A radioactive nucleus A has a single decay mode with half life `tau_(A)`. Another radioactive nucleus B has two decay modes 1 and 2. If decay mode 2 were absent, the half life of B would have been `tau_(A)//2`. If decay mode 1 were absent, the half life of B would have been `3 tau_(A)`, then the ratio `tau_(B)//tau_(A)` is–

Options

A. `(3)/(7)`
B. `(7)/(2)`
C. `(7)/(3)`
D. 1

Answer

A

Explanation

`lamda_(B) = lamda_(1) +lamda_(2)`
`(ln 2)/(tau_(B)) = (2ln 2)/(tau_(A)) + (ln 2)/(3 tau_(A)) = (7 ln 2)/(3 tau_(A)) rArr (tau_(B))/(tau_(A))= (3)/(7)`