Draw a diagram like the one shown in Figure 14.12 to predict

Question

a. the relative intensities of the peaks in a triplet.

Accepted Answer

Welcome back everyone to another video Joy diagram showing the different ways in which the magnetic fields of the protons align for a sex that showing the relative intensities of the peaks. First of all, we're given sex stat and we have to recall the M plus one rule according to the M plus one rule. If we equate it to six. As given to us, we get the number of neighboring hygen N so N is equal to five. And this means that we are considering five arrows for the magnetic field, they might be pointing up or down. And our next step is to understand how many ways we can align them, we can align all of them up, all of them down, one, pointing up four, pointing down and so on. So we can either use Pascal's triangle or we can use the formula for combinations without her petition. The total number of elements is five. We have five arrows. G let's label K as the number of arrows pointing down can be zero arrows pointing down 1234 or five, right? Meaning we can have 01234 or five arrows pointing down in a set of five arrows. So we want to calculate combinations with N of five and K of zero, we can use a calculator and we get one. Now what if we have a total of five arrows and only one is pointing down. If we calculate that we get five, meaning there are five combinations, then we calculate C five comma C, we get some, there are 10 combinations to distribute five arrows such that two are pointing down. Then symmetrically we get C five comma three, which is equal to 10 C five comma four, which is equal to five in C 55. This gives us one. So this is the ratio of intensities. And now we simply want to draw these combinations. So the first combination that we want to draw is five arrows zero, pointing down, meaning all of them must be pointing up. So one to you, we four and five and this is the only possible way, right? Because it says a one. Now, for the second part, we want to draw five arrows such that one is pointing down and there are five ways. So we're going to draw five arrows such that one of them is pointing down. So we can draw four arrows in a row pointing up and one of them at the end pointing down. Now we can draw three arrows pointing up the fourth one pointing down and the final one pointing up. So we can just shift that arrow pointing down until we reach position. Number one, let's do that up, up, down, up, up, then we have up, down, up, up and up and eventually our final combination is to have down, up, up, up and up. So we have listed five possible combinations. Now, we have 10 possible combinations where two arrows must be pointing down. So let's begin with three arrows pointing up and two pointing down. So up, up, up and then two arrows pointing down. Now, it might be confusing because there are a lot of ways. So let's keep the final arrow pointing down and let's keep shifting. The fourth arrow is pointing down at position number four. Now let's shift it or move it to the left. So we have up h down, up him down, well done. Now we're going to move it to position number two, we're going to get up, down, up, up down and finally, we're going to move it to position number one. So we're going to get down three of them up and the final one is going to point down well done. Now, from here, we're going to look at the first arrangement and we are going to move both of our arrows pointing down to the left. So where we can draw a combination where we have up, up, down, down up. So we have five, we need five more. What is the next way while we can keep the fourth arrow in a fixed position and just keep moving the third arrow. So we're going to get up. Now, we move it, we get down, up, down, up. Now, once again, we can move it right. And we are going to get down, up, up, they have down and up. We have 1234567 total. Now, our next strategy is to move both of these arrows pointing down once again. So we will have one another way to combine them, right. So essentially, if we had arrows three and four pointing down, now we are moving them to the left and we will have arrows two and three pointing down. So up down, down, up, up right. Now, from here, we have to consider alternative possibilities. We can now simply keep error number three fixed can only move arrow number two. So if we move arrow number two, we're going to get down, up, down, up and up. And finally, we're going to get two arrows down. So down, down, up, up and up. So we have 123456789, 10, we have all of them well done. Now, the other side of our diagram will be symmetrical. What does that mean? Well, essentially we simply want to reflect those. So we are going to draw opposite to what we are seeing on the left side. So if we start with our next column, if we label columns, 12 and three, notice that the ratio of peaks is 15 and 10. So we can just write 15 and some, the next column is going to have 10 combinations to get those combinations. We simply want to look at the previous column and we want to flip our arrows. So if we had three pointing up, now we're going to have three pointing down and those that we're pointing down are now going to be pointing up, we had up up. So now they're going to be down, down, down, it's going to be up, up is going to come down and down is going to become up well done and we can keep doing this. So up down, it's going to become down, up, up, up is going to become down, down, down is going to become up for the next one down, flips to up, then we have three of them up. So they're going to become down, down, down and the final one becomes up. Now we have up, up, that'll be down, down, down, down is going to become up and up. And the one that was up is now going to point down, then we have down, up, down, up and down, up, down, down, up and down, eventually down, up, up, down and down, up, down, up, down and down. And then we have up up and three of them down. Our next step is to have five combinations we can use the same strategy if we had four of them pointing up. Now we're going to draw four of them pointing down and flip the final one. Now it's going to point up, then we had three pointing up. Now they're going to point down, then we have two pointing up. They will now be pointing down. The middle one is going to be pointing up or the fourth combination down at and then we have three of them pointing down and the final one will have up wet, fall down arrows. Oh, well done. Our final one, which is one in intensity, we have five arrows pointing down. So 1234 and five arrows pointing down. Great job. We have the file diagram and we can conclude the video. Thank you for watching.

Draw a diagram like the one shown in Figure 14.12 to predict
a. the relative intensities of the peaks in a triplet.
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Key Concepts

Nuclear Magnetic Resonance (NMR) Spectroscopy

Spin-Spin Coupling

Peak Intensity and Integration

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