Why does coupling intensity in H-NMR correspond to Pascal's triangle?

AI Thread Summary
In the discussion about NMR (Nuclear Magnetic Resonance) in a first-year college chemistry class, participants highlight the connection between hydrogen coupling and Pascal's triangle. The relative intensities of signals in NMR are influenced by the probabilities of different spin states, which can be represented using combinations from Pascal's triangle. For example, in a quartet, the combinations of up and down spins correspond to the coefficients in Pascal's triangle, illustrating how the number of ways to arrange spins affects the observed signal intensities. This relationship emphasizes the probabilistic nature of spin states in NMR, which is not always clearly explained in textbooks.
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All right, my 1st-year college chemistry class is just beginning NMR, and I really have no clue what's going on. But what caught my eye was how the relative intensities in hydrogen coupling is roughly predicted by Pascal's triangle. Is this because of probability?

For a quartet, the number of combinations for 3 up spins and 0 down spins would be {3 \choose 0} = 1, for 2 up spins and 1 down spin would be {3 \choose 1} = 3, and so on, right?


My textbook just states the fact and doesn't explain why.
 
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Yes, that's exactly the reason.
 

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