A radioactive isotope is being produced at a constant rate in an experiment. The isotope has a half- — Nuclear Chemistry and Radioactivity Chemistry Question
Question
A radioactive isotope is being produced at a constant rate $\text{d}N/\text{dt} = R$ in an experiment. The isotope has a half-life, $t_{1/2}$. After a time $t \gg t_{1/2}$, the number of active nuclei will become constant. The value of this constant is
Answer: C
💡 Solution & Explanation
The net rate of change of nuclei is $\frac{dN}{dt} = R - \lambda N$. Once a steady state is reached, the number of nuclei is constant, so $\frac{dN}{dt} = 0$. This gives $R = \lambda N$, or $N = R/\lambda$. Therefore, correct answer is C.
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