1 00:00:00,890 --> 00:00:03,260 The following content is provided under a Creative 2 00:00:03,260 --> 00:00:04,650 Commons license. 3 00:00:04,650 --> 00:00:06,860 Your support will help MIT OpenCourseWare 4 00:00:06,860 --> 00:00:10,950 continue to offer high-quality educational resources for free. 5 00:00:10,950 --> 00:00:13,490 To make a donation, or to view additional materials 6 00:00:13,490 --> 00:00:17,450 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:17,450 --> 00:00:18,350 at ocw.mit.edu. 8 00:00:21,872 --> 00:00:24,080 MICHAEL SHORT: So I'd like to do a quick two or three 9 00:00:24,080 --> 00:00:25,872 minute review of the stuff we did last time 10 00:00:25,872 --> 00:00:27,578 to get you back into where we were. 11 00:00:27,578 --> 00:00:29,120 We were talking about different types 12 00:00:29,120 --> 00:00:30,920 of technologies that use the stuff you'll 13 00:00:30,920 --> 00:00:33,710 be learning in 22.01. 14 00:00:33,710 --> 00:00:38,590 Everything ranging from nuclear reactors for producing power, 15 00:00:38,590 --> 00:00:42,130 and the Cherenkov radiation that tells you-- well, 16 00:00:42,130 --> 00:00:43,990 that the beta particles are moving faster 17 00:00:43,990 --> 00:00:45,610 than the speed of light in water. 18 00:00:45,610 --> 00:00:46,790 It's a neat thing, too. 19 00:00:46,790 --> 00:00:48,280 I've actually been to this reactor 20 00:00:48,280 --> 00:00:50,200 at Idaho, to the spent fuel pool. 21 00:00:50,200 --> 00:00:53,740 Even the spent fuel, once it comes out of the reactor, 22 00:00:53,740 --> 00:00:55,270 is still giving off betas and still 23 00:00:55,270 --> 00:00:56,890 giving off Cherenkov radiation. 24 00:00:56,890 --> 00:00:59,140 And you can tell how long it's been out of the reactor 25 00:00:59,140 --> 00:01:02,220 by how dim the glow gets, which is pretty cool. 26 00:01:02,220 --> 00:01:04,720 So you can tell how old a fuel assembly is by the blue glow. 27 00:01:04,720 --> 00:01:06,737 So remember, I told you guys, if someone says, 28 00:01:06,737 --> 00:01:08,320 oh, you're nuclear, do you glow green? 29 00:01:08,320 --> 00:01:10,300 You can be like, no, it's blue. 30 00:01:10,300 --> 00:01:12,670 That's the right way of things. 31 00:01:12,670 --> 00:01:14,860 We talked about fusion energy and got 32 00:01:14,860 --> 00:01:16,780 into some of the nuclear reactions involved 33 00:01:16,780 --> 00:01:17,590 in fusion energy. 34 00:01:17,590 --> 00:01:20,320 And I'll be teaching you more about these today. 35 00:01:20,320 --> 00:01:22,000 Why fission and fusion work, it all 36 00:01:22,000 --> 00:01:24,370 has to do with the stability and binding 37 00:01:24,370 --> 00:01:25,750 energy of the nuclei involved. 38 00:01:25,750 --> 00:01:27,820 And that'll be the main topic for today, 39 00:01:27,820 --> 00:01:32,440 is excess mass, binding energy, nuclear stability. 40 00:01:32,440 --> 00:01:34,720 We looked at medical uses of radiation, 41 00:01:34,720 --> 00:01:37,420 from implanting radioactive seeds called 42 00:01:37,420 --> 00:01:41,800 brachytherapy seeds in certain places to destroy tumors, 43 00:01:41,800 --> 00:01:47,500 to imaging, to X-ray therapy, to proton therapy using 44 00:01:47,500 --> 00:01:51,460 accelerators, or cyclotrons, to accelerate protons and send 45 00:01:51,460 --> 00:01:52,920 them into people. 46 00:01:52,920 --> 00:01:55,210 If you remember, last time we ran the SRIM code 47 00:01:55,210 --> 00:01:57,460 of the stopping range of ions and matter, 48 00:01:57,460 --> 00:01:59,050 and actually showed that protons all 49 00:01:59,050 --> 00:02:01,660 stop at a certain distance in tissue, 50 00:02:01,660 --> 00:02:06,050 depending on their energy and what you're sending them into. 51 00:02:06,050 --> 00:02:09,056 Let's see-- we talked about brachytherapy. 52 00:02:09,056 --> 00:02:10,639 We talked about radiotracers, and this 53 00:02:10,639 --> 00:02:13,014 is going to be one of the other main topics for today, is 54 00:02:13,014 --> 00:02:15,890 these decay diagrams, and figuring out not only 55 00:02:15,890 --> 00:02:18,650 what products are made, but what energy levels do 56 00:02:18,650 --> 00:02:20,900 the nuclei have, and how do you calculate 57 00:02:20,900 --> 00:02:22,550 the energy of the radioactive decay 58 00:02:22,550 --> 00:02:26,150 products and the recoil nuclei, which do take away 59 00:02:26,150 --> 00:02:28,730 some of the energy. 60 00:02:28,730 --> 00:02:30,310 We talked about one way to get rich. 61 00:02:30,310 --> 00:02:32,060 If you guys can figure out one of the ways 62 00:02:32,060 --> 00:02:34,640 to solve this moly-99 shortage. 63 00:02:34,640 --> 00:02:36,440 Right now, it's mostly made in reactors. 64 00:02:36,440 --> 00:02:38,390 The future has got to be accelerators 65 00:02:38,390 --> 00:02:40,450 or some sort of switchable device 66 00:02:40,450 --> 00:02:42,680 where you don't need to construct a reactor 67 00:02:42,680 --> 00:02:45,170 to make these medical isotopes for imaging, and tracers, 68 00:02:45,170 --> 00:02:46,273 and such. 69 00:02:46,273 --> 00:02:47,690 And finally, we got all the way up 70 00:02:47,690 --> 00:02:51,980 to space applications, shielding, crazy, different 71 00:02:51,980 --> 00:02:54,770 types of shielding, like electromagnetic shielding, 72 00:02:54,770 --> 00:02:57,920 to protect from high energy protons, all the way 73 00:02:57,920 --> 00:03:01,400 to radiothermal generators, which use alpha decay 74 00:03:01,400 --> 00:03:03,920 to produce a constant amount of energy 75 00:03:03,920 --> 00:03:08,210 on the order of one to 200 watts for like 100 years. 76 00:03:08,210 --> 00:03:09,943 And finally, to a different configuration 77 00:03:09,943 --> 00:03:11,360 of nuclear reactors, where you can 78 00:03:11,360 --> 00:03:15,960 design them to produce thrust, not necessarily electricity. 79 00:03:15,960 --> 00:03:18,558 And that's where we stopped on Friday. 80 00:03:18,558 --> 00:03:20,600 So let's move on to one of the things I'd alluded 81 00:03:20,600 --> 00:03:23,780 to earlier, which is semiconductor processing. 82 00:03:23,780 --> 00:03:26,450 This is actually a diagram from the MIT reactor, 83 00:03:26,450 --> 00:03:28,520 because we have this beam port here. 84 00:03:28,520 --> 00:03:30,260 Has anyone got to see the silicon beam 85 00:03:30,260 --> 00:03:32,760 port at the MIT reactor? 86 00:03:32,760 --> 00:03:35,135 Oh, seven, eight-- OK, about half of you. 87 00:03:35,135 --> 00:03:36,760 For those who haven't, who here has not 88 00:03:36,760 --> 00:03:39,520 had a nuclear reactor tour? 89 00:03:39,520 --> 00:03:40,060 Oh man. 90 00:03:40,060 --> 00:03:40,807 OK. 91 00:03:40,807 --> 00:03:42,640 Well, you'll get one when you get to control 92 00:03:42,640 --> 00:03:44,367 the thing in early October. 93 00:03:44,367 --> 00:03:46,450 So you actually get to go down to the control room 94 00:03:46,450 --> 00:03:48,040 and see the rest of what's going on. 95 00:03:48,040 --> 00:03:50,050 So make sure to ask them, show us the beam port 96 00:03:50,050 --> 00:03:52,120 for silicon ingots. 97 00:03:52,120 --> 00:03:55,420 And I think I already told you the story about the poor UROP 98 00:03:55,420 --> 00:03:57,340 who held the ingots up to their chest, 99 00:03:57,340 --> 00:04:00,358 getting about 10 months of dose, which is not dangerous, 100 00:04:00,358 --> 00:04:01,900 but it meant that for 10 months, they 101 00:04:01,900 --> 00:04:03,370 could have no radiation exposure, 102 00:04:03,370 --> 00:04:05,490 and they had to answer the phone. 103 00:04:05,490 --> 00:04:08,750 So that's how we ensure safety around here. 104 00:04:08,750 --> 00:04:09,835 There's other ones that-- 105 00:04:09,835 --> 00:04:11,210 applications that you're probably 106 00:04:11,210 --> 00:04:13,220 carrying around in your pocket. 107 00:04:13,220 --> 00:04:14,630 You can use the fact that charged 108 00:04:14,630 --> 00:04:17,570 particles have very finite ranges in matter 109 00:04:17,570 --> 00:04:20,760 to separate little bits of that matter from other things. 110 00:04:20,760 --> 00:04:23,090 So this is actually how single-crystal sapphires 111 00:04:23,090 --> 00:04:26,900 can be separated in little slivers for protective phone 112 00:04:26,900 --> 00:04:29,180 covers, because sapphire is one of the most-- 113 00:04:29,180 --> 00:04:31,430 the hardest, or the most scratch-resistant materials 114 00:04:31,430 --> 00:04:33,500 there is. 115 00:04:33,500 --> 00:04:36,350 Single-crystal sapphire is exceptionally strong, 116 00:04:36,350 --> 00:04:39,660 and optically transparent, and expensive. 117 00:04:39,660 --> 00:04:41,780 I know that because on one of our experiments, 118 00:04:41,780 --> 00:04:46,190 we use a single-crystal sapphire window to see into reactor 119 00:04:46,190 --> 00:04:49,790 conditions at like 150 atmospheres, and 350 120 00:04:49,790 --> 00:04:52,550 degrees Celsius, and pretty corrosive chemistry. 121 00:04:52,550 --> 00:04:54,560 So you want to use as little as possible. 122 00:04:54,560 --> 00:04:56,840 So you can use a big, expensive accelerator 123 00:04:56,840 --> 00:04:58,850 to limit the amount of sapphire that you use. 124 00:04:58,850 --> 00:05:01,070 And this is actually done here in Boston. 125 00:05:01,070 --> 00:05:05,060 There's a facility not far from here that uses an accelerator. 126 00:05:05,060 --> 00:05:08,120 And this is their super detailed diagram 127 00:05:08,120 --> 00:05:10,440 of what the radiation looks like-- 128 00:05:10,440 --> 00:05:11,970 yeah, whatever. 129 00:05:11,970 --> 00:05:15,260 But what they do is they take-- they accelerate protons. 130 00:05:15,260 --> 00:05:17,090 They send them through bending magnets 131 00:05:17,090 --> 00:05:19,070 to steer that beam path. 132 00:05:19,070 --> 00:05:21,590 And then they send them into a large piece 133 00:05:21,590 --> 00:05:23,690 of single-crystal sapphire, which is exceptionally 134 00:05:23,690 --> 00:05:25,130 expensive to make. 135 00:05:25,130 --> 00:05:27,530 And they can actually lift off a thin sliver 136 00:05:27,530 --> 00:05:29,480 with micron precision. 137 00:05:29,480 --> 00:05:31,100 The reason for that is the same reason 138 00:05:31,100 --> 00:05:33,050 that we showed with that SRIM code. 139 00:05:33,050 --> 00:05:36,140 If you have this exact energy of protons 140 00:05:36,140 --> 00:05:38,120 going into well-known matter, you 141 00:05:38,120 --> 00:05:40,930 know what its range is going to be with an uncertainty 142 00:05:40,930 --> 00:05:42,740 or so of about a micron. 143 00:05:42,740 --> 00:05:46,070 So you can have things that come out thin, uniformly 144 00:05:46,070 --> 00:05:49,180 thick, and smooth, right away. 145 00:05:49,180 --> 00:05:51,340 There's some other really wacky products-- 146 00:05:51,340 --> 00:05:56,020 like has anyone heard of these betavoltaic batteries? 147 00:05:56,020 --> 00:05:56,990 No? 148 00:05:56,990 --> 00:06:01,040 They rely on beta decay or the direct capture and electricity 149 00:06:01,040 --> 00:06:03,110 generation from a radiation source 150 00:06:03,110 --> 00:06:04,730 like radioactive tritium. 151 00:06:04,730 --> 00:06:08,840 So in this little chip is about 2 curies worth of tritium. 152 00:06:08,840 --> 00:06:10,430 You guys will learn in about a week, 153 00:06:10,430 --> 00:06:13,370 how to go from activity in curies to mass, 154 00:06:13,370 --> 00:06:15,120 or something like that. 155 00:06:15,120 --> 00:06:16,550 And so this chip actually contains 156 00:06:16,550 --> 00:06:18,620 a lot of radioactive tritium that 157 00:06:18,620 --> 00:06:20,770 directly creates electricity. 158 00:06:20,770 --> 00:06:22,520 So you can hook into that chip and produce 159 00:06:22,520 --> 00:06:24,800 nanowatts for years. 160 00:06:24,800 --> 00:06:27,170 So it's one of these batteries that lasts-- well, 161 00:06:27,170 --> 00:06:31,280 as long as a couple half-lives of the isotope that's inside. 162 00:06:31,280 --> 00:06:32,720 Now there's a trade-off here. 163 00:06:32,720 --> 00:06:35,270 The shorter the half-life, the more active 164 00:06:35,270 --> 00:06:38,000 a given isotope will be for the same number of atoms, 165 00:06:38,000 --> 00:06:39,830 but the shorter it will last. 166 00:06:39,830 --> 00:06:43,700 So you can have higher power for lower time, or lower power, 167 00:06:43,700 --> 00:06:44,210 higher time. 168 00:06:44,210 --> 00:06:46,250 It's the classic energy trade-off-- 169 00:06:46,250 --> 00:06:50,440 works the same way with irradiation. 170 00:06:50,440 --> 00:06:52,240 And so now I wanted to get into some 171 00:06:52,240 --> 00:06:54,250 of the more technical stuff, where 172 00:06:54,250 --> 00:06:56,920 we'll be talking about nuclear mass and stability. 173 00:06:56,920 --> 00:07:01,240 And this is where the nuclear stuff really begins in 22.01. 174 00:07:01,240 --> 00:07:04,100 First, I want to make sure that we all agree on notation. 175 00:07:04,100 --> 00:07:07,410 So I'll be writing isotopes in this sort of fashion, 176 00:07:07,410 --> 00:07:09,970 where we refer to A as the atomic mass, or just 177 00:07:09,970 --> 00:07:12,040 the total number of nucleons. 178 00:07:12,040 --> 00:07:14,680 This is not the exact mass of a nucleus. 179 00:07:14,680 --> 00:07:17,830 It just refers to the sum of the protons and neutrons 180 00:07:17,830 --> 00:07:19,123 in the nucleus itself. 181 00:07:19,123 --> 00:07:21,040 And a lot of what we'll be talking about today 182 00:07:21,040 --> 00:07:25,300 is the difference between this nice integer mass number, 183 00:07:25,300 --> 00:07:27,100 and the actual mass of the nucleus, 184 00:07:27,100 --> 00:07:29,950 and that difference is given by the binding energy, 185 00:07:29,950 --> 00:07:33,170 or the excess mass, which are directly related. 186 00:07:33,170 --> 00:07:35,420 Z is just referred to as the atomic number, 187 00:07:35,420 --> 00:07:36,550 or the number of protons. 188 00:07:36,550 --> 00:07:38,450 It's what makes the element what it, 189 00:07:38,450 --> 00:07:41,510 which makes the name kind of redundant. 190 00:07:41,510 --> 00:07:43,760 But it's-- humans learned by association. 191 00:07:43,760 --> 00:07:46,430 It's easier to remember element names or symbols 192 00:07:46,430 --> 00:07:50,320 than which element is which just by the number of protons. 193 00:07:50,320 --> 00:07:52,820 So a lot of times we'll use the name, or at least the symbol 194 00:07:52,820 --> 00:07:54,280 just so we know what's going on. 195 00:07:54,280 --> 00:07:57,950 And anything up here is some sort of a charge. 196 00:07:57,950 --> 00:08:01,520 I do want to warn you guys of the dreaded multiple symbol 197 00:08:01,520 --> 00:08:03,860 use or multiple use of symbols. 198 00:08:03,860 --> 00:08:06,760 I'll try to stick for a lower case q-- 199 00:08:06,760 --> 00:08:08,270 will be charged. 200 00:08:08,270 --> 00:08:10,490 And uppercase Q is going to refer 201 00:08:10,490 --> 00:08:13,190 to the Q value or the energy consumed or released 202 00:08:13,190 --> 00:08:14,420 by a nuclear reaction. 203 00:08:14,420 --> 00:08:16,310 So they're both Q's but we're going to keep 204 00:08:16,310 --> 00:08:17,882 one upper and lower case. 205 00:08:17,882 --> 00:08:19,340 And like we mentioned before, let's 206 00:08:19,340 --> 00:08:21,920 say we were to write a typical nuclear reaction, 207 00:08:21,920 --> 00:08:25,520 like the capture of neutrons by boron 208 00:08:25,520 --> 00:08:29,180 to produce lithium-7, helium-4, better 209 00:08:29,180 --> 00:08:33,200 known as an alpha particle, and some amount of energy. 210 00:08:33,200 --> 00:08:36,440 There's two places where we actually use this reaction. 211 00:08:36,440 --> 00:08:38,960 One of them is as control rods. 212 00:08:38,960 --> 00:08:41,960 A lot of reactors use boron for carbide, 213 00:08:41,960 --> 00:08:46,910 or this compound B4C, which is conveniently solid, fairly 214 00:08:46,910 --> 00:08:50,450 dense, and contains a whole lot of boron in one place. 215 00:08:50,450 --> 00:08:52,850 Specifically, enriched in boron-10, 216 00:08:52,850 --> 00:08:55,910 because boron-10 has a high cross section, or probability, 217 00:08:55,910 --> 00:08:57,308 for neutron capture. 218 00:08:57,308 --> 00:08:58,850 And the other one is in what's called 219 00:08:58,850 --> 00:09:01,120 boron neutron capture therapy. 220 00:09:01,120 --> 00:09:04,003 Have I discussed this with you guys already, BNCT? 221 00:09:04,003 --> 00:09:05,420 Good, because that's what we'll be 222 00:09:05,420 --> 00:09:07,250 talking about for a few slides. 223 00:09:07,250 --> 00:09:09,980 And to write this whole reaction is the same thing 224 00:09:09,980 --> 00:09:12,330 as writing this shorthand nuclear reaction. 225 00:09:12,330 --> 00:09:14,412 So this is often how you see them in the reading, 226 00:09:14,412 --> 00:09:16,370 and in papers, because it's shorter to do that. 227 00:09:16,370 --> 00:09:19,187 But it's the exact same thing. 228 00:09:19,187 --> 00:09:21,270 So I have a couple of questions for you guys then. 229 00:09:21,270 --> 00:09:23,870 I have this extra Q here. 230 00:09:23,870 --> 00:09:26,210 Where does that Q actually go? 231 00:09:26,210 --> 00:09:29,420 So let's say boron and neutron absorb, 232 00:09:29,420 --> 00:09:32,660 it produces two nuclei with different binding energies. 233 00:09:32,660 --> 00:09:34,670 What happens to the excess energy 234 00:09:34,670 --> 00:09:38,260 created from the conversion of mass to energy? 235 00:09:38,260 --> 00:09:38,840 Yeah, Alex? 236 00:09:38,840 --> 00:09:39,910 AUDIENCE: That could be heat. 237 00:09:39,910 --> 00:09:40,640 MICHAEL SHORT: Yep. 238 00:09:40,640 --> 00:09:41,973 And heat, and more specifically? 239 00:09:41,973 --> 00:09:43,450 AUDIENCE: Kinetic energy. 240 00:09:43,450 --> 00:09:47,027 MICHAEL SHORT: Kinetic energy of the radiation released. 241 00:09:47,027 --> 00:09:48,610 And so that kinetic energy is actually 242 00:09:48,610 --> 00:09:53,350 used to our benefit in BNCT, or Boron Neutron Capture Therapy. 243 00:09:53,350 --> 00:09:54,670 The way this works-- 244 00:09:54,670 --> 00:09:56,440 once I hit play-- 245 00:09:56,440 --> 00:10:00,100 is you can either-- you can use any sort of source of neutrons, 246 00:10:00,100 --> 00:10:02,860 either a reactor or an accelerator, 247 00:10:02,860 --> 00:10:05,267 through a lower complex chain of events, like this. 248 00:10:05,267 --> 00:10:07,600 In this case, an accelerator-- so you don't need a whole 249 00:10:07,600 --> 00:10:08,680 reactor-- 250 00:10:08,680 --> 00:10:11,590 fires a beam of high-energy protons 251 00:10:11,590 --> 00:10:13,475 into a beryllium target. 252 00:10:13,475 --> 00:10:15,310 Does that sound fairly familiar? 253 00:10:15,310 --> 00:10:17,980 Firing something at beryllium, releasing neutrons, 254 00:10:17,980 --> 00:10:19,690 like what Chadwick was doing? 255 00:10:19,690 --> 00:10:22,000 Except he was firing alpha particles into it. 256 00:10:22,000 --> 00:10:23,890 This releases neutrons. 257 00:10:23,890 --> 00:10:27,040 What they don't have labeled here is slowing down stuff, 258 00:10:27,040 --> 00:10:29,470 or probably hydrogenous material, 259 00:10:29,470 --> 00:10:32,890 so that the neutrons slow down to a lower energy. 260 00:10:32,890 --> 00:10:35,950 And their probability of capture increases 261 00:10:35,950 --> 00:10:37,530 or their cross section increases. 262 00:10:37,530 --> 00:10:39,447 And if you don't know what a cross section is, 263 00:10:39,447 --> 00:10:41,760 the definition is two slides away. 264 00:10:41,760 --> 00:10:45,280 And the idea here is that these neutrons then enter the brain 265 00:10:45,280 --> 00:10:47,650 or wherever the tumor happens to be. 266 00:10:47,650 --> 00:10:51,130 And we rely on the fact that tumor cells consume resources 267 00:10:51,130 --> 00:10:54,370 much faster than regular cells, especially neurons, which 268 00:10:54,370 --> 00:10:57,170 after you're about five, don't tend to grow very much. 269 00:10:57,170 --> 00:11:00,340 So it's all downhill by the time you enter kindergarten. 270 00:11:00,340 --> 00:11:04,390 And we use that to our advantage so that the neutrons coming in 271 00:11:04,390 --> 00:11:06,850 will hit the cancer cells, which will preferentially 272 00:11:06,850 --> 00:11:10,120 uptake the borated compounds, leaving most 273 00:11:10,120 --> 00:11:11,470 of the normal cells intact. 274 00:11:11,470 --> 00:11:14,200 And the difference in dose can be a factor of 5 275 00:11:14,200 --> 00:11:15,760 or a factor of 10. 276 00:11:15,760 --> 00:11:18,370 So that the cancer gets fried while doing as little damage 277 00:11:18,370 --> 00:11:21,250 as possible to the remaining brain cells, of which we 278 00:11:21,250 --> 00:11:23,320 have fewer and fewer every day. 279 00:11:23,320 --> 00:11:24,910 So I say statistically speaking you 280 00:11:24,910 --> 00:11:26,440 guys are probably smarter than me 281 00:11:26,440 --> 00:11:28,670 if we go by number of neurons in your brain, 282 00:11:28,670 --> 00:11:31,630 because I think I'm the oldest person in the room. 283 00:11:31,630 --> 00:11:35,200 And so now we can start to explain, how does BNCT work, 284 00:11:35,200 --> 00:11:37,900 and why did we make the choices that we did? 285 00:11:37,900 --> 00:11:41,350 For example, they use 30 MeV protons in order 286 00:11:41,350 --> 00:11:43,198 to induce these neutrons. 287 00:11:43,198 --> 00:11:45,740 So we have a nuclear reaction that looks something like this. 288 00:11:45,740 --> 00:11:50,860 We start off with beryllium-9 plus a proton-- 289 00:11:50,860 --> 00:11:52,450 let's just call it hydrogen to stick 290 00:11:52,450 --> 00:11:54,520 with our normal notation-- 291 00:11:54,520 --> 00:11:58,540 and becomes-- well, can someone help me balance this reaction? 292 00:11:58,540 --> 00:12:01,790 We know we get a neutron. 293 00:12:01,790 --> 00:12:02,975 What else is left? 294 00:12:02,975 --> 00:12:06,650 So Monica, what would you say? 295 00:12:06,650 --> 00:12:07,646 AUDIENCE: Let's see-- 296 00:12:13,930 --> 00:12:16,430 MICHAEL SHORT: Even just say number of protons and neutrons, 297 00:12:16,430 --> 00:12:18,040 and we'll figure out the symbol later. 298 00:12:18,040 --> 00:12:20,648 AUDIENCE: Number of protons should be-- 299 00:12:20,648 --> 00:12:22,190 MICHAEL SHORT: Sorry, oh, that's a 4. 300 00:12:22,190 --> 00:12:25,718 AUDIENCE: The number of protons should be five. 301 00:12:25,718 --> 00:12:26,510 MICHAEL SHORT: Yep. 302 00:12:26,510 --> 00:12:30,420 Five protons, which means it's boron. 303 00:12:30,420 --> 00:12:32,578 And number of neutrons in the nucleus? 304 00:12:32,578 --> 00:12:33,120 Someone else? 305 00:12:35,917 --> 00:12:36,417 Yeah? 306 00:12:36,417 --> 00:12:37,437 AUDIENCE: Nine. 307 00:12:37,437 --> 00:12:38,270 MICHAEL SHORT: Nine. 308 00:12:38,270 --> 00:12:41,450 So we have boron-9. 309 00:12:41,450 --> 00:12:44,330 Not a stable isotope of boron, but it doesn't really matter, 310 00:12:44,330 --> 00:12:47,960 because boron-9 almost immediately decays into 311 00:12:47,960 --> 00:12:52,310 an alpha, and an alpha, and a hydrogen. 312 00:12:52,310 --> 00:12:54,628 But this nuclear reaction right here 313 00:12:54,628 --> 00:12:56,420 is what we'll be studying for a little bit. 314 00:12:56,420 --> 00:13:00,830 And there'll also be some amount of energy. 315 00:13:00,830 --> 00:13:04,490 And this Q can actually be positive or negative. 316 00:13:04,490 --> 00:13:06,710 No one said there had to be energy released 317 00:13:06,710 --> 00:13:09,450 in a nuclear reaction, because in this case, 318 00:13:09,450 --> 00:13:18,540 we actually start off with 30 MeV protons and roughly zero 319 00:13:18,540 --> 00:13:19,998 MeV beryllium. 320 00:13:19,998 --> 00:13:21,540 If you want to get really exact, it's 321 00:13:21,540 --> 00:13:25,050 on the order of about 0.01 eV, which 322 00:13:25,050 --> 00:13:27,810 is why we neglect the kinetic energy of beryllium 323 00:13:27,810 --> 00:13:29,870 at room temperature. 324 00:13:29,870 --> 00:13:31,960 There are other reactions that when 325 00:13:31,960 --> 00:13:34,150 you fire a proton into them will produce 326 00:13:34,150 --> 00:13:36,547 neutrons, such as the absorption of lithium. 327 00:13:36,547 --> 00:13:38,380 But can anyone think of why we'd want to use 328 00:13:38,380 --> 00:13:39,880 beryllium instead of lithium? 329 00:13:46,895 --> 00:13:48,020 Kristin, what do you think? 330 00:13:48,020 --> 00:13:50,340 What could be a bad thing about using lithium? 331 00:13:53,140 --> 00:13:54,984 You ever throw in water? 332 00:13:54,984 --> 00:13:55,880 AUDIENCE: No. 333 00:13:55,880 --> 00:13:56,630 MICHAEL SHORT: OK. 334 00:13:56,630 --> 00:13:58,088 Then I should show you what happens 335 00:13:58,088 --> 00:14:00,110 when you throw it in water. 336 00:14:00,110 --> 00:14:01,850 There's a few bad things about lithium. 337 00:14:01,850 --> 00:14:04,400 It does this when you throw it in water. 338 00:14:04,400 --> 00:14:06,170 It's one of the alkali metals. 339 00:14:06,170 --> 00:14:08,540 It's got an awfully low melting point. 340 00:14:08,540 --> 00:14:10,910 It reacts with oxygen to produce an oxide almost 341 00:14:10,910 --> 00:14:11,880 instantaneously. 342 00:14:11,880 --> 00:14:13,760 So if you ever take a lithium battery apart, 343 00:14:13,760 --> 00:14:16,700 which you shouldn't, but if you watch the video of somebody 344 00:14:16,700 --> 00:14:19,340 else doing it, you'll see that the lithium foil turns black 345 00:14:19,340 --> 00:14:20,570 almost instantly. 346 00:14:20,570 --> 00:14:22,550 It also has a pretty poor thermal conductivity 347 00:14:22,550 --> 00:14:25,610 and doesn't hold that structural integrity when it melts. 348 00:14:25,610 --> 00:14:28,518 So it's not that good of a target to use. 349 00:14:28,518 --> 00:14:30,560 Beryllium's pretty cool in that it's the lightest 350 00:14:30,560 --> 00:14:32,275 structural material there is. 351 00:14:32,275 --> 00:14:33,650 Folks tend to make satellites out 352 00:14:33,650 --> 00:14:35,690 of it, because it costs a lot of money 353 00:14:35,690 --> 00:14:37,077 to launch things into space. 354 00:14:37,077 --> 00:14:39,410 And if you want something that has a high melting point, 355 00:14:39,410 --> 00:14:42,440 and is light, and is structural, beryllium's your way to go. 356 00:14:42,440 --> 00:14:45,800 It also happens to be a great neutron generator. 357 00:14:45,800 --> 00:14:48,230 And then why 30 MeV? 358 00:14:48,230 --> 00:14:51,950 In this case, we're going to use a table called JANIS, 359 00:14:51,950 --> 00:14:56,230 which I've got open over here. 360 00:14:56,230 --> 00:14:59,407 And I just have to clone my screen so you can see it. 361 00:14:59,407 --> 00:15:01,990 This is a resource that I think you guys are going to be using 362 00:15:01,990 --> 00:15:03,670 quite a lot in this course. 363 00:15:03,670 --> 00:15:06,038 We have a link to it on the learning module site. 364 00:15:06,038 --> 00:15:08,080 And I'm going to show you how it works right now. 365 00:15:08,080 --> 00:15:10,690 So I tend to use the web version because it works 366 00:15:10,690 --> 00:15:13,460 on any browser, any computer. 367 00:15:13,460 --> 00:15:16,080 And now you can start to pick which nuclear reaction you're 368 00:15:16,080 --> 00:15:16,830 looking at. 369 00:15:16,830 --> 00:15:20,230 And you can get tabulated cross sections. 370 00:15:20,230 --> 00:15:23,760 So I'm going to start by zooming all the way out. 371 00:15:23,760 --> 00:15:25,715 We can pick our incident particle. 372 00:15:25,715 --> 00:15:27,090 Since in this case, we're looking 373 00:15:27,090 --> 00:15:30,870 at the firing of protons into beryllium, 374 00:15:30,870 --> 00:15:34,680 I'll pick the incident proton data right here. 375 00:15:34,680 --> 00:15:37,410 There's a lot of different databases with sometimes 376 00:15:37,410 --> 00:15:39,450 conflicting information. 377 00:15:39,450 --> 00:15:42,870 I tend to go with the most recent one you can find. 378 00:15:42,870 --> 00:15:45,850 And click on cross sections. 379 00:15:45,850 --> 00:15:48,190 And this is, again another table of nuclides, anything 380 00:15:48,190 --> 00:15:49,990 in green there's data for. 381 00:15:49,990 --> 00:15:53,640 Anything in gray, there isn't. 382 00:15:53,640 --> 00:15:57,980 So let's go all the way back to the light nuclei, 383 00:15:57,980 --> 00:16:01,840 zoom in, go back down to the light nuclei 384 00:16:01,840 --> 00:16:03,910 again until we find beryllium-9. 385 00:16:07,310 --> 00:16:12,110 Double-click on that, and let's look for the anything 386 00:16:12,110 --> 00:16:15,700 cross section. 387 00:16:15,700 --> 00:16:17,870 And this is a pretty wide energy scale. 388 00:16:17,870 --> 00:16:20,990 So you can actually change your X minimum and maximum. 389 00:16:20,990 --> 00:16:22,970 So let's change it to a minimum and maximum-- 390 00:16:22,970 --> 00:16:24,590 I don't know-- a maximum of 50 MeV. 391 00:16:24,590 --> 00:16:30,260 We don't have to see all of that other stuff going on. 392 00:16:30,260 --> 00:16:35,020 50 MeV and maybe a minimum of 10. 393 00:16:35,020 --> 00:16:36,970 If you notice-- actually, I'll go back to 1. 394 00:16:36,970 --> 00:16:39,490 And I want to point something out. 395 00:16:39,490 --> 00:16:43,775 You can actually get a good yield of beryllium. 396 00:16:43,775 --> 00:16:46,150 Let's see-- you can actually get a good yield of neutrons 397 00:16:46,150 --> 00:16:48,940 by firing protons at beryllium in lower energies. 398 00:16:48,940 --> 00:16:52,090 But I notice there's this interesting feature 399 00:16:52,090 --> 00:16:53,410 right around there. 400 00:16:53,410 --> 00:16:54,577 The cross section's flatter. 401 00:16:54,577 --> 00:16:55,827 And so if you want to get an-- 402 00:16:55,827 --> 00:16:57,310 ensure that you get the right dose, 403 00:16:57,310 --> 00:16:59,530 you might want to deal with a flatter cross 404 00:16:59,530 --> 00:17:01,308 section or a flatter probability region, 405 00:17:01,308 --> 00:17:03,100 so that you have something more predictable 406 00:17:03,100 --> 00:17:06,230 instead of in a really high slope region. 407 00:17:06,230 --> 00:17:07,849 But some of these nuclear reactions 408 00:17:07,849 --> 00:17:11,480 actually take extra energy in order to move forward. 409 00:17:11,480 --> 00:17:15,690 And we'll show you another example pretty quickly. 410 00:17:15,690 --> 00:17:19,020 Let's go back to our slides here. 411 00:17:19,020 --> 00:17:21,240 Then another question is, how does the boron 412 00:17:21,240 --> 00:17:23,220 only get into the cancer cells? 413 00:17:23,220 --> 00:17:24,810 Like we mentioned before, cancer cells 414 00:17:24,810 --> 00:17:26,609 are actively growing, which means 415 00:17:26,609 --> 00:17:29,820 they need a very large and active blood supply. 416 00:17:29,820 --> 00:17:32,670 And so it's one way for things to, let's say, 417 00:17:32,670 --> 00:17:34,980 not quite cross the blood-brain barrier. 418 00:17:34,980 --> 00:17:38,190 If the cancer cells are growing and your neurons aren't, then 419 00:17:38,190 --> 00:17:40,605 your cancer cells are going to use more energy, take 420 00:17:40,605 --> 00:17:43,290 in more sugar, which might be doped with boron, 421 00:17:43,290 --> 00:17:45,005 or some other compound doped with boron, 422 00:17:45,005 --> 00:17:47,130 and that's all you can get the boron into the cells 423 00:17:47,130 --> 00:17:48,960 that you want. 424 00:17:48,960 --> 00:17:51,870 And then why was boron selected for the therapy? 425 00:17:51,870 --> 00:17:53,130 Let's think about that. 426 00:17:53,130 --> 00:17:58,490 What happens after the neutron is created? 427 00:17:58,490 --> 00:18:02,180 And let's write the next stage of the reaction. 428 00:18:02,180 --> 00:18:03,870 In boron neutron capture therapy, 429 00:18:03,870 --> 00:18:10,260 we rely on doping the patient with boron-10 to release 430 00:18:10,260 --> 00:18:21,510 an alpha particle, and lithium-7 and a gamma ray. 431 00:18:21,510 --> 00:18:22,922 So now what we can start doing is 432 00:18:22,922 --> 00:18:25,380 look at the table of nuclides, which I'm going to teach you 433 00:18:25,380 --> 00:18:27,630 how to read now, to figure out-- let's 434 00:18:27,630 --> 00:18:31,560 say that this neutron had an energy of about zero eV 435 00:18:31,560 --> 00:18:36,120 and the boron nucleus had an energy of about zero eV. 436 00:18:36,120 --> 00:18:42,780 And in the end, all this stuff here has gained or lost 437 00:18:42,780 --> 00:18:45,360 some sort of energy cue, Q. And today we're 438 00:18:45,360 --> 00:18:47,200 going to teach you how to calculate this Q. 439 00:18:47,200 --> 00:18:51,330 So I want to skip ahead to how to read the table of nuclides. 440 00:18:51,330 --> 00:18:53,320 So there's all-- this is like the poster you'll 441 00:18:53,320 --> 00:18:54,570 see in every nuclear building. 442 00:18:54,570 --> 00:18:57,303 It's kind of what makes us, us. 443 00:18:57,303 --> 00:18:59,220 What you'll notice is that there's a whole lot 444 00:18:59,220 --> 00:19:01,070 of nuclei at the lower left. 445 00:19:01,070 --> 00:19:02,940 They are the light ones. 446 00:19:02,940 --> 00:19:05,340 At the upper right, they are the heavier ones. 447 00:19:05,340 --> 00:19:08,040 And they're colored by half-life. 448 00:19:08,040 --> 00:19:10,620 In general, the blue ones will be stable, 449 00:19:10,620 --> 00:19:13,320 and the further away you get from blue, the less stable 450 00:19:13,320 --> 00:19:14,185 they get. 451 00:19:14,185 --> 00:19:16,560 So right away, without even delving deeper, what patterns 452 00:19:16,560 --> 00:19:17,560 do you guys notice here? 453 00:19:20,140 --> 00:19:22,310 Yeah, Alex? 454 00:19:22,310 --> 00:19:24,897 AUDIENCE: As they get bigger, heavier, they're more unstable. 455 00:19:24,897 --> 00:19:25,730 MICHAEL SHORT: Yeah. 456 00:19:25,730 --> 00:19:29,082 There's a whole section where there's no more blue. 457 00:19:29,082 --> 00:19:30,290 There are no stable elements. 458 00:19:30,290 --> 00:19:33,590 So stability drops off after a certain point. 459 00:19:33,590 --> 00:19:36,890 And what about in the region of stable isotopes? 460 00:19:36,890 --> 00:19:38,950 Does anybody notice any repeating patterns here? 461 00:19:42,960 --> 00:19:45,000 Take a look at every other row. 462 00:19:45,000 --> 00:19:47,040 There's a bunch of blues and then one, 463 00:19:47,040 --> 00:19:51,090 and then a bunch and then one, and then more and then none. 464 00:19:51,090 --> 00:19:53,310 That must be technetium, because that's 465 00:19:53,310 --> 00:19:55,920 the only element around there that doesn't have any. 466 00:19:55,920 --> 00:19:57,050 And then a bunch of blues. 467 00:19:57,050 --> 00:19:59,310 So every other row-- 468 00:19:59,310 --> 00:20:02,550 and in this case, it's increasing number of protons-- 469 00:20:02,550 --> 00:20:05,490 has more or fewer stable isotopes. 470 00:20:05,490 --> 00:20:08,280 It turns out that the even numbered 471 00:20:08,280 --> 00:20:11,070 isotopes have a lot more stable ones, for reasons that we'll 472 00:20:11,070 --> 00:20:12,900 get into pretty soon. 473 00:20:12,900 --> 00:20:14,598 If you zoom in a little bit, you can 474 00:20:14,598 --> 00:20:16,140 see all the different isotopes so you 475 00:20:16,140 --> 00:20:18,460 can select which ones you want. 476 00:20:18,460 --> 00:20:20,600 And again, if you look really closely, that's-- 477 00:20:20,600 --> 00:20:23,370 let's say, neon right here has got a few stable ones. 478 00:20:23,370 --> 00:20:24,840 Sodium has one. 479 00:20:24,840 --> 00:20:25,890 Magnesium as three. 480 00:20:25,890 --> 00:20:27,240 Aluminum has one. 481 00:20:27,240 --> 00:20:28,872 And this pattern repeats all the way up 482 00:20:28,872 --> 00:20:30,330 to the point where you don't really 483 00:20:30,330 --> 00:20:32,730 get any more stable isotopes. 484 00:20:32,730 --> 00:20:34,525 If you double-click on one of them, 485 00:20:34,525 --> 00:20:36,150 you get all the information that you'll 486 00:20:36,150 --> 00:20:38,740 need for the next three or so weeks of the course. 487 00:20:38,740 --> 00:20:41,250 So in this case, I picked on sulfur-32, 488 00:20:41,250 --> 00:20:43,530 one of the stable isotopes of sulfur. 489 00:20:43,530 --> 00:20:46,800 So if you notice it doesn't have any decay mechanisms here, 490 00:20:46,800 --> 00:20:49,200 but it does say its atomic abundance. 491 00:20:49,200 --> 00:20:51,270 So you can know how-- what percentage is normally 492 00:20:51,270 --> 00:20:52,470 found in nature. 493 00:20:52,470 --> 00:20:54,660 And then there's a few other quantities 494 00:20:54,660 --> 00:20:58,180 that is going to be the topic of what's going on here. 495 00:20:58,180 --> 00:20:59,670 Let's start with the atomic mass. 496 00:20:59,670 --> 00:21:04,290 If you notice, the atomic mass is slightly less than 32, 497 00:21:04,290 --> 00:21:07,950 32 being the mass number, or the total number of protons 498 00:21:07,950 --> 00:21:09,690 plus neutrons in the nucleus. 499 00:21:09,690 --> 00:21:15,140 The actual mass is a little lower by that amount 500 00:21:15,140 --> 00:21:17,655 right there, the binding energy. 501 00:21:17,655 --> 00:21:19,280 It might be a little funny because I've 502 00:21:19,280 --> 00:21:23,060 given you a mass in AMU, and a binding energy in kiloelectron 503 00:21:23,060 --> 00:21:24,110 volts. 504 00:21:24,110 --> 00:21:28,410 I want to remind you that these are the same thing. 505 00:21:28,410 --> 00:21:32,000 The conversion factor you'll be using over and over again 506 00:21:32,000 --> 00:21:35,270 throughout this course, especially on the next p sets, 507 00:21:35,270 --> 00:21:46,600 is one atomic mass unit is 931.49 MeV c squared. 508 00:21:46,600 --> 00:21:51,172 Yeah-- I'm sorry. 509 00:21:51,172 --> 00:21:53,470 Yeah, never mind, put that there. 510 00:21:53,470 --> 00:21:55,763 So then, again, one, don't round-- 511 00:21:55,763 --> 00:21:57,430 because we've had times when folks said, 512 00:21:57,430 --> 00:21:59,380 ah, this is about 931. 513 00:21:59,380 --> 00:22:01,922 And when you're off by half an MeV, 514 00:22:01,922 --> 00:22:03,880 you could be at a totally different decay level 515 00:22:03,880 --> 00:22:05,838 or get a positive Q when it should be negative, 516 00:22:05,838 --> 00:22:07,050 or vice versa. 517 00:22:07,050 --> 00:22:09,220 And let's take a quick look here to say, 518 00:22:09,220 --> 00:22:15,292 if this atomic mass is 31.9720707 AMU-- 519 00:22:15,292 --> 00:22:16,750 this is why I brought a calculator. 520 00:22:16,750 --> 00:22:18,520 Normally I do mental, math but since I 521 00:22:18,520 --> 00:22:20,770 told you guys don't round, I can't 522 00:22:20,770 --> 00:22:23,950 do eight significant digits in my head. 523 00:22:23,950 --> 00:22:26,025 So I'm going to get that in there-- 524 00:22:26,025 --> 00:22:27,043 0707. 525 00:22:27,043 --> 00:22:28,710 If any of you guys want to follow along, 526 00:22:28,710 --> 00:22:30,570 I encourage you to. 527 00:22:30,570 --> 00:22:34,660 And say minus 32, which is the mass number. 528 00:22:34,660 --> 00:22:40,260 So in this case we're taking the actual atomic mass 529 00:22:40,260 --> 00:22:42,150 minus the actual-- 530 00:22:42,150 --> 00:22:43,560 the mass number. 531 00:22:43,560 --> 00:22:44,700 In this case, it's 32. 532 00:22:44,700 --> 00:22:52,070 In this case it's, 31.9720707. 533 00:22:52,070 --> 00:22:54,580 And we end up with minus 0.0-- 534 00:22:54,580 --> 00:22:57,070 I'm going to put all the digits here-- 535 00:22:57,070 --> 00:23:01,840 293 AMU. 536 00:23:01,840 --> 00:23:04,750 If we convert this to MeV-- 537 00:23:04,750 --> 00:23:18,270 times 931.49, we get minus 26.0159 MeV. 538 00:23:18,270 --> 00:23:23,170 See this number anywhere on the KAERI table? 539 00:23:23,170 --> 00:23:25,435 Right there-- that's the excess mass. 540 00:23:28,000 --> 00:23:31,110 And in this case, we usually give this the symbol delta 541 00:23:31,110 --> 00:23:33,220 for the excess mass. 542 00:23:33,220 --> 00:23:34,800 And these are how these quantities 543 00:23:34,800 --> 00:23:38,030 are directly related. 544 00:23:38,030 --> 00:23:39,620 The excess mass-- well, actually, 545 00:23:39,620 --> 00:23:41,450 what does the excess mass really mean? 546 00:23:41,450 --> 00:23:44,450 It's the difference between the actual mass 547 00:23:44,450 --> 00:23:47,870 and a fairly poor approximation of the mass. 548 00:23:47,870 --> 00:23:50,060 So the excess mass doesn't really 549 00:23:50,060 --> 00:23:53,160 have that much of a physical connotation. 550 00:23:53,160 --> 00:23:56,180 But it is nice, because if you know very well 551 00:23:56,180 --> 00:23:58,790 the tabulated atomic number-- 552 00:23:58,790 --> 00:24:02,240 I'm sorry, the-- yeah, the mass number and the excess mass, 553 00:24:02,240 --> 00:24:04,100 you can figure out-- 554 00:24:04,100 --> 00:24:06,020 let's see-- yeah, you can figure out 555 00:24:06,020 --> 00:24:07,640 what the real atomic mass is. 556 00:24:10,350 --> 00:24:14,130 And I want to switch now to the actual table of nuclides 557 00:24:14,130 --> 00:24:16,420 and show you one example. 558 00:24:16,420 --> 00:24:18,510 If you want to very quickly jump between isotopes, 559 00:24:18,510 --> 00:24:21,302 you can type them in right up here. 560 00:24:21,302 --> 00:24:23,760 And does anyone know what the gold standard for atomic mass 561 00:24:23,760 --> 00:24:24,260 is? 562 00:24:24,260 --> 00:24:26,010 And I'll give you a hint, it's not gold. 563 00:24:26,010 --> 00:24:26,510 Yep? 564 00:24:26,510 --> 00:24:27,510 AUDIENCE: Carbon-12. 565 00:24:27,510 --> 00:24:28,860 MICHAEL SHORT: Carbon-12. 566 00:24:28,860 --> 00:24:31,653 What do you think the excess mass of carbon-12 567 00:24:31,653 --> 00:24:33,570 is going to be without doing any calculations? 568 00:24:33,570 --> 00:24:34,500 AUDIENCE: Zero. 569 00:24:34,500 --> 00:24:35,600 MICHAEL SHORT: Exactly. 570 00:24:35,600 --> 00:24:36,990 Zero. 571 00:24:36,990 --> 00:24:40,230 So if we go to carbon-12, because that 572 00:24:40,230 --> 00:24:44,250 is set as the standard, the way atomic masses were done 573 00:24:44,250 --> 00:24:48,540 was carbon-12 weighs exactly 12 AMU. 574 00:24:48,540 --> 00:24:51,480 The excess mass here is zero. 575 00:24:51,480 --> 00:24:55,320 And that's why the atomic mass is 12.0 to as many decimals 576 00:24:55,320 --> 00:24:58,060 as we care to note. 577 00:24:58,060 --> 00:25:00,230 So is everyone clear on what excess mass is? 578 00:25:00,230 --> 00:25:00,730 Yep? 579 00:25:00,730 --> 00:25:04,360 AUDIENCE: What's the point of c squared for that conversion? 580 00:25:04,360 --> 00:25:06,970 MICHAEL SHORT: So mass does not actually equal-- 581 00:25:06,970 --> 00:25:09,035 oh right, and it's actually on the-- 582 00:25:09,035 --> 00:25:10,700 where did my chalk go? 583 00:25:10,700 --> 00:25:14,830 It's actually down below. 584 00:25:14,830 --> 00:25:18,180 The point is that energy is related to mass by c squared. 585 00:25:18,180 --> 00:25:19,930 So they're not the same units, but they're 586 00:25:19,930 --> 00:25:21,536 directly convertible. 587 00:25:21,536 --> 00:25:22,410 AUDIENCE: OK. 588 00:25:22,410 --> 00:25:23,470 MICHAEL SHORT: Yep. 589 00:25:23,470 --> 00:25:26,410 And so this way, you have an E over a c squared. 590 00:25:26,410 --> 00:25:28,610 You get an m, and there we go. 591 00:25:28,610 --> 00:25:31,620 I had the units upside down. 592 00:25:31,620 --> 00:25:38,570 However, carbon-12 does not have a zero binding energy. 593 00:25:38,570 --> 00:25:39,370 Yeah, Luke? 594 00:25:39,370 --> 00:25:41,815 AUDIENCE: How come when you did that calculation, 595 00:25:41,815 --> 00:25:44,140 you didn't use the c squared? 596 00:25:44,140 --> 00:25:49,750 So like, it seems like then that would be 26.0159-- 597 00:25:49,750 --> 00:25:51,840 MICHAEL SHORT: MeV per c squared. 598 00:25:51,840 --> 00:25:52,340 Yeah. 599 00:25:52,340 --> 00:25:54,980 AUDIENCE: But they don't say that up there-- 600 00:25:54,980 --> 00:25:57,435 or it didn't say that on the table. 601 00:25:57,435 --> 00:25:58,810 MICHAEL SHORT: Yeah, that's true. 602 00:25:58,810 --> 00:26:02,650 AUDIENCE: [INAUDIBLE] 603 00:26:02,650 --> 00:26:04,660 MICHAEL SHORT: So it is funny, right? 604 00:26:04,660 --> 00:26:07,090 The binding energy is give it in keV, and that's correct. 605 00:26:07,090 --> 00:26:08,500 An energy is an energy. 606 00:26:08,500 --> 00:26:10,730 An excess mass, it really should say 607 00:26:10,730 --> 00:26:14,290 keV per c squared, because if we're talking in units of mass, 608 00:26:14,290 --> 00:26:16,540 it's got to be in m. 609 00:26:16,540 --> 00:26:21,710 Or in this way, you could say m is an energy per c squared. 610 00:26:21,710 --> 00:26:26,020 So this, to me, is a semantic inconsistency in the table. 611 00:26:26,020 --> 00:26:28,120 But you guys will know that a mass is always 612 00:26:28,120 --> 00:26:31,270 going to be an AMU, or kilograms, or MeV 613 00:26:31,270 --> 00:26:32,730 per c squared. 614 00:26:32,730 --> 00:26:37,150 And energies will be in MeV, keV, some sort of eV, 615 00:26:37,150 --> 00:26:39,370 usually, in this course. 616 00:26:39,370 --> 00:26:41,520 The binding energy, though, that's correct. 617 00:26:41,520 --> 00:26:44,280 That's in keV, because that's an actual energy. 618 00:26:44,280 --> 00:26:46,530 Now then the question is, what does the binding energy 619 00:26:46,530 --> 00:26:47,580 actually represent? 620 00:26:47,580 --> 00:26:49,680 Does anyone remember from Friday or Thursday? 621 00:26:54,762 --> 00:26:56,470 I can refresh your memory, because that's 622 00:26:56,470 --> 00:26:58,800 what I'm here to do. 623 00:26:58,800 --> 00:27:00,850 The binding energy is as if-- let's say 624 00:27:00,850 --> 00:27:05,600 we're assembling carbon-12 from its constituent nucleons. 625 00:27:05,600 --> 00:27:06,970 There's going to be 12 of them. 626 00:27:09,750 --> 00:27:14,565 Let's say we had six protons and six neutrons. 627 00:27:17,300 --> 00:27:21,080 We can calculate the total mass energy 628 00:27:21,080 --> 00:27:24,560 of this ensemble of nucleons when they're infinitely 629 00:27:24,560 --> 00:27:25,730 far apart from each other. 630 00:27:25,730 --> 00:27:27,110 And forgive the little-- 631 00:27:27,110 --> 00:27:28,370 it's not to scale. 632 00:27:28,370 --> 00:27:31,820 But they are infinitely far apart from each other. 633 00:27:31,820 --> 00:27:34,350 And we can say that-- 634 00:27:34,350 --> 00:27:37,780 let's say there is Z number of protons. 635 00:27:37,780 --> 00:27:40,080 So we'll say the binding energy is 636 00:27:40,080 --> 00:27:44,910 the number of protons times the mass of a proton 637 00:27:44,910 --> 00:27:48,150 plus the number of neutrons-- 638 00:27:48,150 --> 00:27:51,600 A minus Z-- times the mass of a neutron 639 00:27:51,600 --> 00:27:55,950 minus the energy of the assembled carbon-12 nucleus. 640 00:28:03,700 --> 00:28:05,860 So there's actually a measurable difference 641 00:28:05,860 --> 00:28:10,590 in mass between six protons and six neutrons, 642 00:28:10,590 --> 00:28:16,980 and the actual mass of a nucleus with atomic number A and-- 643 00:28:16,980 --> 00:28:22,026 I'm sorry, with atomic number Z and mass number A c squared. 644 00:28:25,760 --> 00:28:28,360 So is everyone clear on how we arrived at this formula? 645 00:28:28,360 --> 00:28:30,310 It's effectively the energy released 646 00:28:30,310 --> 00:28:34,180 when you take the individual nucleons, assemble the nucleus. 647 00:28:34,180 --> 00:28:36,430 You don't have as much mass as when you started. 648 00:28:36,430 --> 00:28:38,620 Or in some cases, you might have a little more mass 649 00:28:38,620 --> 00:28:42,760 than when you started if things are particularly unstable. 650 00:28:42,760 --> 00:28:45,730 And you can use the excess mass and binding energies 651 00:28:45,730 --> 00:28:50,320 in relative amounts to see, is a nucleus going to be stable? 652 00:28:50,320 --> 00:28:53,500 For example, let's look at iron-55 I'm 653 00:28:53,500 --> 00:28:56,150 going to jump here, make it a little bigger 654 00:28:56,150 --> 00:28:59,560 so the important stuff is easier to see. 655 00:28:59,560 --> 00:29:03,657 And if you notice, the binding energy of iron-55-- 656 00:29:03,657 --> 00:29:04,740 there's quite a bit of it. 657 00:29:04,740 --> 00:29:05,940 It's very well-bound. 658 00:29:05,940 --> 00:29:09,780 In fact, this is one of the most well-bound nuclei 659 00:29:09,780 --> 00:29:12,330 in the whole chart of nuclides. 660 00:29:12,330 --> 00:29:13,830 Let's look at something that we know 661 00:29:13,830 --> 00:29:16,400 to be particularly unstable. 662 00:29:16,400 --> 00:29:18,670 Someone have any idea? 663 00:29:18,670 --> 00:29:21,580 Let's just add like 20 neutrons to iron 664 00:29:21,580 --> 00:29:23,810 let's see if it even exists. 665 00:29:23,810 --> 00:29:25,260 No-- doesn't happen. 666 00:29:25,260 --> 00:29:28,930 Let's try adding 10 neutrons to iron-- 667 00:29:28,930 --> 00:29:30,100 or go even crazier. 668 00:29:32,720 --> 00:29:35,570 What about 70? 669 00:29:35,570 --> 00:29:39,090 Too small-- all right, let's meet somewhere in the middle-- 670 00:29:39,090 --> 00:29:40,780 68. 671 00:29:40,780 --> 00:29:42,238 Still a pretty high binding energy, 672 00:29:42,238 --> 00:29:43,822 but you can look at it as a difference 673 00:29:43,822 --> 00:29:45,175 in binding energy per nucleon. 674 00:29:48,190 --> 00:29:50,500 So in this case, the binding energy per nucleon-- 675 00:29:50,500 --> 00:29:52,660 if you take the binding energy and divide 676 00:29:52,660 --> 00:29:54,580 by the total number of nucleons, will give you 677 00:29:54,580 --> 00:29:58,660 a relative measure of how tightly bound that nucleus is. 678 00:29:58,660 --> 00:30:00,430 Now these are not absolute things. 679 00:30:00,430 --> 00:30:02,630 You can't just say, certain binding energy 680 00:30:02,630 --> 00:30:04,630 leads to certain stability, but they do give you 681 00:30:04,630 --> 00:30:06,752 pretty good trends to follow. 682 00:30:06,752 --> 00:30:08,710 And we're actually going to be coming up with-- 683 00:30:08,710 --> 00:30:10,570 probably on Thursday-- 684 00:30:10,570 --> 00:30:14,050 a semi-empirical formula to get the rough binding energy 685 00:30:14,050 --> 00:30:17,110 of any particular assembly of protons and neutrons. 686 00:30:17,110 --> 00:30:21,580 And it follows experimental calculations pretty well-- 687 00:30:21,580 --> 00:30:24,382 surprisingly so. 688 00:30:24,382 --> 00:30:26,090 I want to jump back to here, because I've 689 00:30:26,090 --> 00:30:29,720 mentioned cross sections, and I want to actually define 690 00:30:29,720 --> 00:30:32,120 what a cross section is, because this is a quantity 691 00:30:32,120 --> 00:30:34,850 that you're going to be using everywhere. 692 00:30:34,850 --> 00:30:37,130 Let's say that we fired a beam of particles-- 693 00:30:37,130 --> 00:30:38,960 it doesn't matter what it is-- 694 00:30:38,960 --> 00:30:41,630 at a target of other particles. 695 00:30:41,630 --> 00:30:44,450 Let's say, the beam particles are atom A, 696 00:30:44,450 --> 00:30:46,970 and the target particles are atom B. 697 00:30:46,970 --> 00:30:50,210 And once these A particles pass through the target 698 00:30:50,210 --> 00:30:52,790 B, a little bit fewer of them come 699 00:30:52,790 --> 00:30:56,780 out the other side reacted, or unscathed, or unscattered. 700 00:30:56,780 --> 00:31:00,050 And some of them are absorbed, or scattered, or bounced off, 701 00:31:00,050 --> 00:31:02,870 or scattered backwards, or what have you. 702 00:31:02,870 --> 00:31:04,790 We can write the sort of proportionality 703 00:31:04,790 --> 00:31:09,140 constant between the change in intensity of our A beam 704 00:31:09,140 --> 00:31:12,230 and the thickness of our slab. 705 00:31:12,230 --> 00:31:14,000 And we give that proportionality constant 706 00:31:14,000 --> 00:31:17,500 this symbol, little sigma. 707 00:31:17,500 --> 00:31:19,490 We'll get something going up here. 708 00:31:19,490 --> 00:31:22,225 Little sigma, which we call the microscopic cross section. 709 00:31:30,340 --> 00:31:32,970 It's in effect, a constant of proportionality 710 00:31:32,970 --> 00:31:35,910 that relates the probability of absorbing 711 00:31:35,910 --> 00:31:37,640 an atom from this beam I-- 712 00:31:37,640 --> 00:31:41,220 or from this beam of atoms A through a slab of B. 713 00:31:41,220 --> 00:31:43,800 And then if you take this formula, 714 00:31:43,800 --> 00:31:46,350 you divide by that delta X-- 715 00:31:46,350 --> 00:31:49,210 so I'm going to take what's on there 716 00:31:49,210 --> 00:31:55,530 and say delta I over delta X equals minus cross section 717 00:31:55,530 --> 00:31:57,990 ABn-- 718 00:31:57,990 --> 00:32:01,180 which refers here to the number density. 719 00:32:01,180 --> 00:32:03,150 So I'll keep our table of symbols 720 00:32:03,150 --> 00:32:05,265 altogether so it's a little easier to follow. 721 00:32:05,265 --> 00:32:15,490 n is our number density, which means the number of atoms 722 00:32:15,490 --> 00:32:17,740 per unit volume. 723 00:32:17,740 --> 00:32:21,670 Usually, in nuclear quantities, we use centimeters 724 00:32:21,670 --> 00:32:24,520 because these are things that are actually fairly measurable, 725 00:32:24,520 --> 00:32:26,410 and cross sections are actually in units 726 00:32:26,410 --> 00:32:31,880 of centimeters squared. 727 00:32:31,880 --> 00:32:34,160 And let me finish that expression. 728 00:32:34,160 --> 00:32:36,050 We had the number density of our target 729 00:32:36,050 --> 00:32:43,300 B. We had our initial intensity, and that's it. 730 00:32:43,300 --> 00:32:47,360 Anyone know how to solve this differential equation? 731 00:32:47,360 --> 00:32:51,856 If we take the limit of small deltas, 732 00:32:51,856 --> 00:32:55,888 it should start to look like a differential equation. 733 00:32:55,888 --> 00:32:57,680 The final answer is up there on the screen. 734 00:32:57,680 --> 00:32:59,810 Does anyone remember the method to actually solve 735 00:32:59,810 --> 00:33:00,935 this differential equation? 736 00:33:03,920 --> 00:33:04,990 This is the easy one-- 737 00:33:04,990 --> 00:33:07,130 separate the variables. 738 00:33:07,130 --> 00:33:09,970 So in this case, we can divide each side by I of of X, 739 00:33:09,970 --> 00:33:13,720 multiply each side by X. I'm going to bring this up 740 00:33:13,720 --> 00:33:16,630 so I'm not bending down. 741 00:33:16,630 --> 00:33:25,300 So we have dI over I equals minus sigma ab n of B times dX. 742 00:33:28,150 --> 00:33:33,340 Integrate both sides and we get log of I 743 00:33:33,340 --> 00:33:45,160 equals minus sigma ab n of BX, and some integration constant. 744 00:33:45,160 --> 00:33:49,780 You can apply an initial boundary condition to say at X 745 00:33:49,780 --> 00:33:53,050 equals zero, the intensity of the being 746 00:33:53,050 --> 00:33:55,690 x was some intensity I naught. 747 00:33:55,690 --> 00:33:57,700 Whatever intensity of the beam that we initially 748 00:33:57,700 --> 00:34:00,020 fired at the target. 749 00:34:00,020 --> 00:34:02,200 And by combining these two, you end up 750 00:34:02,200 --> 00:34:04,420 with the expression you get right there, 751 00:34:04,420 --> 00:34:08,440 which is that the intensity of the beam coming out 752 00:34:08,440 --> 00:34:14,230 is the initial intensity times e to the minus sigma ab nbx. 753 00:34:17,320 --> 00:34:19,370 And we've kind of derived the idea 754 00:34:19,370 --> 00:34:21,670 of exponential attenuation. 755 00:34:21,670 --> 00:34:26,480 For those who haven't seen that word before, 756 00:34:26,480 --> 00:34:30,440 attenuation or the gradual removal of the beam of incident 757 00:34:30,440 --> 00:34:32,870 particles by whatever the target happens to be. 758 00:34:36,080 --> 00:34:38,870 This quantity right here, we actually 759 00:34:38,870 --> 00:34:45,480 have another symbol for it, which we give big sigma. 760 00:34:45,480 --> 00:34:50,248 And in this case, big sigma we call the macroscopic cross 761 00:34:50,248 --> 00:34:50,847 section. 762 00:34:58,490 --> 00:34:59,940 I'll draw a box around these so we 763 00:34:59,940 --> 00:35:04,020 know these are our symbols that we're keeping defined here. 764 00:35:04,020 --> 00:35:06,960 And so you may see that the microscopic cross section just 765 00:35:06,960 --> 00:35:10,575 depends on single reactions between the incoming atoms 766 00:35:10,575 --> 00:35:14,970 A and the target atoms B. The macroscopic cross section 767 00:35:14,970 --> 00:35:17,650 depends on how much B is there. 768 00:35:17,650 --> 00:35:22,170 So if you want to get per atom probabilities of absorption 769 00:35:22,170 --> 00:35:24,660 scattering, whatever thing you're looking at, 770 00:35:24,660 --> 00:35:27,210 you use the microscopic cross section. 771 00:35:27,210 --> 00:35:29,980 And if you have a finite amount of stuff there, 772 00:35:29,980 --> 00:35:32,640 and you know the number density of your substance B, 773 00:35:32,640 --> 00:35:35,790 you can use the macroscopic cross section 774 00:35:35,790 --> 00:35:38,910 to get actual total probabilities of beam 775 00:35:38,910 --> 00:35:40,260 attenuation-- 776 00:35:40,260 --> 00:35:43,320 or to calculate exponential attenuation. 777 00:35:43,320 --> 00:35:45,750 We're going to see this again in another form when 778 00:35:45,750 --> 00:35:47,970 we talk about designing shielding, 779 00:35:47,970 --> 00:35:49,470 and how much shielding do you need 780 00:35:49,470 --> 00:35:51,930 to remove how much of the beam? 781 00:35:51,930 --> 00:35:54,060 Well, this quantity right here, there's 782 00:35:54,060 --> 00:35:57,360 actually tabulated values for a lot of this stuff at the-- 783 00:35:57,360 --> 00:35:58,680 on the NIST website. 784 00:35:58,680 --> 00:36:01,500 And I have links to that as well on the Stellar website, 785 00:36:01,500 --> 00:36:04,650 so you can-- instead of having to look these all up on JANIS 786 00:36:04,650 --> 00:36:06,150 and multiply number densities, there 787 00:36:06,150 --> 00:36:08,430 are some easier graphical functions you can just 788 00:36:08,430 --> 00:36:10,110 find the value for. 789 00:36:10,110 --> 00:36:11,880 But we'll get back to that in a few days. 790 00:36:14,520 --> 00:36:16,770 So anyway, on reading the KAERI table, 791 00:36:16,770 --> 00:36:19,770 there's a few quantities right there. 792 00:36:19,770 --> 00:36:22,380 We've already defined what the excess mass 793 00:36:22,380 --> 00:36:24,330 and the binding energy is. 794 00:36:24,330 --> 00:36:25,890 And I want to note right here, if you 795 00:36:25,890 --> 00:36:28,710 want to actually calculate binding energies by hand, which 796 00:36:28,710 --> 00:36:31,765 I'm going to ask you to do a bit on problem set 2, 797 00:36:31,765 --> 00:36:33,765 you'll need to know what the mass of the proton, 798 00:36:33,765 --> 00:36:35,910 and the neutron, and the electron 799 00:36:35,910 --> 00:36:38,760 are to, again, usually like six or seven digits 800 00:36:38,760 --> 00:36:41,970 is the idea behind this course. 801 00:36:41,970 --> 00:36:45,240 Notice that they're not exactly one atomic mass unit, 802 00:36:45,240 --> 00:36:46,860 because one atomic mass unit, again, 803 00:36:46,860 --> 00:36:48,523 was set with that carbon-12 standard. 804 00:36:48,523 --> 00:36:50,940 I'm not going to use the word gold standard because that's 805 00:36:50,940 --> 00:36:54,570 a misnomer in this field. 806 00:36:54,570 --> 00:36:56,940 And so like I said, what does excess mass really mean, 807 00:36:56,940 --> 00:36:58,530 physically? 808 00:36:58,530 --> 00:37:00,990 Not much, because it's the comparison 809 00:37:00,990 --> 00:37:03,900 to an arbitrary standard or a rather poor approximation 810 00:37:03,900 --> 00:37:04,890 of the mass. 811 00:37:04,890 --> 00:37:08,250 The binding energy actually does represent the conversion 812 00:37:08,250 --> 00:37:10,290 of mass to energy when you assemble 813 00:37:10,290 --> 00:37:15,980 a nucleus like Voltron-style from its constituent nucleons. 814 00:37:15,980 --> 00:37:18,070 So let's try a few examples in class right here. 815 00:37:18,070 --> 00:37:21,210 I'd like you guys to follow around and try and calculate 816 00:37:21,210 --> 00:37:26,700 the binding energy of each of these three nuclei of sulfur. 817 00:37:26,700 --> 00:37:31,400 Let me get a better blank board so we can follow along. 818 00:37:31,400 --> 00:37:33,660 And there's a few different ways of calculating 819 00:37:33,660 --> 00:37:34,980 that binding energy. 820 00:37:34,980 --> 00:37:37,410 You can do it by the excess mass. 821 00:37:37,410 --> 00:37:38,850 You can do it by-- 822 00:37:38,850 --> 00:37:40,630 let's go back to the table of nuclides 823 00:37:40,630 --> 00:37:43,240 so I can show you how I would do it. 824 00:37:43,240 --> 00:37:45,870 Let's start with sulfur 32. 825 00:37:45,870 --> 00:37:48,426 And we'll write up the quantities that we're-- 826 00:37:48,426 --> 00:37:50,000 that we know. 827 00:37:50,000 --> 00:37:52,860 Let's say the excess mass is the actual mass 828 00:37:52,860 --> 00:37:55,800 minus the mass number. 829 00:37:55,800 --> 00:38:04,950 The binding energy is Z times mass of hydrogen plus A minus Z 830 00:38:04,950 --> 00:38:09,870 mass of a neutron minus the actual mass of that nucleus 831 00:38:09,870 --> 00:38:14,100 with AZ c squared. 832 00:38:14,100 --> 00:38:19,290 And then what we can do is rearrange this excess mass, 833 00:38:19,290 --> 00:38:23,120 isolating the mass term right here, and make a substitution. 834 00:38:23,120 --> 00:38:26,740 So we can say the mass is actually 835 00:38:26,740 --> 00:38:32,820 the excess mass plus A. Stick that in right there, 836 00:38:32,820 --> 00:38:35,730 and now we can calculate and confirm the binding energies 837 00:38:35,730 --> 00:38:40,170 that we see right here from tabulated excess mass values, 838 00:38:40,170 --> 00:38:45,120 atomic number, mass number, and the masses of a hydrogen 839 00:38:45,120 --> 00:38:51,330 atom and a neutron, which, for reference, 840 00:38:51,330 --> 00:38:54,100 I'll write up here as well. 841 00:38:54,100 --> 00:38:57,330 So the mass of a hydrogen is the mass 842 00:38:57,330 --> 00:39:00,120 of a proton plus an electron. 843 00:39:00,120 --> 00:39:10,110 So 1.0072-- 007276 plus 0.000-- 844 00:39:10,110 --> 00:39:12,480 make that a little easier to read-- 845 00:39:12,480 --> 00:39:20,360 how many zeros-- 00054858 AMU. 846 00:39:20,360 --> 00:39:27,180 Mass of a neutron, surprisingly close to Chadwick's prediction. 847 00:39:27,180 --> 00:39:33,120 8664 AMU. 848 00:39:33,120 --> 00:39:37,420 So now I'll head back to the table of nuclides. 849 00:39:37,420 --> 00:39:40,110 And let's see if you guys can follow along. 850 00:39:40,110 --> 00:39:42,750 What we want to do is try to confirm this binding 851 00:39:42,750 --> 00:39:46,020 energy using the atomic mass, the excess mass, 852 00:39:46,020 --> 00:39:48,630 or if we don't even know the atomic mass, 853 00:39:48,630 --> 00:39:53,070 we can use the excess mass plus A right there. 854 00:39:53,070 --> 00:39:58,650 So let's see-- Z, in this case, for sulfur, is 16 times 855 00:39:58,650 --> 00:40:01,740 the mass of hydrogen. This is definitely a calculator 856 00:40:01,740 --> 00:40:04,325 moment, because like I said, I don't know about you guys, 857 00:40:04,325 --> 00:40:06,450 but I can't do eight significant digits in my head. 858 00:40:10,160 --> 00:40:21,930 0054858-- 1.007855-- probably enough digits-- 859 00:40:21,930 --> 00:40:24,510 plus 16, because there's-- 860 00:40:24,510 --> 00:40:26,750 mass number here is 32. 861 00:40:26,750 --> 00:40:28,050 The atomic number is 16. 862 00:40:28,050 --> 00:40:32,370 That leaves us with 16 neutrons times the mass of a neutron, 863 00:40:32,370 --> 00:40:36,120 08664-- 864 00:40:36,120 --> 00:40:47,670 minus the excess mass, which in this case is 26.015 MeV-- 865 00:40:47,670 --> 00:40:52,770 015 MeV per c squared. 866 00:40:52,770 --> 00:40:55,560 So thanks for that-- thank Jared for that question because, 867 00:40:55,560 --> 00:40:57,517 indeed, the excess mass, if you want 868 00:40:57,517 --> 00:40:59,100 to write it in terms of a mass, should 869 00:40:59,100 --> 00:41:04,150 be in MeV or keV per c squared minus A, 870 00:41:04,150 --> 00:41:09,090 which is 32 times c squared. 871 00:41:11,780 --> 00:41:13,490 So let's do all this out-- 872 00:41:13,490 --> 00:41:16,630 shouldn't take too long. 873 00:41:16,630 --> 00:41:20,730 007825 plus 16-- 874 00:41:20,730 --> 00:41:38,610 1.008664 minus 32 minus 26.015 divided by c squared. 875 00:41:38,610 --> 00:41:39,740 It's basically nothing. 876 00:41:42,770 --> 00:41:46,310 Gives us on the order of-- 877 00:41:46,310 --> 00:41:48,845 let's see-- times c squared. 878 00:42:10,975 --> 00:42:12,100 What did we get right here? 879 00:42:18,792 --> 00:42:21,182 AUDIENCE: Is the 26 negative? 880 00:42:21,182 --> 00:42:23,600 MICHAEL SHORT: Ah, let's see. 881 00:42:23,600 --> 00:42:26,400 I believe it is, because we have to subtract the mass, 882 00:42:26,400 --> 00:42:28,758 and we're substituting in this delta-- 883 00:42:28,758 --> 00:42:30,710 AUDIENCE: Isn't the delta negative? 884 00:42:30,710 --> 00:42:32,250 MICHAEL SHORT: Oh. 885 00:42:32,250 --> 00:42:33,150 Good point. 886 00:42:33,150 --> 00:42:35,280 There is a negative there. 887 00:42:35,280 --> 00:42:39,780 So that's minus negative that. 888 00:42:39,780 --> 00:42:40,740 And A is 32. 889 00:42:40,740 --> 00:42:42,222 Thank you. 890 00:42:42,222 --> 00:42:42,930 Yeah, good point. 891 00:42:42,930 --> 00:42:43,847 Let me try this again. 892 00:43:12,865 --> 00:43:16,500 Ah, I know what I'm doing wrong. 893 00:43:16,500 --> 00:43:20,340 This part right here, we want to convert to AMU. 894 00:43:20,340 --> 00:43:23,400 So we can take our minus-- 895 00:43:23,400 --> 00:43:32,670 thank you-- 26.015 MeV per c squared and divide 896 00:43:32,670 --> 00:43:38,544 by our conversion factor, 931.49-- 897 00:43:38,544 --> 00:43:42,350 let's see-- MeV per c squared per AMU. 898 00:43:45,070 --> 00:43:46,590 What does that give us? 899 00:43:46,590 --> 00:43:51,850 26.015 over that. 900 00:43:51,850 --> 00:44:00,630 0.027928 AMU negative. 901 00:44:00,630 --> 00:44:02,460 Let's put that in and see how we do. 902 00:44:13,370 --> 00:44:24,330 So plus 0.027928 minus 32. 903 00:44:24,330 --> 00:44:28,440 And then we get 271.-- 904 00:44:28,440 --> 00:44:32,530 I'll just say 764 MeV. 905 00:44:32,530 --> 00:44:34,630 I think six digits is enough. 906 00:44:34,630 --> 00:44:38,770 The actual binding energy, 271.780 MeV, 907 00:44:38,770 --> 00:44:41,650 so we're off by 16 electron volts-- 908 00:44:41,650 --> 00:44:43,060 close enough. 909 00:44:43,060 --> 00:44:45,710 Also note that I used a five-digit accurate conversion 910 00:44:45,710 --> 00:44:46,210 factor. 911 00:44:46,210 --> 00:44:47,460 That might be part of the source of it. 912 00:44:47,460 --> 00:44:48,870 Does someone have a question? 913 00:44:48,870 --> 00:44:49,515 AUDIENCE: Yeah. 914 00:44:49,515 --> 00:44:52,300 In the equation on top, you did the atomic number 915 00:44:52,300 --> 00:44:54,758 times the mass of the proton, but in the one on the bottom, 916 00:44:54,758 --> 00:44:56,216 you used atomic mass times the mass 917 00:44:56,216 --> 00:44:58,590 of the hydrogen including the electron. 918 00:44:58,590 --> 00:44:59,522 Is there-- 919 00:44:59,522 --> 00:45:00,480 MICHAEL SHORT: Oh yeah. 920 00:45:00,480 --> 00:45:01,800 I actually added the two. 921 00:45:01,800 --> 00:45:05,100 So the mass of an electron, since it's got that extra zero, 922 00:45:05,100 --> 00:45:06,960 makes so much of a-- 923 00:45:06,960 --> 00:45:08,040 so the mass of-- 924 00:45:08,040 --> 00:45:08,683 oh-- yeah. 925 00:45:08,683 --> 00:45:10,350 The mass of hydrogen would be the proton 926 00:45:10,350 --> 00:45:11,983 plus the electron right there. 927 00:45:11,983 --> 00:45:12,650 AUDIENCE: Right. 928 00:45:12,650 --> 00:45:16,423 But why do hydrogen, though, if [INAUDIBLE] just the proton? 929 00:45:16,423 --> 00:45:18,840 MICHAEL SHORT: Oh, because there's an electron there, too. 930 00:45:18,840 --> 00:45:20,850 Now this can usually be neglected 931 00:45:20,850 --> 00:45:22,890 because it's such a small fraction compared 932 00:45:22,890 --> 00:45:23,880 to everything else. 933 00:45:23,880 --> 00:45:25,338 So now we're talking about-- what-- 934 00:45:25,338 --> 00:45:29,410 the fifth or sixth decimal place. 935 00:45:29,410 --> 00:45:32,070 But just for exactness, I stuck on it. 936 00:45:32,070 --> 00:45:34,470 Yeah, in your calculations, you can try with and without, 937 00:45:34,470 --> 00:45:36,845 and I think you'll find that it doesn't matter that much, 938 00:45:36,845 --> 00:45:39,780 because in the end we get the binding energy that we see 939 00:45:39,780 --> 00:45:44,460 on the table to within 16 electron volts for a total 940 00:45:44,460 --> 00:45:45,180 of-- yeah-- 941 00:45:45,180 --> 00:45:46,380 271 MeV. 942 00:45:46,380 --> 00:45:47,790 That's pretty accurate. 943 00:45:47,790 --> 00:45:48,480 Yeah. 944 00:45:48,480 --> 00:45:49,980 AUDIENCE: If you wanted to calculate 945 00:45:49,980 --> 00:45:51,840 the like energy released from a reaction, 946 00:45:51,840 --> 00:45:55,070 would you do the binding energy for [INAUDIBLE] reactants 947 00:45:55,070 --> 00:45:56,868 that's trapped products for the reactants? 948 00:45:56,868 --> 00:45:58,410 MICHAEL SHORT: That's the next slide. 949 00:45:58,410 --> 00:45:59,600 We'll get right there. 950 00:45:59,600 --> 00:46:01,960 Yeah, so you're catching on to where we're going. 951 00:46:01,960 --> 00:46:04,860 So once you can calculate either the excess mass, 952 00:46:04,860 --> 00:46:08,753 or the binding energy, or the total mass of any nucleus, 953 00:46:08,753 --> 00:46:10,170 you can start to put them together 954 00:46:10,170 --> 00:46:11,340 into nuclear reactions. 955 00:46:11,340 --> 00:46:14,500 So since you asked, let's take a quick look at them. 956 00:46:14,500 --> 00:46:16,772 Where is our nuclear reaction board? 957 00:46:16,772 --> 00:46:18,480 Anyone mind if I hide this board for now, 958 00:46:18,480 --> 00:46:20,264 so we can go back to our original? 959 00:46:20,264 --> 00:46:20,764 OK. 960 00:46:24,250 --> 00:46:27,520 Let's take a look at this reaction right 961 00:46:27,520 --> 00:46:33,110 here, the actual boron neutron capture therapy reaction. 962 00:46:33,110 --> 00:46:37,360 And now we can get towards calculating this Q, what 963 00:46:37,360 --> 00:46:39,910 the difference is between the-- 964 00:46:39,910 --> 00:46:42,460 the total energies of the products and the reactants, 965 00:46:42,460 --> 00:46:44,150 and where does that go? 966 00:46:44,150 --> 00:46:46,540 So now we can either look up or calculate 967 00:46:46,540 --> 00:46:49,840 the binding energy of each of these nuclei, 968 00:46:49,840 --> 00:46:52,720 subtract off the energy of the gamma, which I've looked up 969 00:46:52,720 --> 00:46:59,380 already, is about 0.478 MeV. 970 00:46:59,380 --> 00:47:02,770 And we can figure out what the total Q of this reaction is. 971 00:47:02,770 --> 00:47:03,753 So in this case-- 972 00:47:03,753 --> 00:47:05,170 I'll skip ahead to the slide where 973 00:47:05,170 --> 00:47:08,980 I've got it because that way I won't write anything wrong 974 00:47:08,980 --> 00:47:10,420 on the board-- 975 00:47:10,420 --> 00:47:12,220 got everything right up here. 976 00:47:12,220 --> 00:47:14,680 We assume that both boron and the neutron 977 00:47:14,680 --> 00:47:16,720 have roughly zero kinetic energy. 978 00:47:16,720 --> 00:47:18,700 And at the end, they come out with 979 00:47:18,700 --> 00:47:22,180 some other kinetic energies as well as this gamma ray. 980 00:47:22,180 --> 00:47:25,960 The sum of this energy differences, we refer to as Q. 981 00:47:25,960 --> 00:47:28,930 And we can actually confirm this total Q 982 00:47:28,930 --> 00:47:31,195 with a few different methods. 983 00:47:31,195 --> 00:47:33,070 In this case, it's always conserve something. 984 00:47:33,070 --> 00:47:34,750 That's the whole theme of this course, 985 00:47:34,750 --> 00:47:36,880 is you can conserve total masses, 986 00:47:36,880 --> 00:47:38,650 you can conserve total kinetic energies. 987 00:47:38,650 --> 00:47:43,120 We may not know those, but tabulated in the KAERI table 988 00:47:43,120 --> 00:47:45,770 are the binding energies of each of these nuclei. 989 00:47:45,770 --> 00:47:47,320 So let's try that out right now. 990 00:47:50,515 --> 00:47:52,390 So let's look at the binding energies of each 991 00:47:52,390 --> 00:47:55,090 of these nuclei and see what the difference is, 992 00:47:55,090 --> 00:47:56,890 the total energy released. 993 00:47:56,890 --> 00:48:00,760 First of all, what's the binding energy of a lone neutron? 994 00:48:00,760 --> 00:48:02,160 Anyone have any idea? 995 00:48:02,160 --> 00:48:03,220 I see a lot of these-- 996 00:48:03,220 --> 00:48:03,720 zero. 997 00:48:03,720 --> 00:48:04,498 Yep. 998 00:48:04,498 --> 00:48:06,790 You haven't assembled an nucleus out of a lone neutron, 999 00:48:06,790 --> 00:48:14,500 so we'll go with the neutron has a binding energy of zero MeV. 1000 00:48:14,500 --> 00:48:16,480 Boron, not quite the case, but we 1001 00:48:16,480 --> 00:48:21,160 can go back to the table of nuclides and punch that in-- 1002 00:48:21,160 --> 00:48:24,360 boron-10. 1003 00:48:24,360 --> 00:48:25,800 We can look up its binding energy, 1004 00:48:25,800 --> 00:48:29,250 which is about 64.7507-- 1005 00:48:29,250 --> 00:48:40,200 I keep saying about, which is exactly 64.7507 MeV. 1006 00:48:40,200 --> 00:48:43,410 And then our other two nuclei, helium-4-- 1007 00:48:43,410 --> 00:48:48,300 so you can punch in helium-4 here. 1008 00:48:48,300 --> 00:49:03,040 It's got a binding energy of exactly 28.295673 MeV. 1009 00:49:03,040 --> 00:49:10,055 And finally, lithium-7, let's punch that in. 1010 00:49:10,055 --> 00:49:11,430 I think you guys are going to get 1011 00:49:11,430 --> 00:49:12,810 very familiar with this table. 1012 00:49:12,810 --> 00:49:14,580 There's a few versions out there. 1013 00:49:14,580 --> 00:49:16,380 There's a new slick Java version that I 1014 00:49:16,380 --> 00:49:17,620 found a little hard to use. 1015 00:49:17,620 --> 00:49:20,520 So I like the text-only version, because it's just as simple 1016 00:49:20,520 --> 00:49:22,410 and fast as it gets-- 1017 00:49:22,410 --> 00:49:34,180 39.244526-- 526. 1018 00:49:34,180 --> 00:49:38,770 So any sort of increase in total amount of binding energy 1019 00:49:38,770 --> 00:49:42,310 between the reactants and the products 1020 00:49:42,310 --> 00:49:45,190 is going to release or absorb energy. 1021 00:49:45,190 --> 00:49:49,900 Now because boron does capture a thermal neutron, or a neutron 1022 00:49:49,900 --> 00:49:53,170 with approximately zero eV of kinetic energy, 1023 00:49:53,170 --> 00:49:55,210 does anyone have any idea whether this would 1024 00:49:55,210 --> 00:49:58,450 release or consume energy? 1025 00:49:58,450 --> 00:50:01,450 In other words, do think this is an exothermic or endothermic 1026 00:50:01,450 --> 00:50:04,120 reaction? 1027 00:50:04,120 --> 00:50:04,817 Yeah, Alex? 1028 00:50:04,817 --> 00:50:06,400 AUDIENCE: I'm guessing that heat would 1029 00:50:06,400 --> 00:50:08,590 be released through the material-- the capture 1030 00:50:08,590 --> 00:50:10,350 material would be heated up. 1031 00:50:10,350 --> 00:50:11,140 MICHAEL SHORT: OK. 1032 00:50:11,140 --> 00:50:12,610 Indeed. 1033 00:50:12,610 --> 00:50:14,800 If the total Q value is greater than zero, 1034 00:50:14,800 --> 00:50:16,390 we refer to this as exothermic-- 1035 00:50:18,970 --> 00:50:20,960 kind of like in chemistry. 1036 00:50:20,960 --> 00:50:24,550 And if Q is less than zero, we refer to this as endothermic. 1037 00:50:27,130 --> 00:50:30,298 So let's do our binding energy subtraction now. 1038 00:50:30,298 --> 00:50:32,590 We want to figure out how much excess binding energy is 1039 00:50:32,590 --> 00:50:33,110 released. 1040 00:50:33,110 --> 00:50:35,100 So I'm going to take the reactants-- 1041 00:50:35,100 --> 00:50:36,850 I'm sorry-- I'm going to take the product. 1042 00:50:36,850 --> 00:50:47,110 So helium 295673-- add lithium 244526-- 1043 00:50:47,110 --> 00:50:53,560 subtract boron 0.7507-- subtract the neutron, which is zero, 1044 00:50:53,560 --> 00:51:01,820 and we're left with 2.79 MeV. 1045 00:51:01,820 --> 00:51:05,265 And because it's positive, this is an exothermic reaction, 1046 00:51:05,265 --> 00:51:07,640 which is what we'd expect, because this reaction actually 1047 00:51:07,640 --> 00:51:09,050 happens. 1048 00:51:09,050 --> 00:51:10,970 If this was an endothermic reaction, 1049 00:51:10,970 --> 00:51:12,660 what could you do to make it occur? 1050 00:51:17,780 --> 00:51:18,280 Yeah? 1051 00:51:18,280 --> 00:51:21,248 AUDIENCE: Heat up the reactants. 1052 00:51:21,248 --> 00:51:22,790 MICHAEL SHORT: Like with temperature, 1053 00:51:22,790 --> 00:51:24,384 or what do you mean? 1054 00:51:24,384 --> 00:51:26,753 AUDIENCE: Make them have higher kinetic energy or-- 1055 00:51:26,753 --> 00:51:27,920 MICHAEL SHORT: There you go. 1056 00:51:27,920 --> 00:51:30,378 So actually-- yeah-- you kind of said the same thing twice. 1057 00:51:30,378 --> 00:51:32,690 Heating things up does give them higher kinetic energy. 1058 00:51:32,690 --> 00:51:34,107 If you rely on temperature, you'll 1059 00:51:34,107 --> 00:51:37,425 be imparting eV worth of kinetic energy. 1060 00:51:37,425 --> 00:51:39,050 But if you accelerate them, or get them 1061 00:51:39,050 --> 00:51:40,467 from a different nuclear reaction, 1062 00:51:40,467 --> 00:51:42,810 and you get them up to the MeV level, 1063 00:51:42,810 --> 00:51:45,590 where whatever this Q value could be might be negative, 1064 00:51:45,590 --> 00:51:47,760 then you can get the reaction to occur. 1065 00:51:47,760 --> 00:51:53,390 For example, what is the Q of that reaction? 1066 00:51:56,708 --> 00:51:59,080 AUDIENCE: Negative 2.79. 1067 00:51:59,080 --> 00:52:00,560 MICHAEL SHORT: Negative that. 1068 00:52:00,560 --> 00:52:03,190 So in this case, if you want lithium 1069 00:52:03,190 --> 00:52:07,060 to absorb an alpha particle, and make boron and a neutron, 1070 00:52:07,060 --> 00:52:09,190 you would have to accelerate the alphas 1071 00:52:09,190 --> 00:52:12,850 to that same amount of energy in order to get this to occur. 1072 00:52:12,850 --> 00:52:16,600 So nuclear reactions do go both ways, just not as easily. 1073 00:52:16,600 --> 00:52:18,100 Kind of like chemical reactions, you 1074 00:52:18,100 --> 00:52:20,290 can drive them in different directions 1075 00:52:20,290 --> 00:52:22,690 by changing the temperature or changing the concentration 1076 00:52:22,690 --> 00:52:23,800 of the reactants. 1077 00:52:23,800 --> 00:52:25,730 Here the concentration doesn't matter. 1078 00:52:25,730 --> 00:52:29,440 But the kinetic energy related directly to the temperature 1079 00:52:29,440 --> 00:52:31,710 definitely is. 1080 00:52:31,710 --> 00:52:34,740 And so in this case, it's 2.79 MeV. 1081 00:52:34,740 --> 00:52:39,540 If I tell you the gamma ray takes off 0.478 MeV of that, 1082 00:52:39,540 --> 00:52:45,150 we're left with 2.31 MeV between the lithium 1083 00:52:45,150 --> 00:52:48,120 nucleus and the helium nucleus. 1084 00:52:48,120 --> 00:52:50,460 Now my next question-- my last question for you today-- 1085 00:52:50,460 --> 00:52:52,100 oh man-- 1086 00:52:52,100 --> 00:52:53,542 is what's the split? 1087 00:52:53,542 --> 00:52:55,750 I think I don't want to keep you longer, because it's 1088 00:52:55,750 --> 00:52:56,973 one minute of 10:00. 1089 00:52:56,973 --> 00:52:58,390 So this is the question that we're 1090 00:52:58,390 --> 00:53:00,110 going to pick up with on Thursday, 1091 00:53:00,110 --> 00:53:03,190 which is how much of the energy is taken off by helium? 1092 00:53:03,190 --> 00:53:06,530 And how much is taken off by lithium? 1093 00:53:06,530 --> 00:53:09,640 Sorry, I should have kept better track of the time.