A counter rate meter is used ot measure the activity of radioactive sample. At a certain instant the count rate was recorded as 475 counters per minute. Five minutes later, the count rate recorded was 270 counts per minute. Calculate the decay constant and half life period of the sample.

Explanation

Let `N_(0)` and N be the number of atoms of the radioactive substance present in the start and after 5 minutes respectively.
Rate of disintegration of the start `= lambda N_(0) = 475`
and rate of disintegration after 5 minutes `= lambda N = 270`
Dividing both, `(lambda N_(0))/(lambda N) = (475)/(270)`
or `(N_(0))/(N) = 1.76`
What know that, `lambda = (2.303)/(t) log_(10) (N_(0))/(N)`
`lambda = (2.303)/(5) log_(10) 1.76 = 0.113 "minute"^(-1)`
Half life period `= (0.693)/(lambda) = (0.693)/(0.113) = 6.1` minute