A particular radioactive sample has a half life of 12 years. The fraction of it that remains undecayed after 48 years, will be :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( \displaystyle\frac{1}{16}^{\mathrm{th}} \) of its initial amount
In each half-life the number of undecayed nuclei falls to half. After \( n \) half-lives (the number of half-lives is the time divided by the half-life)
\( \displaystyle \frac{N}{N_0} = \frac{1}{2^{n}} \)
\( \displaystyle n = \frac{t}{T_{1/2}} = \frac{48\,\mathrm{years}}{12\,\mathrm{years}} = 4 \)
\( \displaystyle \frac{N}{N_0} = \frac{1}{2^{4}} = \frac{1}{16} \)
So \( \frac{1}{16} \)th of the sample remains undecayed.