Question

The half-life of the isotope \(_{11}\text{Na}^{24}\) is 15 hr. How much time does it take for \((\frac{7}{8})^{\text{th}}\) of a sample of this isotope to decay ?

• A. \(45\) hour
• B. \(60\) hour
• C. \(75\) hour
• D. \(90\) hour

Hint:

If \(\frac78\) decays, \(\frac18\) remains, which takes three half-lives.

Answer 1

The Correct Option is A

Step 1: Track the fraction
After 15 h: $\tfrac12$ left. After 30 h: $\tfrac14$ left. After 45 h: $\tfrac18$ left.

Step 2: Read
$\tfrac18$ left means $\tfrac78$ decayed, which happens at 45 h, option (A).

Final Answer:
It takes 45 hours, option (A). \[ \boxed{45\ \text{hours}} \]