Applying the effective-mass approach, the energy eigenvalues of excitonic states in amorphous semiconductors are derived. It is shown that Wannier-Mott-type excitons can indeed be formed in amorphous solids. The results show that the occurrence of the double photoluminescence (PL) lifetime distribution peak, fast and slow, in hydrogenated amorphous silicon (a-Si:H) and hydrogenated amorphous germanium (a-Ge: H) can unambiguously be assigned to radiative recombinations from singlet and triplet excitonic states respectively. The dependence of PL peaks on the temperature and generation rate in a-Si: H and a-Ge: H is also discussed. The approach is general and simple and can be applied to study the charge-carrier transport and PL properties in any amorphous solid.