Final answer:
After 1,000 years, approximately 97.66% of Plutonium-239 would remain, due to its half-life being about 24,000 years.
Step-by-step explanation:
Plutonium-239 is a radioactive isotope with a half-life of about 24,000 years, meaning that after this period, only half of the initial amount of the isotope remains due to radioactive decay.
To determine what fraction or percent of plutonium-239 would remain after a certain period, you can apply the half-life formula.
Assuming you want to know the fraction remaining after 1,000 years, you would calculate how many half-lives (24,000-year intervals) fit into 1,000 years.
Using the formula for exponential decay N(t) = N(0) * (1/2)^(t/T), where N(t) is the remaining quantity at time t, N(0) is the initial quantity, and T is the half-life, we find that after 1,000 years, around 97.66% of plutonium-239 would remain.
This is because 1,000 is 1/24 of the half-life period, so the fraction remaining would be (1/2)^(1/24), which equals approximately 0.9766 or 97.66%.