Question

Radon is pumped off and sealed into tiny seeds using a 300 mg source of 226Ra. (a) What activity (in mCi) of radon will be available at each pumping if this is done at 7-day intervals? (b) How much time will be required to accumulate 200 mCi of the gas?

Answer 1

Ra-226 decays to Rn-222 with half-life T_1/2 = 1600 y

Rn-222 haas an half-life T_1/2 = 3.82 d

We can assume production of Rn-22 from Ra-226 is at a const rate but it decays with its own decay rate and Rn builds up over time

production rate of Rn-222 = decay rate of Ra-226 = N_RaRa = 300mCi

                                                  = 1.11e+10 atoms/s

Rn activity at any instant of time t is given by

N(t) = 1.11e+10( 1- exp(-t) )

            = 300mCi * (1 -exp( -0.693*7/3.82) )

             = 94.47 mCi

b) activity

200 mCi = 300( 1-exp(-0.693t/7))

t = 11.1 days