Question

There are n number of radioactive nuclei in a sample that undergoes beta decay. If from the sample, n' number of $\beta$-particles are emitted every 2 s, then half-life of nuclei is

• A. n'/2
• B. $0.693\times \left(2n/n^{\prime }\right)$
• C. 0.693 ln(2n/n')
• D. $0.693\times n/n^{\prime }$

Answer 1

The correct option is B $0.693\times \left(2n/n^{\prime }\right)$

$\frac{dN}{dt}=-\lambda N$

Given rate of decay $=\frac{n^{\prime }}{2}$
$\frac{n^{\prime }}{2}=\lambda n$
$\frac{n^{\prime }}{2}=\frac{ln2}{t_{1/2}}n$

$t_{1/2}=2nln2/n^{\prime }$

$t_{1/2}=0.693\times \left(2n/n^{\prime }\right)$