After 17,190 years, approximately 62.5 grams of a pure 500 gram sample of carbon-14 would remain.
If you had a pure 500 gram sample of carbon (parent isotope), after 17,190 years, approximately 62.5 grams would be remaining. This can be calculated using the concept of half-life, which is the time it takes for half of a radioactive substance to decay. Since the half-life of carbon-14 is about 5,730 years, we can determine the fraction of the original sample remaining after 17,190 years.
Knowing that three half-lives have passed (1/2 * 1/2 * 1/2 = 1/8), we can calculate the remaining mass with the equation Remaining Mass = (Original Mass) * (1/2)^3 = (500 g) * (1/8) = 62.5 g. Therefore, approximately 62.5 grams of the original 500 gram sample would be left after 17,190 years.