Question

A radioactive sample consists of two distinct species having the equal number of atoms initially. The mean-life time 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 represent the form of this plot ?

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

When a radioactive sample decays simultaneously with different processes,

The effective decay constant is goven by,

$\lambda ={\lambda }_1+{\lambda }_2$

By law of radioactivity,

$N=N_0{e}^{-\lambda t}$

Therefore, total number of nuclei decrease exponentially with time as represented by option $\left(A\right)$

The total number of nuclei neither remains constant, as in option $\left(B\right)$ nor can ever increase, as in option $\left(C\right)$ and $\left(D\right)$.

Hence, option $\left(A\right)$ is correct.