For a proton or carbon-13 nucleus I is 1/2, hence mI can be only ± 1/2 and two energy levels, or spin
states, are produced (Figure 9.28):
Figure 9.28
Nuclear spin energy levels for a
proton or carbon-13, I = 1/2.For energy to be absorbed, radiation of a frequency equivalent to E 2 – E 1 must be supplied. Thus, using
the Planck relation, the condition for absorption is defined as
Equation (9.24) shows that the absorption frequency is directly proportional to the strength of the
applied magnetic field at the nucleus.
In practice, using a CW instrument, the absorption of energy may be detected by subjecting the sample
to radiation of varying frequency at a fixed value of the applied field or vice versa until the conditions
required by equation (9.24) are met. At this point, the system is said to be in resonance, both upward
and downward transitions occur, and a net absorption of energy is observed because of the small excess
of nuclei in the lower level.
The width of an absorption band in NMR spectrometry is determined by the rate at which nuclei
absorbing energy return to the lower level. This relaxation process is complex, involving dissipation of
the excess energy throughout the whole sample, and giving a decaying emission signal which FT
spectrometers (p. 413) can detect and computer-process. The rate of relaxation in liquid samples is such
that absorption bands are narrow (~ 0.5 Hz) thus enabling well-resolved spectra to be readily obtained.