Question

A sample of a particular radioisotope is placed near a Geiger counter, which is observed to register 160 counts per minute. Eight hours later, the detector counts at a rate of 10 counts per minute. What is the half-life of the material (in minutes)?

Answer 1

Rf/Ri=(1/2)^t, where Ri is initial decay rate, Rf is final decay rate, t is the number of half lives.

Here,Ri=160 counts per minute, Rf =10 counts per minute.

So,10/160=(1/2)^t

=>(1/2)^t=1/16

=>t=4.

So, 8 hours contain 4 half lives.

Hence,half life=8/4=2 hours=2*60=120 minutes.