Question

Radioactivity of a radioactive element remains $1/10$ of the original radioactivity after $2.303$ seconds. The half life period is

• A. $2.303sec$
• B. $0.2303sec$
• C. $0.693sec$
• D. $0.0693sec$

Answer 1

Answer: (C)

$0.693sec$

Let original activity be 1.
After $t=2.303\approx ln10seconds$
Using integrated rate law:
$\frac{1}{10}=e^{-\lambda ln10}$
$\Rightarrow ln\left(\frac{1}{10}\right)=-\lambda ln10\Rightarrow ln10=ln{10}^{\lambda }$
$\Rightarrow \lambda =1$
So, half life $=\frac{ln2}{\lambda }=\frac{ln2}{1}=0.693seconds$