Final answer:
Approximately 97% of Plutonium-239 remains after 1000 years, according to the calculations based on its half-life of 24,000 years using the exponential decay formula.
Step-by-step explanation:
The question is asking what percentage of Plutonium-239 remains after 1000 years, knowing that the half-life of Plutonium-239 is 24,000 years. Since half-life is the time it takes for half of a radioactive substance to decay, after one half-life, 50% of the original material remains. To calculate the remaining amount after 1000 years, we will use the formula for exponential decay:
N(t) = N0 * (1/2)^(t/T)
Where:
- N(t) is the remaining quantity of the substance after time ‘t’
- N0 is the initial quantity of the substance
- t is the time that has passed
- T is the half-life of the substance
Using the given values:
- t = 1000 years
- T = 24000 years
We substitute the values into the formula:
N(t) = N0 * (1/2)^(1000/24000)
After calculating:
N(t) = N0 * (1/2)^(1/24)
Since the calculations might not be straightforward, we can approximate using logarithms or a scientific calculator to find that the remaining amount approximately equals to 97% of the original quantity. Therefore, the answer is (c) 97%.