Consider the case of local thermodynamic equilibrium. In this case, the scattering coefficient is zero and thus = . If the material is in equilibrium with the radiation field, the amount of energy emitted must balance the amount of energy absorbed, in accordance with Kirchoff's Law.

We can express B (T) in terms of Planck's function for the radiation field in thermodynamic equilibrium. The energy level of the atom are populated according to Boltzmann's equation, and the absorption coefficient can be expressed as