WEBVTT 00:01.933 --> 00:03.933 J. MICHAEL MCBRIDE: OK, welcome back. 00:03.933 --> 00:07.133 I hope you had a good break. 00:07.133 --> 00:09.903 Can you remember back to when we, before break, what we were 00:09.900 --> 00:11.800 talking about? 00:11.800 --> 00:14.970 The last thing we did was this gyroscope bicycle-wheel 00:14.967 --> 00:19.267 precession to show what would happen to a nucleus that was 00:19.267 --> 00:23.197 spinning in a magnetic field, or an 00:23.200 --> 00:24.830 electron for that matter. 00:24.833 --> 00:27.673 Just to rehearse it a little bit, remember the idea of a 00:27.667 --> 00:31.797 pulse, a 90 degree pulse, that if you have a big magnetic 00:31.800 --> 00:33.870 field-- the blue one there, really enormous-- 00:33.867 --> 00:40.927 and then the little magnet of the nucleus precesses at 100 00:40.933 --> 00:44.933 MHz, for example, in a certain field. 00:44.933 --> 00:48.273 And that gives rise to a constant vertical field, but a 00:48.267 --> 00:51.397 rotating horizontal field from that one. 00:51.400 --> 00:54.230 So the question is whether that rotating horizontal 00:54.233 --> 00:56.833 field, which as you see it will be going back and forth 00:56.833 --> 00:59.133 and back and forth, will act as an antenna 00:59.133 --> 01:00.573 and give you a signal. 01:00.567 --> 01:02.297 You should be able to pick up a radio 01:02.300 --> 01:04.070 signal at 100 MHz. 01:04.067 --> 01:06.867 Indeed, you should be able to, except that there's not just 01:06.867 --> 01:08.097 one proton. 01:08.100 --> 01:11.070 There are lots of protons, and they're in different phases of 01:11.067 --> 01:12.997 precession. 01:13.000 --> 01:15.930 So although they all add vertically, and you have a 01:15.933 --> 01:20.073 substantial vertical magnetism from those, their horizontal 01:20.067 --> 01:23.497 components cancel, so you don't see anything. 01:23.500 --> 01:27.230 In fact, the energy is so small, of the interaction of 01:27.233 --> 01:30.003 each of these magnets with the field, that there are ones 01:30.000 --> 01:33.500 pointing the opposite direction, with higher energy, 01:33.500 --> 01:36.330 almost exactly the same population. 01:36.333 --> 01:38.303 Just a tiny, tiny difference. 01:38.300 --> 01:40.370 But we'll look just at the excess. 01:40.367 --> 01:44.067 Obviously, ones down will cancel ones up. 01:44.067 --> 01:48.727 But if we look just at the net ones up, even they cancel, 01:48.733 --> 01:51.033 because they're at different phases of rotation or 01:51.033 --> 01:54.203 precession about that axis. 01:54.200 --> 01:55.670 But you can do a trick. 01:58.833 --> 02:03.073 We could consider that we're rotating with them, so that they 02:03.067 --> 02:05.227 look like they're standing still. 02:05.233 --> 02:09.873 And then in our frame we'll put on a little bit of a 02:09.867 --> 02:14.027 magnetic field that's horizontal, a very weak field. 02:14.033 --> 02:18.073 And now, as far as we can see, we don't care about the big 02:18.067 --> 02:21.267 field anymore, because we've compensated for it by orbiting 02:21.267 --> 02:23.867 around this thing as we're looking at it. 02:23.867 --> 02:27.427 But what we see is that these will begin to process in our 02:27.433 --> 02:31.133 frame around that horizontal field, so they'll do a slow 02:31.133 --> 02:33.703 precession, all of them, in that direction. 02:33.700 --> 02:35.130 So they'll be going like this. 02:35.133 --> 02:37.973 They'll start here, they'll go there, then they'll go down, 02:37.967 --> 02:40.497 then they'll go back, and then back up again. 02:40.500 --> 02:43.570 But we're going to put on a pulse only long enough, of 02:43.567 --> 02:47.367 this field, so that they go down to here. 02:47.367 --> 02:50.327 That's called a 90 degree pulse, and they'll 02:50.333 --> 02:52.333 rotate down like that. 02:52.333 --> 02:55.103 And now forget the rotating frame. 02:55.100 --> 02:57.470 They'll look like they're just pointing out toward us in the 02:57.467 --> 02:58.827 rotating frame. 02:58.833 --> 03:03.103 But if we go back to the real frame, the laboratory frame, 03:03.100 --> 03:04.870 what we see is this whole bunch 03:04.867 --> 03:07.897 precessing around the field. 03:07.900 --> 03:11.800 And now as they precess around the field in the laboratory 03:11.800 --> 03:17.200 frame, there will be a net horizontal field that they're 03:17.200 --> 03:19.030 generating, a magnetic field. 03:19.033 --> 03:21.973 And that will be the antenna that broadcasts a signal that 03:21.967 --> 03:23.827 we can hear. 03:23.833 --> 03:26.673 And what will determine the frequency of that signal 03:26.667 --> 03:29.367 that's going to be coming out from going back and forth, and 03:29.367 --> 03:31.497 back and forth or around? 03:31.500 --> 03:33.300 What will its frequency be? 03:33.300 --> 03:37.070 How rapidly are they precessing? 03:37.067 --> 03:40.097 It says 100 MHz. 03:40.100 --> 03:42.670 And what determined the 100 MHz? 03:42.667 --> 03:44.897 The strength of this big magnetic field. 03:44.900 --> 03:46.830 Remember, the more you twist on something, 03:46.833 --> 03:49.033 the faster it precesses. 03:49.033 --> 03:50.833 So we could make it 100 MHz. 03:50.833 --> 03:53.533 If we had half as big a big field, it'd be 50 MHz. 03:53.533 --> 03:58.303 Or twice the field, it would be 200 MHz, and so on. 03:58.300 --> 04:02.100 So we get a signal that's 100 MHz radio frequency in 04:02.100 --> 04:06.130 the laboratory frame, that we could detect with an antenna. 04:06.133 --> 04:08.233 But in time it will relax. 04:08.233 --> 04:10.803 This is a non-equilibrium situation when we put the 04:10.800 --> 04:12.500 energy in to make it go down. 04:12.500 --> 04:15.070 And in time it'll come back to equilibrium. 04:15.067 --> 04:17.997 And that process is called relaxation. 04:18.000 --> 04:19.870 And there are various things that control 04:19.867 --> 04:22.897 how fast that happens. 04:22.900 --> 04:26.100 But it will reestablish equilibrium, and it will be 04:26.100 --> 04:29.870 very important later in the lecture about this relaxation, 04:29.867 --> 04:32.897 and you'll see why. 04:32.900 --> 04:36.400 So a 90 degree pulse makes the spinning nuclei, protons, or 04:36.400 --> 04:41.500 C-13s broadcast a frequency that tells what their local 04:41.500 --> 04:43.330 magnetic field is. 04:43.333 --> 04:45.973 The higher the field, the faster they precess, the 04:45.967 --> 04:47.527 higher the frequency. 04:47.533 --> 04:51.403 Now let's first look at this as it arises in magnetic 04:51.400 --> 04:55.430 resonance imaging, where the purpose is to locate protons 04:55.433 --> 05:00.633 within the body using a non-uniform magnetic field. 05:00.633 --> 05:04.173 Now, the idea of tomography is important here. 05:04.167 --> 05:09.197 I've taken this from a Colorado Physics 2000-page. 05:09.200 --> 05:12.130 So this is a slice through somebody's body, show their 05:12.133 --> 05:14.703 rib cage, spine, and so on, and they're wearing some sort 05:14.700 --> 05:18.070 of jacket that's opaque to X-rays. 05:18.067 --> 05:21.097 And we're interested in finding what it looks like 05:21.100 --> 05:23.770 inside, where these things are. 05:23.767 --> 05:26.827 So what we do is we take X-rays, and send an X-ray beam 05:26.833 --> 05:29.803 straight through and see how much gets through. 05:29.800 --> 05:33.100 And we scan the X-ray from top to bottom, and see how much 05:33.100 --> 05:35.700 gets through at every different x-coordinate. 05:35.700 --> 05:38.700 So we do a scan, and it starts at the top, but oops, there's 05:38.700 --> 05:39.200 something there. 05:39.200 --> 05:40.270 And there's even more there. 05:40.267 --> 05:42.167 And lots, then a little bit more. 05:42.167 --> 05:44.167 And for when we hit the spine there's going to be quite a 05:44.167 --> 05:46.567 bit, and so on. 05:46.567 --> 05:49.127 But that's just a one-dimensional 05:49.133 --> 05:51.833 picture of the density. 05:51.833 --> 05:53.703 Now what we're going to do is take that same picture and 05:53.700 --> 05:57.270 just smear it out to the right. 05:57.267 --> 06:02.867 So that's the profile, top to bottom, or stomach to back, of 06:02.867 --> 06:06.697 this particular slice through the body of bones 06:06.700 --> 06:08.500 or whatever it is. 06:08.500 --> 06:11.530 Now the neat trick is that you rotate that, 06:11.533 --> 06:14.003 rotate it by 15 degrees. 06:14.000 --> 06:18.170 And now do the same thing again, and superimpose the new 06:18.167 --> 06:20.497 one on the old one. 06:20.500 --> 06:24.130 And now rotate another 15 degrees and do the same trick, 06:24.133 --> 06:26.873 scan top to bottom and add it up. 06:26.867 --> 06:31.197 And do it again, and again, and again, and again, and 06:31.200 --> 06:35.370 again, again, again, and again. 06:35.367 --> 06:37.967 And see what you got now? 06:37.967 --> 06:40.497 When you superimpose all those, you get what it looked 06:40.500 --> 06:43.030 like, the two-dimensional slice through the thing. 06:43.033 --> 06:45.573 So that's called tomography. 06:45.567 --> 06:49.197 If you can get a one-dimensional projection, 06:49.200 --> 06:52.030 and do it in lots of different directions and add them 06:52.033 --> 06:54.873 together, you can get the two-dimensional, or in fact, a 06:54.867 --> 06:58.627 three-dimensional picture of what's going on inside. 06:58.633 --> 07:01.173 So that's the trick that's used, except you want to do it 07:01.167 --> 07:04.627 for protons, not for bone. 07:04.633 --> 07:07.003 So we want to find protons in the body. 07:07.000 --> 07:09.000 For example, let's find where there's fluid 07:09.000 --> 07:11.000 water in the body. 07:11.000 --> 07:16.700 So there's a body, and we put it inside this cylinder and 07:16.700 --> 07:20.770 wrap the cylinder with special wire, that if we cool it to 07:20.767 --> 07:23.667 liquid helium temperature is superconducting. 07:23.667 --> 07:28.197 So essentially, we've made a big solenoid magnet that goes 07:28.200 --> 07:31.600 along the body's axis. 07:31.600 --> 07:33.800 Now, what will happen? 07:33.800 --> 07:37.570 Well, suppose that field is 1.5 Tesla, which 07:37.567 --> 07:39.797 means 15,000 Gauss. 07:39.800 --> 07:42.270 A Gauss, you remember, is about the size of the earth's 07:42.267 --> 07:46.827 magnetic field more or less, so 15,000 times as strong as 07:46.833 --> 07:49.903 the earth's magnetic field. 07:49.900 --> 07:52.170 So what will happen to the protons in there? 07:52.167 --> 07:55.927 Well, they're going to precess. 07:55.933 --> 07:59.973 And in that field, at 15,000 Gauss or 1.5 Tesla, they'll 07:59.967 --> 08:03.467 precess at 63 MHz. 08:03.467 --> 08:06.797 So if we put an antenna in there and give a 90 degree 08:06.800 --> 08:10.700 pulse, we're going to hear a signal at 63 MHz. 08:10.700 --> 08:13.830 Our radio will pick that up. 08:13.833 --> 08:17.033 So we know there are protons in the body. 08:17.033 --> 08:18.503 Surprised? 08:18.500 --> 08:20.670 No. 08:20.667 --> 08:24.667 The question is, where are the protons in the body? 08:24.667 --> 08:28.127 Now here's an analogy to figure this out. 08:28.133 --> 08:30.903 Suppose we had a cricket in this room, and 08:30.900 --> 08:33.030 wondered where it was. 08:33.033 --> 08:35.073 But I'm blind. 08:35.067 --> 08:39.167 I can hear, but with only one ear, so I can't hear it. 08:39.167 --> 08:41.997 I don't have spatial resolution with my ear. 08:42.000 --> 08:44.600 How can I find out where the cricket is in this room? 08:44.600 --> 08:45.830 Anybody got an idea? 08:49.433 --> 08:52.973 Well, I have one bit of control over the room. 08:52.967 --> 08:56.027 I can make a temperature gradient in the room, make it 08:56.033 --> 08:59.473 cold in front and warm behind. 08:59.467 --> 09:00.767 Suppose I can do that. 09:00.767 --> 09:03.797 Now how can I find the cricket? 09:03.800 --> 09:04.930 What? 09:04.933 --> 09:05.333 Derek? 09:05.333 --> 09:07.003 STUDENT: Crickets chirp at different speeds at different 09:07.000 --> 09:07.170 temperatures. and different intervals. 09:07.167 --> 09:08.667 PROFESSOR: You hear it chirping. 09:08.667 --> 09:15.097 You count how many there are in 13 seconds and add 40. 09:15.100 --> 09:17.000 You establish a temperature gradient and you 09:17.000 --> 09:18.430 listen with a stopwatch. 09:18.433 --> 09:21.333 And if you go to Snopes, you can see that this is not an 09:21.333 --> 09:23.533 urban legend or a rural legend. 09:23.533 --> 09:25.473 It's true that you can do that. 09:25.467 --> 09:30.427 And they actually show this picture of Doctor LeMone from 09:30.433 --> 09:33.403 Boulder, Colorado, who actually did this with 09:33.400 --> 09:36.830 crickets, and showed that it gives a very good measure of 09:36.833 --> 09:38.003 the temperature. 09:38.000 --> 09:40.670 So if I could establish a temperature gradient from 09:40.667 --> 09:43.697 front to back, and count for 13 seconds and add 40, and 09:43.700 --> 09:45.200 knew what the temperature was, I'd know how far 09:45.200 --> 09:46.000 from front to back. 09:46.000 --> 09:51.200 What would I do next if I want to find the cricket? 09:51.200 --> 09:53.730 I'd fiddle with the air conditioning controls and make 09:53.733 --> 09:57.273 a temperature gradient from left to right. 09:57.267 --> 09:59.967 I could even make one from top to bottom, and then I'd 09:59.967 --> 10:04.397 know what its x-, and its y-, and its z-coordinates are. 10:04.400 --> 10:05.830 So I could find the cricket that way. 10:05.833 --> 10:07.973 So we're going to do the same thing with the protons in the 10:07.967 --> 10:10.297 water in the body. 10:10.300 --> 10:13.030 So back to the body here. 10:13.033 --> 10:16.773 What I need is not a uniform field where all the protons 10:16.767 --> 10:18.727 are going at 63 MHz. 10:18.733 --> 10:22.103 I want to make them faster in some regions than others. 10:22.100 --> 10:25.900 So what I do is I put two coils around this solenoid. 10:25.900 --> 10:28.770 And in the one near the head, I make the current go that 10:28.767 --> 10:31.067 way, which reinforces the field. 10:31.067 --> 10:33.497 And in the one near the feet I make it go that way, which 10:33.500 --> 10:35.530 subtracts from the field. 10:35.533 --> 10:39.033 So now I've generated a gradient along the body. 10:39.033 --> 10:41.973 And it turns out to be that what's actually used is about 10:41.967 --> 10:45.297 40 microtesla per millimeter. 10:45.300 --> 10:50.730 So if I went, like, 25 millimeters, about an inch, 10:50.733 --> 10:57.433 that would be 1000 microtesla, that is a millitesla. 10:57.433 --> 11:01.203 So it'd be about one part in 15,000. 11:01.200 --> 11:03.130 Or, pardon me, one part-- 11:03.133 --> 11:08.233 it's a millitesla out of a 1.5 tesla, so about a part per 11:08.233 --> 11:11.603 1000 difference. 11:11.600 --> 11:20.630 So that means if I slice the body there or there, on the 11:20.633 --> 11:21.903 first slice-- 11:21.900 --> 11:24.470 remember, there's is a gradient from foot to head-- 11:24.467 --> 11:26.827 so there we have the average. 11:26.833 --> 11:30.103 63 MHz is going to be a signal coming out from protons 11:30.100 --> 11:32.070 that are in that first slice. 11:32.067 --> 11:35.897 But in the second slice they're going to be at 63.05, 11:35.900 --> 11:39.070 about a part per 1000, because there's a higher 11:39.067 --> 11:40.767 field near the head. 11:40.767 --> 11:43.997 And if I did another slice another inch or so along, it'd 11:44.000 --> 11:46.370 be 63.1 MHz. 11:46.367 --> 11:48.897 So if I had an antenna and could hear all these different 11:48.900 --> 11:52.930 frequencies and how strong the signal was, I'd get a profile 11:52.933 --> 11:56.503 of the proton distribution from foot to head. 11:56.500 --> 11:59.500 So just like we did with the X-rays scanning down. 11:59.500 --> 12:02.730 I now know how much water there is at different places 12:02.733 --> 12:06.303 along the height of the body, or the length of the body. 12:06.300 --> 12:07.630 What did we want to do next? 12:14.767 --> 12:15.667 Matt? 12:15.667 --> 12:17.627 STUDENT: You do it in a different direction-- 12:17.633 --> 12:19.273 PROFESSOR: So we want to make a gradient 12:19.267 --> 12:21.497 in a different direction, so I stop the current in those 12:21.500 --> 12:25.000 green coils and put on yellow coils with current going that 12:25.000 --> 12:29.430 way, which adds to the big field on the right. 12:29.433 --> 12:32.473 And then I put other coils over here, which the current 12:32.467 --> 12:36.567 goes that way and subtracts from the current from the 12:36.567 --> 12:38.597 field on the left. 12:38.600 --> 12:42.970 And when I do that, I get a gradient from right to left. 12:42.967 --> 12:46.227 So then I can do a slice and find out how water is 12:46.233 --> 12:47.203 oriented that way. 12:47.200 --> 12:50.100 And then I can put coils on the top and bottom, analogous 12:50.100 --> 12:53.430 to these, and get a vertical gradient, and get it that way. 12:53.433 --> 12:56.003 And in fact, by putting a certain amount of current in 12:56.000 --> 12:58.700 all these coils at the same time, different amounts in 12:58.700 --> 13:01.200 different coils, I can make a slice that goes in any 13:01.200 --> 13:05.300 direction I want to, and find out how much is there. 13:05.300 --> 13:07.530 So now in three dimensions I can do one of these 13:07.533 --> 13:11.503 tomographic reconstructions, and get where the 13:11.500 --> 13:14.470 water is in the body. 13:14.467 --> 13:16.967 Now, much more interesting than that, which is itself 13:16.967 --> 13:21.727 very powerful, is functional NMR, or MRI, magnetic 13:21.733 --> 13:23.003 resonance imaging. 13:23.000 --> 13:28.300 Where you locate protons whose signal strength is being 13:28.300 --> 13:30.000 fiddled with. 13:30.000 --> 13:33.100 So for example, we talked about relaxation, how fast the 13:33.100 --> 13:35.170 signal goes away. 13:35.167 --> 13:38.127 If you measured this for the different signals you were 13:38.133 --> 13:41.073 getting, how fast they went away, then you'd know 13:41.067 --> 13:43.567 something about a difference from one part of the body to 13:43.567 --> 13:46.467 the other, that the protons in this part, their signal is 13:46.467 --> 13:49.767 going away rapidly, whereas here they're not. 13:49.767 --> 13:52.227 So you could get something about how the protons are 13:52.233 --> 13:56.073 behaving, not just what their local field is. 13:56.067 --> 14:01.497 So for example, blood oxygen level dependent or B-O-L-D, 14:01.500 --> 14:04.330 BOLD imaging, you can do this. 14:04.333 --> 14:07.973 And you get a spatial resolution of about one 14:07.967 --> 14:11.667 millimeter, and a temporal resolution 14:11.667 --> 14:13.497 of about two seconds. 14:13.500 --> 14:17.900 So every two seconds, you can get where oxygen is in the 14:17.900 --> 14:20.400 body, unusual amounts of oxygen, 14:20.400 --> 14:22.030 Now, how is that relevant? 14:22.033 --> 14:25.133 Because if you have cell activity, it increases the 14:25.133 --> 14:30.203 blood oxygen supply, and that speeds the relaxation, how 14:30.200 --> 14:33.100 fast the signal goes away. 14:33.100 --> 14:36.000 So now, these are very weak signals. 14:36.000 --> 14:39.570 So the way you tell something about them, is to take a 14:39.567 --> 14:41.097 difference. 14:41.100 --> 14:43.170 Where did we see a difference map before? 14:43.167 --> 14:44.497 Do you remember? 14:48.767 --> 14:50.097 Remember when we look for 14:50.100 --> 14:55.500 bonds in X-ray, we look at the observed electron density 14:55.500 --> 14:58.070 minus what you'd have for the atoms. That different signal, 14:58.067 --> 15:00.397 tells you how it shifted for bonds. 15:00.400 --> 15:02.130 Well, you do a similar kind of thing here. 15:02.133 --> 15:03.633 You get a difference map. 15:03.633 --> 15:04.703 Now, this is a bunch of different 15:04.700 --> 15:07.200 slices through the brain. 15:07.200 --> 15:11.400 And what's lit up is where there's relaxation. 15:11.400 --> 15:14.470 That is, where there's oxygen, where the brain cells are 15:14.467 --> 15:19.797 active under one circumstance, minus how active they are 15:19.800 --> 15:22.000 under some other circumstance. 15:22.000 --> 15:23.800 It's a difference. 15:23.800 --> 15:28.300 So the brain is working harder when it's in one 15:28.300 --> 15:29.270 state than the other. 15:29.267 --> 15:30.797 Now, what are the two states? 15:30.800 --> 15:37.970 It's the subject being shown donuts minus the signal when 15:37.967 --> 15:41.227 the subject is being shown car keys. 15:41.233 --> 15:44.103 So these are places where the brain lights up when it sees 15:44.100 --> 15:48.400 donuts, but doesn't light up when it sees car keys. 15:48.400 --> 15:53.170 Now, this particular subject had recently been fed. 15:53.167 --> 15:56.927 And they did it also for someone who had not been fed, 15:56.933 --> 15:58.533 who was fasting. 15:58.533 --> 16:00.603 And their brain really lit up when they saw 16:00.600 --> 16:02.630 donuts versus car keys. 16:02.633 --> 16:06.403 So you can imagine that this is very, very popular with 16:06.400 --> 16:09.030 psychologists and so on, people interested in brain and 16:09.033 --> 16:12.073 all sorts of things, where you can use this trick of 16:12.067 --> 16:14.627 differences to see where something's happening in one 16:14.633 --> 16:16.103 case versus another. 16:16.100 --> 16:19.670 So that's MRI, and, of course, it's not fundamentally our 16:19.667 --> 16:22.167 business here to talk about MRI. 16:22.167 --> 16:26.467 Except, we want to see things happening in molecules. 16:26.467 --> 16:29.597 Now, why can't we do exactly the same trick with molecules 16:29.600 --> 16:32.770 to find out where protons are in a molecule? 16:32.767 --> 16:36.867 How do we know that something is here, rather than here, 16:36.867 --> 16:39.427 rather than here in the brain? 16:39.433 --> 16:42.073 We establish a magnetic gradient so that you get a 16:42.067 --> 16:44.227 different field here and here, and you get different 16:44.233 --> 16:44.903 frequencies. 16:44.900 --> 16:47.730 And you can distinguish where it is in the brain. 16:47.733 --> 16:50.033 What's the problem with doing that for a molecule, and 16:50.033 --> 16:51.703 looking at different protons in molecules? 16:56.633 --> 16:59.973 What's the difference between my brain and a molecule? 17:01.433 --> 17:02.773 There are lots of differences, 17:02.767 --> 17:06.597 but one of them is, that I hope my brain is an awful lot 17:06.600 --> 17:09.470 bigger than a molecule. 17:09.467 --> 17:12.927 So you can't establish a gradient big enough across the 17:12.933 --> 17:16.103 small dimensions of a molecule, so that protons in 17:16.100 --> 17:19.570 different regions will have different frequencies. 17:19.567 --> 17:22.397 Within any one molecule it should all be the same field 17:22.400 --> 17:24.370 for practical purposes. 17:24.367 --> 17:28.897 So we can't do this trick, or can we? 17:28.900 --> 17:32.200 So we want to locate protons within molecules. 17:32.200 --> 17:35.830 And now we want to have, not a gradient, we want to have a 17:35.833 --> 17:38.633 uniform field. 17:38.633 --> 17:41.273 If we could make the gradient big enough, maybe that would 17:41.267 --> 17:43.097 be useful, but we can't make it big enough. 17:43.100 --> 17:44.830 So let's go the other direction and make it 17:44.833 --> 17:47.673 absolutely the same everywhere, a uniform field. 17:50.767 --> 17:54.697 Now, and then what we're going to do is listen until we hear-- 17:54.700 --> 17:58.430 and put up one of these pulses in-- and hear the frequency 17:58.433 --> 17:59.933 with which these protons-- 17:59.933 --> 18:02.573 if there are protons there in the sample, we'll hear them. 18:02.567 --> 18:04.767 Of course, most organic substances 18:04.767 --> 18:06.127 have protons in them. 18:06.133 --> 18:09.273 So it doesn't surprise you that as I scan 18:09.267 --> 18:11.867 the magnetic field-- 18:11.867 --> 18:14.967 increasing the magnetic field, which changes the precession 18:14.967 --> 18:15.727 frequency-- 18:15.733 --> 18:19.003 while listening with a radio that's tuned to just one 18:19.000 --> 18:22.070 frequency, as I go along, at someplace I'm going to have 18:22.067 --> 18:23.397 the right frequency. 18:23.400 --> 18:27.370 And the protons are going to give me a signal. 18:27.367 --> 18:29.267 Of course, if I had different nuclei in there that were 18:29.267 --> 18:31.867 different magnetic strengths, then I'd get signals at 18:31.867 --> 18:33.627 different places. 18:33.633 --> 18:34.973 But I'm going to only look at-- 18:34.967 --> 18:37.497 only listen for protons. 18:37.500 --> 18:38.670 OK, so there it is. 18:38.667 --> 18:39.027 Bingo! 18:39.033 --> 18:40.103 Protons. 18:40.100 --> 18:40.770 Whoop! 18:40.767 --> 18:42.727 Protons again. 18:42.733 --> 18:44.233 Protons again. 18:44.233 --> 18:46.633 There are different signals for protons. 18:46.633 --> 18:50.233 Not all protons are equivalent. 18:50.233 --> 18:53.433 Now, the difference here, between this signal and this 18:53.433 --> 18:56.933 signal, and how big the magnetic field is, is very, 18:56.933 --> 18:57.833 very small. 18:57.833 --> 19:00.403 It differs by only that fraction, 19:00.400 --> 19:03.570 2.48 parts in a million. 19:03.567 --> 19:07.097 They're almost exactly the same. 19:07.100 --> 19:10.300 But they're a little bit different, just parts per 19:10.300 --> 19:12.300 million different. 19:12.300 --> 19:16.200 Now, when this was discovered it was an annoyance for the 19:16.200 --> 19:19.430 physicists who were mostly interested in things like 19:19.433 --> 19:22.403 measuring how strong the magnetic moment was, how fast 19:22.400 --> 19:25.470 the precession was for protons. 19:25.467 --> 19:27.767 But they put something in there that has protons and 19:27.767 --> 19:29.567 they find out there are different protons. 19:29.567 --> 19:32.567 Which one is the real proton? 19:32.567 --> 19:36.527 So they called this the chemical shift, because these 19:36.533 --> 19:38.703 differences had something to do with a chemical 19:38.700 --> 19:40.470 environment. 19:40.467 --> 19:45.097 But this was a gold mine for chemists, because since the 19:45.100 --> 19:46.700 beginning people have been-- 19:46.700 --> 19:49.170 since 1850, at least-- people have been interested in 19:49.167 --> 19:51.497 chemical structure. 19:51.500 --> 19:54.530 But the only way they could do it was convert one molecule to 19:54.533 --> 19:55.933 another, count isomers-- 19:55.933 --> 19:59.103 as we discussed last semester with Koerner, and so on-- 19:59.100 --> 20:02.200 and try to use logic to figure out what structure would be 20:02.200 --> 20:06.730 consistent for these various transformations, chemical 20:06.733 --> 20:09.433 transformations. 20:09.433 --> 20:12.273 And, of course, then there was X-ray, which really did show 20:12.267 --> 20:13.667 where atoms were. 20:13.667 --> 20:16.997 But here's something that could work in liquids. 20:17.000 --> 20:18.470 Not everything can be a crystal. 20:18.467 --> 20:20.697 So this looked really, really promising. 20:20.700 --> 20:23.900 Now, this sample was ethanol. 20:23.900 --> 20:25.570 Now, what do you think the three different 20:25.567 --> 20:27.667 signals are in ethanol? 20:27.667 --> 20:30.727 Well, one must be the OH. 20:30.733 --> 20:33.933 One must be the H's of the CH2, and one must be the H's 20:33.933 --> 20:35.203 of the CH3. 20:38.233 --> 20:43.533 Now, doing such an experiment requires that the field be 20:43.533 --> 20:47.903 very, very uniform, because if, as you go from one part of 20:47.900 --> 20:51.130 your sample to another, the field changes by a couple 20:51.133 --> 20:54.673 ppm, then the methyl protons in this part of 20:54.667 --> 20:58.197 the sample will appear the same place that the CH2 20:58.200 --> 21:01.600 protons appear in this part of the sample, or the OH does in 21:01.600 --> 21:06.230 this part of the sample, even if the gradient across the 21:06.233 --> 21:09.833 sample is only a part per million or so, a couple parts 21:09.833 --> 21:11.103 per million. 21:11.100 --> 21:13.800 And that's one of the reasons these peaks are not 21:13.800 --> 21:14.770 infinitely sharp. 21:14.767 --> 21:17.127 One of the reasons they're broad is that the field isn't 21:17.133 --> 21:18.633 perfectly uniform. 21:18.633 --> 21:19.403 But it's very good. 21:19.400 --> 21:24.300 It's within a fraction of a part per million. 21:24.300 --> 21:27.830 Now, in the late 1950s, as it says here, chemistry 21:27.833 --> 21:31.273 departments began buying commercial NMR spectrometers. 21:31.267 --> 21:33.997 This one was called the Varian A-60, and it's the one I 21:34.000 --> 21:35.230 learned to operate. 21:37.200 --> 21:41.130 And they had to have fields that were homogeneous enough to 21:41.133 --> 21:42.703 determine molecular structure. 21:42.700 --> 21:45.100 So they had to have fields that were different, that 21:45.100 --> 21:48.170 didn't vary by more than a small part of a part per 21:48.167 --> 21:52.397 million, so that you could tell things about chemical 21:52.400 --> 21:54.530 shifts and spin-spin splittings, which we're going 21:54.533 --> 21:57.033 to be talking about in the rest of this lecture. 21:57.033 --> 21:59.373 But, of course, these things were expensive and many 21:59.367 --> 22:02.997 different people were using them, so it was a challenge to 22:03.000 --> 22:05.830 keep the field homogeneous to obtain sharp lines. 22:05.833 --> 22:08.533 Now, there were knobs in there that you could turn the 22:08.533 --> 22:12.273 current to coils, to cancel a gradient in one direction or 22:12.267 --> 22:14.497 another, or another, or another. 22:14.500 --> 22:18.470 And most of them were hidden behind that door, and the door 22:18.467 --> 22:21.427 said on it, Do Not Open. 22:21.433 --> 22:24.733 Because someone who knew what he was doing came in at the 22:24.733 --> 22:27.103 beginning of the day and turned all those knobs just 22:27.100 --> 22:29.300 right, so the field was very uniform. 22:29.300 --> 22:31.930 And if anybody else came in and twiddled them, then the 22:31.933 --> 22:35.403 next guy to come in was really up a creek. 22:35.400 --> 22:37.700 So do not touch these gradient knobs. 22:37.700 --> 22:41.500 In fact, there was one there, the y gradient, which would 22:41.500 --> 22:46.130 have its own special sign, Do not touch this. 22:46.133 --> 22:51.833 Now, this was fine, but across New Haven... or across the Long 22:51.833 --> 22:55.103 Island Sound here, you see the smokestacks of Port Jefferson 22:55.100 --> 22:58.430 and the medical building at State University in New York 22:58.433 --> 22:59.573 at Stony Brook. 22:59.567 --> 23:02.397 And there was a physical chemist at Stony Brook who 23:02.400 --> 23:03.530 fiddled with them. 23:03.533 --> 23:05.673 His name was Paul Lauterbur. 23:05.667 --> 23:10.397 And in 1972 he would take over this machine every night, and 23:10.400 --> 23:13.430 he'd just wreck the field homogeneity. 23:13.433 --> 23:15.903 And, of course, late at night before he left, or early 23:15.900 --> 23:18.570 morning, he would turn all the knobs back, because he was 23:18.567 --> 23:23.297 really an expert at NMR. But the reason he did this was to 23:23.300 --> 23:26.300 establish gradients in different directions so that 23:26.300 --> 23:27.830 he could locate-- 23:27.833 --> 23:30.133 he had a sample tube, and he filled it 23:30.133 --> 23:32.773 with D20, not protons. 23:32.767 --> 23:37.727 And in it he put two capillary tubes that had water in them. 23:37.733 --> 23:39.973 So he did exactly the kind of experiment we 23:39.967 --> 23:41.227 were talking about. 23:41.233 --> 23:45.873 And in Nature in 1973, he published this, where he 23:45.867 --> 23:49.697 scanned vertically and got this, scanned horizontally and 23:49.700 --> 23:53.600 got this, scanned at 45 degrees or -45 degrees and got those, 23:53.600 --> 23:59.530 and could find out where these water samples were inside D2O. 23:59.533 --> 24:04.373 And he called that zeugmatography, but the name 24:04.367 --> 24:06.297 didn't catch on. 24:06.300 --> 24:09.330 But the good news was that 30 years later he got the Nobel 24:09.333 --> 24:12.703 Prize in Physiology or Medicine, for inventing MRI. 24:12.700 --> 24:16.800 And that's what he worked on the rest of his life. 24:16.800 --> 24:18.800 So it was a chemist who invented MRI. 24:21.800 --> 24:27.770 So there are lots and lots of magnetic resonance 24:27.767 --> 24:28.927 spectrometers. 24:28.933 --> 24:32.503 And I already showed you some X-ray diffractomers around, 24:32.500 --> 24:35.330 which have put classical structure proof by chemical 24:35.333 --> 24:38.003 transformation, the kind of thing that we talked about 24:38.000 --> 24:39.000 Koerner doing, 24:39.000 --> 24:42.730 and even IR, mostly out of business, although there are 24:42.733 --> 24:45.733 still things for which IR is as good or even better than 24:45.733 --> 24:49.373 NMR. And, in fact, there was a Yale-- 24:49.367 --> 24:52.667 before I came here, there was a organic chemistry professor 24:52.667 --> 24:55.397 who was in the field called natural products, where the 24:55.400 --> 24:57.830 job was to take something that came from nature and figure 24:57.833 --> 24:59.403 out what its structure was. 24:59.400 --> 25:02.870 And the way to do it, in those days, was to do these chemical 25:02.867 --> 25:05.797 transformations and try to make it from something or make 25:05.800 --> 25:10.200 it into something whose structure you knew. 25:10.200 --> 25:12.900 So these were great puzzles, and it was 25:12.900 --> 25:15.400 really a big operation. 25:15.400 --> 25:19.570 But when NMR came along, he abandoned organic chemistry 25:19.567 --> 25:22.427 and took up fundamental research on quantum theory. 25:22.433 --> 25:25.273 And in fact, later he became a professional studio 25:25.267 --> 25:26.867 photographer. 25:26.867 --> 25:30.867 He was just wiped out by NMR coming along, which is the way 25:30.867 --> 25:32.627 people know structures now. 25:32.633 --> 25:35.433 We haven't really talked about that much, about how people 25:35.433 --> 25:37.503 knew-- we've talked about different structures, but not 25:37.500 --> 25:40.130 really how people figured them out, except 25:40.133 --> 25:41.873 when they used X-ray. 25:41.867 --> 25:44.327 But this is an even more common way of determining 25:44.333 --> 25:46.773 structures routinely, is spectroscopy. 25:46.767 --> 25:49.167 And in particular, nowadays, magnetic resonance 25:49.167 --> 25:50.227 spectroscopy. 25:50.233 --> 25:52.803 So a couple of years ago I took a tour through the 25:52.800 --> 25:55.030 department and took photographs of magnetic 25:55.033 --> 25:57.503 resonance spectrometers to show you here. 25:57.500 --> 26:00.070 So across from your lab you may have noticed this door 26:00.067 --> 26:02.897 which says Chemical Instrumentation Center, and it 26:02.900 --> 26:06.130 says warning over here, about magnetic fields, so if you 26:06.133 --> 26:08.503 have a pacemaker, be careful. 26:08.500 --> 26:11.230 And you go inside there, and some of these have now been 26:11.233 --> 26:13.203 moved since I took the pictures, but you see these 26:13.200 --> 26:16.800 things sticking up like here, and here. 26:16.800 --> 26:21.530 And if you go around, you see these big cans, WARNING: 26:21.533 --> 26:22.833 strong magnetic field. 26:22.833 --> 26:23.873 Here's another one. 26:23.867 --> 26:24.667 Here's another one. 26:24.667 --> 26:26.997 That's a 500 MHz spectrometer. 26:27.000 --> 26:28.830 Here's a 500 MHz spectrometer. 26:28.833 --> 26:31.203 Here's a 600 MHz spectrometer. 26:31.200 --> 26:33.770 Here's another 600 MHz spectrometer. 26:33.767 --> 26:36.827 And out in the courtyard, behind your lab, there's this 26:36.833 --> 26:41.773 special little building that was constructed specially for 26:41.767 --> 26:43.197 a big magnet. 26:43.200 --> 26:46.600 And it has this one, which is an 800 MHz spectrometer, 26:46.600 --> 26:49.700 which turns out to be 8 to the third power. 26:49.700 --> 26:54.630 That is 512 times as sensitive as a 100 MHz 26:54.633 --> 26:58.033 spectrometer, not to mention other advantages that we're 26:58.033 --> 27:00.903 going to talk about below. 27:00.900 --> 27:02.930 Now, why is it 8 cubed? 27:02.933 --> 27:05.073 It's because of the Boltzmann factor. 27:05.067 --> 27:07.497 Remember, this signal comes because there are more that 27:07.500 --> 27:09.500 point with the field than against the field. 27:09.500 --> 27:12.530 We only see the difference between those two. 27:12.533 --> 27:14.703 And if you have a bigger energy difference, you'll get 27:14.700 --> 27:16.230 a bigger population difference. 27:16.233 --> 27:18.803 So you get an eightfold factor from that. 27:18.800 --> 27:21.600 But the energy quantum that you're dealing with, in going 27:21.600 --> 27:24.530 from one level to another, becomes eight times as big. 27:24.533 --> 27:28.103 That's an advantage in your signal. 27:28.100 --> 27:31.530 And the sensitivity of the electronics, when it's eight 27:31.533 --> 27:32.973 times bigger, is also better. 27:32.967 --> 27:36.167 So all these things go together to make it 500 times 27:36.167 --> 27:40.127 better, and even more than 500 times better when you consider 27:40.133 --> 27:42.733 what we'll talk about soon, the chemical shift advantage. 27:42.733 --> 27:45.473 So that's why one pays the big bucks to have a 27:45.467 --> 27:46.927 machine like that. 27:46.933 --> 27:49.433 Here are just some others that I took around. 27:49.433 --> 27:54.273 And now by the cross hall there, next to your lab when you 27:54.267 --> 27:57.667 walk down there on this side of it, there's a room that has 27:57.667 --> 28:00.697 electron paramagnetic resonance spectrometers. 28:00.700 --> 28:03.470 So this is a much smaller magnet, not one of these big 28:03.467 --> 28:05.267 liquid helium cooled things. 28:05.267 --> 28:09.897 And the reason is that this is to study free radicals, which 28:09.900 --> 28:12.230 have magnetic electrons. 28:12.233 --> 28:17.503 Mostly electrons come in pairs and their magnetisms cancel. 28:17.500 --> 28:20.200 But in certain molecules, free radicals, there's an odd 28:20.200 --> 28:23.230 electron, whose magnetism is detectable. 28:23.233 --> 28:26.273 So this is to study free radicals. 28:26.267 --> 28:30.127 And the electron magnet is 660 times 28:30.133 --> 28:32.303 stronger than the proton. 28:32.300 --> 28:36.570 So you don't need such a big field to make it precess. 28:36.567 --> 28:42.667 So you can use just 0.3 Tesla instead of several Tesla for 28:42.667 --> 28:44.467 electron paramagnetic resonance. 28:44.467 --> 28:46.397 So there are two of those spectrometers. 28:46.400 --> 28:48.870 And in fact, we don't have one of these, but there's now 28:48.867 --> 28:52.597 commercially available a 1000 MHz spectrometer, which 28:52.600 --> 28:56.730 is 23.5 Tesla. 28:56.733 --> 29:01.833 And at the Florida State University National High Field 29:01.833 --> 29:04.333 Magnet Lab, there's a field that's pulsed 29:04.333 --> 29:06.503 that goes to 45 Tesla. 29:06.500 --> 29:08.300 And it's a national lab. 29:08.300 --> 29:09.400 You don't pay to use it. 29:09.400 --> 29:12.830 But you have to have a great experiment to be assigned time 29:12.833 --> 29:14.873 to do things there. 29:14.867 --> 29:16.227 So there are lots of these things around. 29:16.233 --> 29:18.903 Now let's go back and see why it's so good. 29:18.900 --> 29:21.500 OK, we have these three signals, and as we said, we're 29:21.500 --> 29:24.030 interested in which peak is which set of protons. 29:24.033 --> 29:27.303 Now, how do we know which is which? 29:27.300 --> 29:30.670 Can anybody see a way of figuring out which is the CH3, 29:30.667 --> 29:32.467 which is the CH2, and which is the OH? 29:36.433 --> 29:37.603 Any guesses? 29:37.600 --> 29:37.800 Yeah. 29:37.800 --> 29:39.630 STUDENT: The size of the peaks. 29:39.633 --> 29:41.033 PROFESSOR: Ah! 29:41.033 --> 29:44.373 If you have twice as many protons, there should be twice 29:44.367 --> 29:46.267 as strong a signal. 29:46.267 --> 29:49.497 You measure the strength of the signal by how much area is 29:49.500 --> 29:51.200 under it, by integrating it. 29:51.200 --> 29:54.130 So if we measure the integrals, we see they're in 29:54.133 --> 29:59.473 the ratio of 1:2:3, so it's clear that that's the 1, 29:59.467 --> 30:01.997 that's the 2, and that's the 3. 30:02.000 --> 30:06.470 Now, we couldn't do this in IR, because we had these 30:06.467 --> 30:07.727 normal modes, 30:07.733 --> 30:10.133 an had for example, C=O. 30:10.133 --> 30:12.573 And remember, as the C=O vibrated, something else 30:12.567 --> 30:15.127 vibrated at the same time, and other things, and they could 30:15.133 --> 30:17.003 cancel or reinforce. 30:17.000 --> 30:20.300 So the signal intensities were very, very different for 30:20.300 --> 30:22.200 different groups. 30:22.200 --> 30:27.000 But here the protons are all essentially exactly the same. 30:27.000 --> 30:30.030 They differ only by a part per million, or a few parts per 30:30.033 --> 30:33.903 million, so the intensities are proportional to the number 30:33.900 --> 30:38.230 of protons, because the difference is so subtle. 30:38.233 --> 30:43.973 So you can count protons by the area under these peaks. 30:43.967 --> 30:44.767 That's what it says here. 30:44.767 --> 30:47.397 The number is proportional to the number protons because 30:47.400 --> 30:51.770 they're so similar, not like IR peaks. 30:51.767 --> 30:52.997 Now, how can you use this? 30:53.000 --> 30:56.300 Here was one of the very first uses of a subtle organic 30:56.300 --> 30:57.530 chemistry question. 30:57.533 --> 31:00.673 This was an advertisement by the Varian Corporation in 31:00.667 --> 31:04.327 1955, who were trying to sell those machines I showed you, 31:04.333 --> 31:05.673 that the guy over at-- 31:05.667 --> 31:09.127 Paul Lauterbur messed up the field on every night. 31:09.133 --> 31:12.433 So this was 20, the use of integrated 31:12.433 --> 31:14.773 intensities in structural analysis. 31:14.767 --> 31:19.167 So there's a question of the structure of C7H8, whether 31:19.167 --> 31:20.627 it's this or this. 31:20.633 --> 31:23.373 And notice that those two are related to one another, 31:23.367 --> 31:26.197 because if we shifted the electrons like that, one would 31:26.200 --> 31:27.470 go to the other. 31:27.467 --> 31:30.567 So you could imagine them going back and forth by an 31:30.567 --> 31:31.697 electrocyclic reaction. 31:31.700 --> 31:34.530 And the question is, which is it really? 31:34.533 --> 31:36.973 Well, you could try to figure out by chemical 31:36.967 --> 31:40.197 transformation, and people did that. 31:40.200 --> 31:41.670 So which is it? 31:41.667 --> 31:44.867 Well, let's try ozonolysis. 31:44.867 --> 31:47.267 Now, do you remember what happens with ozonolysis and 31:47.267 --> 31:49.067 then oxidation? 31:49.067 --> 31:52.967 You cleave C=C double bonds and make carbonyl groups there, an 31:52.967 --> 31:59.197 acid, make a carboxylic acid group when you add the H2O2. 31:59.200 --> 32:01.930 So these would give different products. 32:01.933 --> 32:05.573 Notice that on the left, you would cleave three bonds, on 32:05.567 --> 32:08.667 the right, you'd cleave only two double bonds. 32:08.667 --> 32:13.297 So on the left, you would get that diacid. On the right, 32:13.300 --> 32:17.830 you'd get the diacid that has two more carbons. 32:17.833 --> 32:20.573 Now, in fact, that acid on the right was known. 32:20.567 --> 32:24.497 It's called cis-caronic acid, and that's what you got. 32:24.500 --> 32:26.600 So what's the conclusion? 32:26.600 --> 32:30.600 The conclusion is that the structure must be B, not A. So 32:30.600 --> 32:33.370 that's a classical structure proof by chemical 32:33.367 --> 32:34.597 transformation. 32:36.567 --> 32:38.797 But here's a completely different way 32:38.800 --> 32:39.700 of going about it. 32:39.700 --> 32:44.500 Take the NMR spectrum and count the protons. 32:44.500 --> 32:48.500 So the group on the left there are protons that are attached 32:48.500 --> 32:50.830 to double bonded carbons, and on the right, to 32:50.833 --> 32:53.933 single bonded carbons. 32:53.933 --> 32:57.603 And now, notice that the compound B has 32:57.600 --> 33:00.270 four of each kind. 33:00.267 --> 33:05.297 But compound A has six of one kind and two of the other. 33:07.933 --> 33:10.603 And if you integrate, you find that those 33:10.600 --> 33:14.670 ratios are 2.9:1, 3:1. 33:14.667 --> 33:17.267 So which is it? 33:17.267 --> 33:20.397 It must be A that you're taking the spectrum of. 33:24.900 --> 33:27.970 That's the one that's 3:1. 33:27.967 --> 33:31.897 So it must be that that's the structure, but then how do you 33:31.900 --> 33:36.430 explain this misleading chemical transformation? 33:36.433 --> 33:40.003 It must be that there's an equilibrium between these two 33:40.000 --> 33:44.370 things that lies to the left, so when you take the spectrum 33:44.367 --> 33:47.497 that's the stuff you see, that's most of the material. 33:47.500 --> 33:50.000 But it's not as reactive with ozone as the 33:50.000 --> 33:52.170 stuff on the right. 33:52.167 --> 33:54.727 So that little bit of stuff on the right is what reacts with 33:54.733 --> 33:56.473 ozone and gives the product. 33:56.467 --> 34:00.567 So the chemical transformation was misleading. 34:00.567 --> 34:04.667 And this is the kind of thing that made this Yale natural 34:04.667 --> 34:07.427 products organic chemistry professor pull out his hair 34:07.433 --> 34:09.633 and become a quantum chemist, and then a studio 34:09.633 --> 34:11.873 photographer, that you couldn't do what he was 34:11.867 --> 34:14.997 trained to do anymore. 34:15.000 --> 34:18.970 So spectroscopy took over in determining structure, and 34:18.967 --> 34:21.827 we're going to talk a little bit about how you do this. 34:21.833 --> 34:27.933 Now, Chemistry 220 website has a bunch of NMR problems. 34:27.933 --> 34:34.073 There are 40 problems there, and I took this from one of 34:34.067 --> 34:36.167 them and fiddled with it a little bit. 34:36.167 --> 34:40.927 And in fact, let me just see, I think I left an extra-- 34:40.933 --> 34:42.633 well, I'll go through here and-- 34:42.633 --> 34:45.003 there's going to be an extra slide in here. 34:45.000 --> 34:46.030 So we can integrate. 34:46.033 --> 34:49.533 And see that there are 2 and 3, and 3. 34:49.533 --> 34:55.033 So we know that the 2 must be that CH2, but there are two 34:55.033 --> 34:59.203 CH3 groups, one is one and one is the other. 34:59.200 --> 35:01.500 That's at low resolution, where the 35:01.500 --> 35:03.300 field isn't so uniform. 35:03.300 --> 35:06.100 But if you make the field really, really uniform, if you 35:06.100 --> 35:09.330 tweak those knobs just right, so that the peaks don't get 35:09.333 --> 35:12.103 broadened by having different fields in different parts of 35:12.100 --> 35:17.570 the sample, and in fact, spin the sample, so that a given 35:17.567 --> 35:20.827 molecule actually is going around and sampling different 35:20.833 --> 35:25.303 parts to average the field, to make it even more uniform, 35:25.300 --> 35:28.430 then you see this thing with sharp peaks. 35:28.433 --> 35:31.503 So it's the same 3, 3, 2, but they look a 35:31.500 --> 35:32.730 little different here. 35:36.600 --> 35:41.570 So the peak width is about three parts per billion, and 35:41.567 --> 35:44.767 that's just, as you see, a single peak there. 35:44.767 --> 35:47.967 But this next one is a little different. 35:47.967 --> 35:49.797 That's a triplet, 1:2:1. 35:52.900 --> 35:57.830 So that's one of those CH3 groups, but which CH3 group? 35:57.833 --> 35:59.973 Oh, pardon me, I got it backwards. 35:59.967 --> 36:04.527 This was a CH3 group, and it turns out to be this one. 36:04.533 --> 36:07.873 This CH3 group is split into three, and it's that one. 36:07.867 --> 36:10.067 Now, why is it not a single peak? 36:10.067 --> 36:13.227 What's different? 36:13.233 --> 36:18.103 OK, well, that splitting is 0.029 parts per million. 36:18.100 --> 36:20.600 I obviously blew it up in order to be able to see it 36:20.600 --> 36:21.700 clearly here. 36:21.700 --> 36:24.670 And this is a 250 MHz spectrum. 36:24.667 --> 36:27.527 So it means that splitting, the difference in frequency, 36:27.533 --> 36:32.973 of protons in one environment or the other, is 7.3 Hz. 36:32.967 --> 36:38.167 And it's exactly the same there, 7.3 Hz. 36:38.167 --> 36:42.827 Now, if you look here, that's a quartet. 36:42.833 --> 36:45.433 And those are 7.3 Hz as well. 36:49.433 --> 36:51.633 Now, what's that last signal, this little 36:51.633 --> 36:53.303 tiny one down here? 36:53.300 --> 36:57.530 Well, notice that the solvent is CDCl3. 36:57.533 --> 37:00.603 Now, why would they pay the bucks, the big bucks, to get 37:00.600 --> 37:03.530 deuterium rather than just using normal chloroform, 37:03.533 --> 37:05.233 CHCl3, for a solvent. 37:09.400 --> 37:13.430 What would it look like if the solvent were CHCl3? 37:13.433 --> 37:16.233 You'd have an enormous peak from the solvent, that 37:16.233 --> 37:18.203 hydrogen of the solvent. 37:18.200 --> 37:20.230 It would wash out the other things. 37:20.233 --> 37:22.233 So you make it deuterium. 37:22.233 --> 37:24.233 But it's not 100% deuterium. 37:24.233 --> 37:27.503 There's a tiny, tiny amount of protium in there. 37:27.500 --> 37:29.630 So that tiny signal comes from a little bit 37:29.633 --> 37:33.533 of CH3 [correction:CHCI3] in the solvent. 37:33.533 --> 37:37.973 So the 90 degree pulse makes the spinning nuclei broadcast 37:37.967 --> 37:41.997 a frequency that tells their local magnetic field, in a 37:42.000 --> 37:43.900 uniform field. 37:43.900 --> 37:46.530 Now, there's the big uniform field. 37:46.533 --> 37:51.073 But what the nucleus sees is an effective local magnetic 37:51.067 --> 37:53.927 field, which is, of course, the big field-- that's mostly 37:53.933 --> 37:57.433 it-- but little, little tiny differences due to the 37:57.433 --> 37:58.733 chemical environment. 37:58.733 --> 38:01.433 And let's see how we do it. 38:01.433 --> 38:05.803 OK, just to back up at first, you could make the applied 38:05.800 --> 38:08.800 field inhomogeneous, as an MRI. 38:08.800 --> 38:15.200 And then the field can be, for example, 2 Tesla, 30,000 38:15.200 --> 38:17.670 Gauss, with a gradient of 4 Gauss per 38:17.667 --> 38:19.367 centimeter for human samples. 38:19.367 --> 38:20.767 And if you have a tiny thing, you could 38:20.767 --> 38:21.727 make a bigger gradient. 38:21.733 --> 38:25.003 So for small animals you can get 50 Gauss per centimeter 38:25.000 --> 38:26.700 and do the imaging that we talked about. 38:26.700 --> 38:28.530 But in chemistry it's different. 38:28.533 --> 38:31.703 In chemistry, you make it really homogeneous, so the 38:31.700 --> 38:35.000 only differences come not from where the proton is in the 38:35.000 --> 38:39.170 sample, but from where it is in a molecule. 38:39.167 --> 38:43.267 And now we're interested in a molecular field that's added 38:43.267 --> 38:46.627 to or subtracted from the big field. 38:46.633 --> 38:49.733 And mostly it's subtracted from, as you'll see. 38:49.733 --> 38:53.033 So these molecular fields then tell you about the molecular 38:53.033 --> 38:56.033 environment, these tiny shifts. 38:56.033 --> 38:59.473 So there are two sources of these local magnetic fields, 38:59.467 --> 39:02.727 besides the enormous big field that you put on. 39:02.733 --> 39:06.173 One is electrons orbiting. 39:06.167 --> 39:09.397 Now, the electrons come in pairs that tend to orbit in 39:09.400 --> 39:13.200 opposite directions, so they tend to cancel. 39:13.200 --> 39:16.130 But there's a little bit of excess, for reasons we don't 39:16.133 --> 39:19.373 need to go on to, of one orbiting over the other. 39:19.367 --> 39:22.497 So you get effects from electron orbiting. 39:22.500 --> 39:27.870 And the magnitude of this shift is about 12 parts per 39:27.867 --> 39:33.397 million for protons, or 200 ppm for carbon, 39:33.400 --> 39:37.430 the range of values you can get from that. 39:37.433 --> 39:39.433 Which is-- so this is grossly exaggerated. 39:39.433 --> 39:42.803 It should be only parts per million of this, not, you 39:42.800 --> 39:47.830 know, like a 20th or something like that, or a 10th. 39:47.833 --> 39:50.373 OK, so one thing about the environment is how many 39:50.367 --> 39:53.727 electrons are around doing this orbiting? 39:53.733 --> 39:57.803 The other thing is there are other magnetic nuclei nearby 39:57.800 --> 39:59.470 who have fields, too. 39:59.467 --> 40:02.727 So if you're this proton, or listening for this proton, its 40:02.733 --> 40:06.003 field is not only going to be the big field, not only what's 40:06.000 --> 40:08.830 coming from the electrons orbiting, but also what's 40:08.833 --> 40:12.233 coming from other nuclei that are in the vicinity, being 40:12.233 --> 40:15.103 oriented either this way or this way. 40:15.100 --> 40:19.570 OK, and those we measure in Hz, and you'll see why we 40:19.567 --> 40:22.497 measure one in ppm, and the other in 40:22.500 --> 40:25.500 Hz very soon. 40:25.500 --> 40:27.830 So anyhow, when you add all those things together, you get 40:27.833 --> 40:29.373 an effective field. 40:29.367 --> 40:31.827 And that's what determines the frequency of the signal you're 40:31.833 --> 40:34.473 going to hear. 40:34.467 --> 40:36.897 So first we're going to talk about the chemical shift, what 40:36.900 --> 40:40.030 happens from orbiting. 40:40.033 --> 40:44.773 So electron orbiting gives this little red B, but the 40:44.767 --> 40:49.667 reason the electrons orbit is because of the applied field. 40:49.667 --> 40:51.997 And the bigger the applied field, 40:52.000 --> 40:55.030 the bigger the orbiting. 40:55.033 --> 40:56.833 So that says the red field is 40:56.833 --> 40:58.673 proportional to the blue field. 40:58.667 --> 41:02.397 If you spent the money to get a bigger magnet, you'd get 41:02.400 --> 41:05.430 twice as much orbiting, so the red would be twice as big. 41:05.433 --> 41:11.033 So that says that what you measure then is a fractional 41:11.033 --> 41:13.203 thing, because it's not a standard difference. 41:13.200 --> 41:15.400 It depends on how big your magnet is. 41:15.400 --> 41:19.200 If you make your magnet twice as big, the shift is twice as 41:19.200 --> 41:22.400 big, the red field is twice as big. 41:22.400 --> 41:24.570 So it's a fraction of the big one. 41:24.567 --> 41:28.527 So you measure it in parts per million, in a fractional unit 41:28.533 --> 41:31.633 rather than in an absolute unit, like an energy unit, 41:31.633 --> 41:33.373 like Hz. 41:33.367 --> 41:35.827 OK, so here's a scale of parts per million. 41:35.833 --> 41:39.273 Let's see what different values we have. Now, the 41:39.267 --> 41:44.767 standard that's used it's called TMS, tetramethylsilane. 41:44.767 --> 41:48.197 Now, why use such a weird molecule as your standard? 41:48.200 --> 41:52.670 Well, it's a small molecule and it's volatile. 41:52.667 --> 41:56.997 So you can add a drop to your sample, but you can easily get 41:57.000 --> 41:59.430 it out again if you want to recover your sample, because 41:59.433 --> 42:02.903 it evaporates easily. 42:02.900 --> 42:06.770 Now, it has four CH3 groups, but they're all identically 42:06.767 --> 42:11.927 situated, so it will just give one peak rather than a more 42:11.933 --> 42:14.203 complicated molecule, so that's good. 42:14.200 --> 42:17.970 But the thing that's really special is that the silicon 42:17.967 --> 42:21.967 is, being a metal, is partially plus, and the methyl 42:21.967 --> 42:25.527 is largely minus, which means there are more electrons 42:25.533 --> 42:28.303 around the protons, which means 42:28.300 --> 42:29.970 there's a bigger shielding. 42:29.967 --> 42:32.427 This B is bigger than it would be if there were fewer 42:32.433 --> 42:33.633 electrons around. 42:33.633 --> 42:36.573 So it shifted all the way to one end of the spectrum, so it 42:36.567 --> 42:38.727 doesn't overlap other things that you might 42:38.733 --> 42:40.273 have in your sample. 42:40.267 --> 42:44.997 So you have a standard, then, that you can use with high 42:45.000 --> 42:49.800 electron density around the protons, which defines 0. 42:49.800 --> 42:53.070 And now, you get another peak from your sample, and see 42:53.067 --> 42:55.097 where it is compared to this. 42:55.100 --> 42:59.130 For example, if you have a carboxylic acid, the H on a 42:59.133 --> 43:03.973 carboxylic acid is way what's called downfield. 43:03.967 --> 43:04.427 Why? 43:04.433 --> 43:08.973 Why is it very different from the hydrogen in TMS? 43:08.967 --> 43:13.597 Anybody see why the COOH hydrogen might be different? 43:13.600 --> 43:14.870 The environment of it? 43:17.833 --> 43:21.103 The OH is electron withdrawing, especially with the carbonyl 43:21.100 --> 43:23.130 group on it. 43:23.133 --> 43:26.333 So the electrons get sucked away from the hydrogen. 43:26.333 --> 43:31.733 You don't have as much of that red shielding effect, so it's 43:31.733 --> 43:33.703 shifted way down to the other end. 43:36.300 --> 43:39.700 So on the right, it's said to be shielded. 43:39.700 --> 43:43.430 That is, the electrons around the proton cancel the big 43:43.433 --> 43:45.733 field, but only a teeny bit of it, only a 43:45.733 --> 43:47.003 few parts per million. 43:49.333 --> 43:54.433 And it's called upfield, and it's also a place where 43:54.433 --> 43:56.833 there's high electron density. 43:56.833 --> 43:59.673 And it's called a low chemical shift. 43:59.667 --> 44:03.297 This scale is the chemical shift numbers, and that's 44:03.300 --> 44:06.930 defined as zero, so it's a very low number. 44:06.933 --> 44:11.403 And it's also low frequency, because we have lots of 44:11.400 --> 44:14.900 electrons relatively big value here. 44:14.900 --> 44:19.000 There is very small, relatively small, magnet 44:19.000 --> 44:21.400 effective field, relatively small. 44:21.400 --> 44:25.700 So a low precession frequency, not such a big field. 44:25.700 --> 44:30.600 By contrast, the OH is called deshielded, downfield, low 44:30.600 --> 44:32.300 electron density, high chemical 44:32.300 --> 44:33.970 shift, and high frequency. 44:33.967 --> 44:37.597 Now, if you have a proton that's attached to a normal 44:37.600 --> 44:40.300 carbon, not one that's attached to silicon, which is 44:40.300 --> 44:44.530 giving electrons away, then it comes around 1, or 44:44.533 --> 44:46.803 between 1/2 and 2. 44:46.800 --> 44:49.530 And these were found just by putting different known 44:49.533 --> 44:53.803 samples in and seeing where the peaks came. 44:53.800 --> 44:57.530 But if you have oxygen, halogen, or nitrogen attached 44:57.533 --> 45:02.003 to the carbon, in the same way that silicon donated electrons 45:02.000 --> 45:04.770 to carbon, these electronegative atoms take 45:04.767 --> 45:07.667 electrons from the carbon, which take electrons from the 45:07.667 --> 45:10.967 hydrogen, which make B smaller, 45:10.967 --> 45:12.397 which shift it downfield. 45:12.400 --> 45:14.770 So in that region, between 2.5 and 4.5. 45:19.833 --> 45:22.403 If the carbon, to which the hydrogen is attached, is 45:22.400 --> 45:25.100 itself attached to a carbon, not to one of these 45:25.100 --> 45:29.300 electronegative elements, but that carbon has oxygen on it, 45:29.300 --> 45:32.370 then the oxygen is sucking electrons from carbon, from 45:32.367 --> 45:35.897 carbon, from hydrogen, so it's shifted down a little bit. 45:35.900 --> 45:39.370 So a hydrogen on a carbon attached to a carbonyl is in 45:39.367 --> 45:42.067 between there. 45:42.067 --> 45:44.827 If you have a carbon attached to a double bond, it's shifted 45:44.833 --> 45:46.133 down still further. 45:46.133 --> 45:50.433 Now, why should a hydrogen attached to a double bond be 45:50.433 --> 45:54.133 different from a carbon with a double bond, be different from 45:54.133 --> 45:58.773 a hydrogen attached to a carbon with only single bonds? 45:58.767 --> 46:00.167 What difference? Mimi? 46:00.600 --> 46:02.230 STUDENT: The pi bond? 46:02.233 --> 46:03.003 PROFESSOR: It's not the-- 46:03.000 --> 46:07.200 well, actually, to tell you the truth, it probably is the 46:07.200 --> 46:10.300 pi bond, but that's not the explanation that people 46:10.300 --> 46:11.300 usually give. 46:11.300 --> 46:12.100 What other difference? 46:12.100 --> 46:14.070 What difference is there in the sigma system? 46:14.067 --> 46:14.567 Lauren? 46:14.567 --> 46:16.067 STUDENT: Hybridization? 46:16.067 --> 46:16.927 PROFESSOR: Pardon me. 46:16.933 --> 46:17.373 STUDENT: Hybridization. 46:17.367 --> 46:18.827 PROFESSOR: The hybridization, right? 46:18.833 --> 46:23.973 This is an sp squared, more s, more electron withdrawing. 46:23.967 --> 46:27.697 Whereas these carbons are sp cubed, so as you pull 46:27.700 --> 46:29.200 electrons to the carbon, away from the 46:29.200 --> 46:30.830 hydrogen, you shift down. 46:30.833 --> 46:32.103 That makes sense. 46:32.100 --> 46:35.200 In fact, this, you might expect, would be the same. 46:35.200 --> 46:37.600 It's shifted even a little further down. 46:37.600 --> 46:40.470 All these things were discovered empirically, just 46:40.467 --> 46:42.297 by putting known samples in and finding 46:42.300 --> 46:43.970 out where they come. 46:43.967 --> 46:46.867 And then an aldehyde is, you won't be surprised to hear, is 46:46.867 --> 46:49.227 still further down, because it has the oxygen-- it's not only 46:49.233 --> 46:51.473 double bonded, it has an oxygen pulling away. 46:51.467 --> 46:54.827 So all these things more or less make sense, in terms of 46:54.833 --> 46:58.303 electron withdrawal, or donation to the hydrogen. 47:01.267 --> 47:03.497 But in fact, it's a little more subtle than that. 47:03.500 --> 47:09.300 Now ROH is funny, because it can come at lots of different 47:09.300 --> 47:13.530 positions, depending on concentration, and depending 47:13.533 --> 47:14.733 on temperature. 47:14.733 --> 47:17.273 Why would concentration have anything to do with it? 47:17.267 --> 47:19.097 Why would it have come at a different place if 47:19.100 --> 47:21.430 you had more ROH? 47:21.433 --> 47:21.733 Lauren? 47:21.733 --> 47:25.903 STUDENT: The hydrogen bonding between molecules. 47:25.900 --> 47:27.570 PROFESSOR: If you have hydrogen bonding 47:27.567 --> 47:29.427 and that affects the chemical shift, the higher 47:29.433 --> 47:32.703 concentration, more hydrogen bonding, higher temperature, 47:32.700 --> 47:35.530 less hydrogen bonding. 47:35.533 --> 47:39.203 So OH comes at lots of different positions depending 47:39.200 --> 47:42.300 on those factors. 47:42.300 --> 47:44.700 But you can already see from this, that if you take a 47:44.700 --> 47:47.100 spectrum and see peaks in different positions, you can 47:47.100 --> 47:48.370 try to say, aha! 47:48.367 --> 47:51.697 This looks like it has hydrogens that are just 47:51.700 --> 47:53.570 attached to carbons that are all single bonded. 47:53.567 --> 47:56.727 It has hydrogens on double bonded carbons, blah, blah. 47:56.733 --> 47:59.303 You measure the integral and see how many of each kind 47:59.300 --> 48:04.600 there are, and you can then do puzzles, like the ones in that 48:04.600 --> 48:08.330 web page that I mentioned, to try to figure out what 48:08.333 --> 48:09.833 structures are. 48:09.833 --> 48:12.733 Now, let's see if you've learned from this. 48:12.733 --> 48:15.573 Where should you expect the hydrogen that is attached to 48:15.567 --> 48:17.597 the carbon of an acetylene? 48:17.600 --> 48:18.970 Where would you expect it to come? 48:22.833 --> 48:24.203 What's special? 48:24.200 --> 48:26.970 Noelle, you got any idea on this? 48:26.967 --> 48:27.897 What's special about it? 48:27.900 --> 48:28.770 STUDENT: The triple bond. 48:28.767 --> 48:28.997 PROFESSOR: Can't hear. 48:29.000 --> 48:30.470 STUDENT: The triple bond. 48:30.467 --> 48:31.127 PROFESSOR: The triple bond. 48:31.133 --> 48:33.703 So now, how is the triple bond going to affect things? 48:33.700 --> 48:36.530 STUDENT: Hybridization. 48:36.533 --> 48:37.473 PROFESSOR: It will affect the 48:37.467 --> 48:39.297 hybridization, in what way? 48:39.300 --> 48:41.600 STUDENT: Will it be deshielding? 48:41.600 --> 48:43.630 PROFESSOR: It'll be sp. 48:43.633 --> 48:47.503 It'll be an sp hybrid, which is more electron withdrawing, 48:47.500 --> 48:50.370 than sp squared, than sp cubed. 48:50.367 --> 48:54.627 So it should be pulling electrons away, deshielding, 48:54.633 --> 48:57.573 as you say, because the electrons are shielding, so it 48:57.567 --> 49:00.597 should shift to the left, compared to the double bond 49:00.600 --> 49:03.900 ones, right? 49:03.900 --> 49:05.570 Wrong. 49:05.567 --> 49:07.967 It actually comes up there. 49:07.967 --> 49:10.627 So there's more to it than what we're saying. 49:10.633 --> 49:13.473 Now, what is this more to it? 49:13.467 --> 49:16.867 Unfortunately, the clock has run, so you're going to have 49:16.867 --> 49:19.567 to wait for tomorrow to find that out.