The half life of Am-241 is 432 y. If 2.00 g of Am-241 is present in a sample, what mass of Am-241 is present after 1000.0 y?

To determine the mass of Am-241 present after 1000.0 years, we need to use the concept of half-life.

The half-life of a radioactive substance is the time it takes for half of the initial amount of the substance to decay or disintegrate.

In this case, the half-life of Am-241 is given as 432 years, which means that after every 432 years, half of the Am-241 will decay.

To calculate the mass of Am-241 after 1000.0 years, we need to determine how many half-lives have passed in that time frame.

The formula to calculate the number of half-lives is:

Number of half-lives = (Time elapsed) / (Half-life)

In this case:

Number of half-lives = 1000.0 years / 432 years

Number of half-lives = 2.315 (rounded to three decimal places)

This means that approximately 2.315 half-lives have passed in 1000.0 years.

To find the remaining mass of Am-241, we can use the formula:

Remaining mass = Initial mass * (1/2)^(Number of half-lives)

Substituting the values:

Remaining mass = 2.00 g * (1/2)^(2.315)

Remaining mass ≈ 2.00 g * 0.418

Remaining mass ≈ 0.836 g (rounded to three decimal places)

Therefore, after 1000.0 years, approximately 0.836 grams of Am-241 will remain in the sample.

k = 0.693/t1/2

Solve for k and substitute in the equation below.

ln(No/N) = kt
No = 2.00
N = unknown
k from above
t = 1000 years.