Question

The count rate of a Geiger Muller counter for the radiation of a radioactive material of half-life of 30 minutes decreases to 5 second$^{-1}$ after 2 hours. The initial count rate was

• A. 80 second$^{-1}$
• B. 625second $^{-1}$
• C. 20second $^{-1}$
• D. 25 second $^{-1}$

Answer 1

Answer: (A)

80 second$^{-1}$

Answer 2

Half-life time = 30 minutes; Rate of decrease
(N) = 5 per second and total time = 2 hours = 120 minutes.
Relation for initial and final count rate
$\frac{N}{N_0}=\bigg(\frac{1}{2}\bigg)^{time/half-life} =\bigg(\frac{1}{2}\bigg)^{120/30}=\bigg(\frac{1}{2}\bigg)^4=\frac{1}{16}.$
Therefore N$_0$= 16 x N = 16 x 5 = 80 $s^{-1}$