The theory of optical transitions between donor levels and the valence band or between acceptor levels and the conduction band has been examined. Expressions for the optical absorption and radiative lifetime due to such transitions are derived. Application of this theory is made to GaAs and it is shown that at relatively high impurity concentrations optical transitions involving impurities can give rise to moderately high absorption constants and short radiative lifetimes. In the intermetallic semiconductors which have a conduction band effective mass much smaller than that of the valence band, the transition probability between acceptor states and the conduction band may be taken to be a constant up to moderate conduction band energies. To test the limits of validity of band to impurity recombination, the minimum spontaneous radiative lifetimes for electrons and holes are calculated. For electrons in GaAs this minimum lifetime is 0.3 nsec.