We’re being asked to calculate** ****the amount of iodine (I)** remaining after **3 half-lives** if we start with **1 mg sample**.

Recall that ** half-life** is the time needed for the amount of a reactant to decrease by 50% or one-half. One way to determine the amount remaining after x half-lives is:

$\overline{){\mathbf{\left[}\mathbf{A}\mathbf{\right]}}_{{\mathbf{t}}}{\mathbf{=}}\frac{\left[A\right]}{{\mathbf{2}}^{\mathbf{x}}}}$

where **[A] _{t}** = concentration or amount after x half-lives

**[A] _{0}** = initial concentration or amount

and **x** = number of half-lives.

Americium-241 is used in smoke detectors. It has a
first order rate constant for radioactive decay of k = 1.6 x 10^{-3 }yr^{-1}. By contrast, iodine-125, which is used to test for thyroid functioning, has a rate constant for radioactive decay of k = 0.011 day^{-1}.

How much of a 1.00 mg sample of iodine remains after 3 half-lives?