Three fourth of the active decays in a radioactive sample in `3//4 sec`. The half-life of the sample is

Options

A. `1sec`
B. `1//2sec`
C. `(3)/(4)sec`
D. `(3)/(8)sec`

Answer

D

Explanation

`N= (N_(0))/(4) rArr (N)/(N_(0)) = (1)/(4) = ((1)/(2))^(2) = ((1)/(2))^(n)`
Number of half lives `n = 2`
`t = nT_(1//2) rArr 3/4 = 2 xx T_(1//2) rArr T_(1//2) = 3/8 sec`