Samples of two radioactive nuclides, `X` and `Y`, each have equal activity `A` at time `t=0`. X has a half-life of `24 years` and `Y` a half-life of `16 years`. The samples are mixed together. What will be the total activity of the mixture at `t=48` years?

Options

A. `(1)/(2) A_0`
B. `(1)/(4) A_0`
C. `(3)/(16) A_0`
D. `(3)/(8) A_0`

Answer

D

Explanation

(d) Given
`X` has activity `A_0` at `t = 0` and its half-life is `24` years
`Y` has activity `A_0` at `t = 0` and its half-life is `16` years
At `t = 24` years `rArr` activity of `X = (1)/(2) A_0`
At `t = 48 `years `rArr` activity of `X = (1)/(4) A_0`
At `t = 16` years `rArr` activity of `Y = (1)/(2) A_0`
At `t = 32` years `rArr` activity of `Y = (1)/(4) A_0`
At `t = 48` years `rArr` activity of `Y = (1)/(8) A_0`
Thus total activity of the mixture of `X` and `Y` at `t = 48` years is
`(1)/(4) A_0 + (1)/(8) A_0 (3)/(8) A_0`.