A mixture of and has a specific activity of sample. The half-lives of the isotopes are years and yea — Nuclear Chemistry and Radioactivity Chemistry Question
Question
A mixture of $\text{Pu}^{239}$ and $\text{Pu}^{240}$ has a specific activity of $6 \times 10^9 \text{ dps per gram}$ sample. The half-lives of the isotopes are $2.40 \times 10^4$ years and $7.17 \times 10^3$ years, respectively. The mass per cent of $\text{Pu}^{239}$ in the sample is
Answer: A
💡 Solution & Explanation
Let fraction of $\text{Pu}^{239}$ be $x$. Total activity $A = A_{239} + A_{240} = \lambda_{239}N_{239} + \lambda_{240}N_{240}$. By plugging in half lives and solving for $x$, $2.3x \times 10^9 + 7.69(1-x) \times 10^9 = 6.0 \times 10^9$. Solving gives $x \approx 0.311$, or 31.1%. Therefore, correct answer is A.
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