The activity of a radioactive sample falls from $700{\mathrm{s}}^{-1}$ to $500{\mathrm{s}}^{-1}$ in $30$ minutes. Its half life is close to:

From equation of radioactivity. $A_{\mathrm{t}}=A_0{e}^{-\lambda t}$

         $\ln \left[\frac{{\mathrm{A}}_0}{{\mathrm{A}}_{\mathrm{t}}}\right]=\lambda \mathrm{t}$

$\Rightarrow \ln \left[\frac{700}{500}\right]=\lambda \left(30\min \right)$ ------$\left(1\right)$

also

$\Rightarrow \ln 2=\lambda t_{1/2}$ --------$\left(2\right)$

$\left(\mathfrak{ii}\right)/\left(\mathfrak{i}\right)$

$\Rightarrow \frac{\ln 2}{\ln (7/5)}=\frac{t_{1/2}}{\left(30\min \right)} \Rightarrow (2.06004)30=t_{1/2}=61.8\min$

$\approx$      $62\mathrm{}\mathrm{m}\mathrm{i}\mathrm{n}$