Kinetic energy with the electrons emitted from the metal surface due to the photoelectric effect is
A. Independent of the intensity of illumination
B. Independent of the frequency of light
C. Inversely proportional to the intensity of illumination
D. Directly proportional to the intensity of illumination

Hint: When light is incident on a metal surface, electrons are emitted known as photoelectrons. This phenomenon is called the photoelectric effect. The photon of energy \[h\nu \] is incident on the metal surface and this energy is used to remove the electron from its orbit of a particular energy level, providing the kinetic energy for it.

Complete step by step solution:
The kinetic energy of an electron is,
\[K.E = E - W\]
Here, W is the work function and it is constant, then the kinetic energy depends on E, that is the energy of the photon. If E increases the kinetic energy increases and when E decreases kinetic energy also decreases.

Energy of a photon is,
\[E = h\nu \] or \[E = \dfrac{{hc}}{\lambda }\]
The energy of photons depends on frequency or wavelength and it is independent of the intensity of illumination.

The intensity of photon can be written as,
\[I = \dfrac{n}{t}\left( {\dfrac{E}{A}} \right)\]
Here, E and A are constant and the intensity depends only on n (number of photons) and t (time).

We can conclude that the kinetic energy depends on the energy of the photon and the photoelectric current depends on the intensity. If we consider option B, as the frequency increases the kinetic energy increases, that is it depends on the frequency. Similar to the previous justification, the kinetic energy doesn’t depend on intensity, intensity depends on the photoelectric current. Therefore, the Kinetic energy of the electrons that are emitted from the metal surface is independent of the intensity of illumination.

Hence, option A is the correct answer.

Note:The photoelectric effect was first discovered by Einstein in 1905 and he also won the Nobel Prize for it. The kinetic energy of these photoelectrons increases with the frequency of light.