Question

It has been shown that the half-life for this radioactive isotope is 20 years. In the year 2000, an archaeology team unearths pottery and is using this isotope for radiometric dating to place the age of the pottery. It is shown that 95% of the nuclei have decayed. How much mass has decayed? How much mass is left?

I'd prefer to be shown a step-by-step on how to solve for these questions. I do better with seeing the step-by-step, and can retain the information better.

Answer 1

(1/2)*n = .05 by the definition of half-life where n is the number of half-lives

n ln .5 = ln .05

n = ln .05 / ln .5 = 4.32 number of half-lives

So 4.32 * 20 = 86.4 years has passed

Actually, they only want the mass left. However, all that has changed is that

95% of the original radioactive atoms have changed to a different form of about the same amount of mass. The amount of mass remaining would be about the same. Also, one doesn't know the percentage of radioactive atoms

that formed the original mass.