Question

$K^{40}$ decays into $C{a}^{40}$ & $A{r}^{40}$ simultaneously as follows
Ratio of atoms of Ar to K in a rock sample is 3 :10. Calculate age of rock sample assuming that source of Ar is radioactive decay of $K^{40}$ only and no Ar was present at the time of formation of rock.

Answer 1

$\frac{{\lambda }_1}{{\lambda }_2}=\frac{9}{1};\lambda ={\lambda }_1+{\lambda }_2={10}^{-8}y{r}^{-1}$
$t=\frac{1}{\lambda }ln\frac{10+10x}{10}=\frac{10+10\times 3}{10}=\frac{40}{10}=4$
Hence, the age of the rock sample is 4 years.