A point of `gamma`-radiation has a half life of 30 minutes. The initial count rate, recorded by Geiger counter placed 2 m form the source is `360s^(-1)`. The distance between the counter and the source is altered. After 1.5 hours, the count rate recorded is `5s^(-5)`. what is the new distance between the counter and the source?

Explanation

Here, `T=30 mi ns. 0.5h, t=1.5hr. :. N=t/T=1.5/0.5=3`
When distance is changed, count rate after 3 half lives is `5s^(-1)`. Therefore, count rate at the beginning of `1.5 hr=(2)^(3)xx5=40s^(-1)`, which is `1/9xx360s^(-1)=1/9th` of original count rate. i.e., Intensity has been reduced by a factor of 9. As intensity `prop 1/((dist)^(2))`, therefore, distance of source form counter must have increased by a factor of 3 i.e., New distance `=3xx2=6m`