Question

The half-life of a radioactive element is 3.8 days. The fraction left after 19 days will be

• A. 0.124
• B. 0.062
• C. 0.093
• D. 0.031

Hint:

The fraction remaining after \( n \) half-lives is \( \left( \frac{1}{2} \right)^n \).

Answer 1

The Correct Option is D

Step 1: Formula for half-life decay.
The fraction of a substance remaining after \( n \) half-lives is given by \( \left( \frac{1}{2} \right)^n \). The number of half-lives in 19 days is \( \frac{19}{3.8} = 5 \). Therefore, the remaining fraction is: \[ \left( \frac{1}{2} \right)^5 = 0.03125 \]
Step 2: Conclusion.
Thus, the correct answer is option (D).

Final Answer: \[ \boxed{0.031} \]