Question

A point source causes photoelectric effect from a small metal plate. Which of the curves in figure may represent the saturation photo-current as a function of the distance between the source and the metal?
(A)
(B)
(C)
(D)

Answer 1

Hint : In order to solve this question, we are going to see what the photoelectric effect is and what impact the distance has on the current, then, according to the relation between current and the distance, we can directly predict the nature of the curve between current and the distance.
As intensity is inversely proportional to the square of the distance, so,
$I \propto \dfrac{1}{{{r^2}}}$

Complete Step By Step Answer:
The saturation current is that maximum value of the current after which no more current flows no matter what intensity of light we strike on the surface. The saturation current is directly proportional to the number of electrons that are falling on the collector plate per second while it is directly proportional to the number of electrons falling on a cathode per second.
Here the number of photons striking directly impacts the number of electrons being ejected, which further depends on the intensity of the incident light. As intensity is inversely proportional to the square of the distance, so,
$I \propto \dfrac{1}{{{r^2}}}$
So, the correct graph is the one depicting the current decreasing with the power two of distance and it will be rapidly decreasing with higher power of $r$ .
So, option D is the correct answer.

Note :
In the photoelectric effect experiment, we have a light ray striking on a metal surface that causes the electrons from the surface to be ejected and cause a flow of current. The number of the ejected electrons and so the current produced directly depends upon the intensity of the incident light.