Final answer:
To determine how much of the radioactive isotope will be left after 264 years, we can use the formula: Amount Remaining = Initial Amount × (0.5)^Number of Half-Lives. Plugging in the values, we get approximately 1237.13 grams.
Step-by-step explanation:
To determine how much of the radioactive isotope will be left after 264 years, we need to calculate the number of half-lives that have occurred in that time. Since the half-life of the isotope is 347 years, we can divide 264 by 347 to find the number of half-lives. In this case, the number of half-lives is approximately 0.76. To calculate the amount remaining, we can use the formula: Amount Remaining = Initial Amount × (0.5)Number of Half-Lives. Plugging in the values, we get: Amount Remaining = 2471.7 g × (0.5)0.76 which is approximately 1237.13 grams.