Question

Radium has a half-life $1600$ years and its daughter element radon has a half-life $3.82$ days. In an enclosure, the volume of radon was found constant for a week. Explain and calculate the ratio of the number of radium and radon nuclei. Will the ratio be constant after $400$ years?

Answer 1

$\frac{N_1\left(Ra\right)}{N_2\left(Rn\right)}=\frac{t_{1/2}\left(Ra\right)}{t_{1/2}\left(Rn\right)}$
$\frac{N_1}{N_2}=\frac{1600}{3.82}\times 365$ $=1.528\times {10}^5$

Ratio will be constant after 400 years.