A counter rate meter is used to measure the activity of a radioactive sample. If at certain instant, the count rate was recorded as 475 counter per minute. Five minutes later, the count rate recorded was 270 counts per minute. What is the half life period of the sample in minutes ?

Let N0 and N be the number of atoms of the radioactive substance present at the start and after 5 minutes respectively.Rate of disintegration at the start = KN0  = 475 and rate of disintegration after 5 minutes = KN = 270.Dividing both, KN0KN=475270⇒N0N=1.76K=2.303tlog⁡N0NK=2.3035log⁡1.76=0.113 minute −1 Half life period =0.693K=0.6930.113=6.1≈6 minutes.