After four half-lives, what fraction of a sample's original radioactive atoms remains?

• A. 1/2
• B. 1/16
• C. 1/8
• D. 1/4

Answer: (B)

Verified step by step guidance

1. Understand that a half-life is the time required for half of the radioactive atoms in a sample to decay.
2. Recognize that after each half-life, the fraction of the original sample remaining is multiplied by 1/2.
3. Express the fraction remaining after n half-lives as \(\left(\frac{1}{2}\right)^n\).
4. Substitute n = 4 (since the problem asks about four half-lives) into the expression to get \(\left(\frac{1}{2}\right)^4\).
5. Simplify the expression to find the fraction of the original sample remaining after four half-lives.