# Problem: 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?

###### FREE Expert Solution

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.

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###### Problem Details

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?