Am-241 has a half life of roughly 432 years. How much of a 100 gram sample would remain after 1,296 years?
Answer to the nearest tenth.

12.5 g

Explanation:

From the question given above, the following data were obtained:

Half-life (t½) = 432 years.

Original amount (N₀) = 100 g

Time (t) = 1296 years

Amount remaining (N) =?

Next, we shall determine the number of half-lives that has elapse. This can be obtained as follow:

Half-life (t½) = 432 years.

Time (t) = 1296 years

Number of half-lives (n) =?

n = t / t½

n = 1296 / 432

n = 3

Thus, 3 half-lives has elapsed.

Finally, we shall determine the amount of the isotope remaining. This can be obtained as follow:

Original amount (N₀) = 100 g

Number of half-lives (n) = 3

Amount remaining (N) =?

N = 1/2ⁿ × N₀

N = 1/2³ × 100

N = 1/8 × 100

N = 0.125 × 100

N = 12.5 g

Thus, 12.5 g of the isotope is remaining.