The half-life of a radioactive nucleus is `50` days. The time interval `(t_2 -t_1)` between the time `t_2` when `(2)/(3)` of it has decayed and the time `t_1` when `(1)/(3)` of it had decayed is

Options

A. 30 days
B. 50 days
C. 60 days
D. 15 days

Answer

B

Explanation

(b) Active fraction at instant `t_2, (1)/(2^(t_2//T_(1//2)) = (1)/(3)`
Active fraction at instant `t_1, (1)/(2^(t_1//T_(1//2)) = (2)/(3)`
`(2^(t_2//T_(1//2)))/(2^(t_1//T_(1//2))) = 2 rArr 2^((t_2 - t_1)/(t_1//2)) = 2`
`t_2 - t_1 = T_(1//2) = 50 days`.