Half life of a radioactive substance A is two times the half life of another radioactive substance B. Initially, the number of nuclei of A and B are `N_(A) and N_(B)` respectively. After three half lives of A, number of nuclei of both are equal. Then the ratio `(N_(A))/(N _(B))` is

Options

A. `(1)/(3)`
B. `(1)/(6)`
C. `(1)/(8)`
D. `(1)/(4)`

Answer

C

Explanation

Three half lives of A are equivalent to six half lives of B. As number of nuclei left are equal in the two cases.
Therefore, `N_(A)((1)/(2))^(3)=N_(B)((1)/(2))^(6)`
`(N_(A))/(N_(B))=((1//2)^(6))/((1//2)^(3))=((1)/(2))^(3)=(1)/(8)`