Final answer:
To find the amount of a radioactive isotope remaining after a specific period, we use the decay formula with the initial mass and the fraction of the half-life that has elapsed. After performing the calculation using the given initial mass and time period relative to the half-life, we would have the remaining amount of the sample.
Step-by-step explanation:
The question involves calculating how much of a radioactive sample remains after a certain period of time, which is less than a single half-life. Since the half-life of the isotope is 347 years and we are interested in the amount remaining after 264 years, we do not expect exactly half of the sample to have decayed.
To calculate the remaining quantity of a radioactive isotope after a certain time, we can use the formula:
Remaining mass = Initial mass × (1/2)(time elapsed / half-life)
For the given isotope with the stated half-life and initial mass, the calculation is as follows:
Remaining mass = 24717 g × (1/2)(264 years / 347 years)
Carefully performing this calculation will provide us with the mass of the radioactive sample that will remain after 264 years.