Question

$1.0g$ of ${}_{88}^{226}Ra$ is placed in a sealed vessel. How much helium will be collected in the vessel in $100$ days? ($t_{1/2}$ of radium $=1600$ years)

Answer 1

$t=\frac{2.303}{K}log\frac{Ao}{A}$

$100=\frac{2.303}{0.693}\times 1600\times 365\times log(1+\frac{\frac{x}{4}}{\frac{1}{226}})$

$100=\frac{2.303}{0.693}\times 1600\times 365log(1+\frac{226x}{4})$

$1.00011=1+\frac{226x}{4}$

$x=2.10\times {10}^{-6}g$