Q 12-13-021NEETJEE MainMedium
A radioactive sample has $N_0$ nuclei at $t = 0$ and decay constant $\lambda$. The number of nuclei that have decayed after time $t$ is
Answer: (D) $N_0(1 - e^{-\lambda t})$
Concept. Undecayed nuclei: $N = N_0e^{-\lambda t}$. Decayed $=$ initial $-$ undecayed.
Step 1. Subtract.
$$N_0 - N_0e^{-\lambda t} = N_0(1 - e^{-\lambda t})$$
Answer. $N_0(1 - e^{-\lambda t})$ (Option D).
Solution by Sreeraj P, M.Sc Physics