The half life of ${ }_{92}^{238} \mathrm{U}$ against $\alpha$-decay is $13.86 \times 10^{16} \mathrm{~s}$.…
The half life of ${ }_{92}^{238} \mathrm{U}$ against $\alpha$-decay is $13.86 \times 10^{16} \mathrm{~s}$. The activity of $1 \mathrm{~g}$ sample of ${ }_{92}^{238} \mathrm{U}$ is
$1.26 \times 10^4 \mathrm{~s}^{-1}$
$1.26 \times 10^{-4} \mathrm{~s}^{-1}$
$12.6 \times 10^4 \mathrm{~s}^{-1}$
$12.6 \times 10^{-4} \mathrm{~s}^{-1}$
Solution
Activity of a sample is
$\begin{aligned}
R & =\left|\frac{d N}{d t}\right|=\mid-\lambda N \models \lambda N=\frac{0.6931}{T_{1 / 2}} \times N \\
& =\frac{0.6931}{T_{1 / 2}} \times n \times N_A=\frac{0.6931}{T_{1 / 2}} \times \frac{m}{M} \times N_A
\end{aligned}$
With values, we get $R=1.26 \times 10^4 \mathrm{~s}^{-1}$