Two radioactive elements `A` and `B` have half life of `t` and `2t` respectively. If we start an experiment with 1 mole of each of them, the mole ratio after a time interval of `6t` so `x:y`. Find the value of `x+y`

Answer

`9`

Explanation

NO. of half-lives of `A` in `6t, n_(A) = (6t)/(t) = 6`
No. of half-lives of `B` in `6t, n_(B) = (6t)/(2t) = 3`
`:'` Initial amount of `A` and `B = 1` mole
Let after time `6t, N_(A)` and `N_(B)` moles of `A` and `B` be left.
`:. N_(A) = N_(0) xx ((1)/(2))^(n_(A)) = 1xx ((1)/(2))^(6)`
`N_(B) = N_(0) xx ((1)/(2))^(n_(B)) = 1 xx ((1)/(2))^(3)`
`(N_(A))/(N_(B)) = (1)/(8) = (x)/(y)`
`x + y = 1 + 8 = 9`