A model for radon gas adsorption on charcoal for open-faced canisters in an active environment

It was previously suggested that the calibration factor (CF) relating the detected activity (A) of the radon decay products 214Bi and 214Pb within a charcoal canister to the radon concentration (CR) in air be defined as CF = A/(E x DF x CR), where E is the counting efficiency of the detector for 214Bi and 214Pb gamma rays, and DF is a factor accounting for decay during the time (tD) from the end of the exposure until the canister is counted; i.e., DF = exp(-lambda RPtD), where lambda RP is the physical decay constant for radon. With CF defined as above, a kinetic model for the adsorption of radon gas on charcoal in humid air predicts that CF (in m3) can be written for CR in Bq m-3, A in cpm, and E in cpm Bq-1 as CF = alpha[1-exp(-delta t)] + beta[1 - exp(-delta t)]M(t), where alpha, beta, and delta are free parameters, t is the canister exposure time in hours, and M(t) is the canister water mass gain in grams in time t. For CF data for the U.S. Environmental Protection Agency's open-faced canisters in an active (with respect to air flow) environmental chamber, delta = (0.046 +/- 0.002)h-1, and exp(-delta t) much less than 1 for t greater than or equal to 3 d. Also, alpha = (0.342 +/- 0.002)m3, and beta = -(0.0123 +/- 0.0001)m3g-1.