The half-life of a particular radioactive isotope of element X is 100 years.If you know that 400 years ago a fossil contained 10 mg of this isotope, you would expect to find about _______ mg in that fossil today.

Question

Quizplus · Accepted Answer

Since the half-life of the isotope is 100 years, we can calculate how many half-lives have elapsed since the fossil was created:

400 years / 100 years/half-life = 4 half-lives

Each half-life reduces the amount of isotope by a factor of 2, so after 4 half-lives the amount remaining would be:

10 mg / 2^4 = 10 mg / 16 = 0.625 mg

Rounding this to one decimal place gives us the nearest answer choice, which is C: 0.6 mg.

The Half-Life of a Particular Radioactive Isotope of Element X