Half - lives of two radioactive . Initially . The samples have equal number of nuclie After `80` minutes ,the ratio of decyed number of `A and B` nuclei will be

Options

A. `1 : 16`
B. `4 : 1`
C. `1 : 4`
D. `5 : 4`

Answer

d

Explanation

Amount remaining after n half lives `(N) = N_(0) ((1)/(2))^(n)`
`:.` Ratio of decayed nuclei of A to that of B will be
`(N_(0) - N_(A))/(N_(A) - N_(B)) = (N_(0)[1-((1)/(2))^(4)])/(N_(0)[1-((1)/(2))^(2)]) = (1-(1)/(16))/(1- (1)/(4))`
`= ((15)/(16))/((3)/(4)) = (5)/(4) `