A radioactive sample has a half-life of 3 years. What fraction remains after 9 years?

A radioactive sample has a half-life of 3 years. What fraction remains after 9 years?

• A. 1/4 (25%)
• B. 1/8 (12.5%)
• C. 1/16 (6.25%)
• D. 1/2 (50%)

Answer: (B)

The idea tested is how a half-life reduces the amount of a radioactive sample over time. Each half-life cuts what you have in half. Since the half-life is 3 years, after 9 years you’ve gone through 9 ÷ 3 = 3 half-lives. Halving three times gives: (1/2) × (1/2) × (1/2) = 1/8. So the remaining fraction is 1/8 (which is 12.5%).

The idea tested is how a half-life reduces the amount of a radioactive sample over time. Each half-life cuts what you have in half. Since the half-life is 3 years, after 9 years you’ve gone through 9 ÷ 3 = 3 half-lives. Halving three times gives: (1/2) × (1/2) × (1/2) = 1/8. So the remaining fraction is 1/8 (which is 12.5%).