A radium source contains 1.00 mg of 226Ra, which decays with a half-life of 1600 y to produce 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 (c) the total mass of 222Rn?

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Chapter1: Units, Trigonometry. And Vectors
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A radium source contains 1.00 mg of 226Ra, which decays with
a half-life of 1600 y to produce 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 (c) the total mass of 222Rn?

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