Half - lives of two radioactive . Initially . The samples have equal number of nuclie After `80` minutes ,the ratio of decyed number of `A and B` nuclei will be

Options

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

Answer

D

Explanation

Here, `n_(A)=80/20=4, n_(B)=80/40=2`
form `(N_(A))/(N_(0))=(1/2)^(n_(A))=(1/2)^(4)=1/16, N_(A)=(N_(0))/16`
Decayed no. of atoms of `A = N_(0) - N_(A) = (15)/(16)N_(0)`
`(N_(B))/(N_(0)) = ((1)/(2))^(n_(B)) = ((1)/(2))^(2) = (1)/(4) N_(b) = (N_(0))/(4)`
Decayed no. of atoms of `B=N_(0)-N_(B)`
`=N_(0)-(N_(0))/4=3/4 N_(0)`
Required ratio `=(15/16N_(0))/(3//4N_(0))=15/16xx4/3=5/4`