Half-life of a radioactive substance A is `4 days`. The probability that a nuclear will decay in two half-lives is

Options

A. `1/4`
B. `1/2`
C. `3/4`
D. `1`

Answer

C

Explanation

`N/N_0 = (1/2)^(t//T)` but it is given that t = 2T
`therefore N/N_0 = (1/2)^2 = 1/4`
`therefore N = (N_0)/(4)` i.e. after 2 half lives, `(N_0)/(4)` atoms will remains undecayed and `(3N_0)/(4)` atom will decay .
`therefore` The probability that the number of atoms disintegrate (decay) in time is
`P= (N_0 - N)/(N_0) = 1- (N)/(N_0) = 1 - 1/4 = 3/4`