Americium-241 is a 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?
a
0.5 g
b
1.0 g
c
0.25 g
d
0.125 g
To solve this problem, we can use the formula for radioactive decay:
N(t) = N₀ * (1/2)^(t/τ)
where N(t) is the amount of substance remaining at time t, N₀ is the initial amount of substance, τ is the half-life, and t is the time elapsed.
In this case, N₀ = 1 gram, τ = 432 years, and t = 1,296 years. Substituting these values into the formula:
N(1,296) = 1 * (1/2)^(1,296/432)
Simplifying the exponent:
N(1,296) = 1 * (1/2)^3
N(1,296) = 1/8
Therefore, only 1/8 of the original amount will remain after 1,296 years.
So the answer is d) 0.125 g.