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

Answer

A

Explanation

`t=80 min=4 T_(A)=2T_(B)`
`:.` no. of nuclei of A decayed `=N_(0)-N_(0)/2^(4)=(15 N_(0))/16`
`:.` no. of nuclei of B decayed `=N_(0)- N_(0)/2^(2)=(3N_(0))/4`
required ratio `=5/4`