The count rate meter is used to measure that activity of a given amount of a radio active element. At one instant, the meter shows 475 counts/minute. Exactly 5 minutes later, is shown 270 counts/minute then
The decay constant is

Explanation

(a) Initial activity `=A_(0)=-(dN)/(dt)" at "t=0`
`"Final activity "=A_(t)=-(dN)/(dt)" at "t=t`
`(dN)/(dt)|_(t=0)=-lambdaN_(0) and (dN)/(dt)|_(t=5)=-lambdaN_(t) rArr (4750)/(2700)=(N_(0))/(N_(t))`
Using `lambdat=2.303 log""(N_(0))/(N_(t))`
`rArr" "lambda(5)=2.303log((4750)/(2700))`
`rArr" "lambda=(2.303)/(5)log((4750)/(2700))=0.1129" min"^(-1)`
(b) `T_(1//2)=(0.693)/(0.1129)="6.14 min."`