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

Step 1: Find how many half-lives have passed. Number of half-lives = total time divided by half-life = 6 hours / 2 hours = 3 half-lives.

Step 2: In each half-life, the remaining amount becomes half of what it was before. So after 3 half-lives, the fraction remaining is \( \left(\frac{1}{2}\right)^3 \).

Step 3: Calculate this value. \( \left(\frac{1}{2}\right)^3 = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8} \).

Step 4: So after 6 hours, only 1/8 of the original radioactive sample is left, the rest has decayed. This matches option C.