between the component peaks of each doublet is the same and is known as the coupling constant JAX
usually measured in Hz. It should be noted that J is independent of the applied field whereas the
chemical shift difference between HA and HX (∆ν), measured between the mid-points of the doublets, is
directly proportional to the strength of the applied field. A shorthand notation for the appearance of this
spectrum is 'AX' and it is classed as a first-order spectrum. This treatment is readily extended to
adjacent groups with two or more protons (i.e. methylene and methyl groups). The number of peaks in a
multiplet is determined by the number of protons in the adjacent group n and is simply n + 1.
Furthermore, protons on the same carbon atom do not 'split each other' unless free rotation is hindered
or there is an adjacent centre of asymmetry. Such protons, and those which are adjacent but have the
same chemical shift, are said to be equivalent. (N.B. in some instances this may not be the case, but
further discussion is beyond the scope of this book.) The intensity ratios within a multiplet follow the
coefficients of the binomial expansion of (a + b)n, or Pascal's triangle, and are a result of the statistical
weighting given to the various possible combinations of the two spin states for the protons in the
adjacent group. The total area of a multiplet is proportional to the number of protons producing the
absorption, thus the triplet and quartet arising from an ethyl group have areas in the ratio 3:2. Figure
9.33 summarizes this information for some common saturated molecular structures.
A first-order spectrum is observed only if the chemical shift difference
Figure 9.33
First-order splitting patterns for some common molecular
structures. (Numbers in circles represent relative total areas of
the multiplets)