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

`t_(B) = (1n2)/(lambda_("eff"))`
`lambda_(eff) = lambda_(1) + lambda_(2)`
`= (2 1n 2)/(t_(A)) + (1n2)/(3t_(A))`
Radioactivity and Nuclear Transformation
`:. T_(B) = (1n2)/((21n 2)/(t_(A)) + (1n2)/(3t_(A))) = ((3)/(7)) t_(A))`
`(t_(B))/(t_(A)) = (3)/(7)`