1 00:00:00,040 --> 00:00:01,440 I want you to close your eyes for a second. 2 00:00:01,440 --> 00:00:02,920 We're going to take a trip. OK, I'm with. 3 00:00:02,960 --> 00:00:06,440 You We are leaving Earth behind. We're traveling about, what, 140 4 00:00:06,440 --> 00:00:10,320 million miles outward through the vacuum of space to a place 5 00:00:10,320 --> 00:00:15,440 that is cold, desolate and covered in a fine, rusty dust. 6 00:00:15,480 --> 00:00:17,880 We're on Mars. We are standing on the surface 7 00:00:17,880 --> 00:00:19,880 of Mars. It is a haunting image, isn't 8 00:00:19,880 --> 00:00:22,240 it? That endless red dust covering 9 00:00:22,240 --> 00:00:25,640 everything. The silence, the the thin 10 00:00:25,640 --> 00:00:27,120 atmosphere. It is. 11 00:00:27,400 --> 00:00:30,240 And reeling through that dust, let's imagine one of the NASA 12 00:00:30,240 --> 00:00:32,640 Rovers, maybe Spirit or Opportunity. 13 00:00:32,880 --> 00:00:35,240 We always picture them taking those incredible panoramic 14 00:00:35,240 --> 00:00:38,440 photos, you know, or drilling into rocks with those mechanical 15 00:00:38,440 --> 00:00:40,680 arms. The classic Mars postcard shots. 16 00:00:40,680 --> 00:00:43,360 Exactly. But there was an instrument on 17 00:00:43,360 --> 00:00:46,440 those Rovers, a specific piece of technology that was doing 18 00:00:46,440 --> 00:00:49,080 something that frankly sounds like magic. 19 00:00:49,080 --> 00:00:50,720 It does. It wasn't just looking at the 20 00:00:50,720 --> 00:00:53,040 rocks. It was interrogating the atomic 21 00:00:53,040 --> 00:00:57,360 nuclei inside the rocks to sniff out the history of water on the 22 00:00:57,360 --> 00:00:58,320 planet. That's right. 23 00:00:58,840 --> 00:01:01,760 And to do that it was using a technique that bridges 2 worlds 24 00:01:01,760 --> 00:01:03,560 that you know, they usually ignore each other. 25 00:01:03,920 --> 00:01:07,680 Nuclear physics and geology. Today we are doing a deep dive 26 00:01:07,680 --> 00:01:10,200 into that technique. It's called Mussbauer 27 00:01:10,200 --> 00:01:13,040 spectroscopy. And look, I know the name sounds 28 00:01:13,040 --> 00:01:14,680 a bit intimidating. Oh, it really does. 29 00:01:14,680 --> 00:01:16,960 It sounds like something you'd fail a test on in grad school. 30 00:01:16,960 --> 00:01:20,440 It definitely has that reputation, but it is genuinely 31 00:01:20,440 --> 00:01:24,240 one of the most elegant, precise concepts in all of physics. 32 00:01:24,360 --> 00:01:27,880 Once you get past the name, the mechanism is it's just 33 00:01:27,880 --> 00:01:30,440 beautiful. And that is our mission today. 34 00:01:30,440 --> 00:01:32,440 We're going to unpack this. We've got a stack of research 35 00:01:32,440 --> 00:01:35,720 papers, lecture notes, and diagrams here, and we are going 36 00:01:35,720 --> 00:01:40,720 to figure out how probing the tiny, dense nucleus of an atom 37 00:01:41,000 --> 00:01:43,480 can tell us about the chemistry happening on the outside. 38 00:01:43,720 --> 00:01:46,160 Right, the electrons. How the nucleus tells you about 39 00:01:46,160 --> 00:01:48,120 the electrons? It's a story about radioactive 40 00:01:48,120 --> 00:01:52,080 decay, relativity, quantum mechanics, and a tuning fork. 41 00:01:52,200 --> 00:01:54,520 A tuning fork is actually the perfect place to start. 42 00:01:54,520 --> 00:01:57,240 It's the best analogy we have for the core phenomenon. 43 00:01:57,240 --> 00:02:00,240 OK, so let's set the stage. The year is 1957. 44 00:02:00,680 --> 00:02:04,880 Who is the hero of our story? Our hero is a German physicist 45 00:02:04,880 --> 00:02:08,080 named Rudolf Musbauer. He was quite young at the time, 46 00:02:08,080 --> 00:02:11,560 actually working on his doctoral thesis in Heidelberg. 47 00:02:11,760 --> 00:02:15,080 So this was a PhD project. This was his PhD project, and 48 00:02:15,080 --> 00:02:17,960 like many great discoveries, he stumbled onto something that 49 00:02:17,960 --> 00:02:20,680 broke the existing rules, or at least the rules as people 50 00:02:20,680 --> 00:02:21,840 understood them. At the time. 51 00:02:22,240 --> 00:02:25,720 He was looking at a phenomenon called nuclear resonance. 52 00:02:25,720 --> 00:02:28,840 Nuclear Resonance? That sounds like the title of a 53 00:02:28,840 --> 00:02:30,520 Tom Clancy novel. It really does. 54 00:02:30,680 --> 00:02:33,800 But let's break that down. I know what resonance is in 55 00:02:33,800 --> 00:02:36,480 music. If I have two guitar strings 56 00:02:36,480 --> 00:02:40,400 tuned to the same note and I pluck one, the other one starts 57 00:02:40,400 --> 00:02:41,880 vibrating. Exactly. 58 00:02:42,040 --> 00:02:44,760 Or think of two identical tuning forks. 59 00:02:45,360 --> 00:02:49,680 If you strike one, let's say it's an A note at 440 Hertz, it 60 00:02:49,680 --> 00:02:53,200 sends out sound waves. If you bring a second identical 61 00:02:53,200 --> 00:02:56,360 tuning fork close to it, that second fork will catch those 62 00:02:56,360 --> 00:02:57,920 sound waves. And it starts to hum. 63 00:02:57,920 --> 00:02:59,800 It absorbs the energy and starts to sing. 64 00:02:59,800 --> 00:03:02,960 That's resonance. Because they match the key fits 65 00:03:02,960 --> 00:03:04,400 the lock. Precisely. 66 00:03:04,720 --> 00:03:06,960 Now, physicists knew this happened with sound. 67 00:03:06,960 --> 00:03:09,480 They also knew it happened with light and atoms. 68 00:03:09,960 --> 00:03:13,760 If you shine a specific color of light at an atom, the electrons 69 00:03:13,760 --> 00:03:16,960 can absorb that light and jump to a higher energy level. 70 00:03:17,040 --> 00:03:18,760 Right, that's standard spectroscopy. 71 00:03:18,960 --> 00:03:20,520 That's how we know what stars are made of. 72 00:03:20,880 --> 00:03:22,840 It is. That's how neon signs work. 73 00:03:22,840 --> 00:03:26,000 Essentially energy goes in, light comes out, or vice versa. 74 00:03:26,000 --> 00:03:28,560 OK. But Mussbauer was interested in 75 00:03:28,560 --> 00:03:31,960 the nucleus. He wanted to know, can we do 76 00:03:31,960 --> 00:03:35,960 this with the core of the atom? Can one nucleus emit a particle 77 00:03:35,960 --> 00:03:39,600 of light, A photon, and have another nucleus of the same type 78 00:03:39,600 --> 00:03:41,880 catch it? A nuclear tuning fork. 79 00:03:42,120 --> 00:03:45,280 So instead of electrons jumping between their shells, we are 80 00:03:45,280 --> 00:03:48,480 talking about the nucleus itself jumping between its own energy 81 00:03:48,480 --> 00:03:50,240 levels. Yes, and this is a crucial 82 00:03:50,240 --> 00:03:51,640 distinction you have to appreciate. 83 00:03:51,640 --> 00:03:54,120 The energy scales here are vastly different. 84 00:03:54,120 --> 00:03:55,920 How different? Well, when electrons jump 85 00:03:55,920 --> 00:03:59,440 around, they release visible light or maybe UV light X-rays 86 00:03:59,440 --> 00:04:00,920 if you're hitting the core electrons. 87 00:04:01,320 --> 00:04:04,480 But when a nucleus jumps, when it rearranges its protons and 88 00:04:04,480 --> 00:04:07,600 neutrons, it releases gamma rays. 89 00:04:07,600 --> 00:04:09,200 Gamma rays. That's Hulk territory. 90 00:04:09,200 --> 00:04:11,480 That's high energy. Extremely high energy. 91 00:04:11,480 --> 00:04:14,760 We are talking about transitions that are thousands, even 92 00:04:14,760 --> 00:04:17,320 millions of times more energetic than visible light. 93 00:04:17,800 --> 00:04:20,279 So the theoretical idea was simple enough. 94 00:04:20,640 --> 00:04:23,080 Nucleus A is excited. It's in a high energy state. 95 00:04:23,080 --> 00:04:26,120 It drops to a lower energy state and shoots out a gamma ray. 96 00:04:26,360 --> 00:04:29,240 Nucleus B is sitting there in its ground state. 97 00:04:29,520 --> 00:04:32,880 It should catch that gamma ray and jump up to the excited 98 00:04:32,880 --> 00:04:34,840 state. Simple catch and release. 99 00:04:35,960 --> 00:04:40,840 If the nuclei are identical, say they're both atoms of iron, the 100 00:04:40,840 --> 00:04:42,720 frequency should match perfectly. 101 00:04:43,040 --> 00:04:45,080 The tuning forks are tuned to the same note. 102 00:04:45,080 --> 00:04:47,040 That that was the theory. That's what everyone thought 103 00:04:47,040 --> 00:04:49,720 should happen. But for decades, nobody could 104 00:04:49,720 --> 00:04:52,280 get it to work in a practical, consistent way. 105 00:04:52,360 --> 00:04:55,040 What would happen? They would fire gamma rays from 106 00:04:55,040 --> 00:04:57,880 a source at a target of the same material and nothing. 107 00:04:58,520 --> 00:05:01,520 The gamma rays would just pass right through, no resonance. 108 00:05:02,120 --> 00:05:03,840 The second tuning fork stayed silent. 109 00:05:04,000 --> 00:05:06,080 Why? I mean, if they were the same 110 00:05:06,080 --> 00:05:08,240 element, shouldn't the key fit the lock? 111 00:05:08,480 --> 00:05:10,080 It feels like it should be automatic it. 112 00:05:10,120 --> 00:05:13,880 Feels like it, but it comes down to a fundamental law of physics, 113 00:05:13,960 --> 00:05:16,520 the conservation of momentum. Or, as we need to discuss it 114 00:05:16,520 --> 00:05:19,400 here, recoil. Recoil like firing a gun. 115 00:05:19,480 --> 00:05:22,480 Exactly like firing a gun. Imagine you are standing on a 116 00:05:22,480 --> 00:05:25,200 perfectly frictionless skateboard and you are holding a 117 00:05:25,200 --> 00:05:26,440 very heavy medicine. Goal. 118 00:05:26,440 --> 00:05:28,040 Yeah, I'm picturing it. I'm on the skateboard. 119 00:05:28,160 --> 00:05:31,680 No, you want to throw that ball to a friend who is also on a 120 00:05:31,680 --> 00:05:33,160 skateboard forward a few yards away. 121 00:05:33,400 --> 00:05:35,760 You heave the ball forward with all your might. 122 00:05:36,240 --> 00:05:38,880 What happens to you? I roll backward. 123 00:05:39,960 --> 00:05:43,240 For every action there is an equal and opposite reaction. 124 00:05:43,720 --> 00:05:46,920 I recoil. Right, you recoil. 125 00:05:47,320 --> 00:05:50,840 Now here's the problem. You put energy into that throw. 126 00:05:51,120 --> 00:05:53,640 You wanted all that energy to go into the ball so it would reach 127 00:05:53,640 --> 00:05:56,760 your friend with maximum speed. But it didn't, no. 128 00:05:56,800 --> 00:06:00,160 Yeah, because you recoiled. You stole some of that energy. 129 00:06:00,320 --> 00:06:02,840 The kinetic energy of your backward motion creates A 130 00:06:02,840 --> 00:06:05,120 deficit. The ball leaves your hands 131 00:06:05,120 --> 00:06:07,720 moving slightly slower than it theoretically should have. 132 00:06:07,720 --> 00:06:12,000 So the bullet is underpowered. Yes, the gamma ray has slightly 133 00:06:12,000 --> 00:06:14,560 less energy than the transition inside the nucleus actually, 134 00:06:14,560 --> 00:06:16,960 provided. We call this recoil energy or E 135 00:06:16,960 --> 00:06:19,000 sub R. So the emitted photon has the 136 00:06:19,000 --> 00:06:23,440 transition energy minus ER. OK, so I throw a weak ball, but 137 00:06:23,440 --> 00:06:25,120 what about my friend who is trying to catch it? 138 00:06:25,160 --> 00:06:26,480 Your. Friend has the same problem, 139 00:06:26,480 --> 00:06:28,840 just in reverse. If they are on their skateboard 140 00:06:28,840 --> 00:06:31,240 and they try to catch that heavy ball flying at them, what 141 00:06:31,240 --> 00:06:32,960 happens on impact? They get pushed backward. 142 00:06:32,960 --> 00:06:34,720 They recoil too. Exactly. 143 00:06:34,800 --> 00:06:37,920 And to absorb that impact and stop the ball, they need to 144 00:06:37,920 --> 00:06:41,200 expend energy. Essentially, for the nucleus to 145 00:06:41,200 --> 00:06:45,120 absorb the gamma ray, it needs the full transition energy, plus 146 00:06:45,120 --> 00:06:47,840 a little extra to account for the fact that it's going to get 147 00:06:47,840 --> 00:06:50,240 kicked backward by the photon. Oh, I see the gap now. 148 00:06:50,240 --> 00:06:53,000 There's a double whammy. The emitter is shooting low 149 00:06:53,000 --> 00:06:56,720 energy minus recoil. The absorber has a high bar to 150 00:06:56,720 --> 00:06:59,920 clear energy plus recoil. And in the world of nuclear 151 00:06:59,920 --> 00:07:03,400 physics, where the energy levels are incredibly sharp, that gap 152 00:07:03,480 --> 00:07:07,800 is twice the recoil. Energy to ER is a chasm. 153 00:07:07,880 --> 00:07:10,800 It's an insurmountable gap. So the photon arrives at the 154 00:07:10,800 --> 00:07:13,720 target nucleus and the nucleus says sorry this isn't enough 155 00:07:13,720 --> 00:07:16,560 energy, I can't make the jump. Your key is just slightly too 156 00:07:16,560 --> 00:07:19,560 small for my lock. The photon either bounces off or 157 00:07:19,560 --> 00:07:22,000 passes straight through. The resonance fails. 158 00:07:22,000 --> 00:07:24,200 And this is what was happening in those early experiments. 159 00:07:24,200 --> 00:07:27,160 Yes, because they were often using gases or liquids where the 160 00:07:27,160 --> 00:07:29,520 atoms are just, you know, floating around, free to move. 161 00:07:29,520 --> 00:07:31,200 So they were all on tiny little skateboard. 162 00:07:31,200 --> 00:07:32,480 They were all on tiny skateboards. 163 00:07:32,480 --> 00:07:34,560 If the atom is free to move, it recoils. 164 00:07:34,840 --> 00:07:36,640 If it recoils, you lose the resonance. 165 00:07:37,560 --> 00:07:39,760 So how did Rudolf Musbauer fix this? 166 00:07:40,400 --> 00:07:42,320 How do you stop an atom from recoiling? 167 00:07:42,840 --> 00:07:44,640 You can't exactly hold it down with tweezers. 168 00:07:44,640 --> 00:07:46,400 No, you can't. But you can change its 169 00:07:46,400 --> 00:07:49,440 environment. This was Musbauer's Nobel Prize 170 00:07:49,440 --> 00:07:52,800 winning insight. He realized that if you lock the 171 00:07:52,800 --> 00:07:57,080 atom inside a solid rigid crystal lattice, everything 172 00:07:57,080 --> 00:07:59,280 changes. Because it's chemically bonded 173 00:07:59,280 --> 00:08:00,920 to all of its neighbors. Exactly. 174 00:08:00,920 --> 00:08:03,560 It's handcuffed to the atoms next to it, which are handcuffed 175 00:08:03,560 --> 00:08:06,560 to the atoms next to them, and so on for the entire crystal. 176 00:08:06,840 --> 00:08:10,040 So now when the nucleus tries to kick back after emitting the 177 00:08:10,040 --> 00:08:13,200 gamma ray, it can't just move the single atom. 178 00:08:13,200 --> 00:08:15,240 It has to try to move the entire crystal. 179 00:08:15,320 --> 00:08:17,640 The entire crystal. I see where this is going. 180 00:08:17,920 --> 00:08:20,800 It's the difference between throwing that medicine ball 181 00:08:21,040 --> 00:08:24,360 while standing on a skateboard versus throwing it while bracing 182 00:08:24,360 --> 00:08:27,160 yourself against a brick wall. That is the perfect analogy. 183 00:08:27,160 --> 00:08:29,400 If you are braced against a building, you don't move, you 184 00:08:29,400 --> 00:08:31,440 don't recoil. All the energy goes into the 185 00:08:31,440 --> 00:08:33,919 ball. The ball flies at full speed. 186 00:08:33,919 --> 00:08:37,520 And your friend, who's also braced against a wall can catch 187 00:08:37,520 --> 00:08:41,000 it without getting knocked over. And physically, this works 188 00:08:41,000 --> 00:08:44,000 because of the mass, right? The formula for recoil energy 189 00:08:44,000 --> 00:08:46,640 has mass little M in the denominator. 190 00:08:47,000 --> 00:08:50,680 If M is the mass of one single atom, the recoil energy is 191 00:08:50,680 --> 00:08:53,120 significant. But if the atom is part of a 192 00:08:53,120 --> 00:08:56,720 crystal, the effective mass becomes the mass of the entire 193 00:08:56,720 --> 00:09:00,160 lattice. That number is huge, billions 194 00:09:00,160 --> 00:09:02,600 and billions of times larger. So if you divide by a 195 00:09:02,600 --> 00:09:06,360 practically infinite number, the recoil energy drops to 0. 196 00:09:06,440 --> 00:09:08,800 Effectively 0. It's not truly 0, but it's so 197 00:09:08,800 --> 00:09:12,280 small it becomes negligible. We call this recoiless nuclear 198 00:09:12,280 --> 00:09:14,560 resonance. By freezing the atoms in a 199 00:09:14,560 --> 00:09:18,240 solid, the emission line and the absorption line now overlap 200 00:09:18,240 --> 00:09:20,680 perfectly. The key fits the lock. 201 00:09:20,840 --> 00:09:23,880 The second tuning fork. That is, it's a physics magic 202 00:09:23,880 --> 00:09:25,480 trick. You're using the collective 203 00:09:25,480 --> 00:09:28,200 stiffness of a crystal to enable a nuclear measurement. 204 00:09:28,200 --> 00:09:29,680 And that is the Mussbauer effect. 205 00:09:29,720 --> 00:09:32,760 It opened the door to some of the most precise measurements in 206 00:09:32,760 --> 00:09:35,720 the history of physics. It turned a theoretical 207 00:09:35,720 --> 00:09:38,440 impossibility into a practical, powerful tool. 208 00:09:38,480 --> 00:09:42,160 OK, so we have the method. We have this this recoilless 209 00:09:42,160 --> 00:09:46,400 trick to make nuclei talk to each other, but we aren't just 210 00:09:46,400 --> 00:09:47,760 doing this for the sake of physics. 211 00:09:47,920 --> 00:09:50,840 We want to learn something about the stuff we are studying. 212 00:09:50,840 --> 00:09:53,120 We want to do chemistry. We want to do chemistry, and to 213 00:09:53,120 --> 00:09:55,360 do that we need a specific element. 214 00:09:55,400 --> 00:09:58,600 The outline mentions iron. Is iron the only one this works 215 00:09:58,600 --> 00:09:59,840 for? It's not the only one. 216 00:09:59,840 --> 00:10:02,520 There are, I think over 40 elements where this effect has 217 00:10:02,520 --> 00:10:05,640 been observed. Things like tin, europium, gold, 218 00:10:05,720 --> 00:10:10,400 nickel, but iron specifically the isotope Iron 57 is the 219 00:10:10,440 --> 00:10:12,800 absolute superstar. The king of Mussbauer. 220 00:10:12,840 --> 00:10:16,200 Absolutely. I'd say 90%, maybe even more, of 221 00:10:16,200 --> 00:10:18,120 all Mussbauer publications are on iron. 222 00:10:18,240 --> 00:10:19,600 Why? Is it just because iron is 223 00:10:19,600 --> 00:10:20,480 common? That helped. 224 00:10:20,480 --> 00:10:23,360 I mean, it's everywhere in geology, biology, and industry. 225 00:10:23,360 --> 00:10:25,960 Corrosion, Hemoglobin Magnets. Mars. 226 00:10:26,120 --> 00:10:29,280 It's everywhere. It is, but physically Iron 57 227 00:10:29,280 --> 00:10:31,560 just happens to have the Goldilocks properties. 228 00:10:31,720 --> 00:10:33,160 The energy levels are just right. 229 00:10:33,360 --> 00:10:35,640 The lifetime of the excited state is convenient for 230 00:10:35,640 --> 00:10:40,240 measurements, and, crucially, it works reasonably well at room 231 00:10:40,240 --> 00:10:41,800 temperature. So it's practical. 232 00:10:41,920 --> 00:10:44,680 It's very practical. Many other elements require you 233 00:10:44,680 --> 00:10:49,240 to cool your sample down to near absolute zero temperatures to 234 00:10:49,240 --> 00:10:52,120 get a strong enough effect, which is, you know, a hassle and 235 00:10:52,120 --> 00:10:55,080 expensive. OK, so Iron 57 is our player, 236 00:10:55,720 --> 00:10:57,920 but here's a detail from the notes that confused me 237 00:10:57,920 --> 00:11:01,440 initially. To study iron, we don't start 238 00:11:01,440 --> 00:11:03,840 with iron, we start with cobalt. Right. 239 00:11:04,040 --> 00:11:06,080 This is about how we generate the gamma rays. 240 00:11:06,080 --> 00:11:09,640 You can't just buy a bag of excited iron nuclei. 241 00:11:09,640 --> 00:11:12,200 Excited states decay very, very quickly. 242 00:11:12,320 --> 00:11:14,760 So you need a generator. You need a parent isotope that 243 00:11:14,760 --> 00:11:17,840 decays into the thing you want, conveniently leaving it in that 244 00:11:17,840 --> 00:11:20,240 excited state for you. So cobalt is the parent. 245 00:11:20,360 --> 00:11:23,920 Yes, Cobalt 57, it's radioactive and it has a half life of about 246 00:11:23,920 --> 00:11:26,240 270 days. That's a nice half life. 247 00:11:26,400 --> 00:11:28,240 Not too hot, not too cold. It's great. 248 00:11:28,240 --> 00:11:30,520 It means you can buy a force from a supplier and it will be 249 00:11:30,520 --> 00:11:33,240 useful in your lab for a year or two before it gets too weak. 250 00:11:33,240 --> 00:11:37,120 And what does this Cobalt 57 do? It undergoes a process called 251 00:11:37,120 --> 00:11:38,960 electron capture. What is that? 252 00:11:39,120 --> 00:11:40,400 It's exactly what it sounds like. 253 00:11:40,800 --> 00:11:44,720 The nucleus, which is positively charged, reaches out and grabs 254 00:11:44,720 --> 00:11:47,120 one of its own inner electrons from the K shell. 255 00:11:47,120 --> 00:11:50,920 Usually it pulls that electron in a proton plus an electron 256 00:11:50,920 --> 00:11:53,440 becomes a neutron. So the atomic number drops by 1. 257 00:11:53,520 --> 00:11:56,840 The atomic number drops by 1. Cobalt is element 27. 258 00:11:57,200 --> 00:11:59,960 It captures an electron. A proton becomes a neutron, and 259 00:11:59,960 --> 00:12:02,640 now it has 26 protons. It's iron. 260 00:12:02,760 --> 00:12:04,440 Alchemy in action. Indeed. 261 00:12:04,840 --> 00:12:08,200 But the iron nucleus it creates is born in a highly excited 262 00:12:08,200 --> 00:12:09,960 state. It's vibrating with excess 263 00:12:09,960 --> 00:12:11,960 energy. It wants to calm down. 264 00:12:11,960 --> 00:12:14,960 So it sheds that energy. It cascades down first. 265 00:12:14,960 --> 00:12:18,560 It drops from a very high spin state of 52 down to a lower 266 00:12:18,560 --> 00:12:23,440 excited state of 32. In doing so, it emits A136KV 267 00:12:23,440 --> 00:12:25,320 gamma ray, which we don't care about. 268 00:12:25,320 --> 00:12:27,320 We just filter that one out. Noise. 269 00:12:27,440 --> 00:12:30,440 It's noise, but now it's sitting in that 32 excited state, which 270 00:12:30,440 --> 00:12:32,640 has a lifetime of about 100 nanoseconds. 271 00:12:32,760 --> 00:12:34,160 And then it makes the final drop. 272 00:12:34,160 --> 00:12:37,480 It drops from the 32 state to the ground state, which is 12. 273 00:12:37,560 --> 00:12:39,200 And that final drop is the money shot. 274 00:12:39,280 --> 00:12:41,680 That's the one. That specific transition 275 00:12:41,680 --> 00:12:46,640 releases a gamma ray with a very precise energy of 14.4 qv. 14 276 00:12:46,640 --> 00:12:50,280 point 4K electron volts. I'm guessing that number is 277 00:12:50,280 --> 00:12:53,320 burned into the brain of every Musbauer spectroscopist. 278 00:12:53,560 --> 00:12:56,840 It is the sacred number that is our probe, that is our perfectly 279 00:12:56,840 --> 00:12:59,880 tuned key. That gamma ray flies out of the 280 00:12:59,880 --> 00:13:03,760 cobalt source, travels towards our sample, and if everything is 281 00:13:03,760 --> 00:13:07,120 right, it gets absorbed. So let's visualize the machine. 282 00:13:07,600 --> 00:13:11,120 We have the source which is the Cobalt 57 embedded in some kind 283 00:13:11,120 --> 00:13:12,960 of matrix. Usually a rhodium foil, yeah. 284 00:13:13,000 --> 00:13:15,760 OK, so the cobalt source, then we have the absorber, which is 285 00:13:15,760 --> 00:13:19,080 our sample, let's say a piece of that Martian rock. 286 00:13:19,360 --> 00:13:21,120 And behind the rock, we have a detector. 287 00:13:21,160 --> 00:13:22,880 Correct. It's a transmission experiment, 288 00:13:22,880 --> 00:13:24,960 just like an X-ray at the doctor's office. 289 00:13:25,400 --> 00:13:27,920 You're looking for the shadow. You are counting the gamma rays 290 00:13:27,920 --> 00:13:30,880 that don't get through. So if the iron in the rock 291 00:13:30,880 --> 00:13:34,480 absorbs the gamma rays, the detector sees a dip in the count 292 00:13:34,480 --> 00:13:35,760 rate. It sees a shadow. 293 00:13:35,760 --> 00:13:37,680 Exactly. You get a plot of gamma ray 294 00:13:37,680 --> 00:13:41,440 transmission versus something else and you look for the dips. 295 00:13:41,680 --> 00:13:45,240 But wait. We have a problem if we have the 296 00:13:45,240 --> 00:13:48,080 perfect resonance we just talked about, no recoil, wouldn't we 297 00:13:48,080 --> 00:13:50,760 just see a total blackout? If the source is emitting from 298 00:13:50,760 --> 00:13:54,040 an iron 57 nucleus and the sample is also iron 57, 299 00:13:54,120 --> 00:13:55,680 shouldn't they always match perfectly? 300 00:13:55,680 --> 00:13:58,840 Now that is the billion dollar question, and the answer is what 301 00:13:58,840 --> 00:14:02,040 makes this technique useful? If every iron atom in the 302 00:14:02,040 --> 00:14:06,040 universe were identical and floating in a vacuum, yes you 303 00:14:06,040 --> 00:14:08,640 would see one single strong absorption line. 304 00:14:08,640 --> 00:14:09,520 But. But. 305 00:14:09,800 --> 00:14:11,560 They're not. Atoms aren't in a vacuum. 306 00:14:11,560 --> 00:14:13,640 They're in molecules. They are in crystals. 307 00:14:13,640 --> 00:14:15,120 They are surrounded by electrons. 308 00:14:15,440 --> 00:14:18,200 Chemistry gets in the way. So chemistry messes with the 309 00:14:18,200 --> 00:14:20,080 nucleus. Chemistry gets in the way, and 310 00:14:20,080 --> 00:14:21,680 this is the whole point of the deep dive. 311 00:14:22,000 --> 00:14:25,480 The chemical environment, the oxidation state, the atoms it's 312 00:14:25,480 --> 00:14:28,200 bonded to, the whole cloud of electrons whizzing around the 313 00:14:28,200 --> 00:14:30,960 nucleus actually affects the nucleus itself. 314 00:14:30,960 --> 00:14:33,040 It subtly shifts the nuclear energy levels. 315 00:14:33,040 --> 00:14:35,960 So the lock in the sample is slightly jammed or slightly 316 00:14:35,960 --> 00:14:38,120 modified compared to the key from the source. 317 00:14:38,240 --> 00:14:41,720 Exactly. The source nucleus is in a nice 318 00:14:41,720 --> 00:14:44,760 clean, symmetric rhodium metal environment. 319 00:14:45,120 --> 00:14:48,720 The sample nucleus might be in a rusty, distorted, messy mineral. 320 00:14:48,960 --> 00:14:51,440 Their energy levels are no longer a perfect match. 321 00:14:51,440 --> 00:14:54,320 So the resonance is lost again. The gamma rays just pass right 322 00:14:54,320 --> 00:14:57,080 through, correct? So we broke it. 323 00:14:57,200 --> 00:15:00,040 We did all this work to get recoil, this resonance, and that 324 00:15:00,040 --> 00:15:01,600 chemistry has come along and broken it. 325 00:15:01,640 --> 00:15:03,360 We didn't break it, we made it sensitive. 326 00:15:03,360 --> 00:15:05,000 We've turned a bug into a feature. 327 00:15:05,680 --> 00:15:09,480 Now to find the resonance again, we have to tune our gamma ray. 328 00:15:10,200 --> 00:15:13,560 We have to slightly change its energy to match the new 329 00:15:13,760 --> 00:15:15,960 chemically shifted requirement of the sample. 330 00:15:16,040 --> 00:15:18,360 How do you tune a gamma ray? You can't just turn a knob on 331 00:15:18,360 --> 00:15:20,720 the nucleus. No, but you can move the source. 332 00:15:20,720 --> 00:15:23,760 We use the Doppler effect the. Train whistle effect the Neos as 333 00:15:23,760 --> 00:15:26,680 it passes by. The very same If a train moves 334 00:15:26,680 --> 00:15:29,800 towards you, the sound waves get squashed, the frequency goes up 335 00:15:29,800 --> 00:15:33,360 and the pitch sounds higher. If it moves away, the waves 336 00:15:33,360 --> 00:15:35,000 stretch out and the pitch goes down. 337 00:15:35,360 --> 00:15:38,000 We do the exact same thing with the gamma ray source. 338 00:15:38,080 --> 00:15:40,120 So you physically move the radioactive source. 339 00:15:40,480 --> 00:15:44,560 We mount the radioactive cobalt source on a motor, a high 340 00:15:44,560 --> 00:15:48,480 precision linear motor, and we vibrate the source back and 341 00:15:48,480 --> 00:15:50,760 forth very smoothly. You're kidding. 342 00:15:50,760 --> 00:15:53,160 Not at all. When the source moves toward the 343 00:15:53,160 --> 00:15:56,720 sample, the gamma ray gets a tiny boost of energy, a blue 344 00:15:56,720 --> 00:15:58,720 shift. When it moves away from the 345 00:15:58,720 --> 00:16:02,680 sample, the gamma ray leases a tiny bit of energy, a red shift. 346 00:16:02,840 --> 00:16:05,880 This seems incredibly primitive and incredibly high tech at the 347 00:16:05,880 --> 00:16:09,440 same time. We are mechanically moving a 348 00:16:09,440 --> 00:16:13,560 radioactive rock to tune a quantum nuclear transition. 349 00:16:13,640 --> 00:16:14,760 That's a great description of it. 350 00:16:14,920 --> 00:16:16,720 How fast does this motor have to move? 351 00:16:16,960 --> 00:16:18,720 I'm imagining something blurring back and. 352 00:16:18,720 --> 00:16:20,280 Forth. That's the best part, and this 353 00:16:20,280 --> 00:16:22,840 speaks to the insane precision of the effect. 354 00:16:23,160 --> 00:16:26,280 To shift the energy enough to scan through all the typical 355 00:16:26,280 --> 00:16:29,320 chemical changes, we don't need to move at the speed of light or 356 00:16:29,320 --> 00:16:32,560 even the speed of a car. We need to move it millimeters 357 00:16:32,560 --> 00:16:34,400 per second. Millimeters per second, like 358 00:16:34,400 --> 00:16:36,280 snail speed. Literally snail speed. 359 00:16:36,320 --> 00:16:39,120 The typical range for scanning iron compounds is usually 360 00:16:39,120 --> 00:16:43,080 between -10mm per second and plus 10mm per second and. 361 00:16:43,240 --> 00:16:45,480 That creates enough of an energy shift to matter. 362 00:16:45,680 --> 00:16:50,320 Yes, the nuclear resonance is so incredibly sharp, so exquisitely 363 00:16:50,320 --> 00:16:54,480 tuned, that a tiny Doppler shift is more than enough to scan 364 00:16:54,480 --> 00:16:56,240 across the entire absorption line. 365 00:16:56,680 --> 00:16:59,760 That's why when you look at a Mussbauer spectrum, the X axis 366 00:16:59,760 --> 00:17:03,240 isn't labeled in joules or frequency, it's labeled in 367 00:17:03,360 --> 00:17:05,520 velocity. Is wild. 368 00:17:05,520 --> 00:17:07,680 You're plotting transmission against the speed of a snail. 369 00:17:08,319 --> 00:17:11,319 So we are looking for a dip in the grab a shadow at a specific 370 00:17:11,319 --> 00:17:15,520 speed, maybe at plus .2mm the detector count suddenly drops. 371 00:17:15,520 --> 00:17:18,079 Exactly. And that velocity where the dip 372 00:17:18,079 --> 00:17:21,960 occurs tells us exactly how much the energy levels in the sample 373 00:17:21,960 --> 00:17:24,119 have shifted relative to our source. 374 00:17:24,640 --> 00:17:27,800 And that brings us to our first major data point, the first 375 00:17:27,800 --> 00:17:31,000 piece of chemical information we can extract, the isomer shift. 376 00:17:31,000 --> 00:17:33,440 OK, let's decode this. The isomer shift which is given 377 00:17:33,440 --> 00:17:36,040 the Greek letter delta. I see what is physically 378 00:17:36,040 --> 00:17:37,880 happening in the atom to 'cause this shift. 379 00:17:38,040 --> 00:17:39,720 What is chemistry doing to the nucleus? 380 00:17:39,920 --> 00:17:42,600 It comes down to something that seems very strange at first. 381 00:17:43,040 --> 00:17:44,720 It's about the size of the nucleus. 382 00:17:45,200 --> 00:17:48,080 We usually think of the nucleus as a hard little point, like a 383 00:17:48,080 --> 00:17:52,480 marble, but it's not rigid. When a nucleus gets excited by 384 00:17:52,480 --> 00:17:55,560 absorbing A gamma ray, it actually changes its radius. 385 00:17:55,640 --> 00:17:58,120 It puffs up or it shrinks. For some isotopes it gets 386 00:17:58,120 --> 00:17:59,720 bigger. For others it gets smaller. 387 00:18:00,000 --> 00:18:03,040 For our hero Iron 57, the excited state is actually 388 00:18:03,040 --> 00:18:05,200 smaller in radius than the ground state. 389 00:18:05,480 --> 00:18:09,160 The nucleus physically shrinks a tiny bit when it gets excited. 390 00:18:09,560 --> 00:18:11,800 OK, that's a weird concept to wrap my head around, but I'm 391 00:18:11,800 --> 00:18:13,920 with you. The nucleus changes size. 392 00:18:14,040 --> 00:18:15,560 How does chemistry connect to that? 393 00:18:15,880 --> 00:18:19,080 The connection is the electrons. The nucleus is surrounded by 394 00:18:19,080 --> 00:18:21,680 electrons. But remember your orbital shapes 395 00:18:21,680 --> 00:18:26,280 from high school chemistry SPDF. Vaguely S orbitals are spheres, 396 00:18:26,280 --> 00:18:28,800 P orbals are dumbbells, D orbals are like clovers. 397 00:18:28,880 --> 00:18:31,520 Perfect. The key here is that only the S 398 00:18:31,520 --> 00:18:35,200 electrons, the spherical ones, have a non 0 probability of 399 00:18:35,200 --> 00:18:38,280 being found inside the nucleus. Inside, I thought electrons 400 00:18:38,280 --> 00:18:40,240 orbited around the nucleus like planets. 401 00:18:40,400 --> 00:18:43,480 In the old Bohr model, yes. But in quantum mechanics, 402 00:18:43,480 --> 00:18:45,680 electrons are clouds of probability. 403 00:18:46,240 --> 00:18:49,680 Their wave functions describe where they are likely to be, and 404 00:18:49,680 --> 00:18:52,480 the spherical wave function of an S electron actually 405 00:18:52,480 --> 00:18:55,880 penetrates the nuclear volume. It spends a tiny fraction of its 406 00:18:55,880 --> 00:18:59,200 time literally sitting on top of the protons and neutrons. 407 00:18:59,200 --> 00:19:03,520 So the P&D electrons stay outside, but the S electrons get 408 00:19:03,520 --> 00:19:04,880 in. That's the crucial point. 409 00:19:04,880 --> 00:19:07,880 The nucleus feels the presence of these S electrons. 410 00:19:07,880 --> 00:19:11,000 It's in direct contact with them, and because the nucleus 411 00:19:11,000 --> 00:19:13,400 changes size during the transition from ground to 412 00:19:13,400 --> 00:19:17,240 excited state, the electrostatic interaction between the nucleus 413 00:19:17,240 --> 00:19:19,200 and that S electron density changes. 414 00:19:19,200 --> 00:19:20,640 And that changes the energy levels. 415 00:19:20,640 --> 00:19:23,160 It shifts them. The energy of the ground state 416 00:19:23,160 --> 00:19:26,520 and the excited state are both shifted by this interaction, but 417 00:19:26,520 --> 00:19:29,000 by slightly different amounts because their radii are 418 00:19:29,000 --> 00:19:31,240 different. This creates a change in the 419 00:19:31,240 --> 00:19:34,240 transition energy. This creates the isomer shift. 420 00:19:34,640 --> 00:19:37,720 So if I change the chemical bonding around an atom, I change 421 00:19:37,720 --> 00:19:41,080 its overall electron configuration, which changes the 422 00:19:41,080 --> 00:19:43,760 S electron density, which changes the shift. 423 00:19:43,960 --> 00:19:46,680 Precisely, you've got it. Let's look at the tin example 424 00:19:46,680 --> 00:19:48,400 from your notes. Tin 119. 425 00:19:48,640 --> 00:19:51,440 It's a classic and a great way to visualize oxidation states. 426 00:19:51,560 --> 00:19:54,680 Tin Tin We have two common oxidation states, tin 2 and tin 427 00:19:54,680 --> 00:19:56,880 3. Right, a neutral tin atom has an 428 00:19:56,880 --> 00:20:01,160 electron configuration ending in five shellers, 5 P $2.00, two 429 00:20:01,160 --> 00:20:03,800 airs electrons, 2P electrons and it's outer shell. 430 00:20:03,840 --> 00:20:06,360 Got it? Now consider tin 3 the stanic 431 00:20:06,360 --> 00:20:10,200 ions 7 plus dollars to become four plus thera it. 432 00:20:10,320 --> 00:20:13,560 Loses those 4 outer electrons or it forms bonds where they are 433 00:20:13,560 --> 00:20:15,800 shared so strongly they are basically pulled away. 434 00:20:16,200 --> 00:20:18,720 So the S electron density at the nucleus is lower. 435 00:20:18,720 --> 00:20:21,440 OK, low density for tin 3. Now look at tin 2, the Stannis 436 00:20:21,440 --> 00:20:24,960 ion 70 plus dollar. When tin forms A2 plus ion, it's 437 00:20:25,040 --> 00:20:27,760 energetically favorable to lose the electrons first. 438 00:20:27,960 --> 00:20:31,040 So it loses the five PT 2 electrons, but it keeps the five 439 00:20:31,040 --> 00:20:35,120 PT 2 pair as a lone pair. So TIN 2 has this big fat cloud 440 00:20:35,120 --> 00:20:37,120 of selectrons sitting right on the nucleus. 441 00:20:37,280 --> 00:20:39,600 Exactly. It has a much higher electron 442 00:20:39,600 --> 00:20:43,040 density at the nucleus compared to tin four, and because the 443 00:20:43,040 --> 00:20:45,800 nucleus interacts with that density, the nuclear energy 444 00:20:45,800 --> 00:20:47,520 levels shift by different amounts. 445 00:20:47,520 --> 00:20:50,640 In the case of TIN, this means TIN compounds show up at a much 446 00:20:50,640 --> 00:20:53,120 higher positive velocity than TIN compounds. 447 00:20:53,480 --> 00:20:54,640 So you can just look at the chart. 448 00:20:54,640 --> 00:20:58,360 If the dip is way out of plus 3mm you can say with confidence 449 00:20:58,720 --> 00:21:02,000 that's tin 2. If it's down near 0 you say 450 00:21:02,240 --> 00:21:05,000 that's 10 four. You are reading the oxidation 451 00:21:05,000 --> 00:21:07,520 state directly from the nucleus. You are. 452 00:21:07,560 --> 00:21:10,600 It's an incredibly powerful fingerprint for oxidation state, 453 00:21:11,160 --> 00:21:13,960 and it gets even more subtle. We can see the effect of the 454 00:21:13,960 --> 00:21:17,360 neighbors, the ligands that the atom is bonded to. 455 00:21:17,360 --> 00:21:20,280 The notes mentioned fluorine versus chlorine bonded to tin. 456 00:21:20,360 --> 00:21:22,040 Right, this is all about electronegativity. 457 00:21:22,040 --> 00:21:25,080 Remember that from chemistry and atoms greed for electrons. 458 00:21:25,080 --> 00:21:26,440 Chlorine is the greediest of all. 459 00:21:26,440 --> 00:21:28,800 Fluorine is the bully of the periodic table. 460 00:21:28,880 --> 00:21:31,160 It wants electrons more than anyone else. 461 00:21:31,320 --> 00:21:35,360 So if you bond 10 to 4 fluorine atoms to make 7F4 hills, the 462 00:21:35,360 --> 00:21:38,360 fluorine atoms pull the bonding electrons violently away from 463 00:21:38,360 --> 00:21:40,440 the tin. So the two nucleus is left 464 00:21:40,480 --> 00:21:42,480 naked? Electronically speaking, yeah. 465 00:21:42,640 --> 00:21:46,880 Relatively speaking, yes, it has very low electron density around 466 00:21:46,880 --> 00:21:49,800 it and therefore a very low electron density at the nucleus. 467 00:21:50,160 --> 00:21:53,800 This results in a very low, even negative isomer shift. 468 00:21:54,280 --> 00:21:58,080 The data shows Maddio .47mm for that compound. 469 00:21:58,080 --> 00:22:01,080 OK, now what if we swap the fluorine for chlorine? 470 00:22:01,400 --> 00:22:05,760 We make SNCL 4 SU dollars. Chlorine is also very greedy, 471 00:22:05,840 --> 00:22:07,760 but it's not as greedy as fluorine. 472 00:22:08,000 --> 00:22:11,160 It pulls on the electrons, but it lets the tin keep a little 473 00:22:11,160 --> 00:22:13,080 bit more of the electron density for itself. 474 00:22:13,120 --> 00:22:16,760 So the S electron density at the nucleus goes up and the shift 475 00:22:16,760 --> 00:22:17,720 goes up. Correct. 476 00:22:17,720 --> 00:22:22,560 The isomer shift for SNCL 4 three is +85 millimeters. 477 00:22:22,800 --> 00:22:24,200 That's a huge difference in this world. 478 00:22:24,320 --> 00:22:26,120 It's a completely different part of the spectrum. 479 00:22:26,120 --> 00:22:27,840 I love this because it's so tangible. 480 00:22:28,080 --> 00:22:30,680 You are using a nuclear interaction that's happening on 481 00:22:30,680 --> 00:22:34,360 a femtometer scale to measure how greedy A neighboring atom 482 00:22:34,360 --> 00:22:36,040 is. It is a nuclear spy in the 483 00:22:36,040 --> 00:22:37,920 chemical camp. It's reporting back on the 484 00:22:37,920 --> 00:22:40,400 nature of the chemical bonds. So that's the isomer shift, the 485 00:22:40,400 --> 00:22:41,800 side to side movement of the peak. 486 00:22:42,080 --> 00:22:44,600 But looking at these Martian Spectra, the graphs aren't 487 00:22:44,600 --> 00:22:46,880 always just single dips. Sometimes they look like, well, 488 00:22:46,880 --> 00:22:50,000 they're split in two, or they look like a comb mountain range. 489 00:22:50,200 --> 00:22:53,080 Yes, the single absorption line we've been talking about can 490 00:22:53,080 --> 00:22:55,920 split into multiple lines. This is where we get into the 491 00:22:55,920 --> 00:23:00,040 other hyperfine interactions. The isomer shift is 1, but there 492 00:23:00,040 --> 00:23:01,920 are others. The first one in the outline is 493 00:23:02,160 --> 00:23:05,560 quadrupole splitting. That sounds like a leg exercise 494 00:23:05,560 --> 00:23:07,160 at the gym. What is a quadrupole? 495 00:23:07,480 --> 00:23:11,000 It refers to the shape of the electric charge distribution in 496 00:23:11,000 --> 00:23:13,960 the nucleus. We like to imagine nuclei as 497 00:23:13,960 --> 00:23:16,800 perfect little spheres, like basketballs. 498 00:23:17,280 --> 00:23:19,720 In that case, the chart is distributed symmetrically. 499 00:23:19,800 --> 00:23:22,920 But it's not always like that. For many isotopes, including 500 00:23:22,920 --> 00:23:26,640 Iron 57 in its excited state, the nucleus is deformed. 501 00:23:26,840 --> 00:23:29,520 It's not a sphere. It's shaped more like a rugby 502 00:23:29,520 --> 00:23:32,400 ball or an American football. We call that prolate. 503 00:23:32,600 --> 00:23:35,280 Or it could be flattened like an M&M, which we call oblique. 504 00:23:35,560 --> 00:23:39,120 OK, so we have an asymmetrical nucleus, A football shaped 505 00:23:39,120 --> 00:23:40,720 nucleus. Now imagine you put that 506 00:23:40,720 --> 00:23:44,200 asymmetrical nucleus into an asymmetrical electric field. 507 00:23:44,240 --> 00:23:46,040 What would create an asymmetrical field? 508 00:23:46,320 --> 00:23:50,200 The electrons, if the electrons in the chemical bonds around the 509 00:23:50,200 --> 00:23:53,720 atom aren't distributed evenly in a nice symmetrical way like a 510 00:23:53,720 --> 00:23:57,000 cube or a sphere, they create what's called an electric field 511 00:23:57,000 --> 00:23:59,160 gradient. There's more negative charge in 512 00:23:59,160 --> 00:24:00,760 One Direction than another. Got it? 513 00:24:01,080 --> 00:24:04,560 So you have a non spherical nucleus in a non spherical 514 00:24:04,560 --> 00:24:07,600 electric field. The nucleus experiences a 515 00:24:07,600 --> 00:24:10,120 torque. It tries to align itself, but 516 00:24:10,200 --> 00:24:12,600 quantum mechanics says it can't just point anywhere. 517 00:24:12,880 --> 00:24:16,240 The energy levels split. So instead of 1 jump from the 518 00:24:16,240 --> 00:24:19,760 ground state to the excited state, there are now 2 possible 519 00:24:19,760 --> 00:24:21,520 jumps with slightly different energies. 520 00:24:21,520 --> 00:24:23,560 Exactly. And because there are two 521 00:24:23,560 --> 00:24:26,800 possible transition energies, the single absorption line 522 00:24:26,800 --> 00:24:29,680 splits into a doublet 2 distinct line side by side. 523 00:24:30,120 --> 00:24:31,840 And what does that tell the chemist? 524 00:24:31,840 --> 00:24:34,720 What's the take away from seeing a doublet instead of a singlet? 525 00:24:34,800 --> 00:24:37,600 It tells you about symmetry. If you see a single line, it 526 00:24:37,600 --> 00:24:40,360 means your iron atom is sitting in a very symmetric local 527 00:24:40,360 --> 00:24:42,400 environment. Maybe it's at the center of a 528 00:24:42,400 --> 00:24:45,640 perfect cube of oxygen atoms, or a perfect octahedron. 529 00:24:46,080 --> 00:24:48,920 But if you see that splitting that doublet, you know the 530 00:24:48,920 --> 00:24:52,440 environment is distorted. So if you squash that cube, or 531 00:24:52,440 --> 00:24:55,280 if you replace one of the neighboring oxygen atoms with a 532 00:24:55,280 --> 00:24:57,840 nitrogen atom, you break the symmetry. 533 00:24:57,880 --> 00:25:00,760 You break the symmetry, you create an electric field 534 00:25:00,760 --> 00:25:03,680 gradient, and the quadruple splitting appears. 535 00:25:03,880 --> 00:25:06,720 It's a geometry detector. It tells you if the Adam's house 536 00:25:06,720 --> 00:25:09,280 is perfectly built or if it's a bit lopsided. 537 00:25:09,360 --> 00:25:10,560 That's a great way of putting it. 538 00:25:10,640 --> 00:25:12,560 And then we have the big one, the one that was so important 539 00:25:12,560 --> 00:25:16,520 for Mars, magnetic splitting. Yes, this is also known as the 540 00:25:16,520 --> 00:25:20,160 nuclear Zeeman effect. This is what makes Iron 57 so 541 00:25:20,160 --> 00:25:23,560 incredibly powerful for geology and material science. 542 00:25:23,560 --> 00:25:27,320 So what's the principle here? The nucleus itself, because of 543 00:25:27,320 --> 00:25:31,440 the spin of its protons and neutrons, acts like a tiny bar 544 00:25:31,440 --> 00:25:33,600 magnet. It has a magnetic moment. 545 00:25:33,840 --> 00:25:36,280 A tiny compass needle. Tiny compass needle. 546 00:25:36,560 --> 00:25:40,240 Now, if there is a magnetic field present where that nucleus 547 00:25:40,240 --> 00:25:43,200 is sitting, that compass needle will try to align with it. 548 00:25:43,200 --> 00:25:45,480 And just like with the quadrupole effect, quantum 549 00:25:45,480 --> 00:25:49,240 mechanics says it can only align in a few specific, quantized 550 00:25:49,240 --> 00:25:51,800 ways. This splits the nuclear energy 551 00:25:51,800 --> 00:25:54,880 levels apart dramatically. And this magnetic field, does it 552 00:25:54,880 --> 00:25:56,760 have to be from a big external magnet? 553 00:25:56,960 --> 00:26:00,480 It can be, but often for materials like iron, metal or 554 00:26:00,480 --> 00:26:04,080 iron oxides, the material generates its own incredibly 555 00:26:04,080 --> 00:26:08,160 strong internal magnetic field. OK, so the material itself is 556 00:26:08,160 --> 00:26:10,160 magnetic. How many lines do we get from 557 00:26:10,160 --> 00:26:13,480 this splitting? For Iron 57, due to the specific 558 00:26:13,480 --> 00:26:17,040 spin states of the ground and excited levels, the levels split 559 00:26:17,040 --> 00:26:19,560 in such a way that you get 6 allowed transitions. 560 00:26:19,560 --> 00:26:21,920 So the single line splits into a sex stat A. 561 00:26:21,920 --> 00:26:24,920 Sex Stat 6 lines. 6 lines. It looks like a six fingered 562 00:26:24,920 --> 00:26:28,040 comb, usually with a characteristic 3 to 2 to 1 563 00:26:28,040 --> 00:26:30,400 intensity ratio for the pairs of peaks. 564 00:26:30,520 --> 00:26:32,640 And this is the fingerprint. This is the definitive 565 00:26:32,640 --> 00:26:35,320 fingerprint. Different magnetic iron minerals 566 00:26:35,320 --> 00:26:37,800 have different magnetic strengths and structures. 567 00:26:37,800 --> 00:26:41,200 Magnetite fee three O 4 Chore 3 creates a very wide splitting 568 00:26:41,200 --> 00:26:43,200 pattern. Chemotite from how the main 569 00:26:43,200 --> 00:26:46,000 component of rust has a different very distinct pattern. 570 00:26:46,840 --> 00:26:49,280 Another common iron mineral is different again. 571 00:26:49,320 --> 00:26:51,920 So when the Rover on Mars looked at one of those little spherical 572 00:26:51,920 --> 00:26:55,280 rocks, the blueberries and its must power spectrometer saw a 573 00:26:55,280 --> 00:26:59,520 sextet with a specific spacing and a specific isomer shift. 574 00:26:59,760 --> 00:27:03,400 It knew with 100% certainty that is hematite. 575 00:27:03,880 --> 00:27:06,760 No other mineral gives that exact signal. 576 00:27:07,200 --> 00:27:09,600 And why do we care about hematite on Mars? 577 00:27:09,720 --> 00:27:14,360 Because on Earth, that specific form of hematite almost always 578 00:27:14,360 --> 00:27:17,600 forms in the presence of large amounts of standing liquid 579 00:27:17,600 --> 00:27:20,560 water. Finding those specific magnetic 580 00:27:20,560 --> 00:27:22,840 fingerprints was the smoking gun. 581 00:27:23,120 --> 00:27:26,440 It was the absolute proof that Mars had a wet past. 582 00:27:26,440 --> 00:27:29,360 That is incredible. We found the ghost of an ancient 583 00:27:29,360 --> 00:27:32,760 ocean on another planet by jiggling a radioactive source at 584 00:27:32,760 --> 00:27:35,120 the speed of a snail. It puts it in perspective, 585 00:27:35,120 --> 00:27:37,160 doesn't it? The scales are just mind 586 00:27:37,160 --> 00:27:39,560 boggling. There is one last technical 587 00:27:39,560 --> 00:27:41,680 hurdle I want to touch on because it seems important for 588 00:27:41,680 --> 00:27:43,120 actually doing these experiments. 589 00:27:43,480 --> 00:27:46,360 The notes mentioned temperature and liquid nitrogen. 590 00:27:46,960 --> 00:27:49,240 We talked about how the crystal needs to be solid to absorb the 591 00:27:49,240 --> 00:27:51,360 recoil. Does temperature affect that? 592 00:27:51,600 --> 00:27:54,080 Hugely. Even in a solid crystal, atoms 593 00:27:54,080 --> 00:27:55,840 aren't perfectly still. They vibrate. 594 00:27:55,840 --> 00:27:58,160 They have thermal energy. In solid-state physics, we 595 00:27:58,160 --> 00:28:00,560 describe these collective vibrations as phonons. 596 00:28:00,560 --> 00:28:03,760 Like sound particles. Essentially, yes, quantized 597 00:28:03,760 --> 00:28:06,560 lattice vibrations. Now, if the atom is vibrating 598 00:28:06,560 --> 00:28:10,160 too violently, if the crystal is too hot, the probability of a 599 00:28:10,160 --> 00:28:12,720 purely recoilus event drops. Why? 600 00:28:13,240 --> 00:28:16,120 Because the atom has another way to deal with the recoil energy. 601 00:28:16,120 --> 00:28:19,240 Instead of transferring the momentum to the entire crystal, 602 00:28:19,400 --> 00:28:22,520 it can just absorb the kick. By increasing its own vibration, 603 00:28:22,520 --> 00:28:25,120 it can create a phonon. And if it creates A vibration, 604 00:28:25,120 --> 00:28:28,040 it uses up some of the energy and we lose the perfect energy 605 00:28:28,040 --> 00:28:28,960 match. Exactly. 606 00:28:29,040 --> 00:28:32,320 The recoil free fraction, which has the technical name of the 607 00:28:32,320 --> 00:28:34,920 West Waller factor, goes down as temperature goes up. 608 00:28:35,400 --> 00:28:38,800 If your sample is made of atoms that are weakly bonded, if the 609 00:28:38,800 --> 00:28:42,520 crystal is soft, or if it's too hot, the signal just disappears 610 00:28:42,520 --> 00:28:44,680 into the noise. You get no absorption. 611 00:28:45,080 --> 00:28:49,800 So that's why you see photos of these with giant steaming metal 612 00:28:49,800 --> 00:28:52,560 flasks, doers of liquid nitrogen. 613 00:28:53,040 --> 00:28:56,280 They are freezing the sample. They're freezing the sample to 614 00:28:56,280 --> 00:28:59,760 make the crystal lattice as stiff and rigid as possible. 615 00:28:59,760 --> 00:29:02,440 They're trying to maximize that recoil free fraction. 616 00:29:02,440 --> 00:29:04,320 To quiet down the thermal vibrations. 617 00:29:04,480 --> 00:29:07,560 Exactly. For many isotopes you absolutely 618 00:29:07,560 --> 00:29:11,720 need to go down to 77 Kelvin, which is the temperature of 619 00:29:11,720 --> 00:29:15,040 liquid nitrogen, or for some even more difficult cases, down 620 00:29:15,040 --> 00:29:18,120 to 4 Kelvin with liquid helium to see anything at all. 621 00:29:18,280 --> 00:29:20,840 But Iron 57 works at room temperature, you said? 622 00:29:21,080 --> 00:29:24,840 Iron 57 is robust enough. The bonds in typical iron 623 00:29:24,840 --> 00:29:27,880 compounds are strong enough that we can get a decent signal at 624 00:29:27,880 --> 00:29:30,600 room temperature. The signal gets much sharper and 625 00:29:30,600 --> 00:29:34,240 stronger if you cool it down, but you can do it at 300 Kelvin. 626 00:29:34,320 --> 00:29:35,920 And that's why we could send it to Mars. 627 00:29:35,920 --> 00:29:39,160 That's why you definitely do not want to try and haul a Dewar of 628 00:29:39,160 --> 00:29:41,760 liquid helium 140 million miles to Mars. 629 00:29:41,760 --> 00:29:43,800 No, that seems like a logistical nightmare. 630 00:29:43,800 --> 00:29:46,000 A definite non starter for a Rover mission. 631 00:29:46,200 --> 00:29:48,400 So let's wrap our heads around this entire journey. 632 00:29:48,440 --> 00:29:51,320 It really is a synthesis of so many different fields of 633 00:29:51,320 --> 00:29:52,520 science. It truly is. 634 00:29:52,520 --> 00:29:55,040 We start with the deepest physics, the nucleus. 635 00:29:55,360 --> 00:29:59,040 Radioactive decay, high energy gamma rays, even special 636 00:29:59,040 --> 00:30:01,320 relativity comes into play with some of the temperature effects. 637 00:30:01,480 --> 00:30:03,640 Then we move to solid-state physics. 638 00:30:03,960 --> 00:30:07,600 The crystal lattice phonons the whole idea of the collective 639 00:30:07,600 --> 00:30:11,000 solid absorbing the recoil. Then we use the Doppler effect, 640 00:30:11,120 --> 00:30:14,000 which is pure classical mechanics, the physics of trains 641 00:30:14,000 --> 00:30:16,360 and sound waves, to tune the energy. 642 00:30:16,680 --> 00:30:20,080 And finally, we interpret the data using pure chemistry, 643 00:30:20,400 --> 00:30:23,320 Oxidation states, electronegativity of ligands, 644 00:30:23,320 --> 00:30:26,360 molecular geometry, symmetry. It's a tool that ignores 645 00:30:26,360 --> 00:30:28,240 boundaries. It doesn't care if you call it 646 00:30:28,240 --> 00:30:31,280 physics or chemistry or geology or material science. 647 00:30:31,320 --> 00:30:33,000 And that's. Why it's so powerful? 648 00:30:33,280 --> 00:30:37,760 It allows us to see the local environment of Ecific atom in a 649 00:30:37,760 --> 00:30:40,440 way that other techniques can't always do. 650 00:30:40,560 --> 00:30:42,960 Exactly. Something like X-ray diffraction 651 00:30:42,960 --> 00:30:46,240 is great for finding the long range average structure of a 652 00:30:46,240 --> 00:30:50,120 crystal where the atoms are in the unit cell, but Mussbauer 653 00:30:50,120 --> 00:30:53,600 tells you what that one specific iron atom is feeling. 654 00:30:53,680 --> 00:30:56,520 Is it magnetic? Is it in a distorted site? 655 00:30:56,520 --> 00:30:57,760 Is it you would to or you would to? 656 00:30:57,760 --> 00:31:00,280 Is it giving up its electrons to a greedy neighbor? 657 00:31:00,480 --> 00:31:03,120 It's like interviewing every atom individually instead of 658 00:31:03,120 --> 00:31:04,760 just taking a census of the crowd. 659 00:31:04,760 --> 00:31:06,000 That's a beautiful way to put it. 660 00:31:06,000 --> 00:31:08,840 It gives you that local atom specific perspective. 661 00:31:09,120 --> 00:31:11,000 I want to leave our listener with that thought about 662 00:31:11,000 --> 00:31:13,480 precision. We talked about how we are 663 00:31:13,480 --> 00:31:16,760 moving the source of millimeters per second, but the precision of 664 00:31:16,760 --> 00:31:20,000 the measurement itself is just. It's hard to comprehend. 665 00:31:20,000 --> 00:31:21,560 Let me try to give you a comparison. 666 00:31:21,920 --> 00:31:27,520 The sharpness of the 14.4 KV line in iron 57 is such that we 667 00:31:27,520 --> 00:31:31,360 are detecting a change in the energy of a gamma ray of about 668 00:31:31,520 --> 00:31:34,440 one part in 10 to the 12, so one part in a trillion. 669 00:31:34,440 --> 00:31:36,960 One in a trillion. Now to put that in perspective, 670 00:31:36,960 --> 00:31:39,520 if you were to measure the distance from the Earth to the 671 00:31:39,520 --> 00:31:43,880 Sun, which is about 93,000,000 miles, OK, and you wanted that 672 00:31:43,880 --> 00:31:47,880 same level of precision, one part in 10 to the 12, you would 673 00:31:47,880 --> 00:31:50,760 be measuring that distance to within about 15 centimeters, 674 00:31:50,840 --> 00:31:53,240 about 6 inches. You'd be measuring the distance 675 00:31:53,240 --> 00:31:55,600 to the sun with the accuracy of a school ruler. 676 00:31:55,600 --> 00:31:58,200 That is the level of precision we are talking about, and we do 677 00:31:58,200 --> 00:32:01,680 it on a tabletop or on a Rover millions of miles away. 678 00:32:01,720 --> 00:32:04,240 It's just astounding. Sometimes the quietest, slowest 679 00:32:04,240 --> 00:32:06,720 movements really do reveal the deepest truths. 680 00:32:06,880 --> 00:32:09,200 I couldn't agree more. It's a testament to how 681 00:32:09,360 --> 00:32:12,240 interconnected everything is, from the largest scales to the 682 00:32:12,240 --> 00:32:14,360 smallest. That's our deep dive on 683 00:32:14,360 --> 00:32:18,280 Mussbauer spectroscopy, from the rusty dust of Mars to the 684 00:32:18,280 --> 00:32:20,840 quantum dance of the nucleus. Thanks for coming on this 685 00:32:20,840 --> 00:32:22,880 journey with us. It was an absolute pleasure. 686 00:32:23,000 --> 00:32:26,920 And to you, our listener, next time you see a piece of rust on 687 00:32:26,920 --> 00:32:31,200 an old gate or a nail, remember there was a whole Symphony of 688 00:32:31,200 --> 00:32:34,240 nuclear physics happening inside it, just waiting for the right 689 00:32:34,240 --> 00:32:37,280 tuning fork to make it sing. See you next time on the Deep 690 00:32:37,280 --> 00:32:37,600 Dive.