Problem: Americium-241 is used in smoke detectors. It has a first order rate constant for radioactive decay of k = 1.6 10-3-1. 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 americium remains after 3 half-lives?

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We’re being asked to calculate the amount of americium (Am) 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:


[A]t=[A]2x


where [A]t = concentration after x half-lives, [A]0 = initial concentration 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 10-3-1. 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 americium remains after 3 half-lives?

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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.