A radium source contains 1.00 mg of 256Ra, which decays with a half-life of 1600 y to

Question:

A radium source contains 1.00 mg of 256Ra, which decays with a half-life of 1600 y to produced 222Rn, a noble gas. This radon isotope in turn decays by alpha emission with a half-life of 3.82 d. If this process continues for a time much longer than the half-life of 222Rn, the 222Rn decay rate reaches a limiting value that matches the rate at which 222Rn is being produced, which is approximately constant because of the relatively long half-life of 226Ra. For the source under this limiting condition, what are?

(a) The activity of 226Ra,

(b) The activity of 222Rn, and