Models for calculating dose rates of spherical particles as well as in fuel cracks are important for radionuclide source term estimations. Dose rates from UO₂ based fuels were calculated for planar, spherical, and crack geometries. The escape probability for a-particles in spherical UO₂ particles was derived as a continuous equation. The dose rate increased with increasing spherical radius due to the decreasing relative volume of the surrounding water layer. The model produced escape probabilities that were closely predicted by the theoretical derivation. It was shown that the dose rate in water filled fuel cracks with width smaller than the range of an alpha-particle led to dissolution rates that were lower per unit surface area.