The exergy of nuclear radiation is evaluated by using a simple quantum statistical thermodynamic approach. Only radiation particles with non-zero rest mass are considered (i.e. protons, neutrons, alpha and beta particles). The exergy and the exergy flux involve efficiency-like factors affecting the internal energy and the energy flux, respectively. These factors are generally different from both the usual Carnot factor and the Petela-Landsberg-Press factor that appears in the exergy of blackbody radiation. The efficiency-like factors are higher in the case of charged rather than neutral particles and in the case of enclosed rather than free radiation. The results are compared with those obtained previously by using a classical thermodynamic theory.