Question

The half life period of $N^{13}$ is $10.1$ minute. Its mean life time is :

• A. $5.05$ minutes
• B. $20.2$ minutes
• C. $\frac{10.1}{0.6931}$ minutes
• D. Infinity

Answer 1

The correct option is C $\frac{10.1}{0.6931}$ minutes

For a radioactive decay with decay constant $k$, the half life of the decay is

$\tau =\frac{ln}{k}=10.1minutes$

$⟹k=\frac{ln2}{10.1}perminute$

Hence mean life of the decay $=\frac{1}{k}=\frac{10.1}{ln2}minutes$ $=\frac{10.1}{0.6931}minutes$