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The half-life of ${Tc}^{99}$ is 6.0 hr. The delivery of a sample of ${Tc}^{99}$ from the reactor to the nuclear medicine lab of a certain hospital takes 3.0 hr. What is the minimum amount of ${Tc}^{99}$ that must be shipped in order for the lab to receive 10.0 mg?

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$20.0 mg$

$14.1 mg$

$15.0 mg$

$12.5 mg$

answer is C.

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Detailed Solution

Half life period,

$\frac{0.693}{λ} = 6.0 hr$

So,

$λ = \frac{0.693}{t_{1 / 2}} = \frac{0.639}{6.0}$

Amount of ${Tc}^{99}$ which has to be shifted,

$10 = \frac{a}{(2)^{3 / 6}} \Rightarrow a = 14.1 mg$

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