We have applied the "dressed" state concept, developed in quantum electronics, to the situation in which spin 1/2 ground-state nuclear levels are coupled by rf photons. In particular, we have studied Mossbauer spectroscopy when there is Zeeman splitting of the nuclear levels and a further interaction due to an applied rf-radiation field when the rf frequency is in the neighborhood of the ground-state splitting. The dressed-state approach treats the coupling of the ground nuclear Zeeman levels, due to a radio frequency field, by considering the total system made up of: nucleus, static magnetic field, and rf field as one global quantum system. The energy levels and corresponding eigenstates of the system are calculated as a function of the rf frequency and the magnitude of the rf magnetic flux density. Mossbauer spectra are calculated for the Fe-57 case in which the source is subjected to both the static and radiation fields while the absorber nuclear levels are unsplit.