A model has been developed to stimulate the one-dimensional time-dependent vertical diffusion of 222Rn and its decay products in the atmosphere. Computed activities and activity ratios as a function of height above the ground are in excellent agreement with experimental data. The simulations indicate that near the air-ground interface a quasi steady state is reached within a few hours after establishment of a particular atmospheric mixing regime. Radioactive equilibrium between radon and its short-lived daughters is approached at all heights except for very close to the ground during weak mixing conditions.