If the half-life of a radioactive nuclide is 16 hours, what fraction of original sample will remain undecayed after 48 hours?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( \displaystyle\frac{1}{8} \)
In each half-life the number of undecayed nuclei falls to half. After \( n \) half-lives the fraction left is \( (1/2)^{n} \).
\( \displaystyle n = \frac{t}{T_{1/2}} = \frac{48\,\mathrm{h}}{16\,\mathrm{h}} = 3 \)
\( \displaystyle \frac{N}{N_0} = \left(\frac{1}{2}\right)^{3} = \frac{1}{8} \)
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.”