Question

A radioactive isotope has a half-life of 2 hours. The fraction of the original sample remaining after 6 hours is:

• A. 1/6
• B. 1/3
• C. 1/8
• D. 1/4

Hint:

Count how many half-lives fit into 6 hours, then halve the amount that many times.

Answer 1

The Correct Option is C

Track the amount left after each half-life directly instead of using a formula.

• Start with a sample of amount $N_0$ at time zero.
• After the first half-life (2 hours), the amount left is $N_0/2$.
• After the second half-life (4 hours total), half of that decays again, leaving $N_0/4$.
• After the third half-life (6 hours total), half of that decays again, leaving $N_0/8$.
• Exactly 3 half-lives fit into 6 hours, since $6 \div 2 = 3$, and the fraction remaining after 3 successive halvings is $1/8$.
• The correct option is C.