Calculate the amount of americium-241 consumed in a smoke detector (initially containing 4.0000 µg of Am), in micrograms, that has been used for 1.000 year if the half-life is 433 years.

Question

Americium-241 is widely used in smoke detectors. Calculate the amount of americium-241 consumed in a smoke detector (initially containing 4.0000 µg of Am), in micrograms, that has been used for 1.000 year if the half-life is 433 years.

Answer 1

Fraction remaining (FR) = 0.5ⁿ where n = number of half lives that have elapsed

number of half lives = n = 1.000 year / 433 yrs = 0.00231 half lives elapsed

FR = 0.5^0.00231 = 0.9984 (essentially 99.84% of the americium-241 remains)

How much was consumed?

If 99.84% remains, that means that 0.16% was used.

Number of micrograms (ug) used = 0.16% x 4.0000 ug = 0.006400 ug used