Question

A count rate meter shows a count of $240$ per minute from a given radioactive source. One hour later the meter shows a count rate of $30$ per minute. The half-life of the source is?

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

Answer 1

Answer: (C)

The number of counts left after time t
$N=N_0{\left(\frac{1}{2}\right)}^{t/T_{1/2}}$
$\therefore 30=240{\left(\frac{1}{2}\right)}^{60/T_{1/2}}$
$[\because t=1h=60min]$
or $\frac{30}{240}={\left(\frac{1}{2}\right)}^{60/T_{1/2}}$
or ${\left(\frac{1}{2}\right)}^3={\left(\frac{1}{2}\right)}^{60/T_{1/2}}$
Comparing the powers, we get
$\therefore \frac{60}{T_{1/2}}=3$
$T_{1/2}=\frac{60}{3}$
or $T_{1/2}=20$min.