The diurnal oscillations of radon and thoron and their decay products

Abstract

Periodic and height-dependent solutions are derived for the disturbances of concentrations of Rn222, Rn220, and their first three decay products in the air above the earth's surface, account being taken of turbulent diffusion and radioactive decay. At the surface, sinusoidal oscillations of Rn222 and Rn220 are assumed, but the concentrations of decay products are required to vanish. At large heights, all concentrations are required to vanish. It is shown that the Rn222 (radon) concentration disturbance is influenced mostly by turbulent diffusion and only slightly by decay. The form of the disturbance is very similar to that of the diurnal oscillation of potential temperature for a constant eddy conductivity. Amplitude decreases exponentially upward and phase propagates upward with constant velocity. Daughter products near the surface are not, by reason of the lower boundary condition, in radioactive equilibrium with Rn222. At sufficiently large heights, however, all daughter products approach radioactive equilibrium with Rn222 by reason of their rapid decay. The height at which radioactive equilibrium becomes a good approximation increases with each successive decay product and ranges from tens to hundreds of meters in numerical examples. These results suggest that the inference of Rn222 concentrations from experimentally determined concentrations of its decay products is not justified except at great heights. The Rn220 (thoron) concentration is strongly influenced by decay as well as by turbulent diffusion. The concentration disturbance attenuates and propagates rapidly upward at exponential and constant rates. Since Po216 decays even more rapidly than Rn220, these two approach radioactive equilibrium at sufficiently large heights. Pb212 decays much more slowly than its precursors, so that it is not in radioactive equilibrium with them at any height. Amplitude attenuation and phase propagation are similar in form to those of the enthalpy disturbance. Since Bi212 decays more rapidly than Pb212, these two approach radioactive equilibrium at great heights.