MULTIPLICITY. SIGNAL SPLITTING

When one nucleus is influenced by another nucleus with spin quantum number I0, the two nuclei are said to be coupled, both will show 2 lines instead of 1 line for each nucleus.

                   

 The reason is that the field caused by H_x can be parallel or antiparallel so the H_a can experience not only the applied field but also combination of both fields.

 One signal absorbs at higher field (if H_x is parallel) and one signal absorbs at lower field (if H_x is antiparallel). The two lines are observed for each nucleus. This is called spin-spin splitting. The signal of H_a is split into 2 peaks (doublet) because there is spin-spin coupling between nonequivalent protons (H_a and H_x).

 In order to obtain the signals, the B₀ will be adjusted to maintain the resonance conditions, either lower or higher field than without H_x.

 Each peak of the doublet has nearly equal area and is half in the absence of H_x because the population of H_a in the two spin states are nearly equal according to the Boltzmann Distribution.      - Since H_a and H_x is split by each other, the distance between 2 lines of both H_a and H_x signals is equal.      - If the two nuclei are only neighbors, then their signals are 2 lines (doublet).

 The number of line splitting can be depicted by using the following equation;

multiplicity  =  2nI + 1, where n is no. of neighboring protons.

nuclei	I	multiplicity
1H	1/2	n + 1
2H and 14N	1	2n + 1
35Cl	3/2	3n + 1

Since the spin quantum no. (I) of ¹H is 1/2, therefore,

multiplicity  =  2n + 1

Consider these examples,

Splitting patterns for a proton with 0, 1, 2, and 3 equivalent neighboring protons