After three half-lives, which fraction remains of the original sample?

After three half-lives, which fraction remains of the original sample?

• A. 1/8
• B. 1/4
• C. 1/2
• D. 1

Answer: (A)

In radioactive decay, the amount left after each half-life is halved. After three half-lives, you multiply by 1/2 three times: (1/2) × (1/2) × (1/2) = 1/8. So the fraction remaining is one-eighth of the original. The other options would correspond to fewer half-lives (1/2 after one, 1/4 after two) or the full original amount (no decay), which aren’t what three half-lives produce.

In radioactive decay, the amount left after each half-life is halved. After three half-lives, you multiply by 1/2 three times: (1/2) × (1/2) × (1/2) = 1/8. So the fraction remaining is one-eighth of the original. The other options would correspond to fewer half-lives (1/2 after one, 1/4 after two) or the full original amount (no decay), which aren’t what three half-lives produce.