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

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=48 years`, activity of `X=(1)/(4) A_(0)`
(`2` half-lives have elapesed)
At `t=48` years, activity of `Y=(1)/(8) A_(0)` (`3` half-lives have elapsed)
Thus, total activirty of the mixture of `X` and `Y` at `t=48 years` is
`(1)/(4) A_(0) +(1)/(8)A_(0)=(3)/(8)A_(0)`.