The half-life of a radioactive isotope is 10 days. What fraction of the original sample remains after 30 days? MCQ with Answer and Explanation

The half-life of a radioactive isotope is 10 days. What fraction of the original sample remains after 30 days?
A. 1/4
B. 1/3
C. 1/8
D. 1/2
Answer: Option C
Solution (By JKSSB Mock Tests)
After each half-life, half of the remaining atoms decay. Number of half-lives n = total time / half-life = 30/10 = 3. Fraction remaining = (1/2)ⁿ = (1/2)³ = 1/8. Thus 12.5% remains. Radioactive decay follows first-order kinetics. Exam trick: fraction remaining = (0.5)^(t/T), where T is half-life. After 4 half-lives, 1/16 remains.

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