Question

1. Radon gas ₈₆²²²Rn is one of the products of the decay of uranium which exists in the ground. The maximum safe level of radon has been established by the EPA at 4x10^-12Ci/L. Radon has a half-life of T_1/2 = 1622 years. Also note that 1 Ci = 3.7x10¹⁰Bq.

a. Calculate the concentration of radon atoms in air in units of particles/liter which will give the above activity.

b. What is the ratio (in percent) of the number of radon gas atoms to air molecules?

Answer 1

a) t _ 1/2 = 1622 years A = 4 times 10 ^- 12 ci/L 1 Ci = 3 .7 times 10 ^10 Bq lambda = 0 . 6931/t _ 1/2 = 0 . 6931/1622 times 365 times 60 times 60 sec^- 1 lambda = 3 . 26 times 10 ^- 10 sec ^- 1 A = 4 times 10 ^- 12 times 3 . 7 times 10 ^10 Bq/L A = 0 . 04 times 3 . 7 Bq /L A = 0 . 148 Bq/L A = lambda N N = A/lambda = 0 . 148/3 . 25 times 10 ^- 10 = 4.55 times 10 ^8 atoms/L (b) 1 L t of air at N T P contains = 2 . 46 times 10 ^22 molecules Ratio = 4 . 55 times 10 ^8/2 . 461 times 10 ^22 times 100 = 4 . 55/2 . 461 times 10 ^- 12 ratio = 1 . 848 times 10 ^- 12 %