GATE 2021 CH – Question 29
A source placed at the origin of a circular sample holder (radius $r=1$ m) emits particles uniformly in all directions. A detector of length $l=1$ cm has been placed along the perimeter of the sample holder. During an experiment, the detector registers 14 particles. The total number of particles emitted during the experiment is _____.
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Correct answer: 8796
Explanation
The detector covers a fraction $l/(2\pi r)$ of the circular perimeter. Convert its length to metres: $l=0.01$ m. For uniform emission over the circular holder, the detected fraction is $0.01/(2\pi)$.
If $N$ particles are emitted, $14=N(0.01)/(2\pi)$, so
$$N=\frac{14(2\pi)}{0.01}=2800\pi=8796.459\ldots.$$
The corresponding whole-particle estimate is **8796**.