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) Number if half-lives in two days four substance `1` and `2` respectively are `n_1 = (2 xx 24)/(12) = 4` and `n_2 = (2 xx 24)/(1.6) = 3`
By using `N = N_0((1)/(2))^n rArr (N_1)/(N_2) = ((N_0)_1)/((N_0)_2) xx (((1)/(2))^(n_1))/(((1)/(2))n_2)`
=`(2)/(1) xx ((1)/(2))^4/(((1)/(2))^3) = (1)/(1)`.