Two radioactive nuclides `A` and `B` have half-lives in the ratio `2:3` respectively. An experiment is made with one mole of each of them. Calculate the molar ratio of `A` and `B` after a time interval of three times of half-line of `A`.

Explanation

Let half-lives of `A` and `B` be `2a` and `3a` sec respectively.
For `A`: at `T = 3 xx 2a = 6a sec`
`6a = (0.303xx2a)/(0.693)` log `(1)/(n_(A))`
(Given `n_(O_(A)) = n_(0_(B)) = 1`)
For `B`: at `T = 6a` sec
`6a = (2.303xx3a)/(0.693)` log `(1)/(n_(B))`
`:. (n_(A))/(n_(B)) = (1)/(2)`