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

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SUMMARY

The discussion centers on the relationship between hydrogen coupling intensity in H-NMR and Pascal's triangle. It confirms that the relative intensities of coupling patterns, such as quartets, can be predicted using combinatorial mathematics, specifically the binomial coefficients represented in Pascal's triangle. The example provided illustrates how the combinations of up and down spins correspond to the coefficients, validating the connection between probability and NMR intensity patterns.

PREREQUISITES
  • Understanding of NMR (Nuclear Magnetic Resonance) spectroscopy
  • Familiarity with hydrogen coupling and spin states
  • Basic knowledge of combinatorial mathematics and Pascal's triangle
  • Experience with interpreting NMR spectra
NEXT STEPS
  • Study the principles of NMR spectroscopy in detail
  • Learn about hydrogen coupling and its implications in molecular structure
  • Explore combinatorial mathematics and its applications in chemistry
  • Investigate how to interpret different NMR patterns and their significance
USEFUL FOR

Chemistry students, particularly those in introductory NMR courses, educators teaching spectroscopy, and researchers interested in the mathematical foundations of NMR analysis.

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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 [tex]{3 \choose 0} = 1[/tex], for 2 up spins and 1 down spin would be [tex]{3 \choose 1} = 3[/tex], and so on, right?


My textbook just states the fact and doesn't explain why.
 
Chemistry news on Phys.org
Yes, that's exactly the reason.
 

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