Final answer:
It will take approximately 12619.08 years for plutonium-240 to decay to 25% of its original amount, given that the decay constant is 0.00011 per year.
Step-by-step explanation:
Calculating the Time for Decay of Plutonium-240
To calculate the time it will take for a quantity of plutonium-240 to decay to 25% of its original amount, we can use the following relationship between the decay constant (k) and the half-life (t₁/₂) of a radioactive isotope:
k = ln(2) / t₁/₂
First, solve for the half-life using the provided decay constant k = 0.00011 per year.
t₁/₂ = ln(2) / k
Then use the fact that every half-life reduces the remaining quantity by half. Since we want the quantity to reduce to 25%, we need it to go through two half-lives (from 100% to 50%, and then from 50% to 25%).
Let's calculate the half-life:
t₁/₂ = ln(2) / 0.00011 ≈ 6309.54 years
To decay to 25% of its original value, two half-lives will pass:
Total time = 2 * t₁/₂
Total time = 2 * 6309.54 years
Total time ≈ 12619.08 years
So, it will take approximately 12619.08 years for plutonium-240 to decay to 25% of its original amount.