We’re being asked to **determine the half-life of ${}_{95}{}^{241}\mathrm{Am}$**.

Recall that ** half-life** is the time needed for the amount of a reactant to decrease by 50% or one-half.

The half-life of a first-order reaction is given by:

$\overline{){{\mathbf{t}}}_{\raisebox{1ex}{$\mathbf{1}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{2}$}\right.}{\mathbf{=}}\frac{\mathbf{ln}\mathbf{}\mathbf{2}}{\mathbf{k}}}$

where:

**t**_{1/2} = half-life

**k** = decay constant

${}_{95}{}^{241}\mathrm{Am}$ is used in many home smoke alarms. If 85% of the americium in a smoke detector decays in 1250 years, what is the half-life of this isotope?

a. 5.33x10^{3} yr

b. 4.50x10^{1} yr

c. 4.57x10^{3} yr

d. 5.33x10^{2} yr

e. 4.57x10^{2} yr

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