Step 1
The mass of I-131 left in the body could be calculated as follows:
[tex]\begin{gathered} M\text{ = M}_0xe^{-\lambda xt} \\ \lambda\text{ = }\frac{ln\text{ 2}}{t_{\frac{1}{2}}} \\ t_{\frac{1}{2\text{ }}}=\text{ half-life} \end{gathered}[/tex]--------
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
-------
Step 3
Procedure:
[tex]\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}} \\ \frac{5x10^{-6}}{5}=e^{-0.087\text{ 1/h x t}} \\ ln\text{ }\frac{5x10^{-6}}{5}=-0.087\text{ x t} \\ 159\text{ h = t} \end{gathered}[/tex]Answer: t = 159 h (approx.)
