition? 1191 00:49:25,072 --> 00:49:26,030 MICHAEL SHORT: Correct. 1192 00:49:26,030 --> 00:49:29,010 In our pre-- in our other notation, 1193 00:49:29,010 --> 00:49:31,970 this would be known as an LM electron. 1194 00:49:31,970 --> 00:49:34,700 And probably L1M1 because there is only one 1195 00:49:34,700 --> 00:49:37,665 electron in hydrogen. Yep. 1196 00:49:37,665 --> 00:49:39,290 So don't let the notations trip you up. 1197 00:49:39,290 --> 00:49:39,957 As long as you-- 1198 00:49:39,957 --> 00:49:42,500 I'm sure someone's got a chart of L 1199 00:49:42,500 --> 00:49:45,650 equals 2 equals whatever other Greek letter 1200 00:49:45,650 --> 00:49:47,262 someone has designated it for. 1201 00:49:47,262 --> 00:49:49,470 There's just different ways of saying the same thing. 1202 00:49:49,470 --> 00:49:51,190 So as long as you know the physics, 1203 00:49:51,190 --> 00:49:55,410 looking up the notation is just kind of a little pain. 1204 00:49:55,410 --> 00:49:58,260 Any other questions on radioactive decay or competing 1205 00:49:58,260 --> 00:49:58,950 mechanisms? 1206 00:50:03,470 --> 00:50:04,760 Cool. 1207 00:50:04,760 --> 00:50:06,560 Let's take a 10 minute break. 1208 00:50:06,560 --> 00:50:09,890 So I'll see you guys upstairs in Room 307 in 10 minutes. 1209 00:50:09,890 --> 00:50:13,890 There's no projector there, so we'll do it all on the board. 1210 00:50:13,890 --> 00:50:14,390 All right. 1211 00:50:14,390 --> 00:50:17,690 So I want to start off the second half of today's class 1212 00:50:17,690 --> 00:50:19,595 by posing and answering a question. 1213 00:50:19,595 --> 00:50:24,330 Who's still mentally having trouble grasping this idea? 1214 00:50:24,330 --> 00:50:25,560 What did I tell you? 1215 00:50:25,560 --> 00:50:26,108 Yeah. 1216 00:50:26,108 --> 00:50:28,400 So whoever I said it to, I said at least half the class 1217 00:50:28,400 --> 00:50:30,210 is right there with you, it's true. 1218 00:50:30,210 --> 00:50:31,860 So in a sentence, it's this-- 1219 00:50:31,860 --> 00:50:35,330 Q is the conversion of mass to energy. 1220 00:50:35,330 --> 00:50:37,287 That's all. 1221 00:50:37,287 --> 00:50:39,370 And the whole point of doing this nuclear reaction 1222 00:50:39,370 --> 00:50:42,460 energetics to find out if things are or aren't allowed, 1223 00:50:42,460 --> 00:50:44,140 if they're exo or endothermic is to see 1224 00:50:44,140 --> 00:50:46,660 how much mass is converted to energy 1225 00:50:46,660 --> 00:50:51,360 or how much energy has to be converted to mass. 1226 00:50:51,360 --> 00:50:52,860 And if you have trouble remembering, 1227 00:50:52,860 --> 00:50:54,420 just go back to the equation that I 1228 00:50:54,420 --> 00:50:57,230 see on everybody's T-shirts. 1229 00:50:57,230 --> 00:50:59,135 And like I said on the first day of class, 1230 00:50:59,135 --> 00:51:00,510 everyone's got it on their shirts 1231 00:51:00,510 --> 00:51:03,630 and no one quite understands it, not even the nuclear engineers. 1232 00:51:03,630 --> 00:51:06,870 Because it's very difficult mentally to grasp the idea 1233 00:51:06,870 --> 00:51:09,270 that energy and matter are two sides of the same coin 1234 00:51:09,270 --> 00:51:11,680 or two different forms of the same thing. 1235 00:51:11,680 --> 00:51:15,600 So for a nuclear reaction where Q is greater than 0 1236 00:51:15,600 --> 00:51:21,330 or exothermic, all that means is that energy is spontaneously 1237 00:51:21,330 --> 00:51:24,620 created from the destruction of mass. 1238 00:51:24,620 --> 00:51:25,940 That's all. 1239 00:51:25,940 --> 00:51:32,870 And for a Q less than 0 reaction or endothermic, 1240 00:51:32,870 --> 00:51:35,570 when you inject energy into the system, it is absorbed 1241 00:51:35,570 --> 00:51:40,970 and mass is created straight from this equation. 1242 00:51:40,970 --> 00:51:42,680 So does this make more sense to the folks 1243 00:51:42,680 --> 00:51:46,070 that raised their hands, which is almost everybody? 1244 00:51:46,070 --> 00:51:48,013 Q is nothing but a quantification 1245 00:51:48,013 --> 00:51:49,430 of the amount of matter and energy 1246 00:51:49,430 --> 00:51:51,610 that turn from one to the other. 1247 00:51:51,610 --> 00:51:53,110 And all the balance stuff we've been 1248 00:51:53,110 --> 00:51:56,405 doing for almost the last month has been to serve, to quantify, 1249 00:51:56,405 --> 00:51:58,890 and to predict it. 1250 00:51:58,890 --> 00:52:00,860 So I hope that helps. 1251 00:52:00,860 --> 00:52:04,070 I know that MIT students have this gift for being 1252 00:52:04,070 --> 00:52:05,930 able to hide behind the math, and I 1253 00:52:05,930 --> 00:52:08,660 know that's true because I used to be one myself. 1254 00:52:08,660 --> 00:52:10,070 And you could get through the day 1255 00:52:10,070 --> 00:52:13,970 or get through the class getting the math right without really 1256 00:52:13,970 --> 00:52:16,340 understanding the physics or the mechanism 1257 00:52:16,340 --> 00:52:17,508 behind what's going on. 1258 00:52:17,508 --> 00:52:19,550 So everything we've done for the last three weeks 1259 00:52:19,550 --> 00:52:21,212 can be summed up in one sentence-- 1260 00:52:21,212 --> 00:52:22,670 mass and energy are the same thing. 1261 00:52:25,430 --> 00:52:28,050 We've just had a lot of math to get there and be able to-- 1262 00:52:28,050 --> 00:52:29,633 yeah, it still kind of makes your head 1263 00:52:29,633 --> 00:52:30,930 want to explode, right? 1264 00:52:30,930 --> 00:52:32,640 If you think about it, if you make an-- 1265 00:52:32,640 --> 00:52:35,150 we want to make an endothermic reaction happen, 1266 00:52:35,150 --> 00:52:38,750 you have to put kinetic energy into one of the particles. 1267 00:52:38,750 --> 00:52:43,850 And that system in the just barely-allowed state, 1268 00:52:43,850 --> 00:52:46,170 the nuclei won't really be moving, or at least the-- 1269 00:52:46,170 --> 00:52:46,670 yeah. 1270 00:52:46,670 --> 00:52:48,545 The nuclei won't really be moving afterwards, 1271 00:52:48,545 --> 00:52:51,100 because you'll have turned energy into matter. 1272 00:52:51,100 --> 00:52:55,310 That kinetic energy is turned into mass energy. 1273 00:52:55,310 --> 00:52:58,070 Just like you can turn potential into kinetic or thermal 1274 00:52:58,070 --> 00:53:03,570 into mechanical or vice versa, it's other forms of energy. 1275 00:53:03,570 --> 00:53:05,890 Kind of mind-blowing. 1276 00:53:05,890 --> 00:53:09,670 Well anyway, so now that we finished radioactive decay, 1277 00:53:09,670 --> 00:53:12,568 I want to get into the concept of activity half-life, 1278 00:53:12,568 --> 00:53:14,110 and then we're going to start but not 1279 00:53:14,110 --> 00:53:18,760 finish serial radioactive creation and destruction. 1280 00:53:18,760 --> 00:53:22,150 In your readings, you'll see an equation that looks something 1281 00:53:22,150 --> 00:53:25,660 like this where we're going to be at the end of the day today. 1282 00:53:25,660 --> 00:53:30,610 If you want to show off how much of some isotope N1 1283 00:53:30,610 --> 00:53:32,560 exists as a function of time, you 1284 00:53:32,560 --> 00:53:34,435 may have seen something that looks like this. 1285 00:53:39,360 --> 00:53:40,860 We're going to be able to understand 1286 00:53:40,860 --> 00:53:44,580 how these equations are created, and because this is MIT, 1287 00:53:44,580 --> 00:53:49,650 we're going to take it further and add 1288 00:53:49,650 --> 00:53:54,060 specifically driven mechanisms, like can you 1289 00:53:54,060 --> 00:53:57,060 create an isotope not just by decay 1290 00:53:57,060 --> 00:54:00,150 from one isotope to another, but by intentionally making it? 1291 00:54:00,150 --> 00:54:04,140 Which is exactly how NAA Nuclear Activation Analysis works. 1292 00:54:04,140 --> 00:54:06,450 You fire neutrons into a material. 1293 00:54:06,450 --> 00:54:10,117 They turn into something else and start decaying in series. 1294 00:54:10,117 --> 00:54:12,450 This is what we're going to be working out the math for, 1295 00:54:12,450 --> 00:54:14,850 but I want to make sure at every step 1296 00:54:14,850 --> 00:54:17,100 that we get the physics right. 1297 00:54:17,100 --> 00:54:20,220 So first, a very quick primer on where-- 1298 00:54:20,220 --> 00:54:24,150 what is activity and where does half-life come from? 1299 00:54:24,150 --> 00:54:31,020 So we define the A, the activity of a substance 1300 00:54:31,020 --> 00:54:34,650 as pretty simple. 1301 00:54:34,650 --> 00:54:38,300 It depends on the amount of the substance that's there, 1302 00:54:38,300 --> 00:54:41,190 and it depends on what's called this decay constant. 1303 00:54:41,190 --> 00:54:45,680 So this amount-- let's just say like atoms. 1304 00:54:45,680 --> 00:54:50,780 And this decay constant is in units of 1 over second. 1305 00:54:50,780 --> 00:54:53,570 An activity is in, let's say, atoms 1306 00:54:53,570 --> 00:54:58,950 destroyed or decays per second. 1307 00:54:58,950 --> 00:55:02,720 That thing right there is called the decay constant, lambda. 1308 00:55:06,940 --> 00:55:09,520 And if we want to see, let's say, how much of a substance 1309 00:55:09,520 --> 00:55:12,670 is decaying at a certain time or what's its activity 1310 00:55:12,670 --> 00:55:16,460 and get a measure of how quickly does it take to decay away, 1311 00:55:16,460 --> 00:55:18,400 we can start by saying, well this in effect 1312 00:55:18,400 --> 00:55:21,790 is a destruction rate of isotope N. 1313 00:55:21,790 --> 00:55:25,150 So we can make the simplest of differential equations 1314 00:55:25,150 --> 00:55:30,100 and say, the amount of substance N as a function of time 1315 00:55:30,100 --> 00:55:36,470 is just minus its activity, which equals minus lambda n. 1316 00:55:36,470 --> 00:55:39,260 I hope I don't have to explain how to solve this differential 1317 00:55:39,260 --> 00:55:42,230 equation, so I'm going to go through it pretty quickly. 1318 00:55:42,230 --> 00:55:45,100 What's the method you use for this 1319 00:55:45,100 --> 00:55:46,870 to get n as a function of t? 1320 00:55:49,582 --> 00:55:50,718 AUDIENCE: 3? 1321 00:55:50,718 --> 00:55:51,510 MICHAEL SHORT: Yes. 1322 00:55:51,510 --> 00:55:54,093 You're all in 18-03 or have finished 18-03, right? 1323 00:55:54,093 --> 00:55:55,260 This should have been day 1. 1324 00:55:55,260 --> 00:55:58,200 So we'll just separate variables, divide each side 1325 00:55:58,200 --> 00:56:01,100 by N, multiply side by dt. 1326 00:56:01,100 --> 00:56:06,142 So we get dN over N equals negative lambda dt. 1327 00:56:06,142 --> 00:56:12,810 You can integrate both sides, and we get the natural log of N 1328 00:56:12,810 --> 00:56:17,678 equals minus lambda t plus some integration constant. 1329 00:56:17,678 --> 00:56:19,470 We're going to do a little bit of trickery, 1330 00:56:19,470 --> 00:56:24,220 and to make things in a nice form that we can deal with, 1331 00:56:24,220 --> 00:56:28,190 let's just call this log of N0. 1332 00:56:28,190 --> 00:56:29,450 They're just numbers, right? 1333 00:56:29,450 --> 00:56:33,180 We haven't defined what this constant of integration is. 1334 00:56:33,180 --> 00:56:35,930 Everyone cool with us doing that? 1335 00:56:35,930 --> 00:56:40,220 So then we can subtract log of N0 from each side. 1336 00:56:42,992 --> 00:56:52,910 And we get log N minus log of N0 equals minus lambda t. 1337 00:56:52,910 --> 00:57:01,370 So this is like saying log of N over N0 equals minus lambda t. 1338 00:57:01,370 --> 00:57:03,260 We'll take either the power of both sides 1339 00:57:03,260 --> 00:57:09,580 and we get N over and not equals e to the minus lambda t. 1340 00:57:09,580 --> 00:57:13,560 And right there you've got your exponential decay equation. 1341 00:57:13,560 --> 00:57:16,600 This is the easy part. 1342 00:57:16,600 --> 00:57:19,720 And what this tells you is it is a larger decay constant. 1343 00:57:19,720 --> 00:57:21,370 Well let me ask you a question, then. 1344 00:57:21,370 --> 00:57:24,160 Would a larger decay constant mean a faster 1345 00:57:24,160 --> 00:57:26,358 or a slower decaying isotope? 1346 00:57:30,940 --> 00:57:33,250 A larger decay constant-- correct-- 1347 00:57:33,250 --> 00:57:36,220 means that you've got more of these decays happening 1348 00:57:36,220 --> 00:57:37,780 per second. 1349 00:57:37,780 --> 00:57:43,050 So a larger lambda means faster decay. 1350 00:57:47,620 --> 00:57:49,330 And we also can define a quantity 1351 00:57:49,330 --> 00:58:02,420 called the half-life, which means N at t 1/2 equals 1/2 N0. 1352 00:58:02,420 --> 00:58:07,670 So for that, all you have to do is plug in t 1/2 for t, 1353 00:58:07,670 --> 00:58:12,980 and 1/2 N0 for N0, and you actually get this relation 1354 00:58:12,980 --> 00:58:20,180 where the half-life is just log of 2 over lambda, better known 1355 00:58:20,180 --> 00:58:22,700 as 0.693. 1356 00:58:22,700 --> 00:58:25,690 But we'll just leave it as log of 2 for exactness. 1357 00:58:25,690 --> 00:58:28,610 And that's all there really is for decay in half-life. 1358 00:58:28,610 --> 00:58:30,500 So I'll pose another question to you. 1359 00:58:30,500 --> 00:58:35,420 Something with a larger decay constant, 1360 00:58:35,420 --> 00:58:38,680 will it have a larger or a smaller half-life? 1361 00:58:38,680 --> 00:58:39,540 AUDIENCE: Smaller? 1362 00:58:39,540 --> 00:58:42,210 MICHAEL SHORT: Smaller, because they're inversely related. 1363 00:58:47,790 --> 00:58:49,440 So I'd say from this quick derivation, 1364 00:58:49,440 --> 00:58:51,990 these are the two things to note. 1365 00:58:51,990 --> 00:58:54,870 Is that something with a larger decay constant decays faster 1366 00:58:54,870 --> 00:58:57,210 and therefore has a shorter half-life. 1367 00:58:57,210 --> 00:59:00,000 So when we were separating out our isotopes in nuclear 1368 00:59:00,000 --> 00:59:02,700 activation analysis into what Mike called the shorts 1369 00:59:02,700 --> 00:59:06,840 and the longs, he was separating them by half-life to say that-- 1370 00:59:06,840 --> 00:59:08,670 let's say the same amount of activation 1371 00:59:08,670 --> 00:59:11,100 or the same amount of creation, the ones 1372 00:59:11,100 --> 00:59:15,420 with shorter half-lives will be hotter, more radioactive, 1373 00:59:15,420 --> 00:59:17,052 but for less time. 1374 00:59:17,052 --> 00:59:18,510 And so what we're going to be doing 1375 00:59:18,510 --> 00:59:21,150 is what's called short nuclear activation analysis 1376 00:59:21,150 --> 00:59:23,610 because we don't want to count for like days or weeks 1377 00:59:23,610 --> 00:59:24,120 or months. 1378 00:59:24,120 --> 00:59:24,760 Yep? 1379 00:59:24,760 --> 00:59:27,010 AUDIENCE: So is half-life-- is the decay constant just 1380 00:59:27,010 --> 00:59:29,915 a property of the given substance, given element? 1381 00:59:29,915 --> 00:59:31,290 MICHAEL SHORT: The decay constant 1382 00:59:31,290 --> 00:59:33,090 is a property of the given isotope 1383 00:59:33,090 --> 00:59:35,650 specific to that type of decay. 1384 00:59:35,650 --> 00:59:40,740 So if we were to draw that generalized radioactivity 1385 00:59:40,740 --> 00:59:41,310 diagram-- 1386 00:59:41,310 --> 00:59:46,530 let's say we have potassium-40, which can either go by beta 1387 00:59:46,530 --> 00:59:48,990 decay to-- 1388 00:59:48,990 --> 00:59:51,060 what comes in beta-- what comes after-- 1389 00:59:51,060 --> 00:59:53,490 I think it's calcium-40. 1390 00:59:53,490 --> 01:00:02,560 Or it can go by positron or electron capture to argon-40. 1391 01:00:02,560 --> 01:00:05,433 Each of these processes has a different half-life. 1392 01:00:05,433 --> 01:00:06,850 And then in that chain-- remember, 1393 01:00:06,850 --> 01:00:10,210 let's do the americium-241, and I'm 1394 01:00:10,210 --> 01:00:12,190 going to channel my one-year-old son 1395 01:00:12,190 --> 01:00:14,995 in drawing this decay diagram. 1396 01:00:14,995 --> 01:00:21,720 It looks something like that with all sorts of transitions. 1397 01:00:21,720 --> 01:00:24,010 I didn't scream like he usually does, but whatever. 1398 01:00:24,010 --> 01:00:25,562 We're on camera. 1399 01:00:25,562 --> 01:00:27,520 Each of these decay-- each of these transitions 1400 01:00:27,520 --> 01:00:29,140 may also have its own half-life. 1401 01:00:29,140 --> 01:00:31,210 So between isometric transitions, 1402 01:00:31,210 --> 01:00:34,175 they're usually very, very fast, but once in a while 1403 01:00:34,175 --> 01:00:34,675 they're not. 1404 01:00:38,790 --> 01:00:42,950 Like technetium-99 metastable to technetium-99 1405 01:00:42,950 --> 01:00:46,340 has a half-life of around six days, 1406 01:00:46,340 --> 01:00:50,730 which is why it's so useful as a medical isotope. 1407 01:00:50,730 --> 01:00:53,210 So when you see something marked M for metastable, 1408 01:00:53,210 --> 01:00:57,560 all that means is there is some sort of a gamma, 1409 01:00:57,560 --> 01:01:00,560 also known as an IT transition, with a particularly 1410 01:01:00,560 --> 01:01:01,832 long half-life. 1411 01:01:04,487 --> 01:01:06,070 Everyone clear on what all that means? 1412 01:01:09,950 --> 01:01:10,773 Cool. 1413 01:01:10,773 --> 01:01:12,190 Well, there'll be some time for it 1414 01:01:12,190 --> 01:01:17,560 to sink in because with these definitions in hand, 1415 01:01:17,560 --> 01:01:19,690 I want to pose a problem to you guys. 1416 01:01:19,690 --> 01:01:31,200 Let's say I start off with some amount of an isotope N1. 1417 01:01:31,200 --> 01:01:33,780 And it decays by some mechanism-- 1418 01:01:33,780 --> 01:01:35,350 we don't care what-- 1419 01:01:35,350 --> 01:01:40,350 to isotope N2, and it decays to some isotope N3 1420 01:01:40,350 --> 01:01:45,480 with decay constants lambda 1 and lambda 2. 1421 01:01:45,480 --> 01:01:49,140 This is what we call serial radioactive decay. 1422 01:01:56,150 --> 01:01:58,010 How do we construct a system of equations 1423 01:01:58,010 --> 01:02:03,080 to tell us what is N1 as a function of time, what 1424 01:02:03,080 --> 01:02:06,710 is N2 as a function of time, and what 1425 01:02:06,710 --> 01:02:11,210 is N3 as a function of time? 1426 01:02:11,210 --> 01:02:13,568 Where do we begin in a general sense? 1427 01:02:17,220 --> 01:02:19,980 OK, so let's start with N1. 1428 01:02:19,980 --> 01:02:21,990 We kind of have an expression for N1 already, 1429 01:02:21,990 --> 01:02:24,840 but let's start out with a differential equation. 1430 01:02:24,840 --> 01:02:26,760 So the form of all of these equations 1431 01:02:26,760 --> 01:02:30,090 for everything serial radioactive decay and burning 1432 01:02:30,090 --> 01:02:33,300 isotopes in a reactor and creating isotopes in a reactor 1433 01:02:33,300 --> 01:02:36,060 is going to take the following form. 1434 01:02:36,060 --> 01:02:39,370 The general equation is simple. 1435 01:02:39,370 --> 01:02:46,265 The change equals creation minus destruction. 1436 01:02:48,880 --> 01:02:54,070 Or the simple thing is let's say the change is 1437 01:02:54,070 --> 01:02:57,280 a source minus a sink. 1438 01:02:57,280 --> 01:02:59,920 And we'll have to come up for every one of these isotopes 1439 01:02:59,920 --> 01:03:02,830 for a mathematical way to describe what's the source 1440 01:03:02,830 --> 01:03:04,330 and what's the sink. 1441 01:03:04,330 --> 01:03:08,170 So if we want to measure the change in N1 1442 01:03:08,170 --> 01:03:12,410 as a function of time, what are the sources of isotope N1? 1443 01:03:12,410 --> 01:03:13,825 Yeah? 1444 01:03:13,825 --> 01:03:15,200 AUDIENCE: Isn't there no sources? 1445 01:03:15,200 --> 01:03:17,690 MICHAEL SHORT: No sources. 1446 01:03:17,690 --> 01:03:21,140 We're starting off with some fixed quantity of N1. 1447 01:03:21,140 --> 01:03:24,260 Let's just call it N1,0. 1448 01:03:24,260 --> 01:03:27,320 But you're right, there's no continuous source 1449 01:03:27,320 --> 01:03:29,480 of isotope N1. 1450 01:03:29,480 --> 01:03:33,296 What about its destruction? 1451 01:03:33,296 --> 01:03:35,197 AUDIENCE: Decay to N2? 1452 01:03:35,197 --> 01:03:36,030 MICHAEL SHORT: Yeah. 1453 01:03:36,030 --> 01:03:36,840 Decay to N2. 1454 01:03:36,840 --> 01:03:40,540 So we've got the equation for that right there. 1455 01:03:40,540 --> 01:03:44,410 it depends on the decay constant of number 1 1456 01:03:44,410 --> 01:03:46,347 and the amount of number 1. 1457 01:03:46,347 --> 01:03:47,430 So what we're doing here-- 1458 01:03:47,430 --> 01:03:50,470 I love how this course is timed with 18-03 because you're 1459 01:03:50,470 --> 01:03:53,280 learning ordinary differential equations in 18-03, 1460 01:03:53,280 --> 01:03:55,780 and we're going to be solving everyday ordinary differential 1461 01:03:55,780 --> 01:03:57,722 equations for a fair bit of this course. 1462 01:03:57,722 --> 01:03:59,180 So it's one of those rare times you 1463 01:03:59,180 --> 01:04:01,780 get to like learn math and put it to use at the same time 1464 01:04:01,780 --> 01:04:04,930 instead of six years later, it's just kind of nice. 1465 01:04:04,930 --> 01:04:06,590 So that's easy. 1466 01:04:06,590 --> 01:04:08,430 Let's go to the more challenging one. 1467 01:04:11,390 --> 01:04:13,280 What is the source of isotope N2? 1468 01:04:16,082 --> 01:04:17,272 AUDIENCE: Decay from N1? 1469 01:04:17,272 --> 01:04:18,480 MICHAEL SHORT: Decay from N1. 1470 01:04:18,480 --> 01:04:21,744 So how would I mathematically write that? 1471 01:04:21,744 --> 01:04:23,910 AUDIENCE: Just lambda 1 N1. 1472 01:04:23,910 --> 01:04:27,780 MICHAEL SHORT: Just lambda 1 N1. 1473 01:04:27,780 --> 01:04:33,780 And what is the destruction of isotope N2? 1474 01:04:33,780 --> 01:04:35,679 Anyone else? 1475 01:04:35,679 --> 01:04:36,932 AUDIENCE: Lambda 2 N2? 1476 01:04:36,932 --> 01:04:38,390 MICHAEL SHORT: Takes the same form. 1477 01:04:38,390 --> 01:04:40,640 It depends on the decay concept of isotope 2 1478 01:04:40,640 --> 01:04:43,280 and the amount of isotope 2 that's there. 1479 01:04:47,570 --> 01:04:48,920 How about isotope 3? 1480 01:04:48,920 --> 01:04:50,848 Where does that come from? 1481 01:04:55,186 --> 01:04:56,308 AUDIENCE: Lambda 2 N2? 1482 01:04:56,308 --> 01:04:57,350 MICHAEL SHORT: That's it. 1483 01:04:57,350 --> 01:05:01,310 The source is lambda 2 N2. 1484 01:05:01,310 --> 01:05:03,276 What are the sinks or the destruction? 1485 01:05:03,276 --> 01:05:04,150 AUDIENCE: Nothing. 1486 01:05:04,150 --> 01:05:05,860 MICHAEL SHORT: Nothing. 1487 01:05:05,860 --> 01:05:10,210 So we have a very simple set of posed differential equations 1488 01:05:10,210 --> 01:05:13,540 to describe the production and the destruction of these three 1489 01:05:13,540 --> 01:05:14,830 isotopes. 1490 01:05:14,830 --> 01:05:18,670 So let's imagine now that N1 was, let's say, 1491 01:05:18,670 --> 01:05:22,490 radium, which exists all throughout the soil and rocks; 1492 01:05:22,490 --> 01:05:27,040 N2 is radon, the gas that's produced from radium decay; 1493 01:05:27,040 --> 01:05:30,640 and then N3 could be let's say one of the stable daughter 1494 01:05:30,640 --> 01:05:31,877 products of radon. 1495 01:05:31,877 --> 01:05:33,460 So these are the sorts of calculations 1496 01:05:33,460 --> 01:05:35,688 that are done all the time in real life to see-- 1497 01:05:35,688 --> 01:05:37,480 if you know how much radium is in the rock, 1498 01:05:37,480 --> 01:05:39,850 how much radon do you expect to breathe in? 1499 01:05:39,850 --> 01:05:42,850 Because at the same time you're producing radon 1500 01:05:42,850 --> 01:05:44,740 from radium decay. 1501 01:05:44,740 --> 01:05:47,410 And the radon is decaying itself. 1502 01:05:47,410 --> 01:05:49,750 So you can't just say, oh, the activity of the radium 1503 01:05:49,750 --> 01:05:51,700 equals the amount of radon because it's 1504 01:05:51,700 --> 01:05:54,490 being created and destroyed all at the same time, 1505 01:05:54,490 --> 01:05:56,940 and it depends on how much there is around. 1506 01:05:56,940 --> 01:05:59,650 Same thing with nuclear activation analysis. 1507 01:05:59,650 --> 01:06:05,470 You'll, let's say, you'd start off with sodium-21, 1508 01:06:05,470 --> 01:06:08,440 you can create sodium-22. 1509 01:06:08,440 --> 01:06:12,060 Sodium-22 will decay by positron emission. 1510 01:06:12,060 --> 01:06:14,460 What comes before sodium? 1511 01:06:14,460 --> 01:06:21,200 Probably neon, I think, 22. 1512 01:06:21,200 --> 01:06:22,880 That's my guess. 1513 01:06:22,880 --> 01:06:23,510 Yeah. 1514 01:06:23,510 --> 01:06:26,750 So if you want to say how much sodium-22 is there, 1515 01:06:26,750 --> 01:06:29,690 well you're both creating it from sodium-21 from neutron 1516 01:06:29,690 --> 01:06:33,290 absorption, and you're decaying it naturally 1517 01:06:33,290 --> 01:06:36,178 by positron emission among other processes. 1518 01:06:36,178 --> 01:06:38,720 We're going to get back into how do we deal with the neutrons 1519 01:06:38,720 --> 01:06:42,230 thing probably on Tuesday, But for now, 1520 01:06:42,230 --> 01:06:45,660 let's work on solving this system of equations. 1521 01:06:45,660 --> 01:06:48,020 So I think N1 is pretty easy because we already 1522 01:06:48,020 --> 01:06:49,713 have the solution for it. 1523 01:06:49,713 --> 01:06:50,630 So I'll just write it. 1524 01:06:54,058 --> 01:06:54,558 1t. 1525 01:06:58,990 --> 01:07:01,060 The harder one is N2. 1526 01:07:01,060 --> 01:07:03,940 So what can we start by doing? 1527 01:07:06,450 --> 01:07:10,330 We've got an ordinary differential equation with-- 1528 01:07:10,330 --> 01:07:13,480 it's just this first order, but there's two variables. 1529 01:07:13,480 --> 01:07:14,230 So how do we deal? 1530 01:07:19,870 --> 01:07:21,760 AUDIENCE: Pick another equation? 1531 01:07:21,760 --> 01:07:24,302 MICHAEL SHORT: We do it-- well, we have other equations, so-- 1532 01:07:24,302 --> 01:07:25,510 actually, we've got this one. 1533 01:07:25,510 --> 01:07:26,050 Yes. 1534 01:07:26,050 --> 01:07:30,460 Substitute N1 in here so we get everything in terms of N2 1535 01:07:30,460 --> 01:07:33,280 and constants and type. 1536 01:07:33,280 --> 01:07:41,650 So we'll rewrite this equation as dN2/dt, which I'm also just 1537 01:07:41,650 --> 01:07:43,603 going to write as N2 prime. 1538 01:07:43,603 --> 01:07:45,520 And when you use this a little bit of notation 1539 01:07:45,520 --> 01:07:47,260 that I'll leave up there on the board 1540 01:07:47,260 --> 01:07:49,870 because it's going to be a lot faster in writing. 1541 01:07:49,870 --> 01:07:54,760 Which equals lambda 1 and 10e to the minus lambda 1542 01:07:54,760 --> 01:07:58,260 1t minus lambda 2 N2. 1543 01:08:00,810 --> 01:08:02,440 Can we separate variables here? 1544 01:08:07,340 --> 01:08:10,080 I don't see an easy way. 1545 01:08:10,080 --> 01:08:15,690 So, 18-03 experts, how do we solve this type of first order 1546 01:08:15,690 --> 01:08:18,540 differential equation? 1547 01:08:18,540 --> 01:08:19,486 And I'll give you-- 1548 01:08:19,486 --> 01:08:21,069 l won't give you a hint, I'll give you 1549 01:08:21,069 --> 01:08:22,990 a little bit of consolation. 1550 01:08:22,990 --> 01:08:26,260 No one from last year knew how to approach this. 1551 01:08:26,260 --> 01:08:28,890 So if you don't know, I won't be disappointed. 1552 01:08:28,890 --> 01:08:30,350 Yeah? 1553 01:08:30,350 --> 01:08:33,432 AUDIENCE: You've got N2 dot plus lambda 2 1554 01:08:33,432 --> 01:08:37,280 N2 equals lambda 1 N1 dot-- 1555 01:08:37,280 --> 01:08:39,689 MICHAEL SHORT: Mm-hmm. 1556 01:08:39,689 --> 01:08:41,020 AUDIENCE: So you could put-- 1557 01:08:41,020 --> 01:08:44,200 add lambda 2 N2 to both sides. 1558 01:08:44,200 --> 01:08:46,720 MICHAEL SHORT: Add lambda 2 N2 to the both sides. 1559 01:08:46,720 --> 01:08:48,670 I think you're on to what I'm thinking about. 1560 01:08:56,810 --> 01:08:59,270 Also, if you can't read something I write, 1561 01:08:59,270 --> 01:09:01,830 please stop me and let me know and I'll be happy to erase it. 1562 01:09:01,830 --> 01:09:03,380 I don't think I've said that yet, 1563 01:09:03,380 --> 01:09:05,090 but it takes a lot of control for me 1564 01:09:05,090 --> 01:09:07,279 to get my handwriting legible on the board let alone 1565 01:09:07,279 --> 01:09:08,112 on a piece of paper. 1566 01:09:08,112 --> 01:09:11,189 So if you can't read, please let me know. 1567 01:09:11,189 --> 01:09:11,779 OK. 1568 01:09:11,779 --> 01:09:15,800 So now we've got the N2's separate from the N1's, what 1569 01:09:15,800 --> 01:09:16,460 do we do next? 1570 01:09:16,460 --> 01:09:18,750 AUDIENCE: --N2 has the form A times 1571 01:09:18,750 --> 01:09:21,500 e to the negative lambda 1t? 1572 01:09:21,500 --> 01:09:23,770 MICHAEL SHORT: OK, let's try this. 1573 01:09:23,770 --> 01:09:28,127 Assume N2 has the form e to the what? 1574 01:09:28,127 --> 01:09:30,877 AUDIENCE: Negative lambda 1t? 1575 01:09:30,877 --> 01:09:32,544 MICHAEL SHORT: Negative-- has the form e 1576 01:09:32,544 --> 01:09:34,090 to the lambda negative 1t. 1577 01:09:34,090 --> 01:09:35,560 AUDIENCE: With that A in front-- 1578 01:09:35,560 --> 01:09:37,960 MICHAEL SHORT: With an A, some constant in front. 1579 01:09:37,960 --> 01:09:41,090 What makes you say that? 1580 01:09:41,090 --> 01:09:43,340 AUDIENCE: Like if you take the derivative with respect 1581 01:09:43,340 --> 01:09:45,597 to time, then the next term will still have a e 1582 01:09:45,597 --> 01:09:47,065 to the negative lambda 1t? 1583 01:09:47,065 --> 01:09:47,982 MICHAEL SHORT: Mm-hmm. 1584 01:09:47,982 --> 01:09:50,477 AUDIENCE: Cancel all those out and solve for A. 1585 01:09:50,477 --> 01:09:51,310 MICHAEL SHORT: Cool. 1586 01:09:51,310 --> 01:09:53,450 So that is one way to do it. 1587 01:09:53,450 --> 01:09:55,490 It's going to get a little messy, though. 1588 01:09:55,490 --> 01:09:57,130 There's another method specifically 1589 01:09:57,130 --> 01:09:59,510 for equations of the form. 1590 01:09:59,510 --> 01:10:01,990 Let's call it y prime plus-- 1591 01:10:01,990 --> 01:10:04,340 I'm going to use notation they may have used in 18-03. 1592 01:10:07,651 --> 01:10:09,105 I hear a couple of aha. 1593 01:10:12,020 --> 01:10:15,380 Anything look familiar about this type of equation? 1594 01:10:15,380 --> 01:10:17,690 OK, what is it? 1595 01:10:17,690 --> 01:10:18,690 AUDIENCE: Not following. 1596 01:10:18,690 --> 01:10:21,160 [LAUGHTER] 1597 01:10:21,160 --> 01:10:23,230 MICHAEL SHORT: It's not that hard. 1598 01:10:23,230 --> 01:10:25,570 Anyone remember the word integrating factor? 1599 01:10:31,540 --> 01:10:34,960 And it was probably done horribly and on like six math 1600 01:10:34,960 --> 01:10:35,860 boards or whatever. 1601 01:10:35,860 --> 01:10:39,940 So I'm going to show you the simpler way to do this. 1602 01:10:39,940 --> 01:10:43,180 The idea here is we want to multiply everything 1603 01:10:43,180 --> 01:10:49,030 by something-- by some function mu. 1604 01:10:49,030 --> 01:10:52,260 Put a mu there, put a mu there, put a mu there. 1605 01:10:52,260 --> 01:10:54,010 I think that's the notation that's usually 1606 01:10:54,010 --> 01:10:56,950 used in differential equations, such 1607 01:10:56,950 --> 01:11:01,910 that this thing right here is shrinkable through the product 1608 01:11:01,910 --> 01:11:02,410 rule. 1609 01:11:05,290 --> 01:11:06,960 Or the product rule-- 1610 01:11:06,960 --> 01:11:10,360 I'm not assuming everyone remembers-- 1611 01:11:10,360 --> 01:11:16,315 says that let's say you have some function a of t, 1612 01:11:16,315 --> 01:11:27,220 b of t prime is like a prime times b plus a times b prime. 1613 01:11:27,220 --> 01:11:29,110 So we're kind of getting around to the method 1614 01:11:29,110 --> 01:11:30,693 that Luke was talking about, but we're 1615 01:11:30,693 --> 01:11:33,100 going to do it by a little bit of a cleaner way. 1616 01:11:33,100 --> 01:11:36,880 We multiply every term by some function mu 1617 01:11:36,880 --> 01:11:40,510 such that this part is one of these perfect product 1618 01:11:40,510 --> 01:11:43,090 rules at which point we can shrink and integrate 1619 01:11:43,090 --> 01:11:44,530 the expression. 1620 01:11:44,530 --> 01:11:46,840 Without going through the derivation of how 1621 01:11:46,840 --> 01:11:48,850 integrating factors are done, I'll 1622 01:11:48,850 --> 01:11:52,390 just let you know that this function mu ends up 1623 01:11:52,390 --> 01:11:56,300 being e to the integral of p. 1624 01:11:59,930 --> 01:12:01,595 Hat is our integrating factor. 1625 01:12:01,595 --> 01:12:03,470 So that's the end result of what was probably 1626 01:12:03,470 --> 01:12:05,360 six boards of 18-03. 1627 01:12:05,360 --> 01:12:07,310 Am I right or am I mistaken? 1628 01:12:07,310 --> 01:12:09,230 Well, things haven't changed in 15 years. 1629 01:12:09,230 --> 01:12:10,130 Cool. 1630 01:12:10,130 --> 01:12:16,140 OK, so what is mu for this equation? 1631 01:12:16,140 --> 01:12:21,220 Luckily, p of t is pretty simple. 1632 01:12:21,220 --> 01:12:22,870 Which part of this equation right here 1633 01:12:22,870 --> 01:12:26,624 is our p of t-like term? 1634 01:12:26,624 --> 01:12:28,810 AUDIENCE: Lambda 2 N2. 1635 01:12:28,810 --> 01:12:31,810 MICHAEL SHORT: Actually, just lambda 2. 1636 01:12:31,810 --> 01:12:34,180 Because we've got our variable right here 1637 01:12:34,180 --> 01:12:37,960 that right there is our p of t. 1638 01:12:37,960 --> 01:12:43,780 So we'll just say that mu equals e to the integral of-- 1639 01:12:43,780 --> 01:12:51,700 uh, yep-- of lambda 2 dt, which is just e to the lambda 2t. 1640 01:12:51,700 --> 01:12:54,160 That's our integrating factor right there. 1641 01:12:54,160 --> 01:12:59,560 So we'll multiply every term right here by that. 1642 01:12:59,560 --> 01:13:07,090 So we'll say e to the lambda 2t times and N2 prime plus lambda 1643 01:13:07,090 --> 01:13:09,610 2 e to the lambda 2t. 1644 01:13:09,610 --> 01:13:13,030 Anyone see what is going on here? 1645 01:13:13,030 --> 01:13:15,190 There's the product rule thing going on-- 1646 01:13:15,190 --> 01:13:24,100 times N2 plus e to the lambda 2t times lambda 1 N10 1647 01:13:24,100 --> 01:13:28,210 e to the minus lambda 1t equals 0. 1648 01:13:28,210 --> 01:13:32,350 And we have successfully created something here 1649 01:13:32,350 --> 01:13:34,130 that can be shrunk up with a product rule. 1650 01:13:34,130 --> 01:13:34,310 Yeah? 1651 01:13:34,310 --> 01:13:35,774 AUDIENCE: Should that be a minus e 1652 01:13:35,774 --> 01:13:39,190 to the lambda 2t lambda 1 N1-- 1653 01:13:39,190 --> 01:13:41,142 when you moved it over? 1654 01:13:41,142 --> 01:13:42,322 It's positive-- 1655 01:13:42,322 --> 01:13:43,280 MICHAEL SHORT: Oh yeah. 1656 01:13:43,280 --> 01:13:44,640 There's an equal sign there, isn't there? 1657 01:13:44,640 --> 01:13:45,920 That's what tripped me up. 1658 01:13:45,920 --> 01:13:47,030 Thank you. 1659 01:13:47,030 --> 01:13:50,300 So there is indeed a minus sign there 1660 01:13:50,300 --> 01:13:53,030 because I skipped the step putting everything 1661 01:13:53,030 --> 01:13:54,670 on one side of the equation. 1662 01:13:54,670 --> 01:13:55,170 Yep? 1663 01:13:55,170 --> 01:13:58,905 AUDIENCE: Could we do this with variational parameters instead? 1664 01:13:58,905 --> 01:14:01,530 MICHAEL SHORT: Where you replace one variable with-- or replace 1665 01:14:01,530 --> 01:14:03,256 a couple of variables with another one? 1666 01:14:03,256 --> 01:14:06,588 AUDIENCE: Well yeah, just like the homogeneous solution, 1667 01:14:06,588 --> 01:14:09,450 and then you'll find like a factor-- 1668 01:14:09,450 --> 01:14:10,590 MICHAEL SHORT: Yeah. 1669 01:14:10,590 --> 01:14:12,850 There are lots of ways of solving a first order 1670 01:14:12,850 --> 01:14:13,990 ODE like this. 1671 01:14:13,990 --> 01:14:14,490 Sure. 1672 01:14:14,490 --> 01:14:16,580 So this would work with various parameters. 1673 01:14:16,580 --> 01:14:18,502 It would work with what Luke's talking about. 1674 01:14:18,502 --> 01:14:19,460 It works with this one. 1675 01:14:19,460 --> 01:14:21,810 This just happened to be a particularly simple one 1676 01:14:21,810 --> 01:14:24,990 because the integrating factor's so simple. 1677 01:14:24,990 --> 01:14:27,720 So let's cram this up right here. 1678 01:14:27,720 --> 01:14:32,340 So this is like saying N2 times e 1679 01:14:32,340 --> 01:14:38,310 to the lambda 2t prime minus-- 1680 01:14:38,310 --> 01:14:41,580 and we've got two e to the somethings 1681 01:14:41,580 --> 01:14:43,990 that we can combine right here. 1682 01:14:43,990 --> 01:14:50,580 So I'll just say lambda 1 and 10e to the lambda 1683 01:14:50,580 --> 01:14:57,450 2 minus lambda 1t equals 0. 1684 01:14:57,450 --> 01:15:00,480 So now I will put this term back on the other side 1685 01:15:00,480 --> 01:15:03,820 by doing that. 1686 01:15:03,820 --> 01:15:05,380 And now we just integrate both sides. 1687 01:15:08,600 --> 01:15:16,970 And we get N2 e to the lambda 2t equals, let's see. 1688 01:15:16,970 --> 01:15:21,260 Becomes lambda 1 N10 over lambda 2 1689 01:15:21,260 --> 01:15:26,330 minus lambda 1 e to the lambda 2 minus 1690 01:15:26,330 --> 01:15:33,280 lambda 1t plus some integration constant C. 1691 01:15:33,280 --> 01:15:35,920 And in this case, our initial condition, well, 1692 01:15:35,920 --> 01:15:39,130 how much of isotope N2 did we start with? 1693 01:15:39,130 --> 01:15:41,928 Have we specified that yet? 1694 01:15:41,928 --> 01:15:43,740 No? 1695 01:15:43,740 --> 01:15:46,990 Let's make it simple. 1696 01:15:46,990 --> 01:15:51,450 Let's assume that the initial amount of isotope N2 equals 0. 1697 01:15:51,450 --> 01:15:53,340 We put some isotope in the reactor 1698 01:15:53,340 --> 01:15:56,342 or start it off with some amount of isotope like radium. 1699 01:15:56,342 --> 01:15:57,300 Didn't start off with-- 1700 01:15:57,300 --> 01:16:00,600 it didn't start off with any radon, and just kept going. 1701 01:16:00,600 --> 01:16:04,680 So then all we have to do is divide each side by either 1702 01:16:04,680 --> 01:16:12,680 the lambda 2t, and that cancels those, 1703 01:16:12,680 --> 01:16:20,320 that cancels that and that, and we end up with N2 as a function 1704 01:16:20,320 --> 01:16:28,180 of time equals lambda 1 N1,0 over lambda 2 minus lambda 1 1705 01:16:28,180 --> 01:16:34,010 times e to the minus lambda 1t. 1706 01:16:34,010 --> 01:16:34,510 OK. 1707 01:16:37,430 --> 01:16:40,850 And we've got an expression for N2. 1708 01:16:40,850 --> 01:16:41,810 How about N3? 1709 01:16:41,810 --> 01:16:44,435 Do we even have to solve this one? 1710 01:16:44,435 --> 01:16:48,342 I see a couple of people shaking their heads no, why is that? 1711 01:16:48,342 --> 01:16:50,318 AUDIENCE: Basically you already solved for N1, 1712 01:16:50,318 --> 01:16:52,058 they're just not minus signs. 1713 01:16:52,058 --> 01:16:53,350 MICHAEL SHORT: Well, not quite. 1714 01:16:53,350 --> 01:16:56,230 Because we-- well yeah, I guess we've kind of solved it for N1, 1715 01:16:56,230 --> 01:17:00,760 but now we take this expression for N2, stick it in here, 1716 01:17:00,760 --> 01:17:04,640 and then solve that, it's going to get messy. 1717 01:17:04,640 --> 01:17:06,880 So I'm going to show you something mathematically 1718 01:17:06,880 --> 01:17:08,920 now that I'll show you graphically later. 1719 01:17:08,920 --> 01:17:11,481 There's a conservation equation that we're missing here. 1720 01:17:15,170 --> 01:17:24,270 If we sum up isotopes N1, N2, N3, equals what? 1721 01:17:24,270 --> 01:17:25,800 Conserving total number of atoms. 1722 01:17:28,572 --> 01:17:29,960 AUDIENCE: N1,0? 1723 01:17:29,960 --> 01:17:31,250 MICHAEL SHORT: Exactly. 1724 01:17:31,250 --> 01:17:32,517 N1,0. 1725 01:17:32,517 --> 01:17:34,100 In this situation where we started off 1726 01:17:34,100 --> 01:17:37,280 with some known quantity of isotope 1 only, 1727 01:17:37,280 --> 01:17:40,160 you can't change the number of atoms here, 1728 01:17:40,160 --> 01:17:42,290 you can only change the type of atoms. 1729 01:17:42,290 --> 01:17:44,630 So we don't have to solve for E3-- 1730 01:17:44,630 --> 01:17:52,240 oh sorry, for N3, because N3 is just N1,0 minus N1 minus N2. 1731 01:17:52,240 --> 01:17:56,680 And that takes like an extra 10 minutes out of today's lecture. 1732 01:17:56,680 --> 01:18:00,100 So later on when we have a projector on Tuesday, 1733 01:18:00,100 --> 01:18:02,960 I will show you these equations graphed out where 1734 01:18:02,960 --> 01:18:04,710 I've-- actually, I'll share this with you. 1735 01:18:04,710 --> 01:18:08,630 Did I tell you guys about the Desmos graphical calculator? 1736 01:18:08,630 --> 01:18:10,108 Or have I shown this to you yet? 1737 01:18:12,920 --> 01:18:17,500 Go here for all of your graphing needs. 1738 01:18:20,060 --> 01:18:21,980 It's free, and the best part that I like 1739 01:18:21,980 --> 01:18:23,930 is that anytime you define some parameter, 1740 01:18:23,930 --> 01:18:25,970 it automatically makes a slider bar 1741 01:18:25,970 --> 01:18:28,160 so you can play with the equations. 1742 01:18:28,160 --> 01:18:29,300 And you can just-- 1743 01:18:29,300 --> 01:18:31,610 say, like, well what if L1 and L-- 1744 01:18:31,610 --> 01:18:32,900 lambda 1 and L2 are equal? 1745 01:18:32,900 --> 01:18:34,233 What if they were way different? 1746 01:18:34,233 --> 01:18:36,798 And it just graphs the solutions for you. 1747 01:18:36,798 --> 01:18:37,590 It's pretty useful. 1748 01:18:37,590 --> 01:18:40,040 So I'll show you some of that on Tuesday 1749 01:18:40,040 --> 01:18:42,040 when we actually have a screen. 1750 01:18:42,040 --> 01:18:44,060 Let me see what time it is. 1751 01:18:44,060 --> 01:18:46,295 Oh sweet, we've got plenty of time. 1752 01:18:46,295 --> 01:18:48,170 So now I want to pose the following questions 1753 01:18:48,170 --> 01:18:49,505 to you guys. 1754 01:18:49,505 --> 01:18:51,630 I'm going to erase stuff from here because we still 1755 01:18:51,630 --> 01:18:52,297 have some space. 1756 01:18:58,570 --> 01:19:01,810 How do we model nuclear activation analysis 1757 01:19:01,810 --> 01:19:05,290 using this kind of equation? 1758 01:19:05,290 --> 01:19:09,370 We'll start off with the same equation. 1759 01:19:09,370 --> 01:19:16,590 So let's say we'll have a minus lambda 1 N1, we'll have N2, 1760 01:19:16,590 --> 01:19:21,570 minus lambda 2 N2 minus something. 1761 01:19:21,570 --> 01:19:27,180 N3 equals something-- let's see, there's a lambda 1 N1, 1762 01:19:27,180 --> 01:19:31,080 there's a lambda 2 N2 minus something. 1763 01:19:31,080 --> 01:19:32,880 I've left some trailing minus signs 1764 01:19:32,880 --> 01:19:35,940 to indicate that we don't have complete equations for this 1765 01:19:35,940 --> 01:19:36,930 yet. 1766 01:19:36,930 --> 01:19:41,640 So for the case of nuclear activation analysis where 1767 01:19:41,640 --> 01:19:43,440 we have some imposed flux-- 1768 01:19:46,860 --> 01:19:49,215 flux-- of neutrons. 1769 01:19:51,980 --> 01:19:56,430 So anyone remember from some of our previous flash-forwards 1770 01:19:56,430 --> 01:19:59,370 how do we turn these into creation and destruction rates 1771 01:19:59,370 --> 01:20:00,945 of these different isotopes? 1772 01:20:05,797 --> 01:20:07,130 AUDIENCE: Could you repeat that? 1773 01:20:07,130 --> 01:20:07,922 MICHAEL SHORT: Yep. 1774 01:20:07,922 --> 01:20:12,200 So let's say we've now stuck N1 in the reactor. 1775 01:20:12,200 --> 01:20:15,140 And we're now using the reactor to create different isotopes 1776 01:20:15,140 --> 01:20:19,220 like N2 and N3, but at the same time they're in the reactor, 1777 01:20:19,220 --> 01:20:21,290 they're getting cooked as well by some 1778 01:20:21,290 --> 01:20:24,500 imposed flux of neutrons. 1779 01:20:24,500 --> 01:20:27,955 How do we set up and not solve the system of equations 1780 01:20:27,955 --> 01:20:31,750 to describe this? 1781 01:20:31,750 --> 01:20:38,012 AUDIENCE: Are they-- are N2 and N3 both getting like-- 1782 01:20:38,012 --> 01:20:40,220 MICHAEL SHORT: They're getting destroyed and whatnot? 1783 01:20:40,220 --> 01:20:42,348 AUDIENCE: Are they just like decaying 1784 01:20:42,348 --> 01:20:45,425 or are they also getting like added stuff from neutrons-- 1785 01:20:45,425 --> 01:20:46,300 MICHAEL SHORT: Well-- 1786 01:20:46,300 --> 01:20:48,000 AUDIENCE: Because that depends on the isotope. 1787 01:20:48,000 --> 01:20:49,230 MICHAEL SHORT: That depends on the isotope. 1788 01:20:49,230 --> 01:20:50,740 So let's define what the system-- 1789 01:20:50,740 --> 01:20:52,290 this system is. 1790 01:20:52,290 --> 01:20:56,890 Let's say we stuck in some other isotope N0, 1791 01:20:56,890 --> 01:21:01,680 and we put it in, and we're going to have to say it's-- 1792 01:21:01,680 --> 01:21:08,250 if we have N0 prime, some minus some creation term. 1793 01:21:08,250 --> 01:21:13,620 And in this case, N0 can absorb a neutron to become N1. 1794 01:21:13,620 --> 01:21:21,900 N1 is decaying to N2, N2 is decaying to N3. 1795 01:21:21,900 --> 01:21:24,840 But also, N1 can be burned by neutrons 1796 01:21:24,840 --> 01:21:31,750 N2 can be burned by neutrons and N3 can be burned by neutrons. 1797 01:21:31,750 --> 01:21:34,500 So here I've given you kind of a simplistic situation that 1798 01:21:34,500 --> 01:21:35,940 doesn't usually exist. 1799 01:21:35,940 --> 01:21:38,070 Here I've given you a situation that you 1800 01:21:38,070 --> 01:21:40,200 could replicate in the reactor. 1801 01:21:40,200 --> 01:21:44,310 How do we model this nuclear activation analysis process? 1802 01:21:49,957 --> 01:21:51,540 Well first of all, what's the creation 1803 01:21:51,540 --> 01:21:57,647 rate of N0, the stuff we put in the reactor? 1804 01:21:57,647 --> 01:21:58,480 Are we creating any? 1805 01:22:04,200 --> 01:22:05,140 No? 1806 01:22:05,140 --> 01:22:05,640 Luke? 1807 01:22:05,640 --> 01:22:09,528 AUDIENCE: It's all going to be created if N2 absorbs 1808 01:22:09,528 --> 01:22:11,515 the neutron and [INAUDIBLE]? 1809 01:22:11,515 --> 01:22:12,640 MICHAEL SHORT: It could be. 1810 01:22:12,640 --> 01:22:16,700 So if we had this for the following nuclear reaction, 1811 01:22:16,700 --> 01:22:18,560 now it's getting crazy. 1812 01:22:18,560 --> 01:22:21,060 We can model that, too. 1813 01:22:21,060 --> 01:22:21,670 Let's do it. 1814 01:22:21,670 --> 01:22:23,462 OK, I was going to say no, but let's do it. 1815 01:22:26,990 --> 01:22:29,210 We can-- so what I'm trying to do here is 1816 01:22:29,210 --> 01:22:31,190 give you the mathematical tools to model 1817 01:22:31,190 --> 01:22:33,290 any real physical situation. 1818 01:22:33,290 --> 01:22:35,540 Usually in this class like when I took it, 1819 01:22:35,540 --> 01:22:37,010 the discussion stopped here and we 1820 01:22:37,010 --> 01:22:39,950 got to start looking at different graphs of secular 1821 01:22:39,950 --> 01:22:42,920 versus transient equilibrium like in the reading. 1822 01:22:42,920 --> 01:22:44,990 But I want you guys to have the intuition to say, 1823 01:22:44,990 --> 01:22:47,960 all right, let's take any crazy decay diagram, right? 1824 01:22:47,960 --> 01:22:52,340 And N3 becomes N1, let's just go nuts. 1825 01:22:52,340 --> 01:22:54,140 How do we set up the differential equations 1826 01:22:54,140 --> 01:22:58,860 for this assuming that computers can solve them? 1827 01:22:58,860 --> 01:23:02,490 In every case-- where's my long pointer? 1828 01:23:02,490 --> 01:23:04,440 Go back to this here. 1829 01:23:04,440 --> 01:23:07,440 The change is the creation minus the destruction. 1830 01:23:07,440 --> 01:23:09,240 So what are all the creation sources 1831 01:23:09,240 --> 01:23:10,778 in our new scenario for N0? 1832 01:23:18,110 --> 01:23:20,010 Well I pose you a simpler question. 1833 01:23:20,010 --> 01:23:23,340 If there is no isotope N2, can you create any N0? 1834 01:23:25,950 --> 01:23:26,940 No. 1835 01:23:26,940 --> 01:23:30,540 Because the only way to make N0 is to start with N2. 1836 01:23:30,540 --> 01:23:36,720 So we know its creation term is going to have an N2 in it. 1837 01:23:36,720 --> 01:23:39,312 What else does it depend on? 1838 01:23:39,312 --> 01:23:40,858 AUDIENCE: Cross-section. 1839 01:23:40,858 --> 01:23:43,150 MICHAEL SHORT: I heard both of the pieces of the answer 1840 01:23:43,150 --> 01:23:44,840 correct at the same time. 1841 01:23:44,840 --> 01:23:47,650 It depends on the flux of neutrons, 1842 01:23:47,650 --> 01:23:50,680 and it depends on the cross-section. 1843 01:23:50,680 --> 01:23:52,860 This macroscopic cross-section right here. 1844 01:23:55,716 --> 01:23:57,144 OK? 1845 01:23:57,144 --> 01:23:58,088 Or I'm sorry, no, no. 1846 01:23:58,088 --> 01:23:59,880 It depends on the microscopic cross-section 1847 01:23:59,880 --> 01:24:02,890 because we have an amount of N2. 1848 01:24:02,890 --> 01:24:07,190 But it does depend on how many neutrons you throw at it 1849 01:24:07,190 --> 01:24:10,770 and what is the probability of each of those neutrons 1850 01:24:10,770 --> 01:24:12,910 make some N0. 1851 01:24:12,910 --> 01:24:16,390 So what we've got right here is a reaction rate. 1852 01:24:19,350 --> 01:24:23,050 So who remembers from the like second or third lecture, 1853 01:24:23,050 --> 01:24:25,270 we said a reaction rate can be expressed 1854 01:24:25,270 --> 01:24:29,350 like macroscopic cross-section times of flux, 1855 01:24:29,350 --> 01:24:32,080 which is the same as a microscopic cross-section times 1856 01:24:32,080 --> 01:24:35,960 number density times flux? 1857 01:24:35,960 --> 01:24:38,782 But this is better known as a macroscopic cross-section. 1858 01:24:41,497 --> 01:24:43,830 Remember, I kind of showed this to you very briefly when 1859 01:24:43,830 --> 01:24:45,205 we talk about cross-sections, now 1860 01:24:45,205 --> 01:24:47,108 is where we actually use them. 1861 01:24:47,108 --> 01:24:48,900 So the cross-section's like the probability 1862 01:24:48,900 --> 01:24:54,090 that a neutron coming in to atom N is going to react with it. 1863 01:24:54,090 --> 01:24:58,500 The macroscopic cross-section in units of, let's say, 1864 01:24:58,500 --> 01:25:02,342 1 over centimeters is the total-- 1865 01:25:02,342 --> 01:25:04,800 let's say the total probability accounting for how many are 1866 01:25:04,800 --> 01:25:10,560 there, and the flux is in neutrons per centimeter 1867 01:25:10,560 --> 01:25:12,630 squared per second. 1868 01:25:12,630 --> 01:25:16,650 Combine these together, and you get a reaction rate 1869 01:25:16,650 --> 01:25:22,890 in atoms per centimeter cubed per second, 1870 01:25:22,890 --> 01:25:25,545 a volumetric reaction rate. 1871 01:25:25,545 --> 01:25:26,210 There we go. 1872 01:25:28,810 --> 01:25:31,960 So N1 can be created. 1873 01:25:31,960 --> 01:25:36,430 Let's give this cross-section a designation from N2 to N0. 1874 01:25:36,430 --> 01:25:41,240 So let's call it cross-section 2,0. 1875 01:25:41,240 --> 01:25:43,680 How can N not be destroyed? 1876 01:25:48,452 --> 01:25:52,390 I'll give you a hint, it looks very similar to this term. 1877 01:25:52,390 --> 01:25:53,952 Anyone want to take a guess? 1878 01:25:58,762 --> 01:25:59,724 Yeah? 1879 01:25:59,724 --> 01:26:01,952 AUDIENCE: Could it undergo fission? 1880 01:26:01,952 --> 01:26:03,660 MICHAEL SHORT: We haven't specified that. 1881 01:26:03,660 --> 01:26:06,560 I'm going to cut the craziness at there, I think. 1882 01:26:06,560 --> 01:26:08,310 But just look at the reactions right here. 1883 01:26:08,310 --> 01:26:11,280 N0 can absorb a neutron and become N1. 1884 01:26:11,280 --> 01:26:13,144 So how do we mathematically write that? 1885 01:26:16,126 --> 01:26:18,818 AUDIENCE: Minus the cross-section N-- 1886 01:26:18,818 --> 01:26:19,610 MICHAEL SHORT: Yep. 1887 01:26:19,610 --> 01:26:20,870 Minus the cross-section of? 1888 01:26:20,870 --> 01:26:21,950 AUDIENCE: N1. 1889 01:26:21,950 --> 01:26:23,960 MICHAEL SHORT: Let's say 0 going to 1. 1890 01:26:23,960 --> 01:26:25,340 Let's just call it that. 1891 01:26:25,340 --> 01:26:27,550 Times the neutron flux. 1892 01:26:27,550 --> 01:26:28,520 Times what? 1893 01:26:28,520 --> 01:26:30,290 AUDIENCE: Times N0? 1894 01:26:30,290 --> 01:26:33,170 MICHAEL SHORT: Times the amount that's there, N0. 1895 01:26:33,170 --> 01:26:34,610 So this is your destruction term. 1896 01:26:38,440 --> 01:26:41,440 Using this pattern, we can fill in all the remaining terms 1897 01:26:41,440 --> 01:26:43,570 for all the remaining isotopes. 1898 01:26:43,570 --> 01:26:48,166 So what are the creation mechanisms for isotope N1? 1899 01:26:53,402 --> 01:26:54,610 Well, just follow the arrows. 1900 01:26:54,610 --> 01:26:55,568 AUDIENCE: --same term-- 1901 01:26:55,568 --> 01:26:56,485 MICHAEL SHORT: Mm-hmm. 1902 01:26:56,485 --> 01:26:58,320 AUDIENCE: --on the first equation for N-- 1903 01:26:58,320 --> 01:26:59,200 MICHAEL SHORT: Yep. 1904 01:26:59,200 --> 01:27:00,130 There's this one right here. 1905 01:27:00,130 --> 01:27:00,590 We can have-- 1906 01:27:00,590 --> 01:27:01,270 AUDIENCE: --the sign. 1907 01:27:01,270 --> 01:27:03,640 MICHAEL SHORT: But flip the sign because it's creation. 1908 01:27:03,640 --> 01:27:08,500 So sigma 0,1 flux N0. 1909 01:27:08,500 --> 01:27:11,080 And what else can create N1 because we're just 1910 01:27:11,080 --> 01:27:12,520 going crazy today? 1911 01:27:12,520 --> 01:27:16,460 N3 can create N1 because we said so. 1912 01:27:16,460 --> 01:27:19,360 But-- yeah, because we said so. 1913 01:27:19,360 --> 01:27:23,260 So now we'll say also we'll have this cross-section for 3 1914 01:27:23,260 --> 01:27:28,050 turning into 1 times flux times N3. 1915 01:27:28,050 --> 01:27:33,150 Minus the decay of N1 using our activity expression, minus 1916 01:27:33,150 --> 01:27:34,116 what else? 1917 01:27:37,005 --> 01:27:38,463 AUDIENCE: [INAUDIBLE] cross-section 1918 01:27:38,463 --> 01:27:40,463 of the [INAUDIBLE]? 1919 01:27:40,463 --> 01:27:41,880 MICHAEL SHORT: I heard some-- yep, 1920 01:27:41,880 --> 01:27:44,948 that will be the cross-section of N1. 1921 01:27:44,948 --> 01:27:46,990 Let's call it going to some isotope we don't care 1922 01:27:46,990 --> 01:27:52,360 about times the flux times N1. 1923 01:27:52,360 --> 01:27:55,770 So as long as you can draw a like arrow decay 1924 01:27:55,770 --> 01:27:58,380 and destruction production diagram, 1925 01:27:58,380 --> 01:28:00,382 we can put this to math. 1926 01:28:00,382 --> 01:28:01,340 That's the crazy thing. 1927 01:28:01,340 --> 01:28:02,132 Let's finish it up. 1928 01:28:02,132 --> 01:28:03,500 How about N2? 1929 01:28:03,500 --> 01:28:06,080 We know that N1 can decay to N2. 1930 01:28:06,080 --> 01:28:09,960 What are the other production mechanisms for N2? 1931 01:28:09,960 --> 01:28:12,826 Follow the arrows. 1932 01:28:12,826 --> 01:28:14,280 AUDIENCE: [INAUDIBLE] 1933 01:28:14,280 --> 01:28:15,920 MICHAEL SHORT: That's it. 1934 01:28:15,920 --> 01:28:18,170 Because we're not changing anything at this point. 1935 01:28:18,170 --> 01:28:22,904 What are all the destruction mechanisms for N2? 1936 01:28:22,904 --> 01:28:24,880 AUDIENCE: Decay or [INAUDIBLE] 1937 01:28:24,880 --> 01:28:25,740 MICHAEL SHORT: Yep. 1938 01:28:25,740 --> 01:28:28,830 It can decay, it can be absorbed by a neutron 1939 01:28:28,830 --> 01:28:31,326 to become something we don't care about. 1940 01:28:31,326 --> 01:28:33,460 Let's see, let's call it cross-section 1941 01:28:33,460 --> 01:28:41,380 2 null times flux times N2 minus the cross-section 1942 01:28:41,380 --> 01:28:44,130 from 2 to 0, just this term with a minus sign. 1943 01:28:48,567 --> 01:28:50,300 How about N3? 1944 01:28:50,300 --> 01:28:52,396 What are all the ways we can make N3? 1945 01:28:55,702 --> 01:28:57,077 Could you say it a little louder? 1946 01:28:57,077 --> 01:28:58,178 AUDIENCE: Only from decay. 1947 01:28:58,178 --> 01:28:59,470 MICHAEL SHORT: Only from decay. 1948 01:28:59,470 --> 01:29:02,020 Again, just see which arrows are pointing at it. 1949 01:29:02,020 --> 01:29:06,225 And what about the destruction mechanism for N3? 1950 01:29:06,225 --> 01:29:08,030 AUDIENCE: [INAUDIBLE] 1951 01:29:08,030 --> 01:29:09,030 MICHAEL SHORT: Yep. 1952 01:29:09,030 --> 01:29:11,890 So there's some probability it decays, let's say, 1953 01:29:11,890 --> 01:29:19,800 cross-section 3 null times flux times N3 minus this arrow 1954 01:29:19,800 --> 01:29:21,960 going back to N1. 1955 01:29:21,960 --> 01:29:25,210 Running out of space, too many units. 1956 01:29:25,210 --> 01:29:31,450 From 3 to 1 flux N3. 1957 01:29:31,450 --> 01:29:35,530 So the point of accepting the escalation of this problem 1958 01:29:35,530 --> 01:29:37,240 into something crazy is that it doesn't 1959 01:29:37,240 --> 01:29:39,010 matter how crazy it gets. 1960 01:29:39,010 --> 01:29:42,190 As long as you have like an arrow-based diagram or a flow 1961 01:29:42,190 --> 01:29:45,820 chart to say which isotopes become which other isotopes 1962 01:29:45,820 --> 01:29:49,720 by which other means, you can pose and correctly write 1963 01:29:49,720 --> 01:29:52,390 the set of equations that defines them. 1964 01:29:52,390 --> 01:29:55,450 This is when I would bring in MATLAB or Mathematica. 1965 01:29:55,450 --> 01:29:57,080 I could make you do this analytically, 1966 01:29:57,080 --> 01:30:00,090 but this isn't a course 18 class and-- 1967 01:30:00,090 --> 01:30:01,844 yeah, we don't want to go there. 1968 01:30:01,844 --> 01:30:04,060 Cool. 1969 01:30:04,060 --> 01:30:06,240 So I think-- 1970 01:30:06,240 --> 01:30:09,660 I guess it's probably getting towards 10 of 10 of. 1971 01:30:09,660 --> 01:30:11,220 Close enough. 1972 01:30:11,220 --> 01:30:14,790 It's like three of 10 of. 1973 01:30:14,790 --> 01:30:18,910 So I'd like to open it up to any questions because we let this-- 1974 01:30:18,910 --> 01:30:22,240 I let this escalate freely to prove the point that as long 1975 01:30:22,240 --> 01:30:23,680 as you know what decays into what 1976 01:30:23,680 --> 01:30:25,600 or what creates or destroys what, 1977 01:30:25,600 --> 01:30:28,980 you can set up the equations correctly. 1978 01:30:28,980 --> 01:30:31,800 What we'll be doing on Tuesday is graphing this. 1979 01:30:31,800 --> 01:30:34,920 Where we can pose an arbitrarily complex set of equations 1980 01:30:34,920 --> 01:30:38,010 and you can start looking at, well, the change in one 1981 01:30:38,010 --> 01:30:40,130 depends on the amount of the other, 1982 01:30:40,130 --> 01:30:42,900 and you can almost graphically solve this on paper. 1983 01:30:42,900 --> 01:30:45,878 Forget Mathematica in MATLAB. 1984 01:30:45,878 --> 01:30:47,670 If you look at last year's exam, I actually 1985 01:30:47,670 --> 01:30:49,080 posed a more complex set of these 1986 01:30:49,080 --> 01:30:52,030 and said draw the solution. 1987 01:30:52,030 --> 01:30:54,710 And I'm going to-- we're going to show you how to do that. 1988 01:30:54,710 --> 01:30:59,175 But any question on how we formed these? 1989 01:30:59,175 --> 01:31:00,165 Yep? 1990 01:31:00,165 --> 01:31:02,145 AUDIENCE: What is sigma again? 1991 01:31:02,145 --> 01:31:03,640 I'm sorry. 1992 01:31:03,640 --> 01:31:06,400 MICHAEL SHORT: So we just said let's say N3 decays 1993 01:31:06,400 --> 01:31:08,862 to some isotope we don't care about. 1994 01:31:08,862 --> 01:31:10,570 That's how I initially had it, and then I 1995 01:31:10,570 --> 01:31:12,600 think Luke said, well can N2 become N0? 1996 01:31:12,600 --> 01:31:14,260 And I said, yeah, sure. 1997 01:31:14,260 --> 01:31:17,090 So there can be a cross-section for every type of reaction. 1998 01:31:17,090 --> 01:31:20,350 So in reality, you might have any reaction under the sun, 1999 01:31:20,350 --> 01:31:21,220 right? 2000 01:31:21,220 --> 01:31:23,290 One isotope could absorb a neutron and decay 2001 01:31:23,290 --> 01:31:25,600 by like any three or four different mechanisms 2002 01:31:25,600 --> 01:31:27,297 into something else. 2003 01:31:27,297 --> 01:31:28,797 You may have different probabilities 2004 01:31:28,797 --> 01:31:30,288 for each of these. 2005 01:31:34,261 --> 01:31:34,761 Yeah? 2006 01:31:34,761 --> 01:31:40,665 AUDIENCE: Do those decay constants [INAUDIBLE] 2007 01:31:40,665 --> 01:31:42,290 MICHAEL SHORT: The only time I'd expect 2008 01:31:42,290 --> 01:31:44,630 you to find these decay constants is if I told you 2009 01:31:44,630 --> 01:31:46,400 what these isotopes were. 2010 01:31:46,400 --> 01:31:49,190 Those are also listed on the table of nuclides. 2011 01:31:49,190 --> 01:31:52,610 As in they give you the half-life, 2012 01:31:52,610 --> 01:31:54,800 and you know from this half-life relation 2013 01:31:54,800 --> 01:31:57,350 what the decay constant is. 2014 01:31:57,350 --> 01:32:00,243 If I didn't tell you what these isotopes were, 2015 01:32:00,243 --> 01:32:01,910 I would just have you keep these symbols 2016 01:32:01,910 --> 01:32:03,710 as lambda 1 and lambda 2. 2017 01:32:03,710 --> 01:32:06,830 And I might pose a question which will solve graphically 2018 01:32:06,830 --> 01:32:09,110 on Tuesday, like let's say, solve 2019 01:32:09,110 --> 01:32:12,320 this set of equations for lambda 2 2020 01:32:12,320 --> 01:32:14,203 is much greater than lambda 1. 2021 01:32:14,203 --> 01:32:15,620 I don't care what the numbers are, 2022 01:32:15,620 --> 01:32:18,700 let's just look at that general relation. 2023 01:32:18,700 --> 01:32:21,430 And all the graphs for that sort of situation 2024 01:32:21,430 --> 01:32:26,140 will follow the same pattern. 2025 01:32:26,140 --> 01:32:27,640 Cool. 2026 01:32:27,640 --> 01:32:29,860 Any other questions on how we constructed this set 2027 01:32:29,860 --> 01:32:32,190 of differential equations? 2028 01:32:32,190 --> 01:32:34,820 And know that I'll never ask you to solve them 2029 01:32:34,820 --> 01:32:38,020 numerically or analytically. 2030 01:32:38,020 --> 01:32:38,520 Yeah. 2031 01:32:38,520 --> 01:32:43,060 That's why we have computers and this is the future. 2032 01:32:43,060 --> 01:32:45,492 These I might expect you to know how to derive, 2033 01:32:45,492 --> 01:32:47,117 but this is the simplest possible case. 2034 01:32:52,254 --> 01:32:54,445 All right, if there's no questions, 2035 01:32:54,445 --> 01:32:56,070 then let's take another 10-minute break 2036 01:32:56,070 --> 01:33:00,100 and I'll be here for recitation to go over whatever problems 2037 01:33:00,100 --> 01:33:02,250 you guys would like to do.