Question

A point monochromatic source of light is placed at \( r \) distance from a photoelectric cell; then stopping potential is obtained as \( V \). What would be the effect on the stopping potential, when the same source is placed at \( 3r \) distance? Justify your answer.

Hint:

The stopping potential in the photoelectric effect depends on the energy of the incident photons, which is not affected by the distance from the light source.

Answer 1

Step 1: Stopping Potential and Intensity.
The stopping potential in the photoelectric effect depends on the energy of the incident photons, which in turn depends on the frequency of light. The stopping potential is given by: \[ V = \frac{h f}{e} - W \] where \( h \) is Planck's constant, \( f \) is the frequency of the light, \( e \) is the charge of an electron, and \( W \) is the work function of the material.
Step 2: Effect of Distance on Intensity.
The intensity of light decreases with the square of the distance from the source. The intensity \( I \) is inversely proportional to the square of the distance \( r \), i.e., \[ I \propto \frac{1}{r^2} \] Since the energy of individual photons is not affected by the distance, the stopping potential remains unchanged. The decrease in intensity (due to the increased distance) will result in fewer electrons being emitted, but the energy of the emitted electrons (and thus the stopping potential) remains the same.
Step 3: Conclusion.
The stopping potential remains the same even if the source is moved to \( 3r \) because the energy of the photons is not affected by the distance.