Question

The half life of a radioactive substance is $13$ years. The decay constant is,

• A. $1.69\times {10}^{-10}{\text{sec}}^{-1}$
• B. $1.96\times {10}^{-9}{\text{sec}}^{-1}$
• C. $1.69\times {10}^{-9}{\text{sec}}^{-1}$
• D. $1.29\times {10}^{-7}{\text{sec}}^{-1}$

Answer 1

The correct option is C $1.69\times {10}^{-9}{\text{sec}}^{-1}$

Half life period, $T_{1/2}=13\text{years}$
$T=13\times 365\times 86400\text{sec}$
Decay constant is given by,
$\lambda =\frac{0.693}{T_{1/2}}$

=$\frac{693\times {10}^{-3}}{13\times 365\times 86400}$

$\lambda =1.69\times {10}^{-9}{\text{sec}}^{-1}$

Hence, $\left(C\right)$ is the correct answer.