WEBVTT 00:01.600 --> 00:02.530 J. MICHAEL MCBRIDE: OK, so you have the exams back. 00:02.533 --> 00:05.233 I'll have a good answer key for you soon. 00:05.233 --> 00:08.503 Currently, the answer key just has which slides of the 00:08.500 --> 00:11.930 presentation were the subject of each question. 00:15.733 --> 00:19.973 Maybe good news is that we're moving on to a new topic. 00:19.967 --> 00:21.627 So it's spectroscopy. 00:21.633 --> 00:25.533 And last time we started talking about IR spectroscopy, 00:25.533 --> 00:27.703 where the general idea, you remember, is 00:27.700 --> 00:30.300 that molecules vibrate. 00:30.300 --> 00:35.930 If they change their dipole moment as they vibrate, they 00:35.933 --> 00:37.473 can interact with light. 00:37.467 --> 00:41.127 That is, the electric vector of light can cause them to 00:41.133 --> 00:43.603 vibrate at a higher amplitude, but 00:43.600 --> 00:45.900 always at the same frequency. 00:45.900 --> 00:49.600 And it's important, as in pushing a child on a swing, 00:49.600 --> 00:51.300 that you push at the right time. 00:51.300 --> 00:53.900 If you just go whang, whang, whang, which some little kids 00:53.900 --> 00:56.570 do, the person won't go on the swing. 00:56.567 --> 00:58.967 You have to push just when they're coming back. 00:58.967 --> 01:03.097 So the frequency of the light has to be exactly the same as 01:03.100 --> 01:06.870 the natural frequency with which the molecule vibrates. 01:06.867 --> 01:09.997 But the molecule can vibrate in many ways, and these are 01:10.000 --> 01:12.600 called normal modes, and we were beginning to illustrate 01:12.600 --> 01:14.570 those last time. 01:14.567 --> 01:18.667 We illustrated it with butane, but showed the spectrum of 01:18.667 --> 01:20.827 octane, which has the same features. 01:20.833 --> 01:23.333 And last time we saw that there were lots of degrees of 01:23.333 --> 01:26.673 freedom, even in butane, many more in octane. 01:26.667 --> 01:30.697 There are 36 normal modes there, but 72 in octane. 01:30.700 --> 01:32.470 And we looked at what some of them were. 01:32.467 --> 01:39.467 That that one was the coordinated stretching of the 01:39.467 --> 01:45.297 C-H bonds, as indeed with the field pushing up and down. 01:45.300 --> 01:47.870 And the next one, that blue one there or one of those 01:47.867 --> 01:52.397 peaks, is the hydrogens moving coordinatedly in and out in a 01:52.400 --> 01:56.370 normal mode, where all vibrate at exactly the same frequency. 01:56.367 --> 01:58.697 And that's the frequency of that light. 01:58.700 --> 02:01.470 And that one, notice, the electric vector goes in and 02:01.467 --> 02:05.427 out of the board rather than up and down. 02:05.433 --> 02:07.073 So those were C-H stretches. 02:07.067 --> 02:11.667 There are other C-H stretches like this one, which are sort 02:11.667 --> 02:15.097 of a breathing of the hydrogens, which don't change 02:15.100 --> 02:16.070 the dipole moment. 02:16.067 --> 02:18.167 Therefore light has no handle on it. 02:18.167 --> 02:24.727 And that doesn't appear in the IR spectrum. 02:24.733 --> 02:27.303 There is another kind of spectroscopy, called Raman 02:27.300 --> 02:31.030 spectroscopy, which can see that kind of vibration. 02:31.033 --> 02:36.633 And in fact, of the 10 C-H stretches that combine to give 02:36.633 --> 02:41.233 10 normal modes involving C-H stretching, half of them have 02:41.233 --> 02:44.503 no handle, and you can't see them in the IR. 02:44.500 --> 02:45.900 But we can go on to other peaks. 02:45.900 --> 02:48.900 Now, those were C-H stretching at very high frequency. 02:48.900 --> 02:52.700 Now we're at high low frequency, the high end of the 02:52.700 --> 02:54.170 low frequency peaks. 02:54.167 --> 02:58.497 And that particular peak is this motion of the hydrogens. 02:58.500 --> 03:02.270 What's involved here? 03:02.267 --> 03:08.127 If you had to name that kind of a motion of a CH2 group, 03:08.133 --> 03:10.173 that you see in this one, what would you call it? 03:10.167 --> 03:12.397 STUDENT: Scissors. 03:12.400 --> 03:13.630 PROFESSOR: Exactly, it scissors. 03:16.967 --> 03:18.227 Then this one-- 03:21.867 --> 03:24.567 whoops, I went too far. 03:24.567 --> 03:25.697 Whoops, sorry. 03:25.700 --> 03:28.600 There we go. 03:28.600 --> 03:31.700 Notice the motion is almost entirely in the methyl groups 03:31.700 --> 03:34.470 at the end, not within the chain. 03:34.467 --> 03:35.397 It's a bending. 03:35.400 --> 03:39.630 It's, in fact, similar to the scissors motion of the CH2 03:39.633 --> 03:42.233 groups, but this one is called something else. 03:42.233 --> 03:44.773 Could you give it a fanciful name, of what one 03:44.767 --> 03:46.367 methyl group is doing? 03:51.600 --> 03:54.330 It's called the umbrella mode. 03:57.900 --> 04:01.170 This little peak here turns out to be this motion. 04:03.867 --> 04:07.067 See how they're wagging back and forth and any given CH2 is 04:07.067 --> 04:09.767 going like this? 04:09.767 --> 04:17.367 Sorry, there we go. 04:17.367 --> 04:20.897 And this last peak down here is this one. 04:24.233 --> 04:28.173 So the CH2's are going like this, and 04:28.167 --> 04:29.767 that's the rocking mode. 04:29.767 --> 04:33.767 So bear in mind that we're illustrating with butane but 04:33.767 --> 04:36.467 showing octane, but they have these same motions. 04:36.467 --> 04:41.867 Obviously, octane has those same motions as butane does. 04:41.867 --> 04:44.467 And they're all coordinated together at the same 04:44.467 --> 04:47.997 frequency, so it's a normal mode. 04:48.000 --> 04:49.900 And obviously, the ones that appear in the 04:49.900 --> 04:51.970 spectrum are IR active. 04:51.967 --> 04:54.267 So now, how about functional groups? 04:54.267 --> 04:56.527 Here we were looking just at a saturated alkane. 04:56.533 --> 04:59.203 What IR is especially good for is 04:59.200 --> 05:02.030 identifying functional groups. 05:02.033 --> 05:05.803 So that was octane, and here's octyne. 05:05.800 --> 05:09.130 Incidentally, what does -yne mean as a suffix? 05:09.833 --> 05:10.273 STUDENT: A triple bond. 05:10.267 --> 05:11.527 PROFESSOR: It means a triple bond. 05:11.533 --> 05:16.673 And methylacetylene is methyl on a triple bond, not methyl 05:16.667 --> 05:17.667 on a double bond. 05:17.667 --> 05:20.827 That gave some people problems on the exam. 05:20.833 --> 05:24.173 OK, so most of the peaks are the same. 05:24.167 --> 05:26.867 In fact, there's one peak here, that one, which is 05:26.867 --> 05:28.527 almost precisely the same. 05:28.533 --> 05:30.373 Do you remember what that one was 05:32.933 --> 05:36.173 in octane? Well, we'll 05:37.533 --> 05:38.373 see in just a second. 05:38.367 --> 05:42.067 And now, look at-- that was 4-octyne, and now if we look 05:42.067 --> 05:43.667 at 1-octyne-- 05:43.667 --> 05:45.427 a triple bond in a different position at 05:45.433 --> 05:47.033 the last two carbons-- 05:47.033 --> 05:50.303 then we see exactly that same peak again. 05:50.300 --> 05:55.500 So all these things, octane, 4-octyne, 1-octyne, all have 05:55.500 --> 05:58.670 that sharp peak that's circled there. 05:58.667 --> 05:59.897 And it's this motion. 06:04.567 --> 06:08.027 It's that same umbrella motion. 06:08.033 --> 06:10.103 And why is it so special? 06:10.100 --> 06:12.000 Why does it occur at exactly the same 06:12.000 --> 06:13.570 place in all of these? 06:13.567 --> 06:15.697 Because it has its own frequency, a certain 06:15.700 --> 06:17.530 frequency, different from the frequencies of 06:17.533 --> 06:19.733 the neighboring CH2. 06:19.733 --> 06:22.203 So it doesn't couple with them. 06:22.200 --> 06:25.070 It's a bad energy match for that frequency with the 06:25.067 --> 06:28.067 neighbors, so it doesn't couple very much. 06:28.067 --> 06:32.127 So it stands alone, and is the same, in octane, in octyne, 06:32.133 --> 06:36.533 also in octene, as you'll see shortly. 06:36.533 --> 06:37.833 OK, so that's that one. 06:37.833 --> 06:41.103 Now, there are some other peaks here that are new. 06:41.100 --> 06:46.070 Like, there's one at really high frequency, 3315. 06:46.067 --> 06:47.097 Now what's that? 06:47.100 --> 06:51.130 Here's the molecule, and watch its motion. 06:51.133 --> 06:52.403 What's mostly happening? 06:55.633 --> 07:00.703 And why is it different from anything you saw in octane? 07:00.700 --> 07:02.370 At higher frequency. 07:02.367 --> 07:05.927 First, what's moving mostly? 07:05.933 --> 07:06.633 Ayesha? 07:06.633 --> 07:08.003 STUDENT: The C-H bond. 07:08.000 --> 07:09.970 PROFESSOR: The C-H bond is stretching. 07:09.967 --> 07:13.897 And why is the stretching of this C-H bond different from 07:13.900 --> 07:18.970 the stretching of the bonds we saw in octane? 07:18.967 --> 07:21.927 Why is it a different frequency, so that it doesn't 07:21.933 --> 07:24.333 mix up with other things? 07:24.333 --> 07:28.333 Bad energy match, it doesn't mix. 07:28.333 --> 07:28.833 Ayesha? 07:28.833 --> 07:30.873 STUDENT: It's in the plane... 07:30.867 --> 07:31.767 PROFESSOR: Can't hear very well. 07:31.767 --> 07:32.697 STUDENT: It's in the plane of the molecule. 07:32.700 --> 07:33.170 PROFESSOR: It's true 07:33.167 --> 07:33.997 that it's in the plane. 07:34.000 --> 07:37.000 In fact, it's in the line in this case. 07:37.000 --> 07:40.030 All the atoms except for three hydrogens are on a line. 07:40.033 --> 07:43.303 But what's special about that C-H bond 07:43.300 --> 07:45.700 as compared to others? 07:45.700 --> 07:49.100 We've seen things special about an acetylene C-H bond 07:49.100 --> 07:52.770 before in its chemistry. 07:52.767 --> 07:54.667 STUDENT: It's sp hybridized. 07:54.667 --> 07:56.297 PROFESSOR: It's sp hybridized. 07:56.300 --> 07:57.530 Remember, it's acidic. 07:57.533 --> 07:59.203 It's unusually acidic. 07:59.200 --> 08:03.700 25 is its pKa, because it's a C-H bond, so it's much 08:03.700 --> 08:06.300 stronger than the others. 08:06.300 --> 08:09.300 So it's at higher frequency, as you'd expect 08:09.300 --> 08:12.000 for a stronger spring. 08:12.000 --> 08:14.470 OK, now, at the other end of the spectrum, there's this 08:14.467 --> 08:18.167 really strong peak at 630, and that's this motion. 08:22.567 --> 08:25.697 It's bending the hydrogen up and down, 08:25.700 --> 08:27.730 bending that C-H bond. 08:27.733 --> 08:32.403 And that turns out to be much easier than bending bonds that 08:32.400 --> 08:35.400 are normally hybridized. 08:35.400 --> 08:36.670 So that's that bending. 08:36.667 --> 08:38.367 So that's characteristic of having an 08:38.367 --> 08:40.197 acetylene in a molecule. 08:40.200 --> 08:44.070 If it's a terminal acetylene at the end of the chain, 08:44.067 --> 08:45.097 you'll have these. 08:45.100 --> 08:47.170 If it's not at the end of the chain, then you don't have 08:47.167 --> 08:52.827 this kind of C-H. Now, what's this peak here at 2120? 08:52.833 --> 08:55.033 Give me some thoughts about what that might be. 08:55.033 --> 08:58.633 What kind of peaks come at the far left of the spectrum, at 08:58.633 --> 09:00.673 very high frequency? 09:00.667 --> 09:01.427 STUDENT: C-H. 09:01.433 --> 09:02.273 PROFESSOR: C-H's, 09:02.267 --> 09:04.767 because the H is so light. 09:04.767 --> 09:08.667 And then when you get bendings of C-H's or stretchings of 09:08.667 --> 09:12.327 C-C, those come in the right half of the spectrum. 09:12.333 --> 09:15.203 So this particular peak at 2120 is in 09:15.200 --> 09:17.270 what's a window usually. 09:17.267 --> 09:18.897 Usually, there's nothing... There must be something 09:18.900 --> 09:21.800 really special that vibrates at that frequency. 09:21.800 --> 09:24.100 Any idea of what could make something... 09:24.100 --> 09:27.070 It's not a C-H bond. 09:27.067 --> 09:31.167 It must be a C-C bond, but it's a very special C-C bond. 09:32.100 --> 09:32.670 STUDENT: Triple bond. 09:32.667 --> 09:33.167 PROFESSOR: What is it that would vibrate at a very high 09:33.167 --> 09:33.897 frequency? Derek? 09:33.900 --> 09:34.600 STUDENT: The triple bond 09:34.600 --> 09:36.400 PROFESSOR: The triple bond is three times 09:36.400 --> 09:39.530 as strong as a single bond, so it comes at unusually high 09:39.533 --> 09:43.933 frequency for a CC bond, and here is its motion. 09:43.933 --> 09:45.203 Whoops. 09:47.367 --> 09:48.767 So it's a CC bond stretching. 09:52.933 --> 09:58.173 Now, notice that in the spectrum of 4-octyne, the blue 09:58.167 --> 10:00.767 spectrum, you don't have that peak. 10:00.767 --> 10:06.267 Why don't you see the triple bond stretching in 4-octyne? 10:06.267 --> 10:08.627 How many carbons are there in octyne? 10:08.633 --> 10:10.633 STUDENT: They cancel out. 10:10.633 --> 10:10.873 PROFESSOR: Right. 10:10.867 --> 10:13.127 There's no change in the dipole moment, because it's 10:13.133 --> 10:15.573 symmetrical as you move like that. 10:15.567 --> 10:18.527 If it's at the end of the chain, it's unsymmetrical, 10:18.533 --> 10:19.273 and you can see it. 10:19.267 --> 10:21.267 But if it's in the middle of the chain, it doesn't change 10:21.267 --> 10:22.667 the dipole moment. 10:22.667 --> 10:25.897 OK, so you can tell the difference in two ways here, 10:25.900 --> 10:28.600 between a triple bond that's at the end of the chain and a 10:28.600 --> 10:31.330 triple bond that's in the middle of the chain. 10:31.333 --> 10:33.503 OK, so there's no handle for the light to 10:33.500 --> 10:35.230 interact with that one. 10:35.233 --> 10:36.473 So we've seen octane. 10:36.467 --> 10:40.897 We've seen octynes, two octynes, the 4 and the 1. 10:40.900 --> 10:43.770 Now let's look at octene, a different functional group. 10:43.767 --> 10:47.997 So again, most of the peaks look exactly the same, because 10:48.000 --> 10:50.630 they have long chains of CH2. 10:50.633 --> 10:53.933 But it's trans-4-octene, so there's a 10:53.933 --> 10:56.803 carbon-carbon double bond. 10:56.800 --> 11:02.670 Now, there's this big peak at 967. 11:02.667 --> 11:03.627 Now what could that be? 11:03.633 --> 11:05.173 Now here's cis. 11:05.167 --> 11:09.767 That was trans-4-octene, here's cis-4-octene. 11:09.767 --> 11:13.367 And now you see a peak at 1655. 11:13.367 --> 11:14.597 What do you suppose that is? 11:17.200 --> 11:20.670 It's not involved in an H. It's very high frequency, but 11:20.667 --> 11:24.027 it doesn't involve H. Those are up around 3000. 11:24.033 --> 11:25.603 Any ideas for this one? 11:25.600 --> 11:27.300 STUDENT: The double bonding stretching. 11:27.300 --> 11:28.170 PROFESSOR: The double bond stretching. 11:28.167 --> 11:32.397 Now, why do you see it in cis-4-octene, but you don't 11:32.400 --> 11:33.670 see it in trans-4-octene? 11:37.900 --> 11:41.700 So that's stretching can be symmetrical, right? 11:41.700 --> 11:45.470 And if it's a trans double bond, like this, then it truly 11:45.467 --> 11:46.797 is symmetrical. 11:46.800 --> 11:49.730 There's a center of symmetry there. 11:49.733 --> 11:54.733 But if it's cis-4-octene, then if you stretch the double bond 11:54.733 --> 11:59.803 and change the bonds from carbon to carbon, you change 11:59.800 --> 12:01.170 the dipole moment in this 12:01.167 --> 12:04.867 direction, not in this direction. 12:04.867 --> 12:08.297 So if you have it cis like that, then the dipole change 12:08.300 --> 12:10.570 is actually in a different direction. 12:10.567 --> 12:13.727 Of course, normally you measure these spectra on 12:13.733 --> 12:17.033 solutions, so there'll be some molecules 12:17.033 --> 12:18.733 that are oriented properly. 12:18.733 --> 12:22.803 But if you had molecules that were fixed, like in a crystal, 12:22.800 --> 12:25.730 you could tell which way the double bonds were oriented, by 12:25.733 --> 12:29.333 seeing which direction the electric vector could 12:29.333 --> 12:31.173 interact with it. 12:31.167 --> 12:32.967 But notice that down at the low frequency 12:32.967 --> 12:35.897 end that has a big peak at 710, whereas the 12:35.900 --> 12:40.930 trans isomer had 967. 12:40.933 --> 12:44.833 Now, what was the really low frequency peak 12:44.833 --> 12:46.403 in acetylene, remember, 12:46.400 --> 12:52.000 in the 1-octyne? Remember the one was really down low? 12:52.000 --> 12:53.130 STUDENT: The Bending. 12:53.133 --> 12:54.503 PROFESSOR: That was the bending of the C-H. 12:54.500 --> 12:55.770 So these are down low, 12:55.767 --> 12:59.167 they could be bending of the C-H. 12:59.167 --> 13:03.627 And let's, just to compare, look at a double bond that has 13:03.633 --> 13:06.503 three carbons on it, so just one H that 13:06.500 --> 13:08.070 could bend out of plane. 13:08.067 --> 13:11.067 And it has a peak at 828. 13:11.067 --> 13:13.397 Now, of course, the others that don't have that extra 13:13.400 --> 13:18.870 methyl group are cis and trans, but have two H's, two 13:18.867 --> 13:22.397 H's cis, or two H's trans. 13:22.400 --> 13:25.570 And they'll couple as they vibrate, because they're near 13:25.567 --> 13:26.867 one another. 13:26.867 --> 13:31.867 So there's perfect energy match of these two. 13:31.867 --> 13:34.927 So if you have any overlap, any coupling mechanism, 13:34.933 --> 13:39.373 mechanical coupling, if one can feel the other vibrating, 13:39.367 --> 13:43.927 then you should get two vibrations, coupled vibrations. 13:43.933 --> 13:47.703 That is, if we look at it this way, you have the 828, which 13:47.700 --> 13:51.970 is a single H, but if you had two of them at 828, and they 13:51.967 --> 13:55.897 could interact, you'd get a higher peak and a lower peak, 13:55.900 --> 13:58.400 which looks like what we see, in a way. 13:58.400 --> 14:01.300 But the higher peak comes in one compound, and the lower 14:01.300 --> 14:03.170 peak comes in another one. 14:03.167 --> 14:05.467 Where is the second of those two peaks 14:05.467 --> 14:08.067 that got mixed together? 14:08.067 --> 14:09.627 We could turn it that way to see the 14:09.633 --> 14:14.433 analogue to orbital mixing. 14:14.433 --> 14:17.803 So let's look at pictures of these vibrations. 14:17.800 --> 14:19.770 At the top, you see, is the molecule that 14:19.767 --> 14:21.567 has just one hydrogen. 14:21.567 --> 14:24.967 At the bottom, on the left, are two hydrogens on the 14:24.967 --> 14:27.067 double bond trans, and on the right, 14:27.067 --> 14:28.697 they're cis to one another. 14:28.700 --> 14:32.470 Now, this is the vibration we're looking at, out-of-plane 14:32.467 --> 14:34.727 vibration of the C-H. Everybody see 14:34.733 --> 14:37.003 what I'm talking about? 14:37.000 --> 14:39.930 It's out-of-plane vibration of the C-H at the top. 14:39.933 --> 14:41.973 Now, at the bottom, there are two CH's. 14:41.967 --> 14:46.327 And notice that in this vibration, those two H's move 14:46.333 --> 14:49.033 in the same direction, both up and both 14:49.033 --> 14:50.473 down at the same time. 14:53.000 --> 14:56.870 Why don't I show the one where one moves up and the other 14:56.867 --> 14:57.767 moves down? 14:57.767 --> 15:01.097 Why isn't that relevant for our discussion? 15:01.100 --> 15:03.700 Because there's no dipole moment for that one. 15:03.700 --> 15:04.470 It cancels. 15:04.467 --> 15:07.427 One went up, the other went down. 15:07.433 --> 15:11.603 So to be IR active, to interact with the light, they 15:11.600 --> 15:14.400 have to move the same direction. 15:14.400 --> 15:18.070 But notice, this is interesting, so they move in 15:18.067 --> 15:19.627 the same direction to be active. 15:19.633 --> 15:22.733 That one is at 828. 15:22.733 --> 15:25.373 This one, notice that when they both move up, 15:25.367 --> 15:27.327 it twists the bond. 15:27.333 --> 15:29.973 See how it twists the center carbon bond when the two 15:29.967 --> 15:31.797 hydrogens move up. 15:31.800 --> 15:33.200 But on the right... 15:33.200 --> 15:35.270 so that reduces the pi overlap. 15:35.267 --> 15:38.327 It weakens the pi bond when those p orbitals 15:38.333 --> 15:39.973 don't overlap as well... 15:39.967 --> 15:42.927 But on the right, when they both move the same direction, 15:42.933 --> 15:44.873 the p orbitals still point so that they 15:44.867 --> 15:46.667 overlap with one another. 15:46.667 --> 15:49.697 So the one on the left is harder to do because it 15:49.700 --> 15:51.430 weakens the bond. 15:51.433 --> 15:54.133 It distorts the bond, whereas the one on the right 15:54.133 --> 15:56.073 doesn't distort the bond. 15:56.067 --> 15:58.697 So the one on the left is harder to do 15:58.700 --> 16:00.370 and it's higher frequency. 16:00.367 --> 16:03.267 So folding preserves the overlap. 16:03.267 --> 16:06.627 The harder one and the easier one. The harder one is high 16:06.633 --> 16:09.673 frequency, the easier one is low frequency. 16:09.667 --> 16:13.397 So you can understand why you see only-- when these two 16:13.400 --> 16:16.570 vibrations mix-- why you see only one. 16:16.567 --> 16:19.967 You only see the one where they move in parallel. 16:19.967 --> 16:22.767 And it's easier if they're like this, than if they're 16:22.767 --> 16:25.527 like this, where you're twisting the bond as well. 16:25.533 --> 16:30.033 So not only are the high- and low- frequency peak handy, 16:30.033 --> 16:33.833 because they diagnose being a cis or a trans double bond, 16:33.833 --> 16:36.533 you can tell which one you have, but also you can 16:36.533 --> 16:39.433 understand what it tells you about the bonding, why you 16:39.433 --> 16:43.033 have one that's high and the other low. 16:43.033 --> 16:48.233 OK, but the real jewel in the crown of infrared spectroscopy 16:48.233 --> 16:49.833 is the carbonyl group. 16:49.833 --> 16:52.473 Why should it be such a great group? 16:52.467 --> 16:55.427 Why should it be so good in infrared spectroscopy? 16:55.433 --> 16:59.073 Why should it stand out and be something that you can really 16:59.067 --> 17:02.567 identify what kind of carbonyl group you have? 17:02.567 --> 17:05.097 First, it absorbs very strongly. 17:05.100 --> 17:07.270 It interacts very strongly with light. 17:07.267 --> 17:09.597 What determines how strongly something 17:09.600 --> 17:11.200 interacts with light? 17:11.200 --> 17:13.700 How much you can push the atoms with the 17:13.700 --> 17:17.370 electric field of light? 17:17.367 --> 17:18.867 Luke, you got an idea? 17:18.867 --> 17:22.197 STUDENT: It's the number of electrons? 17:22.200 --> 17:23.170 PROFESSOR: Not just the number of 17:23.167 --> 17:26.097 electrons, but how much the dipole moment 17:26.100 --> 17:27.800 changes when you stretch. 17:30.500 --> 17:33.430 If the electrons change a lot when you stretch it, and it 17:33.433 --> 17:36.833 becomes much more plus-minus, if the plus-minus get 17:36.833 --> 17:42.473 separated more, then that's a strong interaction with light. 17:42.467 --> 17:46.697 And the C-O is a polar bond, so it changes much more than 17:46.700 --> 17:49.030 a C-H bond does as it vibrates. 17:49.033 --> 17:50.903 So it's going to be a very strong peak. 17:50.900 --> 17:54.730 It's not going to be one of these wimpy little peaks. 17:54.733 --> 17:59.903 Now, why does it stand out in its frequency? 17:59.900 --> 18:03.470 From one molecule to the next, you don't have to worry so 18:03.467 --> 18:06.267 much about the coupling in interpreting it. 18:06.267 --> 18:10.197 A certain ketone, a ketone will always be very near where 18:10.200 --> 18:13.870 another ketone is, at the same frequency. 18:13.867 --> 18:14.827 Why? 18:14.833 --> 18:18.233 Because that bond is a double bond and nearby bonds aren't 18:18.233 --> 18:19.703 double bonds. 18:19.700 --> 18:23.000 So the nearby bonds that it could couple its vibration 18:23.000 --> 18:26.200 with have very different frequency. 18:26.200 --> 18:28.930 So you have very little overlap, so you don't change 18:28.933 --> 18:30.603 the frequency very much when it 18:30.600 --> 18:32.170 interacts with its neighbors. 18:32.167 --> 18:36.127 So it stands alone and is characteristic of a particular 18:36.133 --> 18:39.333 kind of carbonyl, and it's very strong so that you can 18:39.333 --> 18:42.003 see it in the IR spectrum easily. 18:42.000 --> 18:44.800 OK, so that's why these are so great, the carbonyls. 18:44.800 --> 18:46.530 So here's a ketone-- 18:46.533 --> 18:49.533 or pardon me, an aldehyde, acetaldehyde. 18:49.533 --> 18:52.603 Notice how very strong a peak it is. 18:52.600 --> 18:55.700 It's strong and it's independent. 18:55.700 --> 18:59.130 It doesn't mix much with its neighbors. 18:59.133 --> 19:01.973 Now, there's a ketone, right? 19:01.967 --> 19:02.727 Acetone. 19:02.733 --> 19:07.373 Notice it's about 12 cm-1 lower frequency, but 19:07.367 --> 19:10.727 that's reproducible. 19:10.733 --> 19:13.403 The ketones would come at a little higher frequency, 19:13.400 --> 19:15.400 aldehydes come at a little lower frequency-- 19:15.400 --> 19:16.670 or pardon me, vice versa. 19:16.667 --> 19:19.967 So you can tell which is which. 19:19.967 --> 19:23.527 Now, here's an amide, where we put a nitrogen on the 19:23.533 --> 19:25.603 carbon=oxygen double bond. 19:25.600 --> 19:27.170 Now, that went to a substantially 19:27.167 --> 19:29.867 lower frequency, 1681. 19:29.867 --> 19:34.567 Why should the C-O bond, double bond of an amide, be 19:34.567 --> 19:38.927 weak and vibrate at lower frequency, a weaker spring? 19:38.933 --> 19:43.833 Anybody got an idea of how the nitrogen would do that to the 19:43.833 --> 19:46.133 C-O double bond? 19:46.133 --> 19:47.873 Yigit how about you? 19:47.867 --> 19:51.167 STUDENT: The interaction between the lone pair of 19:51.167 --> 19:53.927 nitrogen and the pi*-- 19:53.933 --> 19:54.703 PROFESSOR: And pi*. 19:54.700 --> 19:58.570 So you put electrons from the nitrogen into the antibonding 19:58.567 --> 20:02.267 orbital of the C=O, weakening the C=O bond and lowering its 20:02.267 --> 20:03.797 vibration frequency. 20:03.800 --> 20:08.000 So there's the unshared pair, we mix them with pi*, and 20:08.000 --> 20:10.200 it gets to 1681. 20:10.200 --> 20:14.170 So the C=O is weakened by resonance, by 20:14.167 --> 20:16.567 occupancy of the pi*. 20:16.567 --> 20:21.367 OK, now, suppose we look at an ester, where we have an oxygen 20:21.367 --> 20:22.227 next to the carbonyl. 20:22.233 --> 20:24.603 Can I get someone to predict that for me? 20:24.600 --> 20:25.870 Po-Yi, what do you think? 20:25.867 --> 20:29.667 Where is the ester going to come, compared to, say, a 20:29.667 --> 20:33.627 ketone and the amide, the one with nitrogen? 20:36.367 --> 20:40.197 STUDENT: Well, there will still be resonance. 20:40.200 --> 20:41.400 PROFESSOR: There'll still be resonance. 20:41.400 --> 20:42.730 It's an unshared pair on oxygen. 20:42.733 --> 20:45.633 Should it be as strong as that involving the nitrogen? 20:45.633 --> 20:46.433 STUDENT: No. 20:46.433 --> 20:47.673 PROFESSOR: Why? 20:52.567 --> 20:54.527 Why should mixing of the 20:54.533 --> 20:59.033 electrons into the pi* be weaker for oxygen than it is 20:59.033 --> 21:00.333 for nitrogen? 21:04.567 --> 21:06.767 Here are the electrons on the atom we're interested in, on 21:06.767 --> 21:08.427 oxygen or nitrogen. 21:08.433 --> 21:10.403 STUDENT: Bad energy-match? 21:10.400 --> 21:12.070 PROFESSOR: But oxygen, as you say, has a 21:12.067 --> 21:13.227 higher nuclear charge. 21:13.233 --> 21:15.003 Lower it doesn't mix as much. 21:15.000 --> 21:18.770 So it shouldn't lower the frequency as much as 1681. 21:18.767 --> 21:21.497 So I think you would predict that it'd be someplace between 21:21.500 --> 21:24.370 1715 and 1681. 21:24.367 --> 21:25.427 Make sense? 21:25.433 --> 21:26.773 Yep. 21:26.767 --> 21:31.127 There it is, it's higher frequency, 1746! 21:31.133 --> 21:32.773 So there's something different. 21:32.767 --> 21:35.067 Not only is it not as good as nitrogen, it goes 21:35.067 --> 21:36.827 the opposite direction. 21:36.833 --> 21:38.603 Now how about if we put a halogen 21:38.600 --> 21:41.270 on there, like chlorine? 21:41.267 --> 21:44.697 That's higher still, 1806. 21:44.700 --> 21:48.100 It's true its electron pair is lower, so it 21:48.100 --> 21:49.030 won't mix as much. 21:49.033 --> 21:51.903 It won't weaken it as much as nitrogen did. 21:51.900 --> 21:54.800 But why does it strengthen it to have a halogen there? 21:58.800 --> 22:00.930 So here's a different kind of resonance. 22:00.933 --> 22:04.003 You have an unshared pair-- on the on the right, we used an 22:04.000 --> 22:06.500 unshared pair of the adjacent atom to 22:06.500 --> 22:08.400 interact with the carbonyl. 22:08.400 --> 22:11.100 Now we're going to use an unshared pair on the oxygen of 22:11.100 --> 22:15.970 the carbonyl to mix with an orbital of the C-X bond. 22:15.967 --> 22:18.367 What orbital could that mix with? 22:18.367 --> 22:22.527 It could mix with sigma*. 22:22.533 --> 22:27.333 So if you mix that with sigma*, then you 22:27.333 --> 22:29.173 strengthen the C=O bond. 22:29.167 --> 22:33.597 You get a triple bond between oxygen and carbon, and occupy 22:33.600 --> 22:34.230 sigma star. 22:34.233 --> 22:37.603 So the appropriate resonance structure would be one with no 22:37.600 --> 22:39.770 bond to that X group. 22:39.767 --> 22:43.527 Of course, that's not the dominant structure, but it's 22:43.533 --> 22:45.903 one that causes the bond to get 22:45.900 --> 22:46.900 the C=O bond 22:46.900 --> 22:47.830 to get stronger. 22:47.833 --> 22:49.703 So it moves to high frequency. 22:49.700 --> 22:51.800 So we can see that that interaction is important. 22:51.800 --> 22:56.100 And in this case, the mixing with the sigma*, the C-O 22:56.100 --> 22:57.670 is strengthened by resonance. 22:57.667 --> 23:00.367 So in the case of amide, it was weakened by resonance. 23:00.367 --> 23:02.867 In this case, it's strengthened by resonance. 23:02.867 --> 23:06.667 In that case, it was a pi interaction, putting electrons 23:06.667 --> 23:07.927 in pi*. 23:07.933 --> 23:11.973 In this one, it's putting electrons in sigma*, and 23:11.967 --> 23:15.567 making a triple bond. 23:15.567 --> 23:17.267 Look at this case here, where we have a 23:17.267 --> 23:19.267 C=C double bond. 23:19.267 --> 23:23.097 Now we don't have the low sigma*, so we're not going 23:23.100 --> 23:26.430 to get the effect we got in the acid, and the acid 23:26.433 --> 23:28.673 chloride and the ester. 23:28.667 --> 23:31.967 And we have pi electrons that could do the mixing. 23:31.967 --> 23:34.527 So that looks like a case where this resonance structure 23:34.533 --> 23:37.873 could be significant, and it would weaken 23:37.867 --> 23:40.897 the C=O double bond. 23:40.900 --> 23:44.000 But the peak is, in fact, at higher frequency than a 23:44.000 --> 23:46.730 ketone, 1720. 23:46.733 --> 23:48.303 Now, why is this so? 23:48.300 --> 23:52.770 Notice that in this case, you have two double bonds 23:52.767 --> 23:56.667 separated only by one single bond, so they both have a 23:56.667 --> 23:59.467 better energy match, these double bonds, than when you 23:59.467 --> 24:04.527 had a double bond and only single bonds in the vicinity. 24:04.533 --> 24:05.833 So now you can mix them. 24:05.833 --> 24:09.973 You can make them in-phase and out-of-phase. 24:09.967 --> 24:12.567 And here, notice that one is stretching while 24:12.567 --> 24:14.167 the other is shrinking. 24:14.167 --> 24:17.227 It's out of phase, and it's mostly a vibration of the C=O. 24:17.233 --> 24:22.203 And that's the one that's at high frequency. 24:22.200 --> 24:25.970 And notice it's a double peak, because you have the other one 24:25.967 --> 24:27.597 when they're in phase as well. 24:30.600 --> 24:33.400 And here's the one where it's in phase and it's mostly a 24:33.400 --> 24:36.830 vibration of the C=C, rather than the C=O. 24:36.833 --> 24:38.203 But notice, they're both 24:38.200 --> 24:41.230 stretching at the same time. 24:41.233 --> 24:42.633 So we have this situation. 24:42.633 --> 24:51.703 We mix them, and we get 1720 and 1683? 24:51.700 --> 24:55.700 Notice there's this peak at 1618. 24:55.700 --> 24:59.400 This is a really neat case, because the doubling that you 24:59.400 --> 25:02.700 see in that strong peak isn't what you think it is. 25:02.700 --> 25:06.500 It's not the in-phase and the out-of-phase. 25:06.500 --> 25:10.230 What is the 1618? 25:10.233 --> 25:13.803 And what's the source of the doubling? 25:13.800 --> 25:17.070 Well, here's a spectrum of methyl vinyl ketone, that same 25:17.067 --> 25:20.367 compound with a double bond adjacent to the carbonyl, 25:20.367 --> 25:24.167 measured in argon at 13 k. 25:24.167 --> 25:29.827 And you can see it's got those two peaks, 1718, 1696, but 25:29.833 --> 25:32.003 then it's got that 1623. 25:32.000 --> 25:34.670 These aren't exactly the same frequencies we saw in the 25:34.667 --> 25:37.697 previous slide, because that was measured in solution, this 25:37.700 --> 25:39.500 is measured in an argon solid. 25:39.500 --> 25:41.000 So there's a little influence of the 25:41.000 --> 25:43.700 neighbors on the frequency. 25:43.700 --> 25:48.230 But if you photolyze that at 308 nanometers for two and a 25:48.233 --> 25:52.903 half hours, and then look at the difference between the 25:52.900 --> 25:58.000 spectrum you have now and the spectrum you had before, see 25:58.000 --> 26:02.030 that some peaks have gotten stronger, they point up, and 26:02.033 --> 26:04.073 those that have gotten weaker, if you take the 26:04.067 --> 26:06.827 difference, go down. 26:06.833 --> 26:12.233 So you see that peak at 1696 went down, not up. 26:12.233 --> 26:14.873 So what does this mean? 26:14.867 --> 26:18.367 It means that there are two different compounds there. 26:18.367 --> 26:23.027 One is becoming the other, so the one that's being formed is 26:23.033 --> 26:25.803 getting stronger, the one that's going away is getting 26:25.800 --> 26:30.830 weaker and appears negative when you do the difference. 26:30.833 --> 26:32.833 And that's 1696. 26:32.833 --> 26:36.403 So that original doublet we looked at is not from the same 26:36.400 --> 26:38.130 compound, those two peaks, they're from 26:38.133 --> 26:40.173 two different compounds. 26:40.167 --> 26:47.697 But the 1696, if photolyzed, can become the 1718. 26:47.700 --> 26:51.400 So if you calculate the positions for that compound 26:51.400 --> 26:54.770 shown at the top, you see the C=O, and the C=C, 26:54.767 --> 26:59.797 so those are the 1718 and 1623. 26:59.800 --> 27:00.570 We got that. 27:00.567 --> 27:01.997 That's that compound. 27:02.000 --> 27:04.770 So the in-phase and the out-of-phase vibrations. 27:04.767 --> 27:06.627 What's the other one? 27:06.633 --> 27:07.873 It's this. 27:10.300 --> 27:12.430 What's the difference? 27:12.433 --> 27:15.733 It's the conformation around that central bond. 27:15.733 --> 27:20.373 They're both planar, but one is like eclipsed and the other 27:20.367 --> 27:21.597 is like anti. 27:25.167 --> 27:29.267 And if you calculate the spectra for the one where the 27:29.267 --> 27:32.267 two double bonds are trans to one another, you see a very 27:32.267 --> 27:34.567 strong peak at 1696, and hardly 27:34.567 --> 27:36.397 anything at the low frequency. 27:36.400 --> 27:39.200 Why is there hardly anything at the low frequency? 27:39.200 --> 27:42.330 Because that one, which is mostly a C=C vibration and a 27:42.333 --> 27:46.633 little bit of coupled C=O, has them so that one tends to 27:46.633 --> 27:48.073 cancel the other. 27:48.067 --> 27:53.867 The C=O doesn't move very much but it's a big dipole, so it 27:53.867 --> 27:54.767 can cancel it. 27:54.767 --> 27:59.367 And at the top, they reinforce one another, so the mostly C=C 27:59.367 --> 28:02.027 vibration is rather strong, because the C=O 28:02.033 --> 28:05.073 is helping it out. 28:05.067 --> 28:08.167 So one of these just called synperiplanar. 28:08.167 --> 28:11.967 It's flat, periplanar, but adjacent to one another. 28:11.967 --> 28:13.197 And the other is anti periplanar. 28:16.200 --> 28:18.400 OK, there's one more peak there, and I don't know what 28:18.400 --> 28:19.470 that is that went away. 28:19.467 --> 28:23.027 It might be a combination of some other freak transitions. 28:23.033 --> 28:25.073 That's something we don't want to talk about now, it's too 28:25.067 --> 28:26.227 complicated. 28:26.233 --> 28:29.703 But anyhow, here's a picture of these vibrations. 28:29.700 --> 28:32.970 We're in-phase, where that's the low frequency, both 28:32.967 --> 28:34.727 stretching at the same time. 28:34.733 --> 28:40.773 But mostly the C=C, the C=C is stretching nine times as much 28:40.767 --> 28:42.597 as the C=O. 28:42.600 --> 28:45.270 But here's the actual amplitude. 28:45.267 --> 28:49.027 The actual amplitudes are very subtle for these things. 28:49.033 --> 28:52.373 And in fact, we talked about this a little bit last 28:52.367 --> 28:55.797 semester, about how, when we were doing quantum mechanics 28:55.800 --> 28:58.530 and vibration, how much things actually move. 28:58.533 --> 29:03.233 And here's the out-of-phase normal mode, mostly the C=O 29:03.233 --> 29:07.673 vibration, a little bit of C=C. And as one stretches the 29:07.667 --> 29:08.897 other shrinks. 29:11.667 --> 29:15.767 So the C=O is moving six times as much as the C=C, and the 29:15.767 --> 29:17.397 actual amplitude is like that. 29:17.400 --> 29:20.530 And if you look at Lecture 8 last semester, you can 29:20.533 --> 29:24.273 see where we talked about how vibrational amplitudes are. 29:31.400 --> 29:35.170 Here we were talking about two things: identifying functional 29:35.167 --> 29:38.597 groups, characteristic peaks, strong peaks that you can 29:38.600 --> 29:41.070 identify with particular functional groups, and you can 29:41.067 --> 29:43.627 look them up in tables, as I suspect you did in lab 29:43.633 --> 29:45.303 already, to see what functional 29:45.300 --> 29:47.300 group would come where. 29:47.300 --> 29:49.170 And that's very valuable. 29:49.167 --> 29:52.527 We used it here more to understand how strong bonds 29:52.533 --> 29:54.873 are, and resonance and so on. 29:54.867 --> 29:58.667 In the real world, it can enter in a lot of cases. 29:58.667 --> 30:01.367 One interesting case is a multibillion dollar 30:01.367 --> 30:04.767 pharmaceutical, which crystallizes in different 30:04.767 --> 30:10.727 crystal forms, and those forms are separately patented. 30:10.733 --> 30:12.603 The drug is called Paxil. 30:17.500 --> 30:20.500 These are taken from the patent for that compound, 30:20.500 --> 30:22.630 paroxetine hydrochloride. 30:22.633 --> 30:27.903 This is the anhydrate, in called Form A, or Polymorph A. 30:27.900 --> 30:32.900 Polymorph means different shapes, different crystals. 30:32.900 --> 30:34.470 Now, what do we see in this spectrum? 30:34.467 --> 30:39.027 We see C-H stretching peaks over at the left, and we see 30:39.033 --> 30:41.473 fingerprint regions on the right. 30:41.467 --> 30:45.827 All these complicated combinations of things. 30:45.833 --> 30:48.103 But is there anything we can identify? 30:48.100 --> 30:52.800 Well, here, this sort of big shoulder in here, turns out to 30:52.800 --> 30:57.800 be characteristic of ammonium ions, NH+-. 30:57.800 --> 31:01.700 So we know it's an ammonium salt from that. 31:01.700 --> 31:05.470 Now, what are these peaks at really high frequency? 31:05.467 --> 31:07.567 They're much higher. 31:07.567 --> 31:11.967 Those that are hydrogens on a double bond, sp2, are 31:11.967 --> 31:15.827 indeed higher frequency than hydrogens on a single bond, 31:15.833 --> 31:20.173 sp3, but they're not as high as this. 31:20.167 --> 31:24.697 And what those turn out to be due to is water. 31:24.700 --> 31:28.170 And notice than when water is hydrogen bonded like this, you 31:28.167 --> 31:32.197 have OH's that are at the end of the chain, that have a very 31:32.200 --> 31:35.670 high frequency, and OH's that are involved in hydrogen 31:35.667 --> 31:39.297 bonding, which are lower frequency, because they don't 31:39.300 --> 31:40.400 just go one way. 31:40.400 --> 31:43.500 It's not so bad to move toward the other oxygen. 31:43.500 --> 31:47.400 OK, so we see two peaks here, which is interesting because 31:47.400 --> 31:52.100 this molecule is called an anhydrate, but, in fact, it 31:52.100 --> 31:53.530 has water in it. 31:53.533 --> 31:56.603 So that was sort of a weird thing about it. 31:56.600 --> 31:59.770 OK, so here's the second form, Form B. And 31:59.767 --> 32:02.167 again, it has ammonium. 32:02.167 --> 32:04.697 There's ammonium functionality in there, C-H and 32:04.700 --> 32:05.900 fingerprints. 32:05.900 --> 32:09.830 And here's the third form, same deal. 32:09.833 --> 32:13.803 Now, notice incidentally, that they had a lot of sample in 32:13.800 --> 32:17.030 this one, so a lot of it had zero transmittance. 32:17.033 --> 32:21.833 Those C-H peaks didn't go all the way, weren't sharp at the 32:21.833 --> 32:23.573 bottom, because they just got cut off. 32:23.567 --> 32:26.097 No light got through the sample. 32:26.100 --> 32:28.300 OK, now if we look at the fingerprint region, there's 32:28.300 --> 32:37.870 Form C, there's Form A, and here's Form B. Now, what you 32:37.867 --> 32:42.497 look for, if you're going to dispute a patent, is the guy 32:42.500 --> 32:48.100 who's violating your patent, making your compound? 32:48.100 --> 32:51.700 So you try to find peaks in here that are characteristic 32:51.700 --> 32:54.670 of your compound, and see whether there's some of that 32:54.667 --> 32:58.227 in what the other guy's trying to sell. 32:58.233 --> 33:00.973 So you look around here and try to figure out where in 33:00.967 --> 33:03.967 this forest of things can we find a peak, even if we have 33:03.967 --> 33:07.597 no idea what the normal mode is, that we'll be able to 33:07.600 --> 33:08.930 distinguish. 33:08.933 --> 33:12.303 And it turns out that those peaks listed below there in 33:12.300 --> 33:16.570 green, blue, and red are ones that occur in the 33:16.567 --> 33:19.127 corresponding form and not in the others. 33:19.133 --> 33:24.633 And in particular, those peaks there, the 665 and the 675 are 33:24.633 --> 33:28.203 very good for distinguishing B and A, right? 33:28.200 --> 33:31.100 So there was a patent dispute that involved, can one 33:31.100 --> 33:37.100 detect 5% of the B, the 675, in the presence of 95% of the 33:37.100 --> 33:38.000 unprotected one? 33:38.000 --> 33:41.300 In which case, they would be violating the patent on B, if 33:41.300 --> 33:43.070 there were 5% of it there. 33:43.067 --> 33:49.567 So this is the legal world and IR being involved in it. 33:49.567 --> 33:52.667 So we've seen here spectroscopy used both for 33:52.667 --> 33:55.367 structure but also for dynamics, 33:55.367 --> 33:58.297 how things are moving. 33:58.300 --> 34:02.030 And we saw it first in electronic spectra, where we 34:02.033 --> 34:05.673 saw the electrons sloshing up and down at a rate that had to 34:05.667 --> 34:08.567 do with the difference in energy of the two orbitals 34:08.567 --> 34:09.667 that are involved. 34:09.667 --> 34:12.767 We've just seen vibrational, and we're going on to nuclear 34:12.767 --> 34:15.867 magnetic resonance, which is at a much lower frequency, 34:15.867 --> 34:19.827 radio frequencies, and involves magnetism which we 34:19.833 --> 34:22.773 haven't discussed yet. 34:22.767 --> 34:24.997 And it involves precession, which we 34:25.000 --> 34:27.400 haven't discussed yet. 34:27.400 --> 34:31.600 But there are problems on the Chem 125 web page that will 34:31.600 --> 34:34.930 help you understand what's involved in precession. 34:34.933 --> 34:38.303 Now, here's a young Michael Faraday, we showed this 34:38.300 --> 34:41.600 picture last year, and he was a chemist, remember? 34:41.600 --> 34:44.500 And he discovered benzene in illuminating gas. 34:44.500 --> 34:46.330 We talked about that last semester. 34:46.333 --> 34:48.303 But that's not all he discovered. 34:48.300 --> 34:52.000 He also discovered magnetic induction, and he invented the 34:52.000 --> 34:55.570 idea of magnetic and electric fields. 34:55.567 --> 34:57.697 He thought they were real, that there were real little 34:57.700 --> 35:00.470 filaments there for these lines of force. 35:00.467 --> 35:03.797 And the idea that you can get magnetism from electric 35:03.800 --> 35:07.270 current and electricity from changing magnetism. 35:07.267 --> 35:10.497 So that's generators and so on. 35:10.500 --> 35:12.700 If you're interested in seeing things about that, here's a 35:12.700 --> 35:16.230 website at Florida State University Magnet Lab, that 35:16.233 --> 35:18.803 tells you things about Faraday and that. 35:18.800 --> 35:22.600 And 30 years later then, Maxwell, who knew math, which 35:22.600 --> 35:26.630 Faraday didn't, built these into the comprehensive theory 35:26.633 --> 35:29.203 of light and electromagnetism. 35:29.200 --> 35:31.700 Now, precession is involved, and you've 35:31.700 --> 35:33.300 seen precession before. 35:33.300 --> 35:42.130 Here's a top, and remember the amazing thing about this is 35:42.133 --> 35:47.703 that if you put it on here it doesn't fall down. 35:47.700 --> 35:48.930 Whoops. 35:50.833 --> 35:55.203 It stays standing up, and that's an amazing thing. 35:55.200 --> 35:57.930 If it's not spinning-- 35:57.933 --> 36:00.473 let me slow it down just a bit. 36:00.467 --> 36:03.267 And now, that's precession, when it goes around like this. 36:03.267 --> 36:07.867 Remember how a top goes like that, the axis goes like this. 36:07.867 --> 36:11.267 And, of course, if it's not spinning, gravity just makes 36:11.267 --> 36:13.067 it fall down. 36:13.067 --> 36:14.967 So why doesn't it fall down? 36:14.967 --> 36:20.897 Why does it fall around rather than falling down? 36:20.900 --> 36:23.470 Now, you can see it better if we use something bigger, so 36:23.467 --> 36:25.167 we'll go to a bicycle wheel here. 36:28.167 --> 36:30.897 And I think I've got that on the next slide. 36:30.900 --> 36:34.030 OK, so we have a bicycle wheel here. 36:34.033 --> 36:36.333 I hang it up on this thing. 36:36.333 --> 36:37.603 There we go. 36:41.000 --> 36:42.230 Whoa, get it hooked. 36:44.400 --> 36:47.300 There we go. 36:47.300 --> 36:48.900 Now, here I'm holding it up. 36:48.900 --> 36:52.330 The strings pulling that way, but its weight, if I let go, 36:52.333 --> 36:53.473 is going to make it fall. 36:53.467 --> 36:55.127 There's no big deal there. 36:55.133 --> 36:57.273 And that shown. 36:57.267 --> 37:00.967 The force down of gravity at the red arrow and up on the 37:00.967 --> 37:04.327 string puts a twist on it, which makes it move right at 37:04.333 --> 37:06.973 the top and left on the bottom. 37:06.967 --> 37:08.727 No big deal there. 37:08.733 --> 37:11.703 But it's different, as you know, if it's spinning. 37:11.700 --> 37:13.330 So let me start spinning here. 37:13.333 --> 37:19.473 [spins bike wheel] 37:19.467 --> 37:21.127 And now when I let go-- 37:21.133 --> 37:24.033 obviously, when I'm holding it there's no torque on it-- but 37:24.033 --> 37:27.533 if I let go, it falls around rather than falling down. 37:30.500 --> 37:35.070 Now, people talk about vectors and right-hand rules... but why 37:35.067 --> 37:38.527 not a left-hand rule, I wonder... and so on. 37:38.533 --> 37:43.273 But it's something else to really understand why this is 37:43.267 --> 37:48.127 doing-- why there's precession in a situation like this. 37:48.133 --> 37:51.373 So normally it would just fall down, but if it's spinning it 37:51.367 --> 37:53.367 falls around. 37:53.367 --> 37:57.067 And Feynman, in his lectures, said something interesting 37:57.067 --> 37:57.567 about this. 37:57.567 --> 38:01.727 He said, many simple things can be deduced mathematically 38:01.733 --> 38:03.303 more rapidly. 38:03.300 --> 38:05.400 They can be really understood in a 38:05.400 --> 38:07.400 fundamental or simple sense. 38:07.400 --> 38:10.870 The precession of a top looks like some kind of miracle 38:10.867 --> 38:13.697 involving right angles and circles, and twists and 38:13.700 --> 38:15.230 right-hand screws. 38:15.233 --> 38:17.533 What we should do is understand it in a more 38:17.533 --> 38:18.503 physical way. 38:18.500 --> 38:21.930 Why does it move around instead of falling down? 38:21.933 --> 38:24.473 So that's what we're going to do here. 38:24.467 --> 38:28.327 And it turns out to have to do with phase again, and the 38:28.333 --> 38:31.203 difference between force and velocity. 38:34.500 --> 38:37.500 So let's think about this. 38:37.500 --> 38:42.400 Let's take a point on the rim of this. 38:42.400 --> 38:49.700 And say... Notice that there's going to be a torque from this 38:49.700 --> 38:53.000 wanting to go down here and being held up here. 38:53.000 --> 38:56.670 And that's transmitted through the spokes to the rim. 38:56.667 --> 39:01.827 So everything above the center feels a force to your right, 39:01.833 --> 39:04.373 and everything below the center feels a force to your 39:04.367 --> 39:05.867 left when I let go. 39:05.867 --> 39:08.497 Everybody with me on that? 39:08.500 --> 39:11.000 So let's take a point on the rim. 39:11.000 --> 39:14.800 Here it feels no force at all, because it's moving neither 39:14.800 --> 39:16.400 right nor left. 39:16.400 --> 39:20.630 As it goes up it gets more and more force to the right. 39:20.633 --> 39:22.173 Everybody with me? 39:22.167 --> 39:24.467 Still more force to the right, more force to the right. 39:24.467 --> 39:28.327 Now less force to the right, less zero, and now it feels a 39:28.333 --> 39:32.933 force to the left as I let go. 39:32.933 --> 39:35.633 So we can make a plot of the force as a function of 39:35.633 --> 39:38.133 position on the rim. 39:38.133 --> 39:42.133 So if it's in the picture on the screen here, when it's 39:42.133 --> 39:46.233 above, the forces is to the right: below, it's to the left. 39:46.233 --> 39:49.503 And this is what the force should look like. 39:49.500 --> 39:52.270 When it's in the front or in the back, there's no force. 39:52.267 --> 39:56.327 When it's above, there's a force to the right, and when 39:56.333 --> 39:57.833 it's below, there's a force to the left. 40:00.400 --> 40:02.970 Now, I'm going to ask you a different question. 40:02.967 --> 40:09.227 Where is the velocity to the right fastest? 40:09.233 --> 40:12.703 Where's the force to the right fastest-- 40:12.700 --> 40:16.170 largest force at what position on the rim? 40:16.167 --> 40:17.467 STUDENT: Top. 40:17.467 --> 40:19.297 PROFESSOR: At the top. 40:19.300 --> 40:22.470 So it'll move the furthest, it goes the fastest when 40:22.467 --> 40:22.827 I let go [clarification: for non-rotating wheel]. 40:22.833 --> 40:24.733 It goes much slower here. 40:24.733 --> 40:26.933 OK, that's fine. 40:26.933 --> 40:28.773 Now I'm asking a different question. 40:28.767 --> 40:34.097 Where is the velocity fastest to the right? 40:34.100 --> 40:36.070 Well, let's start here. 40:36.067 --> 40:38.227 It's beginning to feel a little bit of force to the 40:38.233 --> 40:41.503 right. But if it's rotating, it's still feeling 40:41.500 --> 40:42.300 force to the right. 40:42.300 --> 40:44.500 More and more, and more, and more force to the right, more 40:44.500 --> 40:45.500 force to the right. 40:45.500 --> 40:47.370 Maximum force to the right. 40:47.367 --> 40:50.197 And now less, and less, and less, and less, and less, and 40:50.200 --> 40:52.530 less, and less, and less, until it gets to zero. 40:52.533 --> 40:57.603 But all this time, during this half rotation, that point that 40:57.600 --> 41:00.930 I'm holding is feeling force to the right, and 41:00.933 --> 41:02.173 what does that mean? 41:02.167 --> 41:05.097 It's accelerating to the right. 41:05.100 --> 41:06.930 Everybody with me on this? 41:06.933 --> 41:11.273 So where is its velocity maximum to the right? 41:11.267 --> 41:13.267 STUDENT: Where force is minimum? 41:13.267 --> 41:15.327 PROFESSOR: Suppose I start pushing 41:15.333 --> 41:18.073 somebody on a bicycle, and I keep pushing and pushing. 41:18.067 --> 41:20.467 At the beginning I don't push very hard, then I push real 41:20.467 --> 41:22.397 hard, and then I don't push very hard, and 41:22.400 --> 41:23.730 finally I let go. 41:23.733 --> 41:26.133 Where are they moving fastest, assuming no 41:26.133 --> 41:27.333 friction and so on? 41:27.333 --> 41:27.633 Yigit? 41:27.633 --> 41:28.503 STUDENT: At the very end. 41:28.500 --> 41:29.330 PROFESSOR: At the very end. 41:29.333 --> 41:31.773 All the time I'm pushing I'm accelerating it. 41:31.767 --> 41:35.867 So where is the velocity fastest on this to the right? 41:35.867 --> 41:37.297 Tell me when I get there? 41:37.300 --> 41:38.100 STUDENT: Now. 41:38.100 --> 41:39.030 PROFESSOR: There. 41:39.033 --> 41:43.373 And that's exactly what it does when it moves like this. 41:43.367 --> 41:46.867 And then it's being slowed down, because you're pushing 41:46.867 --> 41:48.297 to the left. 41:48.300 --> 41:52.070 And here it's got zero velocity, you've cancelled it. 41:52.067 --> 41:54.797 And now it starts moving to the left and reaches its 41:54.800 --> 41:57.570 maximum velocity to the left here. 41:57.567 --> 42:01.797 Then it starts slowing down again and has zero velocity to 42:01.800 --> 42:04.730 the left or right here, and then it has its 42:04.733 --> 42:07.303 maximum. So it moves like this. 42:07.300 --> 42:09.570 Isn't that neat? 42:09.567 --> 42:14.097 So it's the difference between force and velocity. 42:14.100 --> 42:17.900 That velocity, you have to integrate force over the time 42:17.900 --> 42:18.770 that's involved. 42:18.767 --> 42:22.667 So if you look at where is the velocity maximum. 42:22.667 --> 42:28.327 It's going to be 90 degrees after the force is maximum. 42:28.333 --> 42:30.673 So it's going to be the maximum velocity 42:30.667 --> 42:32.997 when it's in front. 42:33.000 --> 42:34.270 Velocity to the right. 42:34.267 --> 42:37.797 And as it keeps going, it then slows down. 42:37.800 --> 42:40.530 And it has its maximum velocity to left at the 42:40.533 --> 42:41.773 bottom [correction: back], and then it comes back up. 42:41.767 --> 42:45.527 So there's this 90 degree phase lag between the periodic 42:45.533 --> 42:47.403 force and the velocity. 42:47.400 --> 42:50.070 And that's why it falls around. 42:50.067 --> 42:52.767 So the velocities look like that. 42:52.767 --> 42:55.467 So there's a 90 degree phase lag, and it falls around 42:55.467 --> 42:56.867 rather than falling down. 42:56.867 --> 43:00.297 Now, you've heard of nuclear spin. 43:00.300 --> 43:04.070 So these protons [correction: nuclei], ones that have an odd 43:04.067 --> 43:11.567 atomic weight, either an odd number or an odd weight, we 43:11.567 --> 43:12.867 know that they spin. 43:12.867 --> 43:15.667 And the reason we know that they spin is that when they're 43:15.667 --> 43:19.267 in a magnetic field they precess. 43:19.267 --> 43:21.197 And how do we know that they're-- 43:21.200 --> 43:23.500 when you put the force on them. 43:23.500 --> 43:26.270 Obviously, if there's no force, this doesn't precess, 43:26.267 --> 43:28.327 it's when you try to twist it. 43:28.333 --> 43:33.103 So if this is a magnet that's spinning, and you put it in a 43:33.100 --> 43:37.000 magnetic field that tries to twist it, then it goes around 43:37.000 --> 43:39.070 and precesses. 43:39.067 --> 43:43.027 So that's how you know that these nuclei are magnetic. 43:43.033 --> 43:45.333 Hydrogen fluorine and phosphorous, those are the 43:45.333 --> 43:48.203 common isotopes, but for carbon and oxygen they're 43:48.200 --> 43:50.200 uncommon isotopes. 43:50.200 --> 43:56.830 And this is how fast they precess in a magnetic field. 43:56.833 --> 44:01.303 They precess like this, and you can measure the frequency 44:01.300 --> 44:03.230 of their going around and around, and we'll mention that 44:03.233 --> 44:04.173 in just a second. 44:04.167 --> 44:07.397 And if a field happens to be 23.5 kilogauss, which is 44:07.400 --> 44:11.170 not an uncommon field, then protons go around the fastest, 44:11.167 --> 44:14.627 100 million times a second. 44:14.633 --> 44:17.603 Fluorine is almost as fast, but phosphorous, carbon, 44:17.600 --> 44:21.370 oxygen are less fast. So that, just to give you-- 44:21.367 --> 44:26.067 Connecticut Public Radio broadcasts at 90.5 MHz, 44:26.067 --> 44:32.197 and WCBS is at 0.88 MHz, 880 kHz. 44:32.200 --> 44:33.800 So these are radio frequencies. 44:33.800 --> 44:37.800 Now, the electron also spins, but it's way off scale up at 44:37.800 --> 44:40.700 the top, 66,000 MHz. 44:40.700 --> 44:46.100 It's a much more powerful magnet than the nuclei. 44:46.100 --> 44:49.870 OK, so a megahertz multiplied by 3 and times 10-5th 44:49.867 --> 44:51.467 is wave numbers. 44:51.467 --> 44:54.997 Remember, in IR we talked about frequencies in wave 44:55.000 --> 44:57.970 numbers, how many waves in a centimeter. 44:57.967 --> 45:02.167 But the radio frequencies are very, very, very 45:02.167 --> 45:04.767 slow compared to that. 45:04.767 --> 45:07.927 10-5th slower. 45:07.933 --> 45:11.833 You can also talk about it in K degrees. 45:11.833 --> 45:15.703 And 100 MHz then, where the proton resonates in this 45:15.700 --> 45:20.030 frequency, is equivalent to 0.01 k. 45:20.033 --> 45:24.703 And it's quantized, so that the direction of the magnetic 45:24.700 --> 45:29.630 field is either more or less with the applied field, or 45:29.633 --> 45:32.103 more or less against the applied field. 45:32.100 --> 45:33.770 But it's not like a compass. 45:33.767 --> 45:36.527 It's not like you can have any angle and different energies 45:36.533 --> 45:37.273 for each angle. 45:37.267 --> 45:39.097 It can either have this or that. 45:39.100 --> 45:41.270 That's quantization of spin. 45:41.267 --> 45:43.997 Actually, quantum mechanics is much easier to do with spin, 45:44.000 --> 45:47.170 because you can only have two values, where for position or 45:47.167 --> 45:49.297 energy, you could, in principal, have any value. 45:54.133 --> 46:02.473 The equilibrium ratio of the up to down is 1.0003. 46:02.467 --> 46:10.827 So that means that if you have 200,000 nuclei, there are 46:10.833 --> 46:14.803 three more pointing up in the favorable direction than 46:14.800 --> 46:15.870 pointing down. 46:15.867 --> 46:19.867 It's really, really wimpy, the Boltzmann factor, the energy 46:19.867 --> 46:23.167 difference between those. 46:23.167 --> 46:28.497 And O-17 occurs at 6% in natural abundance and C-13 at 46:28.500 --> 46:33.430 1%, but these others, like protons, are 99.98%, and only 46:33.433 --> 46:35.973 0.02% deuterium. 46:35.967 --> 46:41.827 OK, now, this is a really neat concept, the rotating frame. 46:41.833 --> 46:44.633 And let me do this and then I'll let you go, because it's 46:44.633 --> 46:46.873 a holiday coming up. 46:46.867 --> 46:50.297 So there's the applied magnetic field, and remember 46:50.300 --> 46:54.770 we said that the nuclear field, the axis about which 46:54.767 --> 46:57.997 it's spinning, can either be more or less up, or more or 46:58.000 --> 46:59.670 less down but at a particular angle. 46:59.667 --> 47:01.927 So suppose it's like that. 47:01.933 --> 47:04.573 And it precesses because it's spinning. 47:04.567 --> 47:06.967 And the rate of precession in that field we just talked 47:06.967 --> 47:11.997 about is 100 MHz, that's how fast it goes around. 47:12.000 --> 47:15.770 So notice that that precessing proton has a 47:15.767 --> 47:18.267 constant vertical field. 47:18.267 --> 47:19.897 That doesn't change as it precesses, 47:19.900 --> 47:21.230 the vertical component. 47:21.233 --> 47:26.273 But the horizontal component goes around like that. 47:26.267 --> 47:29.367 And that looks neat, because if that's going around at 100 47:29.367 --> 47:33.967 MHz, that's going to be like an antenna, and it'll 47:33.967 --> 47:35.867 generate light that's coming out. 47:35.867 --> 47:39.227 It's like the vibration of C=O, charge 47:39.233 --> 47:40.573 going back and forth. 47:40.567 --> 47:42.567 You see it going back and forth as it is like that. 47:42.567 --> 47:45.497 So it looks like we might be able to detect that 47:45.500 --> 47:47.900 broadcasting. 47:47.900 --> 47:50.100 So will it generate a 100 MHz 47:50.100 --> 47:51.630 radio frequency signal? 47:51.633 --> 47:52.873 No. 47:52.867 --> 47:55.697 It would if you just had one proton. 47:55.700 --> 47:58.170 But of course you have a mole of protons, or at least a 47:58.167 --> 48:01.267 millimole or something of protons. 48:01.267 --> 48:03.927 And so some we'll be here, some will be here, some will 48:03.933 --> 48:06.073 be here, some will be here, some will be here. 48:06.067 --> 48:07.997 And if you look at the horizontal component-- 48:08.000 --> 48:11.130 although the vertical components all add-- 48:11.133 --> 48:16.133 the horizontal components that are changing in time cancel. 48:16.133 --> 48:17.373 Everybody see that? 48:17.367 --> 48:21.027 So you don't get any net signal coming out. 48:21.033 --> 48:26.803 So the horizontal fields cancel, but there's a trick 48:26.800 --> 48:28.400 that allows you to do it. 48:28.400 --> 48:32.470 And that is, suppose that instead of us sitting here and 48:32.467 --> 48:35.997 watching them precess, suppose we orbit 48:36.000 --> 48:39.330 around them at 100 MHz. 48:39.333 --> 48:42.633 We would certainly get dizzy if we went around them at a 48:42.633 --> 48:43.533 100 MHz. 48:43.533 --> 48:47.373 But what would a proton look like if we were going around 48:47.367 --> 48:49.927 it at 100 MHz? 48:49.933 --> 48:53.133 And it's going around at 100 MHz? 48:53.133 --> 48:55.433 It would look like it's standing still. 48:55.433 --> 48:59.103 So that makes it much easier to solve the problems, to work 48:59.100 --> 49:02.270 in a rotating frame so that they're not moving around from 49:02.267 --> 49:03.867 our point of view at 100 MHz. 49:03.867 --> 49:05.327 They're just standing still. 49:05.333 --> 49:10.003 So we look at these and they're just standing still, 49:10.000 --> 49:13.230 as if there were no applied field. 49:13.233 --> 49:17.903 Now we take a very weak magnetic field that we 49:17.900 --> 49:22.000 generate, a radio frequency field, that's horizontal. 49:22.000 --> 49:25.530 In our frame it's horizontal, pointing out that way. 49:25.533 --> 49:29.773 Now, of course, in truth, it's going around at 100 MHz. 49:29.767 --> 49:32.797 But from our point of view, it's just sitting there. 49:32.800 --> 49:35.630 And from our point of view, there is no applied field, 49:35.633 --> 49:38.433 because our going around canceled that. 49:38.433 --> 49:42.773 So what will those protons do as we look at them? 49:42.767 --> 49:46.897 They'll precess around that field. 49:46.900 --> 49:48.670 See what I'm saying? 49:48.667 --> 49:51.167 From our point of view they'll just be this one weak little 49:51.167 --> 49:56.097 magnetic field, and it'll appear in a constant position 49:56.100 --> 50:00.030 relative to us, because we're whipping around so fast. And 50:00.033 --> 50:03.733 so these things will precess around that. 50:03.733 --> 50:06.303 But they now they make all different angles, because 50:06.300 --> 50:08.270 they're quantized with respect to that one. 50:08.267 --> 50:10.227 They're quantized with respect to the vertical field. 50:10.233 --> 50:11.703 So they'll precess like that. 50:11.700 --> 50:14.200 That particular one would go, and all the others would go 50:14.200 --> 50:15.930 precessing at the same rate. 50:19.200 --> 50:22.570 So that's about 0.1 MHz rather than 100 MHz, so 50:22.567 --> 50:26.627 this is 1000 times weaker field. 50:26.633 --> 50:28.103 But how long do we do it? 50:28.100 --> 50:31.000 How long do we put this field on? 50:31.000 --> 50:37.900 Just long enough to make them go 90 degrees, like that. 50:37.900 --> 50:42.770 So now they're pointing out toward us like this. 50:42.767 --> 50:45.097 But, in truth, they're not statically 50:45.100 --> 50:46.170 pointing out toward us. 50:46.167 --> 50:49.027 They're going around at 100 MHz, because we're going 50:49.033 --> 50:51.303 around at 100 MHz. 50:51.300 --> 50:57.200 And now there's a net field that's oscillating in time, if 50:57.200 --> 51:01.600 we go back and take ourselves back to the laboratory, and 51:01.600 --> 51:04.130 not spin around like that or orbit like that. 51:04.133 --> 51:07.003 We see this whole set going around like that. 51:07.000 --> 51:11.130 So if we put in this thing called a 90 degree pulse, now 51:11.133 --> 51:14.103 we can hear these things broadcasting. 51:14.100 --> 51:16.270 And what will they tell us? 51:16.267 --> 51:19.497 They'll tell us how strong the torque is. 51:19.500 --> 51:21.570 I didn't do that here, but let me do it. 51:21.567 --> 51:27.397 [spins bike wheel] 51:27.400 --> 51:30.300 Now, if this is a magnet, I can twist it by putting a 51:30.300 --> 51:33.400 magnet field perpendicular to it. 51:33.400 --> 51:39.270 Now, suppose I made the field that's perpendicular stronger, 51:39.267 --> 51:40.867 to twist it harder. 51:40.867 --> 51:43.297 So that's how fast it's precessing. 51:43.300 --> 51:48.270 What happens if I put this wrench on? 51:48.267 --> 51:51.297 Is it going to go faster or slower, if I hang it on here? 51:55.367 --> 51:57.597 Faster or slower? 51:57.600 --> 51:59.100 Let me speed it up again here. 51:59.100 --> 52:00.900 [spins bike wheel] 52:00.900 --> 52:02.870 Incidentally, that's another question. 52:02.867 --> 52:07.327 If I go faster, if I make it spin faster, will it precess 52:07.333 --> 52:08.573 faster or slower? 52:11.233 --> 52:13.503 It precesses only because it's spinning. 52:13.500 --> 52:15.400 If it weren't spinning it wouldn't precess. 52:15.400 --> 52:20.970 So suppose I spin faster, does it go faster or slower? 52:20.967 --> 52:21.327 Faster? 52:21.333 --> 52:23.803 It should go faster? 52:23.800 --> 52:27.430 No, because the amount of time that's involved going here, 52:27.433 --> 52:29.973 that we're pushing is shorter if it's spinning faster. 52:29.967 --> 52:31.327 So in fact, it goes slower. 52:31.333 --> 52:32.133 Isn't that neat? 52:32.133 --> 52:37.203 And now if I twist harder, it goes faster. 52:37.200 --> 52:39.000 See how it's going faster now? 52:39.000 --> 52:40.870 And then it slows down if I take that off? 52:43.733 --> 52:46.473 It's not an ideal demonstration, I grant you. 52:51.500 --> 52:54.930 In fact, it goes slower if you-- 52:54.933 --> 52:58.003 pardon me, it goes faster if you put more torque on and 52:58.000 --> 52:59.800 it's spinning at the same rate. 52:59.800 --> 53:03.070 So that's what these problems are, for you to think about. 53:03.067 --> 53:07.267 So I'll just finish in a second here. 53:07.267 --> 53:09.867 So we went into the rotating frame long enough to get into 53:09.867 --> 53:13.327 90 degrees, and now we go back, and now we see a signal 53:13.333 --> 53:16.103 coming out at 100 MHz. 53:16.100 --> 53:19.000 So that's how you do the NMR experiment. 53:19.000 --> 53:22.370 They don't like that, and that's the signal you see. 53:22.367 --> 53:26.267 So it's 100 MHz in the laboratory frame. 53:26.267 --> 53:30.897 Until they relax and go back to where they started, then 53:30.900 --> 53:33.000 the signal goes away. 53:33.000 --> 53:36.100 So that's what we're going to talk about some more. 53:36.100 --> 53:37.370 Have a good break.