Final answer:
Approximately 2059.2 grams of Element X would remain after 25 years, given its half-life of 13 years and an initial mass of 8800 grams.
Step-by-step explanation:
Understanding Radioactive Half-Life Calculation
Element X has a half-life of 13 years, which means that every 13 years, its mass decreases by half. Knowing the initial mass of Element X is 8800 grams, we want to determine the remaining mass after 25 years. To solve this, we use the formula for the decay of a radioactive substance:
Remaining mass = Initial mass × (1/2)^(time/half-life period)
In this case, the time is 25 years, and the half-life period is 13 years, leading to the following calculation:
Remaining mass = 8800 × (1/2)^(25/13)
= 8800 × (1/2)^(1.923) ≈ 8800 × 0.234
≈ 2059.2 grams
Therefore, approximately 2059.2 grams of Element X would remain after 25 years.