Final answer:
It takes approximately 79734 years for 99% of the plutonium-239 in spent fuel to decay.
Step-by-step explanation:
The half-life of plutonium-239 is 2.41 x 104 years. To determine how many years it takes for 99% of the plutonium-239 to decay, we can use the formula for exponential decay.
In this case, we want to find the time it takes for the amount of plutonium-239 to decrease to 1% of its initial amount. This can be calculated using the formula:
T = (ln(0.01)/ln(0.5)) * half-life
Substituting the given half-life, we get:
T = (ln(0.01)/ln(0.5)) * 2.41 x 104 years
Calculating this, we find that it takes approximately 79734 years for 99% of the plutonium-239 to decay.