Calculate the amount of americium-241 consumed in a smoke detector (initially containing 6.6000 µg of Am), in micrograms

Question

Americium-241 is widely used in smoke detectors. Calculate the amount of americium-241 consumed in a smoke detector (initially containing 6.6000 µg of Am), in micrograms, that has been used for 1.000 year if the half-life is 433 years.

Answer 1

Decay of Am-241 follows first order kinetics.

For a 1st order decay, the fraction remaining (FR) = 0.5ⁿ where n is the number of half lives that have elapsed.

FR = 0.5ⁿ

n = 1 yr / 433 yrs = 0.00231 half lives have elapsed

FR = 0.5^0.00231

FR = 0.998

Since 0.998 is the fraction remaining (99.8%), the fraction used up in 1 year = 1.000 - 0.998 = 0.00200 (0.2%)

In micrograms, this is

0.00200 x 6.600 = 0.0132 micrograms used