**Electron emission: **The phenomenon of emission of electrons from the surface of a metal. The minimum energy needed by an electron to come out from a metal surface is known as “work function” of the metal. It is denoted by Φ_{0} or W_{0} and measured in electron volt (eV).

Work function W= hυ = hc/λ

The electron emission can be obtained from the following physical processes :

**Thermionic emission : **It is the phenomenon of emission of electrons from the metal surface when heated suitably.

**Photoelectric emission :** It is the phenomenon of emission of electrons from the surface of metal when light radiations of suitable frequency fall on it.

**Field emission or cold cathode emission :** It is the phenomenon of emission of electrons from the surface of a metal under the application of a strong electric field.

**Photoelectric effect : **It is the phenomenon of emission of electrons from the surface of metals, when light radiations of suitable frequency fall on them.

**Laws of photoelectric emission : **The laws of photoelectric effect are as follows :

(1) For a given metal and frequency of incident radiation, the number of photoelectrons ejected per second is directly proportional to the intensity of the incident light.

(2) For a given metal, there exists a certain minimum frequency of the incident radiation below which no emission of photoelectrons takes place. This frequency is known as threshold frequency.

(3) Above the threshold frequency, the maximum kinetic energy of the emitted photoelectron is independent of the intensity of incident light but depends only upon the frequency (or wavelength) of the incident light.

(4) The photoelectric emission is an ** instantaneous process**. The time lag between the incidence of radiation and emission of photoelectrons is very small, less than 10

^{–9}second.

**Photoelectric current : **Photoelectric current depends on the intensity of incident light and the potential difference applied between the two electrodes.

**Stopping potential : **The minimum negative potential given to anode plate w.r.t. to cathode plate at which the photoelectric current becomes zero is known as stopping potential or cut off potential. It is denoted by V_{0}. If e is the charge on the photoelectron, then

where m is the mass of photoelectron and v_{max} is the maximum velocity of emitted photoelectrons.

≫Variation of stopping potential V_{0} with frequency υ of incident radiation :

≫Variation of photocurrent with collector plate potential for different intensity of incident radiation :

≫Variation of photocurrent with collector plate potential for different frequencies of incident radiation :

**Einstein’s photoelectric equation : **If a light of frequency u is incident on a photosensitive material having work function (Φ_{0}), then maximum kinetic energy of the emitted electron is given as

where υ_{0} = threshold frequency

λ_{0} = threshold wavelength

λ = incident wavelength

Einstein’s photoelectric equation is in accordance with the *law of conservation of energy*.

**Dual nature of radiation : **Wave theory of electromagnetic radiation explains the phenomenon of interference, diffraction and polarisation. On the other hand, photoelectric effect is supported by particle nature of light. Hence, we assume dual nature of light.

**The photons :** These are the packets of energy (or energy particles) which are emitted by a source of radiation. The photons emitted from a source, travel through space with the same speed c (equal to the speed of light).

≫ Energy of a photon

where, υ = frequency, λ = wavelength, h = Planck’s constant, c = speed of the light

≫ Momentum of photon is

≫ The rest mass of photon is zero.

≫ The moving mass m of photon is

≫ All photons of light of a particular frequency or wavelength have the same energy E and momentum p whatever be the intensity of radiation.

≫ Photon energy is independent of intensity of radiation.

≫ Photons are not deflected by electric and magnetic fields.

≫ In a photon-particle collision (such as photon electron collision), the total energy and total momentum are conserved.

≫ Number of photons emitted per second of frequency υ from a lamp of power P is

**de Broglie waves (Matter waves) : **Radiation has dual nature, wave and particle. The nature of experiment determines whether a wave or a particle description is best suited for understanding the experimental result. Reasoning that radiation and matter should be symmetrical in nature, Louis Victor de Broglie attributed a wave like character to matter (material particles). The waves associated with the moving material particles are known as matter waves or de Broglie waves.

≫ **de Broglie wavelength : **The de Broglie wavelength associated with a moving particle is related to its momentum as de Broglie wavelength,

where m is the mass of the particle, v is the velocity of the particle, p is the momentum of the particle.

** Note: **de Broglie wavelength is independent of the charge and nature of the material particle.

– In terms of kinetic energy K, de Broglie wavelength is given by

– If a particle of charge q is accelerated through a potential difference V, its de Broglie wavelength is given by

For an electron,

– For a gas molecule of mass m at temperature T kelvin, its de Broglie wavelength is given by

where k is the Boltzmann constant.

**Davisson and Germer experiment : **Davisson and Germer performed an experiment to study the wave nature of electrons as suggested by de Broglie.

According this experiment the de-Broglie wave length

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