Rule N+1

Details
Nuclear Magnetic Resonance (NMR)
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From the above discussion it can be deduced that a proton produces a signal with a number of peaks one unit greater than the number of neighboring hydrogens. In the following image we can see the peaks produced by a hydrogen $H^b$ when coupled with a number of variable hydrogens $H^a$

coupling-spin-spin-05

The intensity of the peaks of a signal are given by Pascal's triangle (Tartaglia)

pascal-triangle

Two considerations must be taken into account when applying the N+1 rule:

  • In molecules of the type $A-CH2^{a}-CH2}^{b}-CH2}^{a}-A$ the $H^b$ protons appear as a quintuplet.
  • In molecules of the type $A-CH_2-CH_2-A$, the four protons are equivalent and give a singlet.