The half lives of two radioactive nuclides A and B are 1 and 2 min. respectively . Equal weights of A and B are taken separately and allowed to disintegrate for 4 min. What will be the ratio of weigths of A and B disintegrated ?

Options

A. `1:1`
B. `5:4`
C. `1:2`
D. `1:3`

Answer

B

Explanation

For A
T=4 min
`t_(1//2)=1` min
`N_(0)=x`(say)
`n=4//1=4`
`N=(N_(0))/(2^(n))=(x)/(2^(4))=(x)/(16)`
A disintegrated
`=x-(x)/(16)=(15x)/(16)`
For B
T=4 min
`t_(1//2)=` 2 min
`N_(0)=x` (say)
`n=4//2=2`
`N=(N_(0))/(2^(n))=(x)/(2^(2))`
`=(x)/(4)`
B disintegrated
`x-(x)/(4)=(3x)/(4)`
Ratio of A : B disintegrated
`(15x)/(16):(3x)/(4)`
or 5:4