Question

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 is placed on the perimeter. During the experiment the detector registers 14 particles. The total number of particles emitted is \(\underline{\hspace{2cm}}\).

Hint:

For isotropic emission over a circular perimeter, detected count ∝ detector length ÷ circumference.

Answer 1

Correct Answer: 8790

Detector length:
\[ l = 1\ \text{cm} = 0.01\ \text{m} \]
Circumference of circular holder:
\[ C = 2\pi r = 2\pi(1) = 6.283\ \text{m} \]
Fraction of circle covered by detector:
\[ f = \frac{0.01}{6.283} \approx 0.00159 \]
If 14 particles are detected, total emitted particles:
\[ N = \frac{14}{0.00159} \approx 8800 \]
Thus, the final answer lies in the range 8790–8800.