A radioactive sample consists of two distinct species having equal number of atoms initially. The mean life of one species is `tau` and that of the other is `5 tau`. The decay products in both cases are stable. A plot is made of the total number of radioactive nuclei as a function of time. Which of the following figure best represents the form of this plot?
(a), (b), (c), (d)

Options

A.
B.
C.
D.

Answer

d

Explanation

`N_(1)=N_(0)e^(-t/tau)" "(i) and tau=(1)/(lambda)`
`N_(2)=N_(0) e^(-lambda_(2) t) =N_(0) e^(- t/5tau)" "and 5 tau (1)/(lambda_(2))`.
Adding (i)and (ii), we get
`N=N_(1)+N_(2)=N_(0)(e^(-t//5tau) +e^(-t//5tau))`
(a) is not correct option as there is a time `tau` for which `N` is constant, which means for time `tau` there is no process of radioactive atoms which is impossible as N will only decreases exponentially. Hence, the correct option is (d).