Question

If the sample has 1/8 of the radioactive nuclei left, how many half-lives would the sample have gone through?

Answer 1

The equation for radioactive decay is:

\[m=m_0 \left( 1 \over 2 \right)^n\]
Where m is the final mass of the sample, m0 is your starting mass, and n is the number of half-lives that have passed.

In this case, m=1/8m0:
\[{1 \over 8}m_0=m_0 \left( 1 \over 2 \right)^n\]\[{1 \over 8}= \left( 1 \over 2 \right)^n\]
Solve for n and you have your answer!