Photo-Electric Effect

PHOTO-ELECTRIC EFFECT

In metals, there are large number of free electrons. These free electrons can more freely to a highest energy level, so called Fermi energy level E_F. No electron at E_F can escape from the metal because of the presence of an energy barrier at the surface of the metal. If an electron has to escape beyond the Fermi energy level, we have to supply some additional energy in order to overcome the energy barrier (E_B) of the metal. This additional energy required to make an electron to escape from the metal surface is called work function, denoted by ϕ. [Fig. 4.10].

ϕ = E_B - E_F

The additional energy required to make an electron to escape from a metal can be supplied in many waves, viz.

(i) In the form of heat, and this type of emission is called thermionic emission.

(ii) In the form of light, which is called photo-electric emission.

(iii) In the form electricity, so called Schottky effect and

(iv) When the energy is supplied by energetic charged particles, it is called secondary emission.

Out of these four types of emission, let us discuss briefly about the photo-electric emission.

Photo-electric emission

Einstein proposed a quantum theory on the basis that, "when a photon collides with an electron in a metal, it transfers the energy to the electron in an "all (or) none" process", i.e., either the photon gives out its total energy (hv) to the electron (or) no energy is transferred to the electron.

According to Einstein, the total energy of the photon, which is completely given to the electron is used in two ways viz,

1. A part of energy is used to eject the electron from the surface of the metal. This energy is known as Photo-electric work function (ϕ).

2. The other part of energy is supplied to the electron as the kinetic energy﴾1/2 mv²﴿for it to move with the velocity 'v'.

Total energy of the photon (E) = ϕ+ 1⁄2 mv²

…... (1)

Equation (1) is called Einstein's photo-electric equation.

Special Cases

Case (i): Suppose if the energy of the incident photon is in such a way that it is used only to eject the electron and not to make it move means, the kinetic energy of the electron becomes zero.

Equation (1) becomes, ……..(2)

Where V₀ is called threshold frequency.

and ϕ₀ is the work function of the metal.

Case (ii): Suppose if the energy of the incident photon ejects the electron and makes it to move with maximum velocity (V_max) means, equation (1) becomes

Since ϕ₀ = hv₀ we can write

……..(3)

As the work function is the energy supplied it is generally expressed in eV. The work functions of some of the metals are listed below for reference.