Dual Nature of Radiation and Matter: Work Function of Metals, Photoelectric Effect (For CBSE, ICSE, IAS, NET, NRA 2022)

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The dual nature of matter and the dual nature of radiation were revolutionary concepts of physics.
At the beginning of the twentieth century, scientists unravelled one of the best-kept secrets of nature – the wave particle duality or the dual nature of matter and radiation.

Work Function of Metals

It is referred to minimum amount of energy required to take out one electron from the metal surface.
So, This energy can be supplied through various sources such as a strong electric field or irradiation of light with a suitable frequency.

It is the phenomenon in which the electrons are emitted from the metal surface when the light is illuminated in a suitable frequency.
The photoelectric effect is the conversion of light to electrical energy.
It follows the law of conservation of energy and is an instantaneous process.
Photoelectric current depends upon three factors:
The potential difference applied within the two electrodes
The incident light՚s intensity
The nature of the emitter material
Factors affecting stopping potential
The incident light՚s frequency
The emitter material՚s nature
The frequency of the incident light does not depend on the intensity.
Stopping potential is directly proportional to the kinetic energy of the emitted electrons.

The laws of the Photoelectric effect are as follows:

For a given metal and frequency of incident light, the photoelectric current is directly proportional to the intensity of incident light.
For a given metal, there is a certain minimum frequency, called Threshold frequency, below which there is no photo-electric emission.
The maximum kinetic energy of photoelectrons above a threshold frequency depends upon the frequency of incident light.
The photoelectric emission is an instantaneous process.

Its Principle states that both the momentum and position of a particle cannot be determined simultaneously.
Mathematically, it can be expressed as ∆ x ∆ P ⩾ (h/4π) where ∆ x represents the Uncertainty in position, ∆ P represents the Uncertainty in Momentum.

Light is composed of various discreet packs of energy which are called quanta.
Einstein explained the photoelectric effect on the basis of this theory. Each photon posses an energy E = (hv) and momentum and it depends on the frequency (v) of light incident and never on the intensity.
In metal surface, photoelectric emission occurs due to the photon absorption capability of an electron.

Minimum energy that is required to emit an electron from the surface of a metal can be supplied to the free electrons by either of the three methods given below:
Thermionic Emission: Required thermal energy is provided to the free electrons by suitably heating it so as to enable them to come out of the metal.
Field Emission: Electrons are kept under the strong influence of the electric field to emit the electron out of the metal.
Photo-electric Emission: When the light of appropriate frequency is made to illuminate a metal surface, electrons are emitted from it. These photo-generated electrons are called Photoelectrons.