Question

The half-life of the radioactive nuclei is nearly $(ln2=0.693,ln3=1.0986)$

• A. $2.5h$
• B. $7h$
• C. $5h$
• D. $1.2h$

Answer 1

The correct option is D $1.2h$

Number of nuclei at any time is:

$A=A_0{e}^{-\lambda t}\Rightarrow \frac{dA}{dt}={-\lambda A}_0{e}^{-\lambda t}$

Consider, decay at $t=0$ and $t=0.5h$
$\Rightarrow 20,000={-\lambda A}_{0}14,800={-\lambda A}_0{e}^{-0.5\lambda }$

Dividing both equations gives, $\lambda =0.6h^{-1}$

Half life $=\frac{\ln 2}{\lambda }=\frac{0.693}{0.6}=1.15h$