Draw all of the possible spin states to explain why a hydrogen...

Question

Draw all of the possible spin states to explain why a hydrogen with four neighbors appears as a quintet (quint, five peaks).

Accepted Answer

Welcome back everyone to another video draw all the possible spin states to show how the presence of five neighboring hydrogens results in a six or six peaks signal for hydrogen. We're going to draw a table with our possible spend states and the ratio to get our ratio, we have to recall the pascal triangle, we're going to add one, then we're going to add one along our diagonal. And now let's add our numbers. One plus one is 21 plus two is 31 plus two is another three. Now one plus three is 43 plus three, gives us 63 plus one, gives us another four. Then we add one, we want to have a total of six peaks. We have five in our final row. So we need to add another one, one plus four is five or plus six is 10 or plus six is another 10, 1 plus four is five. And then we have one. So this would be the ratio of our peaks 1 to 5 to San another 10 5 and one. And now we need to think about the possible spin states right now having six different spin states essentially tells us that we will need to add five arrows. Now, let's understand why this is the case. Well, essentially we can have zero down one down, two down, three down pore down or all five spend states down. That makes sense, right? Because we have sat or a total of six peaks, that means we're going to look at our possible combinations. So what if we have zero down? Well, essentially that means we're going to add five spin states winding up. So let's do that 12345, right? And we want to make sure that our diagram is symmetrical. So for five down, we will just flip them right? And we are going to draw five down, 12345, well done. And of course, based on our ratio, we only have one possibility it's really related to combinatorics right. Now, if we look at one down, we can place it as our first arrow making the remaining four pointing up, we can place it as our second arrow. So let's say we have up down and then up, up and up. Now we can place it as our third arrow. So we would have up, up down, up and up. Now we can place it as our fourth arrow and we will keep going. So one, 23, now the fourth one is down, the fifth one is up and our final possibility is to place it as our final arrow. So the down state will be our fifth position. So 1234 and five is pointing down. And now we want to get a symmetrical view for four down, right? We got all five. Now, we need to get 544 down. So if we had one pointing down, now it will be pointing up and we will have four down. So 1234. Now let's continue. Now, we will have down, up, down, down down. Now, we will have down down, we will have that up as our third position. Now, we will have down, down, down, up and down and the final one will be down, down, down, down and up. So we got all five and now we have to continue with some total, right? So two down. Ok. So let's add the first one pointing down and the second one pointing down. So that three of them are pointing up. Now, let's keep the first one fixed and let's just keep changing the position of the second one. So let's say it's down, then we have up down and then we will have up and up. Now the first one is fixed. So it's still down. But now we have up, up and we're moving this one to the fourth position. So it's down and up and finally down, up, up, up and down, right. So now we have to change the position of the first one. So let's suppose that we have the first one pointing up and then both of them are down so that two more are pointing up and now let's keep the second one fixed and let's keep changing the position of the third one. So we will then have up, down, up, down, up and then we will have up, down, up, up and down. Now we need three more, right? Because we have 1234567. Now let's say that first of all, we have both of them up. So let's draw up up and now we can add both of them pointing down immediately. So down, down, up, let's keep the third one thick. So we will have up, up, down, up and down and finally, we are done with this one. So we just need to add, we pointing up, up, up up and two of them pointing down. So we are out of disabilities and now we just want to make a symmetrical sketch for three down, essentially, if we have two of them pointing down, now we will have up up and three down if we have down. Now, we will have up, up, becomes down and on. So let's fill it out, up, down, up, down and down. Now we will have up, down and down, up and down. For the next one that would be up, we have done will be down and the next one will be up. Now for the next one, the first one was up. So now we will have down, up, up, down, down for the next one that'd be down, up, down, up and down. Now, let's continue. We have four more. So we are almost done. So the first one was up, now it be down, up, down, down, up, then we have down, down, up, up, down, down, down, up, down, up and finally down, down, down, up, up and that would be it. We have got our spin states. Thank you for watching.

Draw all of the possible spin states to explain why a hydrogen with four neighbors appears as a quintet (quint, five peaks).

Key Concepts

Spin States and NMR Spectroscopy

Coupling and Multiplet Formation

Pascal's Triangle in NMR

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