After a radioactive sample undergoes two half-lives, what fraction of the original sample remains?

• A. 1/8
• B. 1/4
• C. 2/3
• D. 1/2

Answer: (B)

Verified step by step guidance

1. Recall that a half-life is the time required for half of a radioactive sample to decay.
2. After one half-life, the fraction of the original sample remaining is \(\frac{1}{2}\).
3. After two half-lives, the fraction remaining is the fraction remaining after the first half-life multiplied by \(\frac{1}{2}\) again, so it is \(\frac{1}{2} \times \frac{1}{2}\).
4. Express this multiplication as an exponent: after two half-lives, the fraction remaining is \(\left(\frac{1}{2}\right)^2\).
5. Calculate the fraction \(\left(\frac{1}{2}\right)^2\) to find the fraction of the original sample remaining after two half-lives.