Question

Americium-241 is widely used in smoke detectors. Calculate the amount of americium-241 consumed in a smoke detector (initially containing 5. 00 µg of am) that has been used for one year if the half-life is 433 years.

Answer 1

0.008 μg of americium-241 was consumed in a smoke detector

The half life of a substance is:

$N=N_o(\frac{1}{2} )^\frac{t}{t_\frac{1}{2} } \\\\Where\ N\ is\ the \ amount \ of\ substance\ remaining\ after\ t\ years,\\N_o\ is\ the\ original\ amount, t_\frac{1}{2} \ is\ half\ life.\\\\\\Given\ N_o=5\ \mu g,t=1\ year,t_\frac{1}{2} =433\ years. Hence:\\\\N=5*10^{-6}(\frac{1}{2} )^\frac{1}{433} =4.992\ \mu g$

The amount consumed = 5 - 4.992 = 0.008 μg

0.008 μg of americium-241 was consumed in a smoke detector.

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