Physical Science Semester A exam question 11
Americium-241 is radioactive substance used in smoke detectors. the half life of americium is 432 years. if a smoke detector initially contains 1 gram of americium 241, how much will remain in 1,296 years?
To solve this problem, we can use the formula for radioactive decay:
N(t) = N₀ * (1/2)^(t/t₁/₂)
where:
N(t) = amount of substance remaining after time t
N₀ = initial amount of substance
t₁/₂ = half-life of the substance
t = time in years
In this case, N₀ = 1 gram, t₁/₂ = 432 years, and t = 1,296 years. Plugging these values into the formula, we get:
N(1,296) = 1 * (1/2)^(1296/432)
Now we can calculate this expression:
N(1,296) = 1 * (1/2)^(3)
Simplifying:
N(1,296) = 1 * (1/8)
N(1,296) = 1/8
Therefore, after 1,296 years, there will be 1/8 of a gram or 0.125 grams of americium-241 remaining in the smoke detector.