Rate of reaction at $10\, \mathrm{s}=-0.04 \,\mathrm{mol} \,\mathrm{L}^{-1} \,\mathrm{s}^{-1}$

Rate of reaction at $20\, \mathrm{s}=\mathrm{s}=0.03\, \mathrm{mol} \,\mathrm{L}^{-1} \mathrm{s}^{-1}$

$\therefore$ Half - life period $\left(\mathrm{t}_{1 / 2}\right)=?$

We have the equation for rate $-$ constant $k$ in first order reaction

$\mathrm{k}=\frac{2.303}{\mathrm{t}} \log \frac{\mathrm{A}_{\mathrm{t}}}{\mathrm{A}_{0}}$

$=\frac{2.303}{105} \log \frac{0.04}{0.03}$

$=\frac{2.303}{105} \times 0.124$

$\mathrm{k}=0.028\, \mathrm{s}^{-1}$

We know that, $t_{1 / 2}=\frac{0.693}{k}$

$=\frac{0.693}{0.028773391}=24.14\, \mathrm{s}=24.1\, \mathrm{s}$