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 minutes
• B. 60 minutes
• C. 70 minutes
• D. 80 minutes

Answer 1

Answer: (B)

60 minutes

Answer 2

$R = \frac{dN}{dt} \propto N \Rightarrow \frac{R_{2}}{R_{1}} = \frac{N_{2}}{N_{1}}$

But $\frac{N_{2}}{N_{1}} = \left( \frac{1}{2} \right)^{t_{1/2}} \Rightarrow \frac{25}{200} = \frac{1}{8} = \left( \frac{1}{2} \right)^{3} \Rightarrow \frac{t}{t_{1/2}} = 3$

$\therefore t_{1/2} = \frac{t}{3} = \frac{3}{3} = 1\mspace{6mu} hour = 60$minutes