Question

The mean lives of a radioactive substance are 1620 year and 405 year for $\alpha$-emission and $\beta$-emission respectively. The time (in year) during which three fourth of a sample will decay if it is decaying both by $\alpha$-emission and $\beta$-emission simultaneously is (divide answer by 200 and write the nearest integer).

Answer 1

$\lambda =\frac{1}{T}=\frac{1}{1620}+\frac{1}{405}$

$t_{1/2}=\frac{0.693}{\lambda }=\frac{0.693}{\frac{1}{1620}+\frac{1}{405}}=224.5$
The time (in year) during which three fourth of a sample will decay if it is decaying both by -emission and -emission simultaneously is
$2\times 224.62=449.24$