What percentage of a given mass of a radioactive substance will be le…

The correct answer is Option (2) → 3.125%

In each half-life the amount of undecayed substance falls to half of what it was. After \( n \) half-lives,

    \( \displaystyle \frac{N}{N_0} = \left(\frac{1}{2}\right)^{n} \)

Putting \( n = 5 \):

    \( \displaystyle \frac{N}{N_0} = \left(\frac{1}{2}\right)^{5} = \frac{1}{32} \)

    \( \displaystyle \frac{1}{32} \times 100\% = 3.125\% \)

So 3.125% of the substance is left undecayed.

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.”