Question

A count rate metre shows a count of $240/\min$ from a given radioactive source later the metre shows a count rate of $30/\min$. The half-life of the source is

• A. 80 min
• B. 120 min
• C. 20 min
• D. 30 min

Answer 1

Answer: (C)

20 min

Answer 2

The number of counts left after time $t$ $N=N_{0}\left(\frac{1}{2}\right)^{t / T_{1 / 2}}$ $\therefore 30=240\left(\frac{1}{2}\right)^{60 / T_{1 / 2}}$ $[\because t=1 h =60\, \min ]$ or $\frac{30}{240}=\left(\frac{1}{2}\right)^{60 / T_{1 / 2}}$ $\left(\frac{1}{2}\right)^{3}=\left(\frac{1}{2}\right)^{60 / T_{1 / 2}}$ Comparing the power, we get $\frac{60}{T_{1/2}} = 3$ $\therefore T_{1/2} = \frac{60}{3}$ or $T_{1/2} = 20 \, \min$