The radioactive elements `A` and `B` have half-lives of `15` and 5 minute respectively. Thew experiment begins with 4 times the number the number of `B` atoms as `A` atoms. At which of the followig times does the number fo `A` atoms left equals the number of `B` atoms left:

Options

A. 6 min
B. 12 min
C. 48 min
D. 30 min

Answer

D

Explanation

Let the initial amount of Y = 1
So, the initial amount of X = 8
X decomposes as
`8 overset(1)to 4 overset(2)to 2overset(3)to 1 overset(4)to 1 overset(4)to 1/2 overset(5)to 1/4`
Number of half lives of X = 5
Y decomposes as
`1 overset(1)to 1/2 overset(2) 1/4`
Number of half lives of Y = 2
So, total time t = n `xx t_(1//2)` = `5xx6` = 30 min