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

$\overline{){\mathbf{ln}}{\mathbf{\left[}\mathbf{N}\mathbf{\right]}}_{{\mathbf{t}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{\mathbf{-}}{\mathbf{kt}}{\mathbf{}}{\mathbf{+}}{\mathbf{\hspace{0.17em}}}{\mathbf{ln}}{\mathbf{\left[}\mathbf{N}\mathbf{\right]}}_{{\mathbf{o}}}}$

where:

**[N] _{t}** = concentration at time t

**k** = decay constant

**t** = time

**[N] _{0}** = initial concentration.

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?

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