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. `1:01`
B. `2:01`
C. `1:2`
D. `1:4`

Answer

a

Explanation

Let `(M_(1))/(M_(2))` (mass ratio)`=(1)/(2)`
`2` days `=2 xx 24 h =48 h`
For first substance, `4` half -life periods and for second substance `3` half -life periods are passed, the masses are reduced to
`M'_(1) =M_(1) xx ((1)/(2))^(4)`
`M'_(2) =M_(2) xx ((1)/(2))^(3)`
`:. (M'_(1))/(M'_(2)) =(M_(1))/(M_(2)) xx (1)/(2) =(2)/(1) xx (1)/(2) =(1)/(1)`.