The article proposes the basis for calculation of the evolution in time and space of one of the most important factors causing damages in radiation accidents is radioactive dust. It has been proved that the decontamination of areas contaminated by radioactive dust should be carried out in several stages. If the first stage is related to the process of removing the large particles of the settled dust from the surface, then the second stage comprises removing the very small dust particles from the air, as they are especially dangerous to the respiratory system. Quantitative limits of three modes of evolution of the radioactive dust in the gravitational field have been determined and the influence of the boundary condition has been considered. The equations that give the description of the evolution of dust particles of arbitrary size have been derived.