A metal plate is illuminated with light of a certain frequency. Which of the following determine whether or not electrons are ejected: (a) the intensity of the light, (b) how long the plate is exposed to the light, (c) the thermal conductivity of the plate, (d) the area of the plate, (e) the material of which the plate is made?

Frequency is defined as the number of waves that pass a fixed point in unit time. It also describes the number of cycles or vibrations undergone during one unit of time by a body in periodic motion.

(a)

The term intensity is used to describe the rate at which light spreads over a surface of a given area some distance from a source. The intensity varies with the distance from the source and the power of the source.

Hence, the option is incorrect.

(b)

The maximum kinetic energy of the electron immediately upon ejection is the difference between the energy of the incident photon and the threshold energy.

Hence, this option is incorrect.

(c)

The coefficient of thermal conductivity of a metal plate depends on - When one end of a metal rod is heated, heat flows by conduction from the hot end to the cold end. In this process, each cross-section of the rod receives some heat from the adjacent cross-section towards the hot end.

Hence, the option is incorrect.

(d)

The area of the plates of a parallel plate capacitor is A and the gap between them is d. The gap is filled with a non-homogeneous dielectric whose dielectric constant varies with the distance $\text{'}y\text{'}$from one plate as $K=\lambda sec\left(2d\pi y\right)$, where λ is a dimensionless constant.

Hence, the option is incorrect.

(e)

Intensity of light determines the number of electrons emitted.

Emitted electrons do not depend on how long the plate is exposed to light, thermal conductivity of the plate, or area of the plate.

Emitted electrons do depend on the material from which the plate is made and the frequency of light incident on the plate.

Whether or not electrons are emitted will depend on the threshold frequency of the material. If the incident light is of a higher frequency than the threshold frequency, then the electron will be emitted.

Hence, this option is correct.