1 00:00:01,050 --> 00:00:03,420 The following content is provided under a Creative 2 00:00:03,420 --> 00:00:04,810 Commons license. 3 00:00:04,810 --> 00:00:07,020 Your support will help MIT OpenCourseWare 4 00:00:07,020 --> 00:00:11,110 continue to offer high-quality educational resources for free. 5 00:00:11,110 --> 00:00:13,680 To make a donation or to view additional materials 6 00:00:13,680 --> 00:00:17,640 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:17,640 --> 00:00:18,526 at ocw.mit.edu. 8 00:00:23,190 --> 00:00:24,500 PROFESSOR: OK, guys. 9 00:00:24,500 --> 00:00:26,490 We're actually slightly ahead of where 10 00:00:26,490 --> 00:00:28,500 I thought we'd be at this point, so I'm only 11 00:00:28,500 --> 00:00:30,900 going to spend about half of today's lecture 12 00:00:30,900 --> 00:00:33,120 finishing up some new material on mass parabolas 13 00:00:33,120 --> 00:00:34,200 and stability. 14 00:00:34,200 --> 00:00:36,368 I also got a comment in through the anonymous box 15 00:00:36,368 --> 00:00:38,160 that said please leave a little bit of time 16 00:00:38,160 --> 00:00:40,098 after class for questions. 17 00:00:40,098 --> 00:00:42,390 So you can get them out right away, because I'm usually 18 00:00:42,390 --> 00:00:44,348 running off to teach some other class at, like, 19 00:00:44,348 --> 00:00:46,283 the IDC or some other building. 20 00:00:46,283 --> 00:00:47,700 So from now on, I'll try and leave 21 00:00:47,700 --> 00:00:49,320 about five minutes at the end of class 22 00:00:49,320 --> 00:00:51,090 for questions on today's material, 23 00:00:51,090 --> 00:00:54,180 and we'll make up with the second half-hour or 25 minutes 24 00:00:54,180 --> 00:00:56,740 of this class being for all the questions on the material 25 00:00:56,740 --> 00:00:58,547 so far in the first two weeks. 26 00:00:58,547 --> 00:01:00,630 But first I wanted to give a quick review of where 27 00:01:00,630 --> 00:01:03,780 we were Wednesday and launch back into mass parabolas, which 28 00:01:03,780 --> 00:01:07,170 are ways of looking at nuclear stability in relative numbers 29 00:01:07,170 --> 00:01:09,370 and even or oddness of nuclei. 30 00:01:09,370 --> 00:01:11,100 So you saw last time we intuitively 31 00:01:11,100 --> 00:01:13,860 derived the semi-empirical mass formula 32 00:01:13,860 --> 00:01:19,620 as a sum of volume, surface, coulomb, asymmetry, 33 00:01:19,620 --> 00:01:23,850 and pairing, or whether things are even-even or odd-even terms 34 00:01:23,850 --> 00:01:28,140 with the coefficients in MeV gleaned from data, 35 00:01:28,140 --> 00:01:31,770 and the forms of the-- and the exponents right here gleaned 36 00:01:31,770 --> 00:01:33,420 from intuition. 37 00:01:33,420 --> 00:01:34,950 Here we assume that the nucleus can 38 00:01:34,950 --> 00:01:38,010 be thought of like a big drop of liquid with some charged 39 00:01:38,010 --> 00:01:39,400 particles in it. 40 00:01:39,400 --> 00:01:41,430 And so the droplet should become more stable 41 00:01:41,430 --> 00:01:44,820 the more nuclei there are-- or the more nucleons there are. 42 00:01:44,820 --> 00:01:46,740 But then you have some more outside 43 00:01:46,740 --> 00:01:48,840 on the surface that aren't bonded to the others. 44 00:01:48,840 --> 00:01:52,388 All of the protons are repelling each other over linear length 45 00:01:52,388 --> 00:01:54,305 scales, because the radius of this liquid drop 46 00:01:54,305 --> 00:01:56,560 would scale like A to the 1/3. 47 00:01:56,560 --> 00:01:59,130 There's an asymmetry term, which means if the neutrons 48 00:01:59,130 --> 00:02:01,470 and protons are out of balance, there's 49 00:02:01,470 --> 00:02:04,548 going to be some less binding energy. 50 00:02:04,548 --> 00:02:06,090 And then there's this extra part that 51 00:02:06,090 --> 00:02:09,780 tells you whether the nuclei are even-even or odd-odd. 52 00:02:09,780 --> 00:02:11,820 And this works pretty well. 53 00:02:11,820 --> 00:02:14,580 If you remember, we looked at theory versus experiment 54 00:02:14,580 --> 00:02:17,910 where all the red points here are theoretical predictions, 55 00:02:17,910 --> 00:02:20,730 and all the black points are experimental predictions. 56 00:02:20,730 --> 00:02:22,560 And for the most part, they look spot-on. 57 00:02:22,560 --> 00:02:25,650 It generates the classic binding energy per nucleon 58 00:02:25,650 --> 00:02:27,540 curve that you see in the textbook 59 00:02:27,540 --> 00:02:30,660 and can predict from the semi-empirical mass formula. 60 00:02:30,660 --> 00:02:33,570 Zooming in and correcting for, let's say, 61 00:02:33,570 --> 00:02:35,740 just getting absolute values of errors, 62 00:02:35,740 --> 00:02:38,880 you can see that, except for the very small nuclei 63 00:02:38,880 --> 00:02:41,160 and a few peaks, which we explained 64 00:02:41,160 --> 00:02:44,130 by looking even closer, the formula, well, 65 00:02:44,130 --> 00:02:48,085 it predicts nuclear stability quite well on average. 66 00:02:48,085 --> 00:02:49,710 Again, this line right here, if there's 67 00:02:49,710 --> 00:02:51,790 a dot that lies on this blue line, 68 00:02:51,790 --> 00:02:54,660 it means that theory and experiment agree. 69 00:02:54,660 --> 00:02:58,860 And a deviation by a few MeV here and there, not too bad. 70 00:02:58,860 --> 00:03:01,620 But we started also looking at different nuclear stability 71 00:03:01,620 --> 00:03:05,610 trends, and we noticed that for odd mass number nuclei, 72 00:03:05,610 --> 00:03:10,500 there's usually only one or sometimes none stable isotopes 73 00:03:10,500 --> 00:03:13,830 per Z, whereas for even ones, there's quite a few more. 74 00:03:13,830 --> 00:03:15,540 And we're going to be now linking up 75 00:03:15,540 --> 00:03:18,600 the stability of nuclei versus what mode of decay 76 00:03:18,600 --> 00:03:22,590 they will take in order to find a more stable configuration. 77 00:03:22,590 --> 00:03:25,650 We looked quickly at the number of stable nuclei with even 78 00:03:25,650 --> 00:03:29,370 and odd Z and noted that these places right here where 79 00:03:29,370 --> 00:03:33,300 there are no stable nuclei correspond to technetium 80 00:03:33,300 --> 00:03:34,740 and promethium. 81 00:03:34,740 --> 00:03:37,000 There's no periodic table on the back of this wall, 82 00:03:37,000 --> 00:03:38,765 but behind my back on the other wall, 83 00:03:38,765 --> 00:03:40,140 there's that periodic table where 84 00:03:40,140 --> 00:03:42,510 you can see the two elements that are fairly 85 00:03:42,510 --> 00:03:44,340 light with no stable isotopes. 86 00:03:44,340 --> 00:03:46,290 That's what those correspond to. 87 00:03:46,290 --> 00:03:49,950 And the peaks correspond to what we call magic numbers 88 00:03:49,950 --> 00:03:52,650 or numbers of protons or neutrons 89 00:03:52,650 --> 00:03:54,630 where all available states at some energy 90 00:03:54,630 --> 00:03:56,040 are pretty much filled. 91 00:03:56,040 --> 00:03:59,050 And this goes for both protons and neutrons. 92 00:03:59,050 --> 00:04:03,180 So something with a magic number for both n, number of neutrons, 93 00:04:03,180 --> 00:04:04,740 and Z, number of protons, is going 94 00:04:04,740 --> 00:04:06,625 to be exceptionally stable. 95 00:04:06,625 --> 00:04:08,250 And we'll see how that's used as a tool 96 00:04:08,250 --> 00:04:11,370 to synthesize the super heavy elements that we believe 97 00:04:11,370 --> 00:04:14,070 should exist. 98 00:04:14,070 --> 00:04:16,470 And finally we got into these mass parabolas. 99 00:04:16,470 --> 00:04:18,750 I found this to be a particularly difficult concept 100 00:04:18,750 --> 00:04:20,640 to just get mathematically. 101 00:04:20,640 --> 00:04:23,700 If you remember, we wrote out the semi-empirical mass formula 102 00:04:23,700 --> 00:04:26,880 and said if you take the derivative with respect to Z, 103 00:04:26,880 --> 00:04:31,550 as we did it, you would get the most stable z for a given A. 104 00:04:31,550 --> 00:04:34,350 And we started graphing for a equals 93 105 00:04:34,350 --> 00:04:36,782 where niobium is stable. 106 00:04:36,782 --> 00:04:39,240 That was just the one I had on the brain from some failures 107 00:04:39,240 --> 00:04:41,460 in lab earlier this week. 108 00:04:41,460 --> 00:04:44,830 We started plotting where those nuclei-- 109 00:04:44,830 --> 00:04:48,150 what is it-- the relative masses are for a fixed A. So 110 00:04:48,150 --> 00:04:49,830 let's regenerate that one right now, 111 00:04:49,830 --> 00:04:52,290 because we were a little fast at the end of last lecture. 112 00:04:52,290 --> 00:04:56,132 Then I want to generate one for a equals 40. 113 00:04:56,132 --> 00:04:57,840 And you'll see something kind of curious. 114 00:04:57,840 --> 00:05:00,090 I'm going to leave this up here for a sec. 115 00:05:00,090 --> 00:05:03,150 If you notice, for odd A nuclei, there's 116 00:05:03,150 --> 00:05:06,895 only one parabola, whereas for even A, there are two. 117 00:05:06,895 --> 00:05:08,520 Why that is, we're going to see when we 118 00:05:08,520 --> 00:05:10,090 look at the table of nuclides. 119 00:05:10,090 --> 00:05:12,450 But notice this nucleus right here 120 00:05:12,450 --> 00:05:16,230 can decay by either positron emission or beta emission 121 00:05:16,230 --> 00:05:17,520 to get to a more stable form. 122 00:05:17,520 --> 00:05:18,895 And there are many real examples, 123 00:05:18,895 --> 00:05:22,270 and I'm going to show you how to find them. 124 00:05:22,270 --> 00:05:26,160 So let's start off by going back to the table of nuclides, 125 00:05:26,160 --> 00:05:29,330 finding niobium-93. 126 00:05:29,330 --> 00:05:32,520 Just go up one more chunk. 127 00:05:32,520 --> 00:05:34,650 And there we are. 128 00:05:34,650 --> 00:05:38,280 Niobium-93 is a stable isotope. 129 00:05:38,280 --> 00:05:40,030 And if you want to see where it came from, 130 00:05:40,030 --> 00:05:43,080 you can scroll down a little bit and see its possible parent 131 00:05:43,080 --> 00:05:45,010 nuclides right here. 132 00:05:45,010 --> 00:05:47,670 So let's say that niobium-- 133 00:05:47,670 --> 00:05:49,560 we'll draw it right there-- 134 00:05:49,560 --> 00:05:50,190 is stable. 135 00:05:50,190 --> 00:05:52,850 We'll put it at the bottom of this parabola. 136 00:05:52,850 --> 00:05:57,560 And let's work down in Z. So we'll move to zirconium. 137 00:05:57,560 --> 00:06:02,240 Zirconium-93 ostensibly has a very similar atomic mass. 138 00:06:02,240 --> 00:06:07,040 But if you remember that 93 AMU is a rather poor approximation 139 00:06:07,040 --> 00:06:11,180 for the actual mass of all nuclei with A equals 93. 140 00:06:11,180 --> 00:06:14,330 In fact, if you look very closely at the atomic masses, 141 00:06:14,330 --> 00:06:18,660 zirconium-93 is 92.90. 142 00:06:18,660 --> 00:06:21,060 Niobium-93, well, it looks like we 143 00:06:21,060 --> 00:06:23,310 have to go all the way to another digit there. 144 00:06:23,310 --> 00:06:26,560 92.906. 145 00:06:26,560 --> 00:06:31,680 You have to go to, like, even more digits 92.906375, 146 00:06:31,680 --> 00:06:34,290 92.906475. 147 00:06:34,290 --> 00:06:36,270 So we go down in Z, and we've actually 148 00:06:36,270 --> 00:06:40,170 gone up in mass by looks like the sixth or seventh digit 149 00:06:40,170 --> 00:06:41,470 in AMU. 150 00:06:41,470 --> 00:06:44,430 If we go up in mass, we go down in binding energy. 151 00:06:44,430 --> 00:06:47,010 That tells us that there's something that's less stable. 152 00:06:47,010 --> 00:06:49,650 And if you notice, we went down by a very small-- 153 00:06:49,650 --> 00:06:52,950 or we went up by a very small amount of mass. 154 00:06:52,950 --> 00:06:56,820 Notice also that its beta decay energy is really, really small, 155 00:06:56,820 --> 00:06:59,070 91 kiloelectron volts. 156 00:06:59,070 --> 00:07:03,670 So why don't we put zirconium just above? 157 00:07:03,670 --> 00:07:05,390 And we note that that decay will happen 158 00:07:05,390 --> 00:07:09,860 by beta, where the beta, let's say 159 00:07:09,860 --> 00:07:14,280 if we have an isotope with mass number A, protons Z, 160 00:07:14,280 --> 00:07:17,030 and let's just call it symbol question mark. 161 00:07:17,030 --> 00:07:20,810 In beta decay, we have the same A. 162 00:07:20,810 --> 00:07:22,820 We'll have a different Z. We're going 163 00:07:22,820 --> 00:07:24,740 to have to give these symbols. 164 00:07:24,740 --> 00:07:28,880 Let's call this parent, and we'll call that daughter. 165 00:07:28,880 --> 00:07:32,517 Plus a beta, plus an electron antineutrino. 166 00:07:32,517 --> 00:07:34,850 And what has to happen to that Z in order for everything 167 00:07:34,850 --> 00:07:36,980 to be conserved? 168 00:07:36,980 --> 00:07:39,750 It's the same reaction that we've got here for-- 169 00:07:39,750 --> 00:07:41,640 I'm sorry-- for zirconium. 170 00:07:41,640 --> 00:07:47,100 So you'd have to have one fewer proton to release one electron. 171 00:07:47,100 --> 00:07:49,320 And so that becomes same A but different Z. 172 00:07:49,320 --> 00:07:51,120 And this is the beta decay reaction. 173 00:07:56,670 --> 00:07:58,560 Let's go back a little farther. 174 00:07:58,560 --> 00:08:00,645 We'll look at the possible parent nuclide for-- 175 00:08:00,645 --> 00:08:01,770 did anyone have a question? 176 00:08:01,770 --> 00:08:06,560 AUDIENCE: Don't you need one more proton [INAUDIBLE]?? 177 00:08:06,560 --> 00:08:07,600 PROFESSOR: Let's see. 178 00:08:07,600 --> 00:08:09,580 Which direction are we going in Z here? 179 00:08:12,200 --> 00:08:14,252 That goes to yttrium. 180 00:08:14,252 --> 00:08:16,298 It actually looks like it's going down. 181 00:08:16,298 --> 00:08:17,340 Oh, yeah, for beta decay. 182 00:08:17,340 --> 00:08:21,030 I'm thinking-- I have the reaction backwards. 183 00:08:21,030 --> 00:08:22,870 Sorry. 184 00:08:22,870 --> 00:08:25,380 I need one more proton to account 185 00:08:25,380 --> 00:08:26,630 for the extra negative charge. 186 00:08:26,630 --> 00:08:27,750 You're right. 187 00:08:27,750 --> 00:08:28,290 OK. 188 00:08:28,290 --> 00:08:30,290 Yep, I was thinking backwards, because we're now 189 00:08:30,290 --> 00:08:32,799 climbing up the decay chain in reverse order. 190 00:08:32,799 --> 00:08:35,980 So this could have come from yttrium-93 with a much 191 00:08:35,980 --> 00:08:37,480 higher energy of three MeV. 192 00:08:37,480 --> 00:08:40,809 So let's put yttrium right here. 193 00:08:44,360 --> 00:08:46,330 That gives a beta decay. 194 00:08:46,330 --> 00:08:52,750 And we'll just go one more back to strontium-93 Has 195 00:08:52,750 --> 00:08:56,507 an even higher beta decay energy. 196 00:08:56,507 --> 00:08:57,590 So let's put that up here. 197 00:09:00,710 --> 00:09:03,120 And let's take a look at its mass real quick. 198 00:09:03,120 --> 00:09:08,270 The mass of strontium-93, 92.914 AMU. 199 00:09:08,270 --> 00:09:13,290 If we go back to niobium-93, now it's 200 00:09:13,290 --> 00:09:16,410 noticeably different to, like, four significant digits 201 00:09:16,410 --> 00:09:17,178 instead of six. 202 00:09:17,178 --> 00:09:21,540 92.914 versus 92.906. 203 00:09:21,540 --> 00:09:24,780 And so that shows you that a tiny bit of mass and AMU 204 00:09:24,780 --> 00:09:26,850 corresponds to a pretty significant change 205 00:09:26,850 --> 00:09:30,450 in binding energy by that same conversion factor 206 00:09:30,450 --> 00:09:33,630 that we've been using everywhere. 207 00:09:33,630 --> 00:09:45,910 931.49 AMU per big MeV per C squared. 208 00:09:45,910 --> 00:09:47,570 Let's see. 209 00:09:47,570 --> 00:09:48,170 Yeah. 210 00:09:48,170 --> 00:09:48,670 OK. 211 00:09:50,930 --> 00:09:53,690 So let's go now in the other direction, in the positron 212 00:09:53,690 --> 00:09:54,900 direction. 213 00:09:54,900 --> 00:10:00,410 Niobium can also be made by electron capture 214 00:10:00,410 --> 00:10:01,820 from molybdenum. 215 00:10:01,820 --> 00:10:05,860 So let's put molybdenum right here. 216 00:10:05,860 --> 00:10:08,113 Let's say that around half an-- 217 00:10:08,113 --> 00:10:09,030 what did we have here? 218 00:10:09,030 --> 00:10:10,030 It was like half an MeV. 219 00:10:14,230 --> 00:10:15,697 Like that. 220 00:10:15,697 --> 00:10:16,280 And let's see. 221 00:10:16,280 --> 00:10:19,670 Molybdenum-93 could have been made by electron capture 222 00:10:19,670 --> 00:10:24,905 from technetium-93 with an energy of 3.201 MeV, 223 00:10:24,905 --> 00:10:25,655 even more extreme. 224 00:10:31,220 --> 00:10:34,080 We'll go back one more, because there's a trend that I want 225 00:10:34,080 --> 00:10:35,850 you guys to be able to see. 226 00:10:35,850 --> 00:10:37,830 And this could have come from electron capture 227 00:10:37,830 --> 00:10:40,620 from ruthenium. 228 00:10:40,620 --> 00:10:42,570 I think I may have said rubidium last time, 229 00:10:42,570 --> 00:10:44,350 but Ru is ruthenium-93. 230 00:10:47,460 --> 00:10:52,740 And that 6.3 MeV, something like that. 231 00:10:52,740 --> 00:10:55,400 And this is where we got to yesterday. 232 00:10:55,400 --> 00:10:57,950 Now I'd like us to take a closer look at the decay 233 00:10:57,950 --> 00:11:01,640 diagrams, which tells us what possible decay reactions can 234 00:11:01,640 --> 00:11:04,580 happen in each of these reactions. 235 00:11:04,580 --> 00:11:06,080 Since we're right here on the chart, 236 00:11:06,080 --> 00:11:10,520 let's take a look at ruthenium turning into technetium by what 237 00:11:10,520 --> 00:11:11,840 it says, electron capture. 238 00:11:11,840 --> 00:11:14,900 So note that on the table, you can click on electron capture, 239 00:11:14,900 --> 00:11:17,870 and if it's highlighted, then the decay diagrams are known. 240 00:11:17,870 --> 00:11:20,150 It's not known for every isotope, 241 00:11:20,150 --> 00:11:23,020 but for a lot of the ones you'll be dealing with, it is. 242 00:11:23,020 --> 00:11:26,990 And you get something I have to zoom out for-- 243 00:11:26,990 --> 00:11:29,600 a lot, a lot of different decays. 244 00:11:29,600 --> 00:11:32,150 What I want you to look at is this one here on the bottom 245 00:11:32,150 --> 00:11:35,400 that I'll zoom in to. 246 00:11:35,400 --> 00:11:37,740 That should be a little more visible. 247 00:11:37,740 --> 00:11:42,100 So notice that if you want to go down the entire 6.4-something 248 00:11:42,100 --> 00:11:51,180 MeV, it usually proceeds by B-plus or positron decay, 249 00:11:51,180 --> 00:11:52,980 by either method. 250 00:11:52,980 --> 00:11:56,160 And as you go up the chain, as these energy differences get 251 00:11:56,160 --> 00:11:59,130 smaller, look what happens to the probability 252 00:11:59,130 --> 00:12:00,900 of getting positron decay. 253 00:12:00,900 --> 00:12:03,060 It shrinks lower and lower and lower. 254 00:12:03,060 --> 00:12:05,220 So there's a trend that the larger the decay 255 00:12:05,220 --> 00:12:08,310 energy for this type of reaction, the more likely 256 00:12:08,310 --> 00:12:10,710 you're going to get positron decay. 257 00:12:10,710 --> 00:12:13,650 And in fact, where we left off last time is in order 258 00:12:13,650 --> 00:12:18,120 to get positron decay, the Q value of the reaction 259 00:12:18,120 --> 00:12:23,730 has to be at least 1.022 MeV, better known 260 00:12:23,730 --> 00:12:29,940 as at least two times the rest mass of the electron, 261 00:12:29,940 --> 00:12:32,580 because in this case, to conserve charge and energy, 262 00:12:32,580 --> 00:12:34,890 you shoot out a positron, and you also 263 00:12:34,890 --> 00:12:36,960 have to eject an electron in order 264 00:12:36,960 --> 00:12:40,160 to conserve all the charge going on here. 265 00:12:40,160 --> 00:12:42,940 So there you have it. 266 00:12:42,940 --> 00:12:47,670 Now let's look at the lower energy decay of technetium 267 00:12:47,670 --> 00:12:49,230 to molybdenum, which had something 268 00:12:49,230 --> 00:12:52,620 like 3 MeV associated with it. 269 00:12:52,620 --> 00:12:57,790 So we'll click on technetium, and its energy is 3.2 MeV. 270 00:12:57,790 --> 00:13:00,820 Let's take a look at its electron capture. 271 00:13:00,820 --> 00:13:03,430 Significantly simpler. 272 00:13:03,430 --> 00:13:05,920 Already what do you notice about these positron 273 00:13:05,920 --> 00:13:07,045 to electron capture ratios? 274 00:13:09,568 --> 00:13:10,360 Anyone call it out. 275 00:13:14,072 --> 00:13:16,280 AUDIENCE: Electron capture is much more likely. 276 00:13:16,280 --> 00:13:17,030 PROFESSOR: Indeed. 277 00:13:17,030 --> 00:13:19,070 When the energy of the decay goes down-- 278 00:13:19,070 --> 00:13:21,980 notice that only these decays are allowed-- 279 00:13:21,980 --> 00:13:25,040 The electron capture suddenly becomes much more likely. 280 00:13:25,040 --> 00:13:27,320 But notice that it does not let you go directly 281 00:13:27,320 --> 00:13:29,760 from 3.2 MeV to 0. 282 00:13:29,760 --> 00:13:31,850 There is no allowable decay here. 283 00:13:31,850 --> 00:13:35,240 So this is probably a change of-- that's 3.2. 284 00:13:35,240 --> 00:13:36,830 That's 1.3. 285 00:13:36,830 --> 00:13:38,840 A little less than 2 MeV. 286 00:13:38,840 --> 00:13:40,280 All of a sudden, electron capture 287 00:13:40,280 --> 00:13:43,880 becomes much more likely, but positron decay 288 00:13:43,880 --> 00:13:46,430 is not disallowed yet. 289 00:13:46,430 --> 00:13:50,910 So we can say electron capture or positron decay right there. 290 00:13:50,910 --> 00:13:53,450 Everyone with me so far? 291 00:13:53,450 --> 00:13:56,130 So let's go to the really low energy one. 292 00:13:56,130 --> 00:13:58,840 We'll click on molybdenum-93 and see 293 00:13:58,840 --> 00:14:02,830 how it decays with an energy of 0.405 MeV to niobium. 294 00:14:02,830 --> 00:14:06,224 Anyone want to guess what's allowed? 295 00:14:06,224 --> 00:14:08,000 AUDIENCE: Electron capture only. 296 00:14:08,000 --> 00:14:09,830 PROFESSOR: Electron capture only. 297 00:14:09,830 --> 00:14:12,590 There's not enough energy for positron decay. 298 00:14:12,590 --> 00:14:14,480 And, indeed, it draws funny, because there's 299 00:14:14,480 --> 00:14:16,170 a metastable state. 300 00:14:16,170 --> 00:14:17,990 But if you scroll down here, there 301 00:14:17,990 --> 00:14:21,960 are two pathways allowed, both of which by electron capture. 302 00:14:21,960 --> 00:14:24,132 Decay diagram's quite a bit simpler. 303 00:14:24,132 --> 00:14:26,090 So we leave this one here by saying it can only 304 00:14:26,090 --> 00:14:27,830 decay by electron capture. 305 00:14:30,510 --> 00:14:33,120 Any questions on the odd A before we 306 00:14:33,120 --> 00:14:38,130 move on to the even, which is a little more interesting? 307 00:14:38,130 --> 00:14:38,710 Cool. 308 00:14:38,710 --> 00:14:40,080 OK. 309 00:14:40,080 --> 00:14:42,300 Let's move on to the even case. 310 00:14:42,300 --> 00:14:43,950 So for here, I'm going to go back 311 00:14:43,950 --> 00:14:48,030 to the overall picture of the table of nuclides. 312 00:14:48,030 --> 00:14:51,630 Click on around where I think potassium-40 is. 313 00:14:51,630 --> 00:14:54,020 Looks like I got there. 314 00:14:54,020 --> 00:14:56,310 And I want to point out one of these features. 315 00:14:56,310 --> 00:14:58,890 If you wanted to undergo decay change 316 00:14:58,890 --> 00:15:01,530 and maintain the same mass number, 317 00:15:01,530 --> 00:15:04,140 that's diagonally from upper left to lower right. 318 00:15:04,140 --> 00:15:08,580 See how all the isotopes here have a 40 in front of them. 319 00:15:08,580 --> 00:15:11,580 The really interesting part is as you cross this line, 320 00:15:11,580 --> 00:15:16,350 you go from stable to unstable to stable to unstable again. 321 00:15:16,350 --> 00:15:19,230 The colors here is dark blue represents stable, 322 00:15:19,230 --> 00:15:21,870 and dark gray represents long lifetimes 323 00:15:21,870 --> 00:15:24,330 of over 100,000 years. 324 00:15:24,330 --> 00:15:27,168 So this is one of the reasons you find potassium-40 325 00:15:27,168 --> 00:15:27,960 in the environment. 326 00:15:27,960 --> 00:15:32,550 In fact, 0.011% of all potassium in you and everything 327 00:15:32,550 --> 00:15:33,990 is potassium-40. 328 00:15:33,990 --> 00:15:36,810 It's what's known as a primordial nuclide. 329 00:15:36,810 --> 00:15:38,970 It's not stable, but its half-life 330 00:15:38,970 --> 00:15:42,010 is so long that there's still some 331 00:15:42,010 --> 00:15:45,190 left since the universe began or whatever 332 00:15:45,190 --> 00:15:49,560 supernova that formed Earth got accumulated into the earth. 333 00:15:49,560 --> 00:15:51,613 But notice it can come from-- 334 00:15:51,613 --> 00:15:53,530 it can decay by a couple of different methods. 335 00:15:53,530 --> 00:15:57,600 So let's pick one of those stable isotopes, calcium-40, 336 00:15:57,600 --> 00:16:01,930 and put that as the bottom of the parabola on this diagram. 337 00:16:01,930 --> 00:16:03,700 So we'll put calcium here. 338 00:16:03,700 --> 00:16:08,160 And in a relative sense, we'll put a calcium point right there 339 00:16:08,160 --> 00:16:10,230 for its total mass. 340 00:16:10,230 --> 00:16:12,510 And it could have come from beta decay 341 00:16:12,510 --> 00:16:19,330 from potassium-40 or electron capture from scandium-40 40. 342 00:16:19,330 --> 00:16:21,430 So let's look at potassium-40. 343 00:16:21,430 --> 00:16:26,760 It can beta decay for about, oh, 1.3 MeV. 344 00:16:26,760 --> 00:16:30,150 So potassium is right here. 345 00:16:30,150 --> 00:16:36,520 Let's say it could beta decay with about 1.3 MeV. 346 00:16:36,520 --> 00:16:40,320 And we'll trace potassium back a little bit, 347 00:16:40,320 --> 00:16:43,950 figure out where would it have come from. 348 00:16:43,950 --> 00:16:45,510 Interesting. 349 00:16:45,510 --> 00:16:46,660 Doesn't tell us. 350 00:16:46,660 --> 00:16:49,160 OK, forget that. 351 00:16:49,160 --> 00:16:56,290 Let's trace calcium back and say there's scandium-40. 352 00:16:56,290 --> 00:16:59,030 And scandium-40 can decay with-- wow-- 353 00:16:59,030 --> 00:17:04,430 an enormous 14.32 MeV. 354 00:17:04,430 --> 00:17:05,900 Let's put that like here. 355 00:17:12,050 --> 00:17:15,609 Anyone want to guess which mode, electron capture or positrons, 356 00:17:15,609 --> 00:17:16,390 much more likely? 357 00:17:16,390 --> 00:17:18,121 AUDIENCE: I think positrons. 358 00:17:18,121 --> 00:17:19,329 PROFESSOR: Probably positron. 359 00:17:19,329 --> 00:17:22,180 Let's take a look. 360 00:17:22,180 --> 00:17:22,960 Oh boy. 361 00:17:22,960 --> 00:17:25,030 Another complicated one. 362 00:17:25,030 --> 00:17:27,190 But the whole way down, positron, positron, 363 00:17:27,190 --> 00:17:30,280 positron for all the most likely decays. 364 00:17:30,280 --> 00:17:33,370 You won't find a drawing to every single line. 365 00:17:33,370 --> 00:17:35,650 I believe that they know that at some point, 366 00:17:35,650 --> 00:17:38,290 drawing extra lines is futile, and they just all overlap 367 00:17:38,290 --> 00:17:39,130 each other. 368 00:17:39,130 --> 00:17:41,560 So I don't know exactly how the algorithm works, 369 00:17:41,560 --> 00:17:44,930 but it does draw up to some number of possible decay 370 00:17:44,930 --> 00:17:45,430 chains. 371 00:17:45,430 --> 00:17:48,160 If you want to see every single one, 372 00:17:48,160 --> 00:17:53,058 they are tabulated in a very, very long list down below. 373 00:17:53,058 --> 00:17:55,600 I'm never going to ask you to do something with all of these, 374 00:17:55,600 --> 00:17:57,670 because that would be insane unless it's 375 00:17:57,670 --> 00:18:00,340 a relatively simple decay, like that 376 00:18:00,340 --> 00:18:03,140 has two or three possibilities. 377 00:18:03,140 --> 00:18:04,490 And let's see. 378 00:18:04,490 --> 00:18:06,320 This could have come from electron capture 379 00:18:06,320 --> 00:18:11,210 from titanium-40 with 11.68 MeV. 380 00:18:11,210 --> 00:18:11,810 Wow. 381 00:18:11,810 --> 00:18:13,830 OK. 382 00:18:13,830 --> 00:18:14,330 Up here. 383 00:18:19,400 --> 00:18:20,880 And there's titanium. 384 00:18:23,420 --> 00:18:25,990 And let's go in the other direction. 385 00:18:25,990 --> 00:18:31,780 So I do know that potassium-40 can decay into argon-40. 386 00:18:31,780 --> 00:18:36,330 So let's jump there. 387 00:18:36,330 --> 00:18:39,280 Argon is a stable isotope too. 388 00:18:39,280 --> 00:18:45,800 So potassium-40 can decay into argon-40 by electron capture. 389 00:18:45,800 --> 00:18:46,300 OK, good. 390 00:18:46,300 --> 00:18:56,150 A more respectable 1.505 MeV. 391 00:18:56,150 --> 00:18:57,380 Is positron decay allowed? 392 00:19:01,960 --> 00:19:02,630 AUDIENCE: Yes. 393 00:19:02,630 --> 00:19:03,260 PROFESSOR: Yes. 394 00:19:03,260 --> 00:19:03,760 Why is that? 395 00:19:03,760 --> 00:19:07,800 AUDIENCE: [INAUDIBLE] 396 00:19:07,800 --> 00:19:10,200 PROFESSOR: Over 1.022 MeV. 397 00:19:10,200 --> 00:19:10,920 Yeah. 398 00:19:10,920 --> 00:19:12,720 Anyone have a question? 399 00:19:12,720 --> 00:19:13,220 No? 400 00:19:13,220 --> 00:19:14,218 OK. 401 00:19:14,218 --> 00:19:16,260 So we've got kind of a kink in our mass parabola. 402 00:19:16,260 --> 00:19:16,790 Yeah? 403 00:19:16,790 --> 00:19:18,165 AUDIENCE: Actually, yeah, so it's 404 00:19:18,165 --> 00:19:20,777 possible if it's over 1.022, but it's still very unlikely. 405 00:19:20,777 --> 00:19:21,860 PROFESSOR: That's correct. 406 00:19:21,860 --> 00:19:24,480 AUDIENCE: Until we get to these higher orders, like 10. 407 00:19:24,480 --> 00:19:26,610 PROFESSOR: Yep, so once the Q value's satisfied, 408 00:19:26,610 --> 00:19:28,045 it is technically possible. 409 00:19:28,045 --> 00:19:29,670 But if you had something with the decay 410 00:19:29,670 --> 00:19:34,080 energy of, like, 1.023 MeV, it would be exceedingly unlikely. 411 00:19:34,080 --> 00:19:36,090 So in fact, we can take a look at this. 412 00:19:36,090 --> 00:19:37,740 This, I would say, is also going to be 413 00:19:37,740 --> 00:19:41,120 on the exceedingly unlikely level, and we can take a look. 414 00:19:41,120 --> 00:19:44,030 So if we look at the decay diagram, 415 00:19:44,030 --> 00:19:45,410 we know it makes positrons. 416 00:19:45,410 --> 00:19:48,010 They're not even really listed. 417 00:19:48,010 --> 00:19:49,810 Interesting. 418 00:19:49,810 --> 00:19:51,910 So that process would not be allowed, 419 00:19:51,910 --> 00:19:55,210 but this one, because that's about 1.5 MeV, 420 00:19:55,210 --> 00:19:55,990 should be allowed. 421 00:19:55,990 --> 00:19:59,170 But since that branch ratio or the probability 422 00:19:59,170 --> 00:20:02,020 of that happening is already so low, I wonder if it even says. 423 00:20:02,020 --> 00:20:08,980 Yep, beta ray with a max or average energy of 482.8 MeV. 424 00:20:08,980 --> 00:20:11,230 We're going to go over why that energy is so low when 425 00:20:11,230 --> 00:20:13,180 we talk about decay next week. 426 00:20:13,180 --> 00:20:15,700 With the relative intensity of something with a lot of zeros 427 00:20:15,700 --> 00:20:17,800 before the decimal place. 428 00:20:17,800 --> 00:20:18,480 So there you go. 429 00:20:18,480 --> 00:20:23,100 Like you said, energies near 1.022 MeV, slightly above it, 430 00:20:23,100 --> 00:20:29,325 are extremely unlikely but possible and measurable. 431 00:20:29,325 --> 00:20:30,670 Cool. 432 00:20:30,670 --> 00:20:36,420 And then let's see what could have made argon 40. 433 00:20:36,420 --> 00:20:41,290 Could have been beta decay from chlorine-40. 434 00:20:41,290 --> 00:20:43,060 So chlorine maybe was here. 435 00:20:46,700 --> 00:20:48,450 And I don't think I have to draw any more. 436 00:20:48,450 --> 00:20:51,570 So we've got a funny-looking parabola with a kink in it, 437 00:20:51,570 --> 00:20:54,640 because really, you have two mass parabolas overlapping. 438 00:20:54,640 --> 00:20:56,520 I'm going to go back to the screen 439 00:20:56,520 --> 00:20:58,290 so that the diagram from the notes 440 00:20:58,290 --> 00:20:59,980 makes a little more sense. 441 00:20:59,980 --> 00:21:01,980 What we've kind of traced out here 442 00:21:01,980 --> 00:21:09,050 is that there's two overlapping parabolas here. 443 00:21:09,050 --> 00:21:11,120 There's the one with the-- what is 444 00:21:11,120 --> 00:21:14,120 it-- the odd Z and the even Z. 445 00:21:14,120 --> 00:21:15,363 So there you go. 446 00:21:15,363 --> 00:21:17,030 Just like the one on here, which I think 447 00:21:17,030 --> 00:21:18,060 is for a different mass number. 448 00:21:18,060 --> 00:21:18,560 Yep. 449 00:21:18,560 --> 00:21:19,430 102. 450 00:21:19,430 --> 00:21:22,810 We get the same kind of behavior where things will mostly 451 00:21:22,810 --> 00:21:26,930 follow the lower mass parabola, but sometimes if something 452 00:21:26,930 --> 00:21:32,110 gets stuck here, it can go either way to get more stable. 453 00:21:32,110 --> 00:21:33,670 So I want to stop here for new stuff, 454 00:21:33,670 --> 00:21:35,378 because this is precisely where I thought 455 00:21:35,378 --> 00:21:36,675 we'd be at the end of the week. 456 00:21:36,675 --> 00:21:38,050 And in the next half an hour, I'd 457 00:21:38,050 --> 00:21:40,420 like to open it up to questions or working things 458 00:21:40,420 --> 00:21:42,520 out together on the board or anything else 459 00:21:42,520 --> 00:21:43,440 you might have had. 460 00:21:43,440 --> 00:21:43,940 Yeah? 461 00:21:43,940 --> 00:21:46,150 AUDIENCE: I have a question about the parabola things. 462 00:21:46,150 --> 00:21:46,817 PROFESSOR: Sure. 463 00:21:46,817 --> 00:21:50,480 AUDIENCE: There's-- you said multiple paths, 464 00:21:50,480 --> 00:21:53,910 so it doesn't have to do the little peak in the middle? 465 00:21:53,910 --> 00:21:56,850 Like, could it follow the lower parabola or the upper, 466 00:21:56,850 --> 00:21:58,330 or does it have to jump over? 467 00:21:58,330 --> 00:22:01,090 PROFESSOR: It's going to go in whatever 468 00:22:01,090 --> 00:22:02,230 way makes it more stable. 469 00:22:02,230 --> 00:22:04,147 So you're never going to have a nucleus that's 470 00:22:04,147 --> 00:22:06,365 going to spontaneously gain mass in order 471 00:22:06,365 --> 00:22:07,490 to get to a different path. 472 00:22:07,490 --> 00:22:10,720 You can only go down on the mass axis. 473 00:22:10,720 --> 00:22:13,930 But let's say you happen to be starting here at potassium-40. 474 00:22:13,930 --> 00:22:16,960 You can go down via either mechanism to the next mass 475 00:22:16,960 --> 00:22:18,289 parabola down. 476 00:22:18,289 --> 00:22:21,223 AUDIENCE: But if you were argon, you would go up. 477 00:22:21,223 --> 00:22:22,690 That's what you would do. 478 00:22:22,690 --> 00:22:23,690 PROFESSOR: That's right. 479 00:22:23,690 --> 00:22:25,180 If you're at argon, you're stuck. 480 00:22:25,180 --> 00:22:27,490 And in fact, if you want to take a look, 481 00:22:27,490 --> 00:22:29,980 what do I mean scientifically by "stuck"? 482 00:22:29,980 --> 00:22:31,810 I mean stable. 483 00:22:31,810 --> 00:22:35,380 Argon-40 is a stable nucleus that 484 00:22:35,380 --> 00:22:38,900 comprises 99.6% of the argon. 485 00:22:38,900 --> 00:22:41,710 So that's what I mean by "stuck" is stable. 486 00:22:41,710 --> 00:22:44,110 And if we look at the rest of the table of nuclides 487 00:22:44,110 --> 00:22:46,750 for similar-looking places-- 488 00:22:46,750 --> 00:22:51,810 so let's hunt near potassium-40. 489 00:22:51,810 --> 00:22:53,410 So notice potassium-40 right here 490 00:22:53,410 --> 00:22:57,775 has got stable isotopes to the upper left and the lower right. 491 00:22:57,775 --> 00:23:01,760 If we look back over here, manganese-54. 492 00:23:01,760 --> 00:23:02,300 Same deal. 493 00:23:02,300 --> 00:23:05,330 It's got a stable isotope to the upper left and a stable one 494 00:23:05,330 --> 00:23:07,010 to the lower right. 495 00:23:07,010 --> 00:23:09,740 How much you want to bet that when we click on manganese-54, 496 00:23:09,740 --> 00:23:11,960 it's got two possible parent nuclides-- 497 00:23:11,960 --> 00:23:15,510 or I'm sorry, two possible decay methods. 498 00:23:15,510 --> 00:23:17,360 So let's take a look. 499 00:23:17,360 --> 00:23:23,750 Manganese-54 can either electron capture and positron decay 500 00:23:23,750 --> 00:23:27,668 to chromium-54 or beta decay to iron-54. 501 00:23:27,668 --> 00:23:29,960 Let's take a look at one more to hammer the point home, 502 00:23:29,960 --> 00:23:32,270 and I think that'll probably be enough. 503 00:23:32,270 --> 00:23:36,160 Cobalt-58 right near nickel-58 and iron-58. 504 00:23:39,530 --> 00:23:41,020 Interesting. 505 00:23:41,020 --> 00:23:44,902 That one's not allowed unless there's more down here. 506 00:23:44,902 --> 00:23:46,920 So you can electron capture to iron-58, 507 00:23:46,920 --> 00:23:50,130 but there's no allowed decay to-- 508 00:23:50,130 --> 00:23:51,510 what was it? 509 00:23:51,510 --> 00:23:52,950 Nickel-58. 510 00:23:52,950 --> 00:23:55,250 OK. 511 00:23:55,250 --> 00:23:56,960 Let's look for more. 512 00:23:56,960 --> 00:24:03,200 Chlorine-36 has argon and sulfur on either side. 513 00:24:03,200 --> 00:24:05,890 There it is. 514 00:24:05,890 --> 00:24:07,353 Beta decay and electron capture. 515 00:24:07,353 --> 00:24:09,520 And how much you want to bet there's basically never 516 00:24:09,520 --> 00:24:11,290 a positron here? 517 00:24:11,290 --> 00:24:15,210 But basically, not actually never. 518 00:24:15,210 --> 00:24:19,110 So you get a positron 0.01% of the time and electron 519 00:24:19,110 --> 00:24:21,510 capture 1.89% of the time. 520 00:24:21,510 --> 00:24:25,540 Where is the other 98-and-change percent? 521 00:24:25,540 --> 00:24:28,710 Right here in the beta decay. 522 00:24:28,710 --> 00:24:32,460 So in this case, chlorine-36 will preferentially beta decay. 523 00:24:32,460 --> 00:24:34,510 If you also notice, it's a-- 524 00:24:34,510 --> 00:24:35,010 let's see. 525 00:24:35,010 --> 00:24:36,710 I don't know if that actually matters. 526 00:24:36,710 --> 00:24:38,918 But I am going to say it's more likely to beta decay. 527 00:24:38,918 --> 00:24:40,710 So when you sum these up, you get 528 00:24:40,710 --> 00:24:43,590 100% of the possible decays. 529 00:24:43,590 --> 00:24:47,210 Let's see how many energy levels there are there too. 530 00:24:47,210 --> 00:24:49,670 Hopefully not too many. 531 00:24:49,670 --> 00:24:51,980 That qualifies as not too many. 532 00:24:51,980 --> 00:24:52,480 Yeah? 533 00:24:52,480 --> 00:24:53,684 Sean? 534 00:24:53,684 --> 00:24:57,530 AUDIENCE: Are the changes in mass always going 535 00:24:57,530 --> 00:25:01,520 to be attributed to beta decays or electron 536 00:25:01,520 --> 00:25:03,960 captures or positron [INAUDIBLE]?? 537 00:25:03,960 --> 00:25:05,710 PROFESSOR: They'll be due to those as well 538 00:25:05,710 --> 00:25:08,615 as some other processes, which we're going to cover on decay. 539 00:25:08,615 --> 00:25:10,240 But if you notice, I've been giving you 540 00:25:10,240 --> 00:25:12,730 a lot of flash-forwards in this class. 541 00:25:12,730 --> 00:25:15,540 We've introduced cross-sections as a thing, 542 00:25:15,540 --> 00:25:17,937 the proportionality constant between interaction 543 00:25:17,937 --> 00:25:18,520 probabilities. 544 00:25:18,520 --> 00:25:20,260 We're going to hit them hard later. 545 00:25:20,260 --> 00:25:22,510 I've also been kind of introducing or flash-forwarding 546 00:25:22,510 --> 00:25:24,070 different methods of decay. 547 00:25:24,070 --> 00:25:26,020 So there's also alpha decay. 548 00:25:26,020 --> 00:25:29,470 There's also isomeric transition or gamma emission. 549 00:25:29,470 --> 00:25:32,230 There's also spontaneous fission. 550 00:25:32,230 --> 00:25:33,790 This is the whole basis behind how 551 00:25:33,790 --> 00:25:35,650 fission can get working without some sort 552 00:25:35,650 --> 00:25:37,280 of kick-starting element. 553 00:25:37,280 --> 00:25:40,050 So maybe now's a good time to show you. 554 00:25:40,050 --> 00:25:47,030 Let's go to uranium-235 and see how it decays. 555 00:25:47,030 --> 00:25:51,740 It goes alpha decay to thorium-231 most of the time. 556 00:25:51,740 --> 00:25:55,340 And if you look how, it's not terrible. 557 00:25:55,340 --> 00:25:56,480 We can make sense of this. 558 00:25:58,990 --> 00:26:04,000 It also undergoes SF, which stands for spontaneous fission. 559 00:26:04,000 --> 00:26:08,130 So one out of every seven-- 560 00:26:08,130 --> 00:26:09,010 what is it? 561 00:26:09,010 --> 00:26:12,550 Seven out of every billion times, 562 00:26:12,550 --> 00:26:16,540 it will just spontaneously fizz into two fission products. 563 00:26:16,540 --> 00:26:19,540 And this is why if you put enough uranium-235 together 564 00:26:19,540 --> 00:26:22,780 in one place, you can make a critical reactor. 565 00:26:22,780 --> 00:26:24,280 In reality, you don't tend to want 566 00:26:24,280 --> 00:26:29,560 to put enough U-235 together to just spontaneously go critical. 567 00:26:29,560 --> 00:26:32,740 We use other isotopes as kickstarters. 568 00:26:32,740 --> 00:26:35,770 For example, californium, I think it's 252. 569 00:26:35,770 --> 00:26:36,910 Let's take a quick look. 570 00:26:39,440 --> 00:26:40,520 There we go. 571 00:26:40,520 --> 00:26:44,310 Californium-252 undergoes spontaneous fission 3% 572 00:26:44,310 --> 00:26:44,810 of the time. 573 00:26:44,810 --> 00:26:47,730 It's even heavier, even more unstable. 574 00:26:47,730 --> 00:26:49,850 So there is a reactor called HFIR, 575 00:26:49,850 --> 00:26:53,210 or the high flux isotope reactor at Oak Ridge National Lab. 576 00:26:53,210 --> 00:26:55,850 One of its main outputs is californium kickstarters 577 00:26:55,850 --> 00:26:56,950 for reactors. 578 00:26:56,950 --> 00:26:59,930 So to get things going, you put a little bit of californium 579 00:26:59,930 --> 00:27:02,930 in as a gigantic neutron source, and then you don't really 580 00:27:02,930 --> 00:27:04,787 need it anymore once it gets going. 581 00:27:04,787 --> 00:27:06,620 So it's one of the safer ways of starting up 582 00:27:06,620 --> 00:27:09,470 a reactor is put in a crazy neutron source, 583 00:27:09,470 --> 00:27:12,150 and then once it gets going, take it out or leave it in 584 00:27:12,150 --> 00:27:12,650 and burn it. 585 00:27:12,650 --> 00:27:14,410 I'm not actually sure which one they do. 586 00:27:14,410 --> 00:27:14,988 Yep? 587 00:27:14,988 --> 00:27:16,482 AUDIENCE: Is the name californium 588 00:27:16,482 --> 00:27:18,480 based on California? 589 00:27:18,480 --> 00:27:19,753 PROFESSOR: It is. 590 00:27:19,753 --> 00:27:20,420 When we get to-- 591 00:27:20,420 --> 00:27:22,753 now is a good time to introduce the super heavy elements 592 00:27:22,753 --> 00:27:24,000 since you asked. 593 00:27:24,000 --> 00:27:27,150 So a lot of these older elements were named after-- 594 00:27:27,150 --> 00:27:28,940 actually this is kind of a hobby of mine. 595 00:27:28,940 --> 00:27:32,490 So I don't know if you guys saw the periodic table outside. 596 00:27:32,490 --> 00:27:34,098 I collect elements, because if you're 597 00:27:34,098 --> 00:27:35,640 going to collect something, you might 598 00:27:35,640 --> 00:27:39,280 as well collect everything that everything else is made of. 599 00:27:39,280 --> 00:27:41,670 It's the same reason I went into nuclear energy. 600 00:27:41,670 --> 00:27:45,210 I started off course 6, or 6.1, specifically electrical. 601 00:27:45,210 --> 00:27:47,430 And I was like, well, I could be designing, like, 602 00:27:47,430 --> 00:27:49,270 the next screen for a cell phone, 603 00:27:49,270 --> 00:27:51,218 or we could solve the energy problem, 604 00:27:51,218 --> 00:27:53,260 which is the problem all others are based off of. 605 00:27:53,260 --> 00:27:55,770 So my whole life theme has been go to the source. 606 00:27:55,770 --> 00:27:58,620 That's why I came here in high school and never left. 607 00:27:58,620 --> 00:28:00,540 That's why I declared course 22. 608 00:28:00,540 --> 00:28:03,060 That's why I collect elements and probably is 609 00:28:03,060 --> 00:28:05,940 the reason for many other things which only a psychiatrist could 610 00:28:05,940 --> 00:28:08,460 diagnose. 611 00:28:08,460 --> 00:28:10,860 But let's look at some of the other elements. 612 00:28:10,860 --> 00:28:14,040 For example, yttrium. 613 00:28:14,040 --> 00:28:16,480 I think it has a isotope 40. 614 00:28:16,480 --> 00:28:19,170 Anyone know-- no, it doesn't have a 40. 615 00:28:19,170 --> 00:28:20,935 What about a 50? 616 00:28:20,935 --> 00:28:21,435 60? 617 00:28:23,950 --> 00:28:25,520 100? 618 00:28:25,520 --> 00:28:26,900 Whatever. 619 00:28:26,900 --> 00:28:28,850 At least it knew that Y was yttrium. 620 00:28:28,850 --> 00:28:29,540 Anyone know-- 621 00:28:29,540 --> 00:28:30,082 AUDIENCE: 89. 622 00:28:30,082 --> 00:28:31,707 PROFESSOR: --where this is coming from? 623 00:28:31,707 --> 00:28:32,870 89? 624 00:28:32,870 --> 00:28:33,605 Seems high. 625 00:28:36,430 --> 00:28:36,930 Oh my god. 626 00:28:36,930 --> 00:28:37,472 You're right. 627 00:28:37,472 --> 00:28:38,560 AUDIENCE: I work with it. 628 00:28:38,560 --> 00:28:39,700 PROFESSOR: OK. 629 00:28:39,700 --> 00:28:40,200 Gotcha. 630 00:28:40,200 --> 00:28:41,640 You work with it. 631 00:28:41,640 --> 00:28:42,180 Awesome. 632 00:28:42,180 --> 00:28:44,958 Anyone know what this is all about, yttrium? 633 00:28:48,030 --> 00:28:50,510 There's a town called Ytterby in Sweden 634 00:28:50,510 --> 00:28:53,720 where large deposits of yttrium and ytterbium, or Yb, 635 00:28:53,720 --> 00:28:57,730 tend to be found or Db, named for dubnium. 636 00:28:57,730 --> 00:28:59,600 So let's say the really basic elements tend 637 00:28:59,600 --> 00:29:00,530 to come from Latin. 638 00:29:00,530 --> 00:29:03,730 Fe stands for iron, which actually stands for ferrum. 639 00:29:03,730 --> 00:29:04,700 Lead is plumbum. 640 00:29:04,700 --> 00:29:06,140 Gold is aurum. 641 00:29:06,140 --> 00:29:07,707 Silver, Ag, is argentium. 642 00:29:07,707 --> 00:29:09,290 I don't know if I'm saying that right. 643 00:29:09,290 --> 00:29:10,707 I never took Latin, and I've never 644 00:29:10,707 --> 00:29:13,402 heard it spoken, of course. 645 00:29:13,402 --> 00:29:15,860 And then a lot of the heavier and heavier elements as we go 646 00:29:15,860 --> 00:29:17,527 are being named for more and more famous 647 00:29:17,527 --> 00:29:21,860 scientists or places where they tend to be made like Db. 648 00:29:21,860 --> 00:29:24,260 I'm going to guess 260 for a mass there. 649 00:29:24,260 --> 00:29:25,700 Oh, nice. 650 00:29:25,700 --> 00:29:28,730 For Dubna in Russia that has got one 651 00:29:28,730 --> 00:29:32,690 of the few gigantic super heavy element colliders where they're 652 00:29:32,690 --> 00:29:35,585 constantly synthesizing and characterizing 653 00:29:35,585 --> 00:29:36,710 these super heavy elements. 654 00:29:36,710 --> 00:29:38,247 So finally they said, you know what? 655 00:29:38,247 --> 00:29:39,830 They've made enough of these in Dubna. 656 00:29:39,830 --> 00:29:41,840 Let's name one of the elements after them. 657 00:29:41,840 --> 00:29:44,690 Or Sg, seaborgium, for Glenn Seaborg. 658 00:29:44,690 --> 00:29:48,920 Or No, nobelium, for Alfred Nobel. 659 00:29:48,920 --> 00:29:50,538 Yep? 660 00:29:50,538 --> 00:29:53,740 AUDIENCE: I just have a question for the actual mass parabola. 661 00:29:53,740 --> 00:29:54,490 PROFESSOR: Uh-huh. 662 00:29:57,412 --> 00:30:03,142 AUDIENCE: Like, do the parabolas ever, like, reach each other? 663 00:30:03,142 --> 00:30:04,350 PROFESSOR: Do they intersect? 664 00:30:04,350 --> 00:30:04,980 AUDIENCE: Yeah. 665 00:30:04,980 --> 00:30:07,350 PROFESSOR: I've never seen a case where they intersect. 666 00:30:07,350 --> 00:30:10,440 That would make for a crazy situation indeed. 667 00:30:10,440 --> 00:30:13,050 However, part of what the homework assignment's about 668 00:30:13,050 --> 00:30:16,710 is to derive an analytical form for a mass parabola 669 00:30:16,710 --> 00:30:19,360 and then check the data to see how well it works. 670 00:30:19,360 --> 00:30:22,710 So for any cases where you have an even mass number, 671 00:30:22,710 --> 00:30:26,130 and you have either odd-odd or even-even nuclei, 672 00:30:26,130 --> 00:30:28,260 you can check those equations analytically 673 00:30:28,260 --> 00:30:30,547 to see if they'll intersect. 674 00:30:30,547 --> 00:30:33,956 AUDIENCE: And for the case of A equals 40, 675 00:30:33,956 --> 00:30:38,350 I'm not really sure what the top parabola is. 676 00:30:38,350 --> 00:30:40,410 PROFESSOR: So the top parabola for potassium-40-- 677 00:30:40,410 --> 00:30:44,160 let's take a quick look at how many protons and neutrons it 678 00:30:44,160 --> 00:30:45,330 has. 679 00:30:45,330 --> 00:30:48,720 Potassium has a proton number of 19, which means 680 00:30:48,720 --> 00:30:50,820 it has a neutron number of 21. 681 00:30:50,820 --> 00:30:57,430 So the top parabola is odd N and odd Z, 682 00:30:57,430 --> 00:31:05,040 where the bottom one is even N and even Z. 683 00:31:05,040 --> 00:31:07,140 Whereas for odd mass number nuclei, 684 00:31:07,140 --> 00:31:10,560 it has to be either odd-even or even-odd, 685 00:31:10,560 --> 00:31:13,440 else it would be even, which is a funny sentence when 686 00:31:13,440 --> 00:31:15,170 you say it all out loud. 687 00:31:15,170 --> 00:31:15,670 Yeah. 688 00:31:15,670 --> 00:31:17,770 So that's the idea here is that notice 689 00:31:17,770 --> 00:31:22,330 that the even-even parabola tends to be further down. 690 00:31:22,330 --> 00:31:26,920 All those nuclear magic numbers, 2, 8, 20, 28-- 691 00:31:26,920 --> 00:31:28,340 I'm not going to quote the rest. 692 00:31:28,340 --> 00:31:29,860 Those the little ones I know. 693 00:31:29,860 --> 00:31:32,570 All even numbers. 694 00:31:32,570 --> 00:31:34,070 So any other questions on these mass 695 00:31:34,070 --> 00:31:36,300 parabolas before we launch into super heavy elements? 696 00:31:36,300 --> 00:31:36,800 Yeah? 697 00:31:36,800 --> 00:31:38,830 AUDIENCE: [INAUDIBLE] the bump on the right? 698 00:31:38,830 --> 00:31:39,580 PROFESSOR: Uh-huh. 699 00:31:39,580 --> 00:31:42,606 AUDIENCE: How do you know that that's where [INAUDIBLE]?? 700 00:31:45,270 --> 00:31:47,150 PROFESSOR: Analytically or experimentally? 701 00:31:47,150 --> 00:31:47,775 Which question? 702 00:31:47,775 --> 00:31:49,530 AUDIENCE: Analytically. 703 00:31:49,530 --> 00:31:50,970 PROFESSOR: So analytically. 704 00:31:50,970 --> 00:31:54,780 Analytically there should be some isotope 705 00:31:54,780 --> 00:31:56,370 of-- well, not potassium. 706 00:31:56,370 --> 00:31:57,460 That wouldn't be allowed. 707 00:31:57,460 --> 00:32:01,530 So in this case, the stable element positions 708 00:32:01,530 --> 00:32:04,330 have got to kind of switch off, shouldn't they? 709 00:32:04,330 --> 00:32:08,430 So if that's potassium-40, that would still 710 00:32:08,430 --> 00:32:10,898 have to be potassium. 711 00:32:10,898 --> 00:32:12,440 You don't really have another choice. 712 00:32:12,440 --> 00:32:15,655 There isn't really a position there, is there, analytically? 713 00:32:15,655 --> 00:32:17,780 That's the interesting thing is that you can either 714 00:32:17,780 --> 00:32:21,830 be odd-odd or even-even for an even mass number. 715 00:32:21,830 --> 00:32:25,880 But you can't just take off one neutron from potassium-40, 716 00:32:25,880 --> 00:32:27,430 and then you've got potassium-39. 717 00:32:27,430 --> 00:32:30,110 Then you're on a different mass number. 718 00:32:30,110 --> 00:32:32,810 Or if you exchange a proton and a neutron, 719 00:32:32,810 --> 00:32:35,340 which you pretty much do in either of these directions. 720 00:32:35,340 --> 00:32:38,363 There's no way to get straight down here. 721 00:32:38,363 --> 00:32:39,113 AUDIENCE: Right. 722 00:32:39,113 --> 00:32:39,780 PROFESSOR: Yeah? 723 00:32:39,780 --> 00:32:42,230 AUDIENCE: For odd-odd, delta is negative, right? 724 00:32:42,230 --> 00:32:43,230 PROFESSOR: For odd what? 725 00:32:43,230 --> 00:32:43,850 For-- sorry? 726 00:32:43,850 --> 00:32:45,650 AUDIENCE: For odd-odd, delta is negative? 727 00:32:45,650 --> 00:32:47,483 PROFESSOR: Yeah, let's go back to that slide 728 00:32:47,483 --> 00:32:49,520 just to make sure. 729 00:32:49,520 --> 00:32:52,470 You mean the pairing term in the semi-empirical mass formula? 730 00:32:52,470 --> 00:32:53,115 AUDIENCE: Yeah. 731 00:32:53,115 --> 00:32:54,740 PROFESSOR: Yeah, so for odd-odd nuclei, 732 00:32:54,740 --> 00:32:58,580 indeed, delta's negative, which means lower binding energy, 733 00:32:58,580 --> 00:32:59,720 which means higher mass. 734 00:32:59,720 --> 00:33:03,260 And that's why we see it bump up on the mass right here. 735 00:33:03,260 --> 00:33:05,393 Yeah? 736 00:33:05,393 --> 00:33:07,310 And do you have a second part of the question? 737 00:33:10,286 --> 00:33:14,750 AUDIENCE: It was more so how to relate 738 00:33:14,750 --> 00:33:20,932 [INAUDIBLE] like the binding energy to that mass parabola. 739 00:33:20,932 --> 00:33:22,390 PROFESSOR: We can actually relate-- 740 00:33:22,390 --> 00:33:23,848 so we can relate the binding energy 741 00:33:23,848 --> 00:33:27,130 to the mass and the mass parabola analytically, 742 00:33:27,130 --> 00:33:35,080 because the binding energy is equal to Z times protons plus N 743 00:33:35,080 --> 00:33:40,420 times mass of neutron minus the actual mass 744 00:33:40,420 --> 00:33:45,920 of that same nucleus, A comma Z. So they're actually directly 745 00:33:45,920 --> 00:33:48,740 related, just negatively. 746 00:33:48,740 --> 00:33:50,720 So something with a higher mass is 747 00:33:50,720 --> 00:33:53,300 going to have a low binding energy, which means it's 748 00:33:53,300 --> 00:33:56,030 less bound and less stable. 749 00:33:56,030 --> 00:34:00,180 And indeed, the further up the mass scale we go, 750 00:34:00,180 --> 00:34:02,690 the higher those beta or electron 751 00:34:02,690 --> 00:34:04,757 capture or positron energies are. 752 00:34:04,757 --> 00:34:06,590 And there's another thing you can check too, 753 00:34:06,590 --> 00:34:08,150 which is the half-life. 754 00:34:08,150 --> 00:34:10,760 Half-life is what we'll be talking about on Tuesday. 755 00:34:10,760 --> 00:34:14,000 It's how long before an average amount of a substance 756 00:34:14,000 --> 00:34:16,125 has undergone radioactive decay. 757 00:34:16,125 --> 00:34:17,750 So let's look at some of these isotopes 758 00:34:17,750 --> 00:34:19,790 and start looking at half-life trends 759 00:34:19,790 --> 00:34:21,980 as another measure of stability. 760 00:34:21,980 --> 00:34:26,900 So potassium-40 has an exceptionally long half-life. 761 00:34:26,900 --> 00:34:29,330 So it's relatively stable. 762 00:34:29,330 --> 00:34:31,820 Let's take a look not at either the stable isotopes, 763 00:34:31,820 --> 00:34:33,530 but let's go up the mass parabola 764 00:34:33,530 --> 00:34:34,940 chain in one direction. 765 00:34:34,940 --> 00:34:38,300 Calcium-40, scandium-40. 766 00:34:38,300 --> 00:34:42,050 So let's take a look at scandium-40. 767 00:34:42,050 --> 00:34:47,659 Scandium-40 has a half-life less than a second. 768 00:34:47,659 --> 00:34:51,889 And it's got quite a high decay energy by whatever method 769 00:34:51,889 --> 00:34:53,840 you want to use. 770 00:34:53,840 --> 00:34:56,555 Let's go up to titanium-40. 771 00:34:56,555 --> 00:34:57,430 Anyone want to guess? 772 00:34:57,430 --> 00:35:01,400 Do you think the half-life is going to go up or down? 773 00:35:01,400 --> 00:35:03,460 Let's see if the half-life goes down. 774 00:35:03,460 --> 00:35:07,610 We know the decay energy goes up. 775 00:35:07,610 --> 00:35:08,420 Indeed. 776 00:35:08,420 --> 00:35:11,390 Half-life goes down from 182 milliseconds to 50 777 00:35:11,390 --> 00:35:13,040 milliseconds. 778 00:35:13,040 --> 00:35:17,250 And let's say titanium-40 could have come from-- wow. 779 00:35:17,250 --> 00:35:23,770 Two proton decay from Cr-42 with a half-life of 350 nanoseconds. 780 00:35:23,770 --> 00:35:28,680 So as we go up the mass ladder and down the stability ladder, 781 00:35:28,680 --> 00:35:32,940 the half-life decreases, which kind of follows intuitively. 782 00:35:32,940 --> 00:35:34,560 Something that's exceptionally stable 783 00:35:34,560 --> 00:35:36,548 should have a half-life of infinity, 784 00:35:36,548 --> 00:35:38,340 and something that's exceptionally unstable 785 00:35:38,340 --> 00:35:40,345 should just blow apart instantly. 786 00:35:40,345 --> 00:35:41,970 Like, remember the first week of class, 787 00:35:41,970 --> 00:35:45,600 we talked about helium-4 grabbing a neutron, 788 00:35:45,600 --> 00:35:48,420 becoming helium-5, and instantaneously going back 789 00:35:48,420 --> 00:35:50,200 to helium-4. 790 00:35:50,200 --> 00:35:55,630 If you look at helium-5, its half-life 791 00:35:55,630 --> 00:36:00,970 is measured in MeV, or 7 times 10 to the minus 7 femtoseconds. 792 00:36:00,970 --> 00:36:03,100 So if helium-4 absorbs a neutron, 793 00:36:03,100 --> 00:36:05,830 it simply doesn't want it and gets rid of it 794 00:36:05,830 --> 00:36:09,790 in 10 to the minus 7 femtoseconds, which 795 00:36:09,790 --> 00:36:11,785 would tell us that it's exceptionally unstable. 796 00:36:15,358 --> 00:36:16,900 So I hope that's a long-winded answer 797 00:36:16,900 --> 00:36:20,170 to that question about what does it mean to be going up 798 00:36:20,170 --> 00:36:23,250 in the mass levels. 799 00:36:23,250 --> 00:36:25,890 Any other questions on mass parabolas or the liquid drop 800 00:36:25,890 --> 00:36:29,320 model or stability in general? 801 00:36:29,320 --> 00:36:30,100 Yes. 802 00:36:30,100 --> 00:36:33,012 AUDIENCE: For something that goes upwards [INAUDIBLE] 803 00:36:33,012 --> 00:36:35,377 just because the mass [INAUDIBLE].. 804 00:36:38,627 --> 00:36:40,460 PROFESSOR: So if you're changing one neutron 805 00:36:40,460 --> 00:36:43,820 to a proton in each case, you're switching back and forth 806 00:36:43,820 --> 00:36:47,630 from the odd-odd to the even-even mass parabolas. 807 00:36:47,630 --> 00:36:50,690 So if I were to redraw these dots more to scale, 808 00:36:50,690 --> 00:36:54,800 this would have to be on the odd-odd. 809 00:36:54,800 --> 00:36:58,400 And, well, let me draw them a little better. 810 00:36:58,400 --> 00:36:59,090 Yep. 811 00:36:59,090 --> 00:37:00,050 AUDIENCE: OK. 812 00:37:00,050 --> 00:37:02,330 PROFESSOR: That's on the odd-odd, 813 00:37:02,330 --> 00:37:03,810 and that's on the even-even. 814 00:37:03,810 --> 00:37:04,770 AUDIENCE: OK. 815 00:37:04,770 --> 00:37:05,600 PROFESSOR: Yeah. 816 00:37:05,600 --> 00:37:07,460 So excuse my poor drawing skills. 817 00:37:07,460 --> 00:37:10,340 But if you're switching one proton to a neutron 818 00:37:10,340 --> 00:37:13,370 or vice-versa, by definition, you're 819 00:37:13,370 --> 00:37:17,330 jumping back and forth between these parabolas. 820 00:37:17,330 --> 00:37:18,330 AUDIENCE: OK, thank you. 821 00:37:18,330 --> 00:37:20,497 PROFESSOR: That's a good question for clarification. 822 00:37:20,497 --> 00:37:21,530 You had a question too? 823 00:37:21,530 --> 00:37:24,635 AUDIENCE: Yeah, about the semi-empirical mass formula. 824 00:37:24,635 --> 00:37:28,112 When do you use that to find binding energy as opposed 825 00:37:28,112 --> 00:37:29,445 to, like, any of the other ways? 826 00:37:31,785 --> 00:37:32,660 PROFESSOR: I'm sorry. 827 00:37:32,660 --> 00:37:34,550 The semi-empirical mass formula is a good way 828 00:37:34,550 --> 00:37:37,880 to get an analytical guess at most of them. 829 00:37:37,880 --> 00:37:39,680 If you want an exact answer, always 830 00:37:39,680 --> 00:37:41,420 use the actual binding energy. 831 00:37:41,420 --> 00:37:45,890 AUDIENCE: So, like, how often is it used now? 832 00:37:45,890 --> 00:37:48,758 PROFESSOR: I would not say it's used much now except-- 833 00:37:48,758 --> 00:37:51,050 well, that's going to be one of your homework questions 834 00:37:51,050 --> 00:37:55,460 is this formula predicts that as you get heavier and heavier 835 00:37:55,460 --> 00:37:59,720 and heavier, nuclei should just continuously get less stable. 836 00:37:59,720 --> 00:38:02,180 And that was, as of when this was derived, 837 00:38:02,180 --> 00:38:06,410 let's say decades ago, we now know something different 838 00:38:06,410 --> 00:38:07,683 is happening. 839 00:38:07,683 --> 00:38:09,350 So if you look at the table of nuclides, 840 00:38:09,350 --> 00:38:13,580 you can sort of see some swells in the number of black pixels 841 00:38:13,580 --> 00:38:15,350 until it cuts off. 842 00:38:15,350 --> 00:38:18,320 And this region actually where we think super heavy elements 843 00:38:18,320 --> 00:38:22,160 happen, I want to jump to the actual table of nuclides, which 844 00:38:22,160 --> 00:38:26,180 I'll say is our snapshot of knowledge today, 845 00:38:26,180 --> 00:38:29,210 and go all the way to the top. 846 00:38:29,210 --> 00:38:33,530 And our knowledge kind of cuts off at these elements, which 847 00:38:33,530 --> 00:38:38,030 are, for now, temporarily named in a very uncreative way. 848 00:38:38,030 --> 00:38:40,260 We don't even know anything about them. 849 00:38:40,260 --> 00:38:43,430 Uun is probably going to have a proton number of what? 850 00:38:43,430 --> 00:38:45,620 110. 851 00:38:45,620 --> 00:38:47,330 I don't know what the prefixes are, 852 00:38:47,330 --> 00:38:50,150 but UUU would be un-un-un 111. 853 00:38:50,150 --> 00:38:54,010 Probably has 111 protons. 854 00:38:54,010 --> 00:38:58,540 Beyond here, off the screen or probably up into the next room, 855 00:38:58,540 --> 00:39:02,110 it's predicted that once you approach the next magic number 856 00:39:02,110 --> 00:39:05,110 in nuclei, there should be an island of stability 857 00:39:05,110 --> 00:39:07,847 where it may not necessarily be totally stable, 858 00:39:07,847 --> 00:39:09,430 but the half-lives should go up again. 859 00:39:09,430 --> 00:39:12,160 And we should be able to synthesize super heavy matter. 860 00:39:12,160 --> 00:39:14,400 And if you actually graph neutron number 861 00:39:14,400 --> 00:39:17,260 versus half-life-- so notice how we were looking at half-life 862 00:39:17,260 --> 00:39:19,000 as a measure of stability. 863 00:39:19,000 --> 00:39:21,730 It starts to go up, then comes down, and then, 864 00:39:21,730 --> 00:39:23,590 to the extent of our knowledge, it 865 00:39:23,590 --> 00:39:27,400 is going back up again to the next predicted magic number. 866 00:39:27,400 --> 00:39:29,530 So what we think should be happening 867 00:39:29,530 --> 00:39:31,820 is half-lives should be continuously going up. 868 00:39:31,820 --> 00:39:32,320 And yeah? 869 00:39:32,320 --> 00:39:33,112 You had a question? 870 00:39:33,112 --> 00:39:35,960 AUDIENCE: Like, what do we do with these weird things? 871 00:39:35,960 --> 00:39:37,570 PROFESSOR: Well, whatever you want. 872 00:39:37,570 --> 00:39:39,520 It's going to be-- 873 00:39:39,520 --> 00:39:42,850 it should be dense as all heck, because nuclear matter is quite 874 00:39:42,850 --> 00:39:44,290 a bit denser than ordinary matter, 875 00:39:44,290 --> 00:39:47,030 and quite a bit is quite an understatement. 876 00:39:47,030 --> 00:39:49,450 So what would you do with super heavy matter? 877 00:39:49,450 --> 00:39:52,150 A lot of it could be used to probe the structure of matter. 878 00:39:52,150 --> 00:39:54,100 There's a lot about how the nucleus is 879 00:39:54,100 --> 00:39:56,410 constructed that we don't know. 880 00:39:56,410 --> 00:39:57,940 And beyond the scope of this course 881 00:39:57,940 --> 00:39:59,732 would also be an understatement. 882 00:39:59,732 --> 00:40:01,690 There's folks that are making their careers now 883 00:40:01,690 --> 00:40:04,570 on figuring out what are the forces between nucleons? 884 00:40:04,570 --> 00:40:08,440 Why do things spontaneously fizz at the rates that they do? 885 00:40:08,440 --> 00:40:11,230 You'll even hit a little bit of this in 22.02 886 00:40:11,230 --> 00:40:14,740 when you can calculate the rough half-life for alpha decay using 887 00:40:14,740 --> 00:40:20,480 quantum tunneling through the potential barrier in a nucleus. 888 00:40:20,480 --> 00:40:22,750 And so the more nuclei we have to mess around with, 889 00:40:22,750 --> 00:40:25,540 the more data and real examples we have to study. 890 00:40:25,540 --> 00:40:28,390 But practical applications, well, I could imagine, 891 00:40:28,390 --> 00:40:30,830 we might find something denser than osmium. 892 00:40:30,830 --> 00:40:33,910 Osmium right now has a density of about 22 grams 893 00:40:33,910 --> 00:40:35,390 per cubic centimeter. 894 00:40:35,390 --> 00:40:38,740 This stuff, zirconium, is about 6.9 or so. 895 00:40:38,740 --> 00:40:40,030 Steel is like 8. 896 00:40:40,030 --> 00:40:41,140 Lead's like 11. 897 00:40:41,140 --> 00:40:42,700 Mercury is like 19. 898 00:40:42,700 --> 00:40:46,900 Have any of you ever played with liquid mercury before? 899 00:40:46,900 --> 00:40:49,510 This is a "don't try this at home, kids" kind of moment. 900 00:40:49,510 --> 00:40:51,190 My grandfather happened to be a dentist, 901 00:40:51,190 --> 00:40:54,110 so we happened to have a lot of mercury to mess around with. 902 00:40:54,110 --> 00:40:56,170 And it's, like, unintuitively heavy. 903 00:40:56,170 --> 00:40:57,250 It's unbelievable. 904 00:40:57,250 --> 00:40:59,810 A 1-pound jar is about that big. 905 00:40:59,810 --> 00:41:01,310 I think it would be cool if we could 906 00:41:01,310 --> 00:41:04,710 find something even denser. 907 00:41:04,710 --> 00:41:06,300 And then really, really dense matter 908 00:41:06,300 --> 00:41:09,390 happens to make really, really good photon shields and gamma-- 909 00:41:09,390 --> 00:41:10,390 not the Star Trek thing. 910 00:41:10,390 --> 00:41:13,410 I mean this in the actual nuclear physics sense. 911 00:41:13,410 --> 00:41:16,260 The best way to stop gamma rays for gamma shielding 912 00:41:16,260 --> 00:41:18,420 is just put more matter in front of it. 913 00:41:18,420 --> 00:41:22,290 And if we find a denser state of matter that's earth stable, 914 00:41:22,290 --> 00:41:25,493 you then have a smaller gamma shield. 915 00:41:25,493 --> 00:41:27,660 So there are practical applications too in radiation 916 00:41:27,660 --> 00:41:28,560 shielding. 917 00:41:28,560 --> 00:41:30,863 They also might make awesome nuclear fuel, 918 00:41:30,863 --> 00:41:32,280 because you better believe they're 919 00:41:32,280 --> 00:41:35,110 going to fizz like crazy. 920 00:41:35,110 --> 00:41:35,830 So who knows? 921 00:41:35,830 --> 00:41:39,130 Maybe we can-- I don't think that would be cost-effective, 922 00:41:39,130 --> 00:41:41,050 but it would probably work. 923 00:41:41,050 --> 00:41:44,290 So the way they're doing this is actually 924 00:41:44,290 --> 00:41:50,320 slamming calcium 48 nuclei into other super heavy elements 925 00:41:50,320 --> 00:41:52,730 that have exceptionally long half-lives. 926 00:41:52,730 --> 00:41:54,640 So if you can't read what the screen says, 927 00:41:54,640 --> 00:41:57,820 this here is berkelium, for Berkeley, 928 00:41:57,820 --> 00:42:01,600 with proton number 97, mass number 249. 929 00:42:01,600 --> 00:42:08,450 Let's take a look at the Bk-249, which happens 930 00:42:08,450 --> 00:42:10,020 to be way beyond uranium. 931 00:42:10,020 --> 00:42:12,710 So it's definitely not a stable isotope, 932 00:42:12,710 --> 00:42:15,890 but it has a half-life of 320 days. 933 00:42:15,890 --> 00:42:17,720 That means you can make a bunch of it, 934 00:42:17,720 --> 00:42:20,840 chemically separate it, make it into a target, 935 00:42:20,840 --> 00:42:24,110 and fire calcium-48 nuclei into it. 936 00:42:24,110 --> 00:42:27,680 Anyone want to guess, why do we use calcium-48? 937 00:42:27,680 --> 00:42:30,525 And I'll give you a hint and write the proton number 938 00:42:30,525 --> 00:42:31,025 for calcium. 939 00:42:33,550 --> 00:42:40,230 The isotope that we use is calcium-28-- 940 00:42:40,230 --> 00:42:42,090 or calcium-48. 941 00:42:42,090 --> 00:42:43,830 Anyone want to take a guess? 942 00:42:43,830 --> 00:42:45,970 Why start here? 943 00:42:45,970 --> 00:42:48,570 Why not just smash two berkeliums into each other? 944 00:42:51,690 --> 00:42:56,130 Calcium 48 happens to be exceptionally stable, 945 00:42:56,130 --> 00:42:57,930 because it's got two magic numbers. 946 00:42:57,930 --> 00:43:01,560 Its proton number is 20, one of those peaks of stability. 947 00:43:01,560 --> 00:43:04,200 And its neutron number is 28. 948 00:43:04,200 --> 00:43:07,200 So start with something super stable, 949 00:43:07,200 --> 00:43:10,290 something with a lot more binding energy to begin with, 950 00:43:10,290 --> 00:43:12,600 and you maximize your chance of making something 951 00:43:12,600 --> 00:43:15,210 with more binding energy that won't just spontaneously 952 00:43:15,210 --> 00:43:16,110 disappear. 953 00:43:16,110 --> 00:43:18,630 So there are reasons calcium 48 was chosen 954 00:43:18,630 --> 00:43:20,475 and not something heavier or lighter. 955 00:43:20,475 --> 00:43:22,050 If we go back to that article, you 956 00:43:22,050 --> 00:43:25,650 can see what happens here is you make some element 117, which 957 00:43:25,650 --> 00:43:30,300 has yet to be made, and it undergoes alpha decay until it 958 00:43:30,300 --> 00:43:33,840 reaches some rather stable-- 959 00:43:33,840 --> 00:43:35,580 you know, 17 seconds. 960 00:43:35,580 --> 00:43:37,080 That's pretty exceptional. 961 00:43:37,080 --> 00:43:40,170 And if you notice the trends here, as you decay, 962 00:43:40,170 --> 00:43:43,710 the alpha energy steadily goes down, 963 00:43:43,710 --> 00:43:46,350 and the half-life steadily goes up. 964 00:43:46,350 --> 00:43:49,560 And so what you do is you make a super, super heavy element, 965 00:43:49,560 --> 00:43:51,930 hoping that it will decay and rest 966 00:43:51,930 --> 00:43:54,210 in one of these islands of stability 967 00:43:54,210 --> 00:43:58,630 beyond the magic numbers that we know right now. 968 00:43:58,630 --> 00:44:00,130 Which I thought this was super cool, 969 00:44:00,130 --> 00:44:02,203 because this is actually happening now. 970 00:44:02,203 --> 00:44:03,370 Like, new elements are made. 971 00:44:03,370 --> 00:44:05,200 I think we've been seeing one a year 972 00:44:05,200 --> 00:44:06,867 or so for the past few years on average. 973 00:44:06,867 --> 00:44:09,242 There might have been a year when there was more than one 974 00:44:09,242 --> 00:44:10,437 announced recently. 975 00:44:10,437 --> 00:44:12,520 There's only a few places in the world doing them, 976 00:44:12,520 --> 00:44:15,430 but you can start to-- already with two weeks of 22.01, 977 00:44:15,430 --> 00:44:17,650 you can start to get a handle for why 978 00:44:17,650 --> 00:44:20,410 do they use the nuclei they do, and then what sort of things 979 00:44:20,410 --> 00:44:21,790 are you looking for? 980 00:44:21,790 --> 00:44:24,040 Decays with lower and lower energy 981 00:44:24,040 --> 00:44:27,590 mean you're already starting to get less steep on whatever 982 00:44:27,590 --> 00:44:29,057 imaginary mass parabola. 983 00:44:29,057 --> 00:44:30,640 Don't quite know how to draw this one, 984 00:44:30,640 --> 00:44:32,710 because it's beyond anything we know. 985 00:44:32,710 --> 00:44:34,780 And as the half-lives keep going up, 986 00:44:34,780 --> 00:44:39,350 you can tell that it's reaching a measure of stability. 987 00:44:39,350 --> 00:44:41,750 However, to get you started on the homework, 988 00:44:41,750 --> 00:44:43,453 for the open-ended ended problem-- 989 00:44:43,453 --> 00:44:44,870 I think I'll bring it up right now 990 00:44:44,870 --> 00:44:46,037 so you guys can take a look. 991 00:44:48,812 --> 00:44:53,420 So let's go to the Stellar site. 992 00:45:00,802 --> 00:45:02,010 Hopefully it doesn't call me. 993 00:45:02,010 --> 00:45:02,510 Good. 994 00:45:07,530 --> 00:45:09,017 And two problem set two. 995 00:45:09,017 --> 00:45:10,600 This is the way I know that everyone's 996 00:45:10,600 --> 00:45:13,100 seen the P set seven days before it's due, because I'm going 997 00:45:13,100 --> 00:45:17,270 to put it up on the screen so you can 998 00:45:17,270 --> 00:45:20,070 see it all the way at the end. 999 00:45:20,070 --> 00:45:23,710 Predicting the island of stability. 1000 00:45:23,710 --> 00:45:25,690 Does the semi-empirical mass formula 1001 00:45:25,690 --> 00:45:28,420 predict the island of stability? 1002 00:45:28,420 --> 00:45:30,670 Well, let's start you off with the easier 1003 00:45:30,670 --> 00:45:32,500 part of the question, which is yes or no. 1004 00:45:32,500 --> 00:45:34,840 And I'm going to leave you to the why and the how. 1005 00:45:34,840 --> 00:45:41,050 If we graph binding energy per nucleon versus mass number, 1006 00:45:41,050 --> 00:45:48,050 the semi-empirical mass formula predicts something like this. 1007 00:45:48,050 --> 00:45:51,200 What happens as we go beyond the realm of known mass numbers? 1008 00:45:56,140 --> 00:45:56,640 Anyone? 1009 00:45:56,640 --> 00:45:58,342 How should I extend this curve? 1010 00:46:01,952 --> 00:46:02,910 What did you say, Alex? 1011 00:46:02,910 --> 00:46:03,700 AUDIENCE: I don't know. 1012 00:46:03,700 --> 00:46:04,825 PROFESSOR: Just keep going. 1013 00:46:04,825 --> 00:46:06,330 Yeah. 1014 00:46:06,330 --> 00:46:10,750 Does this predict an island of stability? 1015 00:46:10,750 --> 00:46:12,190 I don't think so. 1016 00:46:12,190 --> 00:46:14,290 So that's one of the few questions I'm 1017 00:46:14,290 --> 00:46:15,970 asking you in this homework. 1018 00:46:15,970 --> 00:46:17,320 And it's up to you guys. 1019 00:46:17,320 --> 00:46:18,340 Use your creativity. 1020 00:46:18,340 --> 00:46:20,020 Again, this is an open-ended problem. 1021 00:46:20,020 --> 00:46:22,330 I'm not looking for a specific answer. 1022 00:46:22,330 --> 00:46:24,220 I want to see how you think and how 1023 00:46:24,220 --> 00:46:27,130 you would change this formula to account 1024 00:46:27,130 --> 00:46:30,130 and actually predict the island of stability while still 1025 00:46:30,130 --> 00:46:33,550 satisfying the mostly correct predictions from the elements 1026 00:46:33,550 --> 00:46:36,330 we know. 1027 00:46:36,330 --> 00:46:37,906 So-- sorry, go ahead. 1028 00:46:37,906 --> 00:46:43,860 AUDIENCE: So should it, like, converge a little bit? 1029 00:46:43,860 --> 00:46:46,170 PROFESSOR: Well, you're on the right track. 1030 00:46:46,170 --> 00:46:47,670 If you want to show stability, you'd 1031 00:46:47,670 --> 00:46:51,300 want it to maybe have a higher value right here. 1032 00:46:51,300 --> 00:46:53,700 Higher binding energy per nucleon 1033 00:46:53,700 --> 00:46:56,460 would correspond to a lower mass, which would 1034 00:46:56,460 --> 00:46:58,560 correspond to higher stability. 1035 00:46:58,560 --> 00:47:04,742 So how would you predict this island of stability? 1036 00:47:04,742 --> 00:47:06,450 And then more specifically, how would you 1037 00:47:06,450 --> 00:47:12,150 reconcile the inaccuracies in the semi-empirical mass 1038 00:47:12,150 --> 00:47:12,990 formula? 1039 00:47:12,990 --> 00:47:15,463 Because we know it doesn't work very well for all cases. 1040 00:47:15,463 --> 00:47:17,880 There are some cases like right around here where it works 1041 00:47:17,880 --> 00:47:21,120 great, and there's some like right here and right here where 1042 00:47:21,120 --> 00:47:21,870 it really doesn't. 1043 00:47:21,870 --> 00:47:24,390 You can get things wrong by like 10 MeV, 1044 00:47:24,390 --> 00:47:26,750 which is pretty significant. 1045 00:47:26,750 --> 00:47:29,288 You know, that's like four digits on the mass scale, like, 1046 00:47:29,288 --> 00:47:30,330 the fourth decimal place. 1047 00:47:30,330 --> 00:47:31,747 That's huge to a nuclear engineer. 1048 00:47:34,220 --> 00:47:36,260 So that's something to get thinking about. 1049 00:47:36,260 --> 00:47:38,300 And remember I did tell you that there will 1050 00:47:38,300 --> 00:47:40,220 be some open-ended problems. 1051 00:47:40,220 --> 00:47:41,720 I'm going to mark them as open-ended 1052 00:47:41,720 --> 00:47:43,310 so you actually know. 1053 00:47:43,310 --> 00:47:45,360 We're not looking for a right or wrong answer. 1054 00:47:45,360 --> 00:47:47,150 This is one of those kinds of things 1055 00:47:47,150 --> 00:47:49,130 where we want to see how you think 1056 00:47:49,130 --> 00:47:50,960 and what do you think is missing. 1057 00:47:50,960 --> 00:47:54,350 There's other hard problems where we give you the answer, 1058 00:47:54,350 --> 00:47:57,080 because I'm not interested in you deriving some insane 1059 00:47:57,080 --> 00:47:59,750 expression and getting it right. 1060 00:47:59,750 --> 00:48:02,300 I'm interested in the derivation process. 1061 00:48:02,300 --> 00:48:04,070 What are the steps you choose? 1062 00:48:04,070 --> 00:48:05,630 What sort of assumptions do you make? 1063 00:48:05,630 --> 00:48:08,120 What sort of terms can you neglect and say, 1064 00:48:08,120 --> 00:48:09,650 that's in the ninth decimal place. 1065 00:48:09,650 --> 00:48:11,223 I'm going to forget it. 1066 00:48:11,223 --> 00:48:12,890 So in this case, we give you the answer, 1067 00:48:12,890 --> 00:48:15,740 because we're going to grade you on the process. 1068 00:48:15,740 --> 00:48:18,050 And you can use the answer to check your process 1069 00:48:18,050 --> 00:48:21,200 and see if you're on the right track or not. 1070 00:48:21,200 --> 00:48:24,520 For the skill-building questions, 1071 00:48:24,520 --> 00:48:25,990 we actually do want you to come up 1072 00:48:25,990 --> 00:48:29,400 with some sort of an answer like explaining 1073 00:48:29,400 --> 00:48:32,250 the terms in the semi-empirical mass formula 1074 00:48:32,250 --> 00:48:35,010 or modifying an equation to calculate something else. 1075 00:48:35,010 --> 00:48:37,150 We will be looking for a right answer there. 1076 00:48:37,150 --> 00:48:39,025 But those are questions to make sure that you 1077 00:48:39,025 --> 00:48:40,350 get the basics of the material. 1078 00:48:40,350 --> 00:48:42,960 If you can answer all of the questions in the first half 1079 00:48:42,960 --> 00:48:45,990 of these P sets fairly quickly, let's say in three or four 1080 00:48:45,990 --> 00:48:48,810 hours, you're totally on the right track. 1081 00:48:48,810 --> 00:48:52,280 The hard ones is because this is MIT. 1082 00:48:52,280 --> 00:48:53,780 And we want you to think beyond just 1083 00:48:53,780 --> 00:48:56,360 knowing what's in the Turner book or the Yit book. 1084 00:48:56,360 --> 00:48:59,760 Like I said, you guys are the leaders of this field. 1085 00:48:59,760 --> 00:49:03,564 So any other questions on stability in general? 1086 00:49:03,564 --> 00:49:04,064 Yes? 1087 00:49:04,064 --> 00:49:06,494 AUDIENCE: Just a real quick reminder. 1088 00:49:06,494 --> 00:49:08,230 When you say, like, even-even, are you 1089 00:49:08,230 --> 00:49:09,680 talking protons, neutrons? 1090 00:49:09,680 --> 00:49:10,700 PROFESSOR: Correct. 1091 00:49:10,700 --> 00:49:13,640 So that would be even N and even Z or odd N 1092 00:49:13,640 --> 00:49:15,350 and odd Z like in the reading and like 1093 00:49:15,350 --> 00:49:18,440 on these mass parabolas. 1094 00:49:18,440 --> 00:49:18,940 Yep. 1095 00:49:18,940 --> 00:49:20,410 Any other questions? 1096 00:49:23,210 --> 00:49:23,710 Yes. 1097 00:49:23,710 --> 00:49:25,990 AUDIENCE: Is the only proof or reason 1098 00:49:25,990 --> 00:49:28,126 that we say that there's an island of stability 1099 00:49:28,126 --> 00:49:33,637 because the mass increases up to the point of unknown? 1100 00:49:33,637 --> 00:49:34,720 PROFESSOR: There's a few-- 1101 00:49:34,720 --> 00:49:36,883 so the question was, is the only reason 1102 00:49:36,883 --> 00:49:39,550 people think there will be super heavy elements because the mass 1103 00:49:39,550 --> 00:49:40,360 increases, right? 1104 00:49:40,360 --> 00:49:41,260 AUDIENCE: Yeah. 1105 00:49:41,260 --> 00:49:44,350 PROFESSOR: So in this case, the mass will always-- 1106 00:49:44,350 --> 00:49:47,150 are you talking about now the total mass or-- 1107 00:49:47,150 --> 00:49:49,696 AUDIENCE: Why is the idea that there 1108 00:49:49,696 --> 00:49:51,317 is this island of stability? 1109 00:49:51,317 --> 00:49:52,520 PROFESSOR: Ah, OK. 1110 00:49:52,520 --> 00:49:53,978 AUDIENCE: If this doesn't prove it, 1111 00:49:53,978 --> 00:49:57,250 do we have other reasons [INAUDIBLE]?? 1112 00:49:57,250 --> 00:49:59,260 PROFESSOR: We have a few things to go on. 1113 00:49:59,260 --> 00:50:03,520 There are a number of different aspects of nuclear stability 1114 00:50:03,520 --> 00:50:06,010 that are all pointing to the same conclusion. 1115 00:50:06,010 --> 00:50:08,140 One of them, you can see on this graph here. 1116 00:50:08,140 --> 00:50:10,180 If you look at the alpha decay half-life 1117 00:50:10,180 --> 00:50:12,070 as a function of neutron number, it 1118 00:50:12,070 --> 00:50:15,400 doesn't just increase or decrease monotonically. 1119 00:50:15,400 --> 00:50:17,470 It swells up and down. 1120 00:50:17,470 --> 00:50:20,770 And it reaches a relative maximum 1121 00:50:20,770 --> 00:50:22,690 near certain magic numbers. 1122 00:50:22,690 --> 00:50:26,110 We can confirm that with the lower mass nuclei. 1123 00:50:26,110 --> 00:50:27,640 It doesn't work for really low mass, 1124 00:50:27,640 --> 00:50:31,210 because tiny things don't tend to undergo alpha decay. 1125 00:50:31,210 --> 00:50:33,760 But there are patterns that we're simply 1126 00:50:33,760 --> 00:50:37,930 recognizing and saying, well, if this is the next magic number, 1127 00:50:37,930 --> 00:50:39,590 it should continue to increase. 1128 00:50:39,590 --> 00:50:43,600 And I should mention too, this scale is logarithmic. 1129 00:50:43,600 --> 00:50:46,900 So the top right here is like 10 to the 4 seconds. 1130 00:50:46,900 --> 00:50:49,930 Just so you know, there are 86,400 seconds 1131 00:50:49,930 --> 00:50:52,060 in-- what is it-- a day. 1132 00:50:52,060 --> 00:50:55,340 And 3 times 10 to the 7 seconds in a year. 1133 00:50:55,340 --> 00:50:56,430 So if this graph-- 1134 00:50:56,430 --> 00:50:59,370 let's say for Z 111-- 1135 00:50:59,370 --> 00:51:02,280 were to continue on its track, it 1136 00:51:02,280 --> 00:51:04,500 should reach like 10 to the 9 or 10 1137 00:51:04,500 --> 00:51:08,160 to the 10, which could be like 100-year lifetimes 1138 00:51:08,160 --> 00:51:10,920 or 100-year half-lives, which means definitely you 1139 00:51:10,920 --> 00:51:13,470 can chemically separate them and do things with them. 1140 00:51:13,470 --> 00:51:16,350 I don't know if they would be safe enough to deal with. 1141 00:51:16,350 --> 00:51:18,790 But we also don't really know what's going to happen. 1142 00:51:18,790 --> 00:51:21,450 You can see that there is some uncertainty, 1143 00:51:21,450 --> 00:51:23,460 and things don't always follow the trend. 1144 00:51:23,460 --> 00:51:26,580 Even the error bars are outside the dashed lines. 1145 00:51:26,580 --> 00:51:27,810 But so we have this to go on. 1146 00:51:27,810 --> 00:51:31,260 We have the alpha decay half-life. 1147 00:51:31,260 --> 00:51:33,630 We also have the alpha decay energy. 1148 00:51:33,630 --> 00:51:35,790 As you approach an island of stability, 1149 00:51:35,790 --> 00:51:37,860 something that's more stable won't give off 1150 00:51:37,860 --> 00:51:40,830 as much kinetic energy to its alpha particle. 1151 00:51:40,830 --> 00:51:44,520 There is also-- for the ones that you can actually 1152 00:51:44,520 --> 00:51:46,320 measure that live long enough, you 1153 00:51:46,320 --> 00:51:48,570 can measure their mass to charge ratio 1154 00:51:48,570 --> 00:51:51,990 and actually get a good picture of their actual mass. 1155 00:51:51,990 --> 00:51:55,290 So we would expect the mass defect 1156 00:51:55,290 --> 00:51:58,650 to follow a certain trend as we go up. 1157 00:51:58,650 --> 00:52:00,240 The mass is always going to increase. 1158 00:52:00,240 --> 00:52:03,600 If you add more nucleons, it's going to increase. 1159 00:52:03,600 --> 00:52:07,800 But the mass defect, which is the real mass 1160 00:52:07,800 --> 00:52:10,920 minus the atomic number mass-- 1161 00:52:10,920 --> 00:52:12,690 if stability were to increase, do you 1162 00:52:12,690 --> 00:52:15,730 think the mass defect would increase or decrease 1163 00:52:15,730 --> 00:52:17,404 with more stability? 1164 00:52:22,290 --> 00:52:23,850 Let's take a quick look at this. 1165 00:52:23,850 --> 00:52:29,730 If A were to stay the same, a shrinking real mass-- 1166 00:52:29,730 --> 00:52:32,550 and remember, lower mass means more stability-- 1167 00:52:32,550 --> 00:52:38,050 would mean a higher or a low mass defect? 1168 00:52:38,050 --> 00:52:42,520 It would mean a lower mass defect or a lower excess mass 1169 00:52:42,520 --> 00:52:43,880 as you'd call it. 1170 00:52:43,880 --> 00:52:48,070 So in this case, you would expect the mass of the nucleus 1171 00:52:48,070 --> 00:52:53,960 to be smaller than its A if it was going more stable. 1172 00:52:53,960 --> 00:52:57,060 And all of these trends work in the same direction, 1173 00:52:57,060 --> 00:53:00,230 which is saying, OK, so we have the alpha energy. 1174 00:53:00,230 --> 00:53:01,610 We have the mass defect. 1175 00:53:01,610 --> 00:53:04,580 We have the half-life all pointing to the same thing 1176 00:53:04,580 --> 00:53:07,250 that something should be more stable. 1177 00:53:07,250 --> 00:53:09,050 And we have some patterns to go on, 1178 00:53:09,050 --> 00:53:12,470 but our understanding is kind of incomplete. 1179 00:53:12,470 --> 00:53:14,700 So-- yeah? 1180 00:53:14,700 --> 00:53:18,220 AUDIENCE: So if there's super heavy elements, 1181 00:53:18,220 --> 00:53:19,810 do they exist somewhere in space, 1182 00:53:19,810 --> 00:53:21,365 or do stars make them, possibly? 1183 00:53:21,365 --> 00:53:21,990 PROFESSOR: Ooh. 1184 00:53:21,990 --> 00:53:22,960 AUDIENCE: Or are they-- 1185 00:53:22,960 --> 00:53:24,756 PROFESSOR: Good question. 1186 00:53:24,756 --> 00:53:26,798 AUDIENCE: --currently made? 1187 00:53:26,798 --> 00:53:29,340 PROFESSOR: So the question is, if super heavy elements exist, 1188 00:53:29,340 --> 00:53:31,410 do they exist out there in space? 1189 00:53:31,410 --> 00:53:34,560 I think there would be a couple places they would exist. 1190 00:53:34,560 --> 00:53:37,950 The source of most of the elements beyond iron 1191 00:53:37,950 --> 00:53:42,660 is supernovas, where regular old fusion doesn't cut it anymore. 1192 00:53:42,660 --> 00:53:47,700 When you hit the maximum of this binding energy per nucleon 1193 00:53:47,700 --> 00:53:50,370 curve, you're at about iron 56. 1194 00:53:50,370 --> 00:53:52,530 That's why stars tend to form a core of iron 1195 00:53:52,530 --> 00:53:55,560 before it goes really bad in whatever way it 1196 00:53:55,560 --> 00:53:56,610 does for a star. 1197 00:53:56,610 --> 00:53:58,440 There are multiple ways. 1198 00:53:58,440 --> 00:54:01,980 When you get a supernova, you have an insane explosion, 1199 00:54:01,980 --> 00:54:03,600 and the core gets compressed from 1200 00:54:03,600 --> 00:54:08,130 the outside, forcing fusion of heavy elements to happen. 1201 00:54:08,130 --> 00:54:10,720 That's because you're putting in extra kinetic energy. 1202 00:54:10,720 --> 00:54:14,970 So it's like you have an endothermic reaction where 1203 00:54:14,970 --> 00:54:19,020 if Q is less than zero, how do you make that reaction happen? 1204 00:54:19,020 --> 00:54:21,240 Add kinetic energy, which can come 1205 00:54:21,240 --> 00:54:24,690 from a tremendous explosion outside of the outer regions 1206 00:54:24,690 --> 00:54:26,128 of the star. 1207 00:54:26,128 --> 00:54:28,420 So who's to say that some of these super heavy elements 1208 00:54:28,420 --> 00:54:30,010 aren't formed in supernovas? 1209 00:54:30,010 --> 00:54:31,820 I think they would be. 1210 00:54:31,820 --> 00:54:35,163 But would they actually make it out to be part of Earth 1211 00:54:35,163 --> 00:54:37,580 and then, let's say, live the 5 billion years that Earth's 1212 00:54:37,580 --> 00:54:38,510 been around? 1213 00:54:38,510 --> 00:54:41,290 We don't know if their half-lives are long enough. 1214 00:54:41,290 --> 00:54:44,940 There very well may have been some 5 billion years ago 1215 00:54:44,940 --> 00:54:46,880 or when the supernova was made. 1216 00:54:46,880 --> 00:54:49,490 But we haven't detected any here on Earth. 1217 00:54:49,490 --> 00:54:53,760 So we know that they're not 5 billion years stable. 1218 00:54:53,760 --> 00:54:56,140 Rather, I wouldn't even say we know that, 1219 00:54:56,140 --> 00:54:58,790 but we have a pretty good idea. 1220 00:54:58,790 --> 00:55:01,932 That's a great question is like, are they naturally made? 1221 00:55:01,932 --> 00:55:04,412 Probably. 1222 00:55:04,412 --> 00:55:06,400 Yeah. 1223 00:55:06,400 --> 00:55:08,020 Any other questions? 1224 00:55:08,020 --> 00:55:09,940 I like these outside the material ones. 1225 00:55:09,940 --> 00:55:13,810 We can take things beyond our known universe, 1226 00:55:13,810 --> 00:55:15,960 start to explain them.