Tritium has a half life of 12.5 years against beta decay. What fraction of a sample of pure tritium disintegrates in 25 years?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( \displaystyle\frac{3}{4} \)
In each half-life, half of the nuclei still present decay. After \( n \) half-lives the fraction remaining is \( 1/2^{n} \).
\( \displaystyle n = \frac{t}{T_{1/2}} = \frac{25}{12.5} = 2 \)
\( \displaystyle \frac{N}{N_0} = \frac{1}{2^{2}} = \frac{1}{4} \)
The question asks for the fraction that has disintegrated, not the fraction left.
\( \displaystyle 1 - \frac{1}{4} = \frac{3}{4} \)
Note: This question is from the pre-rationalised NCERT book (2022-23). The topic was removed from the latest NCERT book (2026-27), and it also appears to be out of the CUET 2026 syllabus.
NCERT (Pre-rationalised edition, 2022-23):
Law of Radioactive Decay – “… Example 13.5 Tritium has a half-life of 12.5 y undergoing beta decay. What fraction of a sample of pure tritium will remain undecayed after 25 y. Solution By definition of half-life, half of the initial sample will remain undecayed after 12.5 y. In the next 12.5 y, one-half of these nuclei would have decayed. Hence, one fourth of the sample of the initial pure tritium will remain undecayed.”