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
0.25 g
b
0.125 g
c
1.0 g
d
0.5 g
The formula to calculate the amount of a radioactive substance remaining after a certain amount of time can be given by:
Amount Remaining = Initial Amount * (1/2)^(Time elapsed / Half-life)
In this case, the initial amount is 1 gram and the half-life is 432 years. We want to find the amount remaining after 1,296 years.
Amount Remaining = 1 gram * (1/2)^(1296 / 432)
Simplifying the exponent:
Amount Remaining = 1 gram * (1/2)^3
Using the exponent rule for negative exponents:
Amount Remaining = 1 gram * 1/8
Amount Remaining = 1/8 gram
So, the amount of americium-241 remaining in the smoke detector after 1,296 years is 0.125 grams.
Therefore, the answer is option b) 0.125 g.