Half lives of two radioactive nuclei `A` and `B` are `10` minutes and `20` minutes respectively, If initially a sample has equal number of nuclei, then after `60` minutes, the ratio of decayed numbers of nuclei `A` and `B` will be :

Options

A. `1:8`
B. `3:8`
C. `8:1`
D. `9:8`

Answer

D

Explanation

Let initially, there are n nuclei of each type.
`n_(A)=n e^(-(t/(t_(1//2)))ln2)= n e^(-(tln2)/10),n_(B)=n e^((-tln2)/20)`
At `t=60` minutes, `n_(A)=n/(2^(6))` and `n_(B)=2/(2^(3))`
Ratio of decayed numbers `=(n-n_(A))/(n-n_(B))=(n-n/(2^(6)))/(n-n/(2^(3)))=(9/8)`