Answer to Question #72 Submitted to "Ask the Experts"

Q

Simple equation for finite cloud for beta dose calcs.

A

The skin dose due to submersion in a cloud of airborne activity can be estimated as half the equilibrium dose. The equilibrium dose assumes that the energy emitted per unit mass is equal to the energy absorbed per unit mass. The factor of one-half in the approximation arises since the skin is irradiated only from one direction; i.e., betas incident on the anterior of the body surface do not contribute to the dose to skin of the posterior surface. Thus the half-space argument for beta particles deals with the body rather than the ground occupying a half-space, which enters the dose considerations for photons. As an example, the beta decays of Kr-85 result in 0.251 MeV per decay of energy. Taking the airborne Kr-85 concentration to be 1 Bq per m3 and assuming an air density of 1.2 kg/m3 then the equilibrium dose rate is D = (1 Bq/m3 * 0.251 MeV/ (Bq-s) * 1.6E-13 J/MeV) / 1.2 kg/m3 = 3.35E-14 Gy/s and the skin dose rate is one-half or 1.67E-14 Gy/s. The skin dose coefficient for Kr-85 in Federal Guidance Report 12 is 1.32E-14 Gy/s per Bq/m3. This estimates includes consideration of the dose-depth profile, the actual beta spectrum, etc. Consideration of these details requires numerical solutions on a computer and hence recourse is made to tabulations such as FGR-12. Keith Eckerman, Ph.D. Oak Ridge National Laboratory