Q 12-13-096JEE MainJEE Main 2021 (27 Jul, Shift 1)Easy
If $f$ denotes the ratio of the number of nuclei decayed $(N_d)$ to the number of nuclei at $t = 0$ $(N_0)$, then for a collection of radioactive nuclei, the rate of change of $f$ with respect to time is given as: [$\lambda$ is the radioactive decay constant]
Answer: (C) $\lambda e^{-\lambda t}$
$N_d = N_0 - N_0e^{-\lambda t}$, so $f = 1 - e^{-\lambda t}$.
$$\frac{df}{dt} = \lambda e^{-\lambda t}$$
Solution by Sreeraj P, M.Sc Physics