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Q.

A point source of γ−radiation has a half-life of 30 minutes. The initial count rate recorded by a Geiger counter placed 1.0m from the source is 360sec−1. The distance between the counter and the source is altered. After 1.5 hour the count rate recorded is 5sec−1. What is the new distance between the counter and the source (in m) ?

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Detailed Solution

λ=ln20.5 hr−1At any moment, Count rate = Activity =λNIf the distance between source and Geiger Counter is d, and area of counter is Athen recorded count rate =λN4πd2AAt t=0 , λN04π12A=360At t=1.5 hr , λN0e−λ1.54πd2A=5Dividing both equation,d2=3608×5=9⇒d=3m

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