what fraction of an original sample of a radioactive isotope remains after three half-lives have passed?
1/8?
2^3 = 8; therefore you will have 1/8 of the original.
To find the fraction of an original sample of a radioactive isotope that remains after three half-lives, you can use the formula: remaining fraction = (1/2)^(number of half-lives).
In this case, we are looking for the fraction of the original sample remaining after three half-lives. So, we can substitute the value 3 into the formula:
remaining fraction = (1/2)^(3) = 1/8
Therefore, the fraction of the original sample that remains after three half-lives is indeed 1/8.