Question

N atoms of a radioactive element emit n alpha particles per second. The half life of the element is

• A. $\frac{n}{N}sec$
• B. $\frac{N}{n}sec$
• C. $\frac{0.693N}{n}sec$
• D. $\frac{0.693n}{N}sec$

Answer 1

The correct option is C $\frac{0.693N}{n}sec$

$\frac{dN}{dt}=-\lambda N\Rightarrow n=-\lambda N(Given\frac{dN}{dt}=n)$
$\therefore \lambda =-\frac{n}{N}$ $\therefore$ Half life = $\frac{0.693}{\lambda }=\frac{0.693}{\lambda }=\frac{0.693N}{n}sec$