Question

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

• A. 50 $min$
• B. 60 $min$
• C. 70 $min$
• D. 80 $min$

Answer 1

The correct option is B 60 $min$

$R=\frac{dN}{dt}\propto N\Rightarrow \frac{R_2}{R_1}=\frac{N_2}{N_1}\frac{N_2}{N_1}={\left(\frac{1}{2}\right)}^{\frac{t}{t_{1/2}}}.....\left(i\right)Now\frac{N_2}{N_2}=\frac{25}{200}=\frac{1}{8}={\left(\frac{1}{2}\right)}^3\mathrm{Putting}\mathrm{this}\mathrm{in}\left(i\right)\Rightarrow \frac{t}{t_{1/2}}=3\therefore t_{1/2}=\frac{t}{3}=\frac{3}{3}=60min$