After three half-lives have elapsed, what fraction of the original radioactive sample remains?

• A. 1/4
• B. 1/16
• C. 1/8
• D. 1/2

Answer: (C)

Verified step by step guidance

1. Recall that the fraction of a radioactive sample remaining after a certain number of half-lives is given by the formula: \(\left( \frac{1}{2} \right)^n\), where \(n\) is the number of half-lives elapsed.
2. Identify the number of half-lives elapsed in the problem, which is 3.
3. Substitute \(n = 3\) into the formula to get the fraction remaining: \(\left( \frac{1}{2} \right)^3\).
4. Simplify the expression by calculating the power: \(\left( \frac{1}{2} \right)^3 = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}\).
5. Express the final fraction as \(\frac{1}{8}\), which represents the fraction of the original sample remaining after three half-lives.