Nuclear shielding

- [Voiceover] Before we get into nuclear shielding, we need to review some physics. So let's say we have current in a loop of wire. So on the left is our loop of wire. And let's say that current is going in this direction. So in physics, you represent current by I. And let's say we're looking down on this loop of wire. And so over here this would be the top view. If we're looking down, current would be going in a clockwise fashion. So, around this loop. In physics, current is thought of as being moving positive charges. So even though that's not really what's happening, but the moving charges, a moving charge creates a magnetic field. And so the current's going to create a magnetic field. We can figure out the direction of the magnetic field by using a variation of the right-hand rule. So if you think about our right hand being right here on our loop, we point our thumb in the direction of the current. So the current's going to the left at this point so we point our thumb to the left. And this is going to be the back of my right hand here. So if you're using your right hand, there's only one direction for your fingers to curl. And in this loop your fingers would curl down. So in this loop, your fingers curl down. And that's the direction of the magnetic field created by the current. And so from a top view, the magnetic field is going into the page. And if you're looking at it from this orientation, the magnetic field would be going down. So a magnetic field, represented by B here, is created by current in our loop of wire. In reality, it's the electrons that are moving. And since the electrons are negatively charged, electrons move in an opposite direction from the current. So the electrons are actually going around this way. So if you look at a top view, the electrons would be going around counter-clockwise. And so this is important, the idea of moving electrons creating a magnetic field. Now let's look at a situation where we have a proton involved. So proton NMR. In the last video, I talked about how in proton NMR you apply an external magnetic field. So this vector here represents our external magnetic field, B naught. And in the presence of an external magnetic field, electron density around our proton circulates. So if you think about this as being a proton, and you think about some electron density going around the proton, so here's some electron density that's circulating, the electron density that's circulating creates and induced magnetic field. So if the electrons are moving this way, you could think about this situation here. And the induced magnetic field would go down. So the induced magnetic field opposes the applied magnetic field. So here's the induced magnetic field. I'm going to use a different color here for that. So this is the induced magnetic field. Which is in a direction, this vector is in a direction opposite to this magnetic field. Alright, this is an effect called diamagnetism. And so the proton right here experiences a smaller overall magnetic field. So let's think about that. So if we have an applied magnetic field of a certain magnitude, so B naught, and the circulating electron density produces an induced magnetic field that opposes the applied field, the proton is going to feel an overall smaller magnetic field. So let me go ahead and draw that in here. So the proton experiences a smaller magnetic field. Which I will call B effective. So the effective magnetic field that the proton experiences. Or you can think about it like this. If you start the effective magnetic field experienced by the proton to be equal to the original magnetic field, the applied magnetic field, minus the induced magnetic field. And so this proton, this nucleus, is shielded from the external magnetic field by electrons. So this proton here is said to be shielded. And if you increase the electron density around the proton, you would therefore increase the shielding of that proton. So shielding has the effect of lowering the effective magnetic field experienced by the proton. So let's think about two examples now. So first let's start with just a bare proton. So over here we have just a proton all by itself. It's completely deshielded. There are no electrons around it. Let me go ahead and write that. So we have a completely deshielded proton here, because there are no electrons. Therefore this deshielded proton is going to experience the full effect of the applied magnetic fields. Alright, so, and we know from the previous video that the applied magnetic field, the external magnetic field, causes your alpha and your beta spin states to be separated by a certain distance here. So here's the alpha spin state, and here's the beta spin state. And this would be a certain energy difference between our two spin states. So this is the energy difference right here. Now let's move to the example on the right. So the example on the right, this proton here is a proton in a molecule, it's shielded. There's electron density around this proton. Alright, so this is a shielded proton. Let me go ahead and write that. Shielded proton. And we've just talked about what that means. A shielded proton has circulating electron density that creates a magnetic field that opposes the applied magnetic field. And so the proton feels a smaller effective magnetic field. So we decrease the magnetic field experienced by this proton. In the previous video, I talked about what happens when you have a decreased magnetic field. The magnetic field strength corresponds to the energy difference between the alpha and the beta states. So if we're decreasing the magnetic field compared to the example on the left, we're going to decrease the energy. So decreasing the magnetic field decreases the energy difference between the alpha and the beta states. So I can go ahead and write that. And I can show the alpha and the beta states here. And I can show a smaller gap between them, right? So there's a decrease in energy. And we know that that energy difference, E is equal to h nu. So if we decrease the energy we're going to decrease the frequency. Alright, so the energy and the frequency are directly proportional. So if you decrease the energy difference, you decrease the frequency. So therefore, a shielded proton absorbs at a lower frequency than a deshielded proton. So a deshielded proton, the energy difference would correspond to a higher frequency. Because there's a larger difference in energy. So that's what we need to think about when we're looking at an NMR spectrum. And so, I just went ahead and drew a, just, generic NMR. This isn't a real NMR. We're just trying to think about this example of these two protons here. So we have one spectrum up here. So this would be, let me go ahead and mark this. So this would be a deshielded spectrum. And then this one down here represents the shielded spectrum. Again, not a real NMR spectrum, just helping to think about what's happening here. And, for the example on the left, for the deshielded protons, let's think about this really fast. So as you go to the left on an NMR spectrum you get more and more deshielded. And if you're more and more deshielded, you experience a greater magnetic field. So a greater magnetic field. A greater magnetic field corresponds to a greater difference in energy and a greater difference in energy corresponds to a higher frequency absorbed. So a higher frequency absorbed here. And so therefore, as we go to the left, we're talking about an increasingly deshielded proton, and this signal that appears at your NMR right here. So this is the signal for this deshielded proton. We're talking about a high frequency signal. So moving to the left on an NMR spectrum, we're talking about higher frequency signal. Alright, let's think about the shielded proton over here on the right. So we're thinking about the shielded proton now. And as you move to the right on your NMR spectrum, so we're moving to the right on our NMR spectrum, we're getting more and more shielded. So this signal is the signal for this proton. So it's more shielded than the one on the left. So as we move to the right you're talking about increasing shielding. And increasing shielding decreases the effective magnetic field. Decreasing the effective magnetic field decreases the energy difference between the alpha and the beta states. And therefore it decreases the frequency absorbed. Alright, so as you move to the right you're talking about a lower frequency signal. So as you move to the right, you're talking about a lower frequency. Alright, so this is the idea of FT NMR, which I briefly introduced in the previous video. So in FT NMR, you're holding the external magnetic field constant. And you're hitting the sample with a short pulse that contains a range of frequencies. And so these frequencies correspond to the energy differences. So one frequency might correspond to this energy difference, and when the proton goes back to the lower energy states, the NMR machine gives you this signal. Another frequency might correspond to this energy difference. And once again the NMR would give you this signal. And so that's the idea about FT NMR. You do all this at once and the NMR machine gives you your NMR spectrum. For older NMRs you would hold the frequency constant and vary the strength of the magnetic fields. And for older NMRs it turns out that as you go to the right, you needed a higher magnetic field strength. And so we called this upfield. So this would be a shift upfield if you will. And as you go to the left on an NMR spectrum, you needed a lower magnetic field strength. And so this is called downfield. So upfield and downfield are two terms that you might hear. And they're older terminology that relate to an older kind of NMR, but you'll still hear them. And I'm sure I will use those terms sometime as well. So in this video, we've talked about two protons with different amounts of shielding. So a completely bare proton, completely deshielded, and a shielded proton here. So two protons with different amounts of shielding are in two different environments. And we get two different signals. Alright, two different signals, and two different, having different frequencies on our NMR. So if you have two protons in the same environment, you should only get one signal. And we'll talk more about this in the next video.