The disintegration rate of a certain radioactive sample at any instant is `4750` disintegrations per minute. Five minutes later the rate becomes `2700` per minute. Calculate
(a) decay constant and (b) half-life of the sample

Explanation

(i) from the reaction ,
`R=R_(0)e^(-)("here -lifeof the sample ")`
substituting the values ,we have ., `27000 = 4750 e^(-5lamda)`
`therefore 5lamda= "in" ((4750)/(2700))=0.56`
`therefore ` Wavelength , `lamda , lamda = 0.113 min^(-1)`
(ii) half - life of the sample , `t_(1//2)=("in 2")/(lamda)= 0.693)/(0.113)=6.132min`