When a group of spins is placed in a magnetic field, each spin aligns in one of the two possible orientations. The relative numbers of spins with different alignments will be given by the Boltzmann distribution.
Definition: if a system of particles, which are able to exchange energy in collisions is in thermal equilibrium, then the relative number (population) of particles, N1 and N2, in two particular energy levels with corresponding energies, E1 and E2, is given by N1/N2 = exp [-(E1 - E2)/kT ] where k is the Boltzmann constant and T is the absolute temperature. For example, in NMR of protons at room temperature in a magnetic field of 0.25 tesla, the difference in relative numbers of spins aligned with the magnetic field and against the field is about one part in a million; the small excess of nuclei in the lower energy state is the basis of the net magnetization and the resonance phenomenon.

The numbers of nuclei or electrons in different energy levels. At thermal equilibrium, the relative populations of the energy levels will be given by the Boltzmann distribution.

See also Boltzmann Distribution.