Final answer:
After 90 days, only 0.78125g of a 100g sample of the element with a half-life of 1 week remains, as calculated using the formula for exponential decay.
Step-by-step explanation:
The student's question involves calculating the remaining amount of a radioactive substance after a period of time, specifically related to its half-life. With a half-life of 1 week for element T, we need to determine how many half-lives pass in a period of 90 days. Since 1 week is equivalent to 7 days, there will be 90/7 = approximately 12.86 half-lives in 90 days. To determine how much of the original 100g sample remains, we use the formula for exponential decay:
Remaining amount = Initial amount × (1/2)^number of half-lives
Thus:
Remaining amount = 100g × (1/2)^(12.86)
Performing this calculation gives us a remaining amount significantly less than 1g, which indicates that option A (0.78125g) is the closest correct answer. Therefore:
After 90 days, 0.78125g of a 100g sample of element T is left.