Final answer:
To find out how much of the 198 Au sample would be left after 8.10 days, we can use the formula for radioactive decay. After calculating the number of half-lives that have passed, we can determine the amount remaining. In this case, the correct answer is 12.5g.
Step-by-step explanation:
To calculate how much of the 198 Au sample would be left after 8.10 days, we need to determine how many half-lives have passed and use the formula:
Final amount = Initial amount * (1/2)^(number of half-lives)
In this case, the half-life of 198 Au is 2.70 days. To find the number of half-lives that have passed in 8.10 days, we divide the total duration by the half-life:
Number of half-lives = 8.10 days / 2.70 days = 3 half-lives
Now we can calculate the final amount:
Final amount = 100g * (1/2)^(3) = 100g * (1/8) = 12.5g
Therefore, the correct answer is 12.5g.