Question

The half-life of a radioactive element is 10 days. The time required for 75% of the element to decay is:

• A. 20 days
• B. 10 days
• C. 30 days
• D. 15 days

Hint:

1 half-life = 50% remains; 2 half-lives = 25% remains; 3 half-lives = 12.5% remains.

Answer 1

The Correct Option is A

Step 1: Concept
Decay follows the rule: $N = N_{0}(1/2)^{n}$, where $n$ is the number of half-lives.
Step 2: Analysis
75% decay means 25% (or $1/4$) remains.
$1/4 = (1/2)^{n} \Rightarrow n = 2$.
Total time $= n \times T_{1/2} = 2 \times 10$.
Step 3: Conclusion
The required time is 20 days.
Final Answer: (A)