Question

If the half-life of a radioactive substance is 32 hours, then the fraction of the substance decayed in 4 days is

• A. \( \frac{1}{16} \)
• B. \( \frac{1}{8} \)
• C. \( \frac{15}{16} \)
• D. \( \frac{7}{8} \)

Hint:

Use the formula for decay fraction: \( \text{decayed fraction} = 1 - \left(\frac{1}{2}\right)^n \), where \( n \) is the number of half-lives elapsed.

Answer 1

The Correct Option is D

4 days = 96 hours. Half-life \( T_{1/2} = 32 \) hours. So, number of half-lives: \[ n = \frac{96}{32} = 3 \] Remaining fraction = \( \left(\frac{1}{2}\right)^3 = \frac{1}{8} \)
Fraction decayed = \( 1 - \frac{1}{8} = \frac{7}{8} \)