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

(a) Let `(M_1)/(M_2) ("mass ratio") = (1)/(2) 2 days = 2 xx 24 hrs = 48 hrs`
For `1^st` substance `4` half-life periods and for `2^(nd)` 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)`.