The count rate of a Geiger Muller counter for the radiation of a radioactive material of half-life `30` min decreases to `5 s^(-1)` after `2 h`. The initial count rate was

Options

A. `20 sec^(-1)`
B. `25 sec^(-1)`
C. `80 sec^(-1)`
D. `625 sec^(-1)`

Answer

C

Explanation

Half -life = 30 minutes , Rate of decrease (N) = 5 per second and total time = 2 hours = 120 minutes . Relation for initial and final count rate
`(N)/(N_(0)) = ((1)/(2))^("time/half - life") = ((1)/(2))^(120//30) = ((1)/(2))^(4) = (1)/(16) ` . Therefore , `N_(0) = 16 xx N = 16 xx 5 = 80 s^(-1)`