# Problem: Am95241 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. 5.33x103 yrb. 4.50x101 yrc. 4.57x103 yrd. 5.33x102 yre. 4.57x102 yr

###### FREE Expert Solution

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:

where:

t1/2 = half-life

k = decay constant

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###### Problem Details

${}_{95}{}^{241}\mathrm{Am}$ 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. 5.33x103 yr
b. 4.50x101 yr
c. 4.57x103 yr
d. 5.33x102 yr
e. 4.57x102 yr