Question

A radioactive element emits 200 particles per second. After three hours 25 particles per second are emitted. The half-life period of element will be

• A. $50\text{minutes}$
• B. $60\text{minutes}$
• C. $70\text{minutes}$
• D. $80\text{minutes}$

Answer 1

The correct option is B $60\text{minutes}$

Activity of a radioactive material is written as
$R=R_0{e}^{\frac{-t}{\tau }}$
or $R=R_0(\frac{1}{2}{)}^{\frac{t}{t_{\frac{1}{2}}}}$

$\therefore \frac{R}{R_0}=\frac{t}{t_{\frac{1}{2}}}$
$\because \frac{R}{R_0}=\frac{25}{100}=\frac{1}{8}=(\frac{1}{2}{)}^3$
by comparing we get,
$\frac{t}{t_{\frac{1}{2}}}=3$
$\Rightarrow t_{\frac{1}{2}}=\frac{t}{3}=\frac{3}{3}=1\text{hour}=60\text{minutes}$