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What is Compton Effect?

Explain why Compton shift is not observed with visible light. Derive an expression for Compton shift and wavelength of a scattered photon; Derive an expression of the kinetic energy of recoil electron in Compton scattering.

Answer:

Compton Effect

The Compton Effect was first demonstrated by A.H. Compton in 1927 (for which he received a 1927 Nobel Prize). According to Compton – “When a high-energy photon colliding (scattered) with loosely bound electrons then there are two components present after scattering i.e. one having lower wavelength (greater frequency) due to inelastic collision and other having unchanged wavelength (unchanged frequency). The photon having unchanged frequency is known as unmodified radiation and one having changed wavelength is known as modified radiation.

Convincing evidence that light is made up of particles (photons), and that photons have momentum, can be seen when a photon with energy collides with a stationary electron. After collision some of the energy and momentum is transferred to the electron; which produce modified and unmodified radiation. Compton Effect

Suppose that a photon having E=hv energy collide with an electron; after collision photon scattered with an angle Theta and electron displaced at certain position and made an angle fi this angle is known as recoil angle and displaced electron is known as recoil electron.

If we consider before collision frequency of a photon is v after collision the changed frequency is v’; Before collision the momentum of an electron should be 0.According to diagram before and after collision the energy (momentum) of photon and electron is defined as:

Before Collision                                                                After collision

Photon                                                                                   Photon

Energy = hv (According to Einstein’s)                         Energy = hv’

Momentum = hv/c            (p=h/l; c=vl)                Momentum = hv’/c

{l = Lembda= Wavelength}

Electron                                                                                Electron

Energy =m₀C² (m₀ = rest mass)                                      Energy = mC²

Momentum = 0                                                              Momentum = mV

Now we are applying the Energy and momentum conservation law because in elastic collision the energy and momentum should be conserved.

1. The Energy conservation law means before and after collision the total energy (energy of photon + electron) should be conserved

Photon Energy + Electron energy (Before collision) = Photon Energy + Electron energy (After collision)

hv + m₀C² = hv’ + mC²                                                                                                       (1)

2. Similarly; The momentum conservation law means before and after collision the total momentum (momentum of photon + electron) should be conserved

Photon momentum + Electron momentum (Before collision) = Photon momentum + Electron momentum (After collision)

Now we also explain that the photon horizontally strike on electron but after collision there are two components possible in photon and electron momentum i.e horizontal components and vertical components of momentum of electron and photon;

horizontal components of momentum is

Compton Effect