Question

The half-life of a radioactive substance is 10 days. After 30 days, fraction remaining is:

• A. 1/4
• B. 1/8
• C. 1/2
• D. 1/16

Hint:

1 $\rightarrow$ 1/2 (10 days) $\rightarrow$ 1/4 (20 days) $\rightarrow$ 1/8 (30 days).

Answer 1

The Correct Option is B

Step 1: Concept
Half-life ($T_{1/2}$) is the time taken for half of the radioactive nuclei in a sample to decay.

Step 2: Meaning
The fraction remaining after $n$ half-lives is given by the formula $(\frac{1}{2})^{n}$.

Step 3: Analysis
Given total time is 30 days and half-life is 10 days, the number of half-lives $n = \frac{30}{10} = 3$.

Step 4: Conclusion
Substituting $n=3$ into the formula, the fraction remaining is $(\frac{1}{2})^{3} = \frac{1}{8}$. Final Answer: (B)