Half-lives of two radioactive elements A and B are 20 minutes and 40 minutes respectively. Initially, the samples have equal number of nuclei. After 80 minutes, the ratio of decayed numbers of A and B nuclei will be

Options

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

Answer

C

Explanation

`N_(A)/N_(B)=(N_(0)e^(-lambdaAt))/(N_(0)e^(-lambdaBt))`
`tau_(A)=20 min, tau_(B)=40` min
`lambda_(A) =(ln(2))/20, lambda_(B)=(ln(2))/40`
`N_(A)/N_(B) =e^(-lambdaAt+ lambdaBt)`
`N_(A)/N_(B)=1/4`