At any instant, the ratio of the amounts of two radioactive substance is `2:1`. If their half-lives be, respectively, `12h` and `16h`, then after two days, what will be the ratio of the substances?

Options

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

Answer

A

Explanation

Number of half lives :
`n_(1)=(48)/(12)=4 and n_(2)=(48)/(16)=3`
`(N_(1))/(N_(0))=((1)/(2))^(4)=(1)/(16) and (N_(2))/(N._(0))=((1)/(2))^(3)=(1)/(8)`
`(N_(1))/(N_(2))xx(N._(0))/(N_(0))=(1)/(16)xx(8)/(1)=(1)/(2)`
`(N_(1))/(N_(2))xx(N._(0))/(N_(0))=(1)/(16)xx(8)/(1)=(1)/(2)`
`(N_(1))/(N_(2))xx(1)/(2)=(1)/(2) or (N_(1))/(N_(2))=1:1`