Question

A radioactive material has a half life of 10 years. What fraction of radioactive nuclei will remain undecayed with respect to the initial sample after 20 years?

• A. 1/2
• B. 1/4
• C. 1/8
• D. 1/16

Hint:

1 Half-life $\rightarrow$ 50% left. 2 Half-lives $\rightarrow$ 25% (1/4) left. 3 Half-lives $\rightarrow$ 12.5% (1/8) left.

Answer 1

The Correct Option is B

Step 1: Concept
The fraction of nuclei remaining after $n$ half-lives is $(\frac{1}{2})^n$.

Step 2: Analysis
Total time = 20 years. Half-life = 10 years.
Number of half-lives ($n$) = $20 / 10 = 2$.

Step 3: Calculation
Fraction remaining = $(\frac{1}{2})^2 = 1/4$.

Step 4: Conclusion
After 20 years, 1/4 of the sample remains. Final Answer: (B)