Two radioactive substances `A` and `B` have half lives of `T` and `2T` respectively. Samples of `a` and `b` contain equal number of nuclei initially. After a time `4T`, the ratio of the number of undecayed nuclei of `A` to the number if undecayed nuclei of `A` to the number of undeacyed nuclei of `B` is

Options

A. `1 : 4`
B. `1 : 2`
C. `2 : 1`
D. `4 : 1`

Answer

A

Explanation

`t = 4T,(T_(1//2))_(A) = T, (T_(1//2))_(B) = 2T`
`A: t = n(T_(1//2))_(A) rArr 4T = nT rArr n = 4`
`N_(A) = N_(0) ((1)/(2))^(n) = N_(0) ((1)/(2))^(4) = (N_(0))/(16)`
`B: t = n(T_(1//2))_(B) rArr 4T = n xx 2T rArr n = 2`
`N_(B) = N_(0)((1)/(2))^(n) = N_(0)((1)/(2))^(2) = (N_(0))/(4)`
`(N_(A))/(N_(B)) = (N_(0)//16)/(N_(0)//4) = (1)/(4)`