Question

A radioactive substance decays at $1/32$ of its initial activity in $25$ days. Its half life is

• A. 4 days
• B. 25 days
• C. 5 days
• D. 20 days

Answer 1

Answer: (C)

Here, $t=25$ days,
$R=\left(\frac{1}{32}\right)R_0$
${\tau }_{1/2}=$ ?
As $R=R_0{e}^{-\lambda t}$
or $\frac{R}{R_o}=e^{-(\frac{\text{In}2}{{\tau }_1}\times t})\left[\because {\tau }_{1/2}=\frac{\text{In2}}{\lambda }\right]$
$32=2^{t/{\tau }_{1/2}};2^5=2^{t/{\tau }_{1/2}}$
$\therefore {\tau }_{1/2}=\frac{t}{5}=\frac{25}{5}=5$ days