# Problem: Americium-241 is used in smoke detectors. It has a first-order rate constant for the radioactive decay of k = 1.6x10-3 yr-1. By contrast, iodine-125, which is used to test for thyroid functioning, has a rate constant for the radioactive decay of k = 0.011 day-1.B) How much of a 1.00 mgmg sample of iodine remains after 4 days?

###### FREE Expert Solution

Recall that radioactive/nuclear decay of isotopes follows first-order kinetics, and the integrated rate law for first-order reactions is:

where:

[N]t = concentration at time t

k = decay constant

t = time

[N]0 = initial concentration.

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###### Problem Details

Americium-241 is used in smoke detectors. It has a first-order rate constant for the radioactive decay of k = 1.6x10-3 yr-1. By contrast, iodine-125, which is used to test for thyroid functioning, has a rate constant for the radioactive decay of k = 0.011 day-1.

B) How much of a 1.00 mg

mg sample of iodine remains after 4 days?