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# Work Function

## Definition of Work Function

Work function is defined as the minimum amount of energy required by an electron to escape from a metal surface.

## Concept of Work Function in Classical Physics

The concept of work function is not to hard to understand. The concept can be explained by either classical physics or quantum mechanism. As per classical physics, when an electron tries to escape from metal surface, it leaves a positive image behind in the metal surface. Due attraction of this positive image negative electron turns back to metal surface hence cannot leave the metal crystal permanently. But to overcome this attraction force an electron requires sufficient energy supplied from outside normally from external light source.

The minimum energy requires to escape an electron form a metal surface is called work function.

## Concept of Work Function in Quantum Physics

Work function can also be explained and defined by quantum physics. For that, we first have to know some basic features.
1. Sir Albert Einstein said that light is in the form of a beam of a huge number of discrete energy packets called photons. The energy contains in each photon is hλ. Where, h is Planck Constant and λ is the frequency of light.
2. Now when the light strikes on a metal surface electrons on the surface of the metal get energy from the light and get emitted from the surface. This is classically termed as photoemission.
3. As the energy of photon Eph = hλ. The energy of each photon depends upon the frequency of light. As the frequency is everything upon which energy of photon rather light depends, it is found that there will be no photoemission from a metal surface below a certain frequency of light. For minimum photoemission frequency of incident light is required.
4. If the frequency of light is higher than that above mention minimum rate for photoemission, then the extra energy of photon will be converted to Kinetic energy of the emitted electron. Hence, how fast the electron will be emitted from the surface of the metal depends upon the frequency of incident light. Not on the intensity (Brightness of the light).
5. But when an intensity of incident light increases without changing its frequency. Obviously, number of photons strike on the metal surface hence more emitted electrons will be produced, but Kinetic energy of each electron will be unchanged as the frequency of incident light is fixed.
6. Hence after a certain minimum frequency the electrons start emitted from a metal surface. Above this frequency, the Kinetic energy of the emitted electron is directly proportional to incident light frequency. But below this minimum frequency, there will be no Kinetic energy in the electrons.

## Graphical Representation of Work Function

Now, If we graphically represent the above points we will get the graph below, Here, the vertical axis represents the energy of an electron and horizontal axis represents the frequency.

After frequency fo Hz, the Kinetic energy of electrons start increasing proportionally with frequency. Below, frequency fo or below energy hfo [ h is Planck Constant ] there will be no kinetic energy i.e. no emission of an electron. This amount of energy i.e. hfo is known and defined as work function λ.

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