Question

$4\times {10}^{23}$ tritium atoms are contained in a vessel. The half life of decay of tritium nuclei is $2.3\text{years}$. The activity of the sample is

• A. $7\times {10}^4{\text{s}}^{-1}$
  
• B. $7\times {10}^{14}{\text{s}}^{-1}$
• C. $7\times {10}^{18}{\text{s}}^{-1}$
• D. $7\times {10}^{24}{\text{s}}^{-1}$

Answer 1

The correct option is B $7\times {10}^{14}{\text{s}}^{-1}$

We know that activity,

$R=\lambda N=\frac{0.693}{T_{1/2}}N$

Given,

$T_{1/2}=12.3\text{years}=12.3\times 365\times 86400\text{s}$

$N=4\times {10}^{23}\text{atoms}$

$\therefore R=\frac{0.693\times 4\times {10}^{23}}{12.3\times 365\times 86400}$

$=\frac{2.772\times {10}^{23}}{3.88\times {10}^8}=7.14\times {10}^{14}{\text{s}}^{-1}$

Hence, $\left(\text{B}\right)$ is the correct answer.