Calculate the amount of americium-241

Question

Americium-241 is widely used in smoke detectors. Calculate the amount of americium-241 consumed in a smoke detector (initially containing 5.0000 µg of Am), in micrograms, that has been used for 1.000 year if the half-life is 433 years.

Answer 1

Radionuclide decay is considered a first order reaction. As such, we can use the following relationship:

FR = 0.5ⁿ

FR = fraction remaining = ?

n = number of half lives that have elapsed = 1.000 yr / 433 yrs = 0.002309 half lives

FR = 0.5^0.002309 = 0.9984 This is the Fraction Remaining

The fraction Consumed would thus be 1.0000 - 0.9984 = 0.00160

Amount consumed = 0.0016 x 5.0000 ug = 0.00800 ug consumed