The half-life of is 6.0 h. The delivery of a sample of from the reactor to the nuclear medicine lab — Nuclear Chemistry and Radioactivity Chemistry Question
Question
The half-life of $\text{Tc}^{99}$ is 6.0 h. The delivery of a sample of $\text{Tc}^{99}$ from the reactor to the nuclear medicine lab of a certain hospital takes 3.0 h. What is the minimum amount of $\text{Tc}^{99}$ that must be shipped in order for the lab to receive 10.0 mg?
Answer: C
💡 Solution & Explanation
The transit time (3.0 h) is exactly 0.5 half-lives. Remaining amount $N = N_0 (1/2)^{0.5} = N_0 / \sqrt{2}$. To receive 10.0 mg, shipped amount $N_0 = 10.0 \times \sqrt{2} \approx 10.0 \times 1.414 = 14.14 \text{ mg}$. Therefore, correct answer is C.
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