Question

A point source of light is used in a photoelectric effect. If the source is removed farther from the emitting metal, the stopping potential:
A. Will increase
B. Will decrease
C. Will remain constant
D. Will either increase or decrease

Answer 1

Recall that photoelectric effect is the release of electrons from a metal surface when light of suitable frequency falls on it, following which electrons on the metal surface absorb sufficient energy to eject themselves from the surface. We also know that stopping potential is the amount of potential that is needed to be applied across the metal to restrain the electrons possessing maximum kinetic energy from being ejected out.
To this end, we know that the photoelectron emission depends on the frequency of incident light from which electrons gain kinetic energy, and is independent of the intensity of light. If this is the case, then think of which factors change when the incident light is moved away, keeping in mind that the stopping potential depends on the kinetic energy possessed by the electrons.

Complete step by step answer:
Let us begin by understanding what photoelectric effect is.
It is a process by which free electrons are emitted from the surface of metals by absorbing electromagnetic radiation (photons) of a suitable frequency that is incident on it. Electrons emitted in this way are called photoelectrons.
Photoelectrons are emitted only when the frequency (energy) of the incident light is greater than the minimum frequency (energy) for photoelectric emission, called the threshold frequency (energy).
Therefore, the electrons on the surface of metals absorb the incident photons and get emitted out by an energetic transfer, i.e., electrons on the surface gain some energy from the photons, and then get emitted with some kinetic energy obtained from the remaining incident energy.
Now, stopping potential is defined as the potential difference that is applied across the metal to prevent or stop electrons possessing maximum kinetic energy from moving across the metal and keep them restrained to the metal surface. Thus, when such a potential is applied, the photocurrent across the metal surface will be zero.
The amount of energy absorbed by the electrons and consequently the kinetic energy possessed by the electrons is directly proportional to the frequency of incident light. And consequently, the amount of stopping potential that is needed to apply to stop the movement of the electrons in the metal surface is proportional to the amount of kinetic energy possessed by the electrons. Therefore, the stopping potential is also directly proportional to the frequency of incident light.
Now, when the point source of light is moved away from the photoelectric metal, the frequency of light it emits remains the same, and it is only the intensity of light incident on the emitting metal that will decrease. But as we mentioned above, the stopping potential is dependent only on the frequency of the incident light and not the intensity of radiation. Therefore, if the source of light is moved away from the emitting metal, the stopping potential that needs to be applied to prevent the emission of photoelectrons will still be the same.
Therefore, the correct choice would be C. Will remain constant.

Note:
Remember that it is according to the contemporary quantum model of light that the maximum kinetic energy of photoelectrons depends on only the frequency of incident light and is independent of the intensity. However, the classical wave model of light predicted that the maximum kinetic energy possessed by the photoelectrons would depend on the light intensity, implying that more intense light imparted greater energy to the electrons on the metal surface. This was later proved to not be true from the fact that no matter what the intensity of radiation was, if the frequency of light was less than the threshold frequency, no photoelectrons were emitted, which meant that no electrons possessed any kinetic energy which ultimately meant that there was no change required in the stopping potential applied across the metal surface, making stopping potential independent of intensity of incident light.