Question

Iodine-131 has a half-life of 8 hours. If a solution containing 5 grams of iodine-131 is injected into a patient, how long will it take until the total amount of iodine-131 left in the patient is 5 μg (5 micrograms)?

Answer 1

Step 1

The mass of I-131 left in the body could be calculated as follows:

`\begin{gathered} M\text{ = M}_0xe^(-\lambda xt) \\ \lambda\text{ = }\frac{ln\text{ 2}}{t_{(1)/(2)}} \\ t_{\frac{1}{2\text{ }}}=\text{ half-life} \end{gathered}`

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Step 2

Data provided:

M = 5 μg (1 g = 1000000 μg) => 5 μg x (1 g/1000000 μg) = 5x10^-6 g

Mo = 5 g

Half-life = 8 hours = 8 h

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Step 3

Procedure:

`\begin{gathered} \lambda\text{ = }\frac{ln\text{ 2}}{8\text{ h}}=\text{ 0.087 1/h} \\ ---------- \\ M/M_0=\text{ }e^{-0.087\text{ 1/h x t}} \\ (5x10^(-6))/(5)=e^{-0.087\text{ 1/h x t}} \\ ln\text{ }(5x10^(-6))/(5)=-0.087\text{ x t} \\ 159\text{ h = t} \end{gathered}`

Answer: t = 159 h (approx.)