Question 11.2: Iodine-131 is a radionuclide that is frequently used in nucl......
Iodine-131 is a radionuclide that is frequently used in nuclear medicine. Among other things, it is used to detect fluid buildup in the brain. The half-life of iodine-131 is 8.0 days. How much, in grams, of a 0.16-g sample of iodine-131 will remain undecayed after a period of 32 days?
Step-by-Step
First, we must determine the number of half-lives that have elapsed.
32 \ \cancel{days}\times (\frac{1 \ half-life}{8.0 \ \cancel{days}} ) = 4 half-lives
Knowing the number of elapsed half-lives and the original amount of radioactive iodine present, we can use the equation
\begin{pmatrix} Amount \ of \ radionuclide \\ undecayed \ after \ n \ half-lives \end{pmatrix} = \begin{pmatrix} original \ amount \\ of \ radionuclid \end{pmatrix}\times (\frac{1}{2^{n}} )= 0.16 g × \frac{1}{2^{4}} 
= 0.16 g × \frac{1}{16} = 0.010 g
Constructing a tabular summary of the amount of sample remaining after each of the elapsed half-lives yields
\begin{matrix} Half-lives \quad\quad \ \ \ & 0 & 1 & 2 & 3 & 4 \\ Number \ of \ days \ \quad & 0 & 8 & 16 & 24 & 32 \\ Amount \ remaining & 0.16 \ g & 0.080 \ g & 0.040 \ g & 0.020 \ g & 0.010 \ g \end{matrix}
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