The activity of a radioactive sample falls from

(2) We know that

Activity, $A=A_{0} e^{-\lambda t}$

$A=A_{0} e^{-t \operatorname{In} 2 / T_{1 / 2}}\left(\because \lambda=\frac{\operatorname{In}_{2}}{T_{1 / 2}}\right)$

$\Rightarrow 500=700 e^{-t \ln 2 / T_{1 / 2}}$

$\Rightarrow \operatorname{In} \frac{7}{5}=\frac{30 \operatorname{In} 2}{T_{1 / 2}}$ ( $\because t=30$ minute)

$\Rightarrow T_{1 / 2}=30 \frac{\operatorname{In} 2}{\operatorname{In} 1.4}=61.8$ minute

$(\because \ln 2=0.693$ and $\ln .1 .4=0.336)$

$\Rightarrow T_{1 / 2} \approx 62$ minute