Answer: Approximately 22.04% of the original.
Explanation: Radioisotopes, like iodine-131, have unstable nuclei. To become stable, they eject some particle (alpha or beta) or energy (gama).
Half-life is a time for half of the substance to decay. Activity is rate of decay, i.e., the number of decays per unit time.
Half-life and Activity are related by the following:
[tex]A=A_{0}.\frac{1}{2^{n}}[/tex]
where
A is activity
[tex]A_{0}[/tex] is initial activity
n is number of half-lives passed in t
For iodine-131, half-live is 8.02, so in 17.5 it has passed:
[tex]n=\frac{17.5}{8.02}[/tex]
n = 2.182
Final activity will be:
[tex]A=\frac{A_{0}}{2^{2.182}}[/tex]
[tex]A = 0.2204A_{0}[/tex]
Which means after 17.5 days, there were 22.04% of the original iodine-101.
