Concept:You must distinguish carefully between the percentage of atoms
remaining and the percentage of atoms that have
decayed.
Formula:$$ \text{Remaining} = N_0 \left(\frac{1}{2}\right)^n $$
$$ \text{Decayed} = 100\% - \text{Remaining} $$
Solution:- A time of \(3T\) means exactly \(n = 3\) half-lives have passed.
- Calculate the remaining fraction: $$ \left(\frac{1}{2}\right)^3 = \frac{1}{8} $$
- Convert \(1/8\) to a percentage: \( \frac{1}{8} = 12.5\% \) of the atoms remain.
- The question asks what percent decayed: $$ 100\% - 12.5\% = 87.5\% $$
Why other options are incorrect:12.5% is the amount remaining, not decayed (this is a very common trap). 50% is the amount decayed after 1 half-life. Radioactive substances never reach 100% mathematical decay in finite time.
Quality & Fidelity Assurance:
Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.