Radon gas as rn-222 is formed by the radioactive decay of u-238, the chief natural isotope of uranium, found in soils and especially granitic rocks. as rn-222, radon decays through several daughter-product isotopes to stable pb-2016. the gas occurs in air at natural levels of 0.1 to 0.2 pci/l, and is considered a health hazard (cancer risk) by the u. s. environmental protection agency at or above 4 pci/l in air. rn-222 decays by the emission of alpha particles (helium nuclei) with a half-life or decay half-time of 3.823 days.
(a) what is its decay rate constant in s-1?
(b) the mole fraction solubility of pure radon gas in water (nrn) from 3 to 970c at 1 atm radon gas pressure, is given by the equation
r in nrn = -499.309 + (25864.2/t) + 69.3241 in t + 0.00101227 t
where r = 1.9872 cal/mol k, and t is in degrees k. calculate the henry's law constant for rn gas at 250 c in m/bar?
(c) well waters pumped from granitic rocks or uraniferous sandstones may be high in radon. exsolution of the gas into the air in a shower stall may result in air levels in excess of 4pci/l. what m concentration of dissolved rn in a groundwater would be in equilibrium with 4 pci/l of radon gas in bathroom air at 250c.