Half-lives of two radioactive substances `A` and `B` are respectively `20` minutes and `40` minutes. Initially, he sample of `A` and `B` have equal number of nuclei. After `80` minutes the ratio of the remaining number of `A` and `B` nuclei is :

Options

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

Answer

D

Explanation

In given tim e interval, there are 4 half-lives of A and 2 half-lives of B.
`N=N_(0)(1/2)^(n)`
`rArr N_(A) =N_(0)(1/2)^(4)` and `N_(B) =N_(0)(1/2)^(2)`
`rArr N_(A)/N_(B)=1/4`