The fractional decay of a radioactive nuclide over time can be mathematically represented. If the in — Nuclear Chemistry and Radioactivity Chemistry Question
Question
The fractional decay of a radioactive nuclide over time $t$ can be mathematically represented. If the initial number of nuclei is $N_0$, what is the fraction of nuclei that has *decayed* at any time $t$ (where $\lambda$ is the decay constant)?
Answer: B
💡 Solution & Explanation
The number of nuclei remaining undecayed is $N_t = N_0 e^{-\lambda t}$. The number that has decayed is $N_0 - N_t = N_0(1 - e^{-\lambda t})$. The fraction decayed is $(N_0 - N_t)/N_0 = 1 - e^{-\lambda t}$.
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