Model for radon diffusion through the lunar regolith

A model for radon diffusion through the lunar regolith is proposed in which the atom migrates by random walk. The regolith is represented by a system of randomly oriented baffles in which the mean distanced which the atom travels between two collisions takes on the role of a mean free path. The effective mean time between two collisions depends on two entities: the actual mean time-of-flight and the mean sticking time on grain surfaces for one collision. The latter depends strongly on the temperature and the heat of adsorption of radon on regolith materials. Bothd (mean free path) as well asQ (heat of adsorption) are either poorly known or unknown for the lunar regolith; hence these quantities are treated as free parameters. Because of the greatly different mean lifetimes against radioactive decay of²¹⁹Rn,²²⁰Rn, and²²²Rn, the regolith acts as a powerful filter for these species.²²²Rn escape is significant (32%) even ford = 1µ,Q = 7.0 kcal/mole and a regolith depth of 4 m. Calculations of radon escape from a 4 m thick regolith, usingd = 1, 10 and 80µ andQ = 4.0, 5.2 and 7.0 kcal/mole show that the²²²Rn/²²⁰Rn escape ratio can be as small as 7.7 and as large as, or larger than 47. The small value of 7.7 is of particular interest, because it is nearly equal to the escape ratio inferred by Turkevichet al. from their Surveyor 5 results.