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?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Integrated Rate Law concept. You can view video lessons to learn Integrated Rate Law. Or if you need more Integrated Rate Law practice, you can also practice Integrated Rate Law practice problems.