Two radioactive nuclides A and B have half life of t and 2t respectively . If we start an experiment with one mole of each of them, what will be the mole ratio after a time interval of 6 t ?

Options

A. `1:2`
B. `1:8`
C. `1:6`
D. `1:1`

Answer

B

Explanation

Number of half lives of A in 6t, `n_(A)=(6t)/(t)=6`
Number of half lives of B in 6 t, `n_(B)=(6t)/(2t)=3`
Initial amount of A and B =1mole each.
Suppose `N_(A)` and `N_(B)` are the moles left after the expiry of 6 t
`N_(A)=N_(0)xx((1)/(2))^(nA)`
`N_(A)=1xx((1)/(2))^(6)" "...(i)` ltbr gt `N_(A)=N_(0)xx((1)/(2))^(nB)`
`N_(B)=1xx((1)/(2))^(3)" "...(2)`
Dividing `(N_(A))/(N_(B))=((1//2)^(6))/((1//2)^(3))=((1)/(2))^(3)=(1)/(8)`
Thus `N_(A):N_(B)=1:8`