Scattering of Photons (Compton Effect)

When a photon strike with a charge particle it scatters with some angle and the wavelength of the scattered photon is larger than before. This effect was studied by Arther Holly Compton. He discovered that when a beam of x-rays strike the target, it scattered from the target, the wavelengths of the scattered x-rays are greater than the incident rays. This effect is called Compton Scattering.

A beam of x-rays of wavelength λ falls on a carbon target (Graphite). Compton observed that the wavelength of x-rays that were scattered at various angles θ is larger than the wavelength of the incident rays. This effect is Compton scattering. Compton scattering is an example of an inelastic collision in which a high energy photon strikes with an electron and scattered at some angle. A part of the energy of the photon is transferred to the electron. In the case of x-rays, x-rays have much greater energy (≊17KeV) than the binding energy of the electron (≊11ev) that holds the electron in an atom, so electrons could be considered as free particles. When x-rays strike the electron a part of their energy is transferred to the electron and they scattered at various angles. Compton observed the scattered x-rays and found that their wavelength was larger than the incident rays. This change in wavelength is called the Compton shift. FIG-1 shows the experimental arrangements.

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The wavelengths λ^’ of the scattered rays are larger by an amount of Δ λ. This Compton shift depend upon the angle at which the scattered x-rays are observed or in other words Compton shift Δ λ depends upon the angle of scattering of rays.

Description of the phenomenon:

Compton derived an expression for Δ λ by studying the interaction between the photon and the free electron as the collision of two particles. The photon with energy ( E = $hf$ ) strike the electron and transferred some of its energy to it, now energy of the photon decreased and become E’ ( E  =hf^’ ).

Because E > E’ we must have f > f’ which requires λ < λ^’. As the energy of photon decreased, frequency of the scattered photon must be lower than the incident photon which requires a difference in the wavelengths of the photon. That is the scattered x-rays must have larger wavelength than incident x-rays. Expression for the Compton shift (Δ λ) is:

$$

 Left hand side of this expression shows the Compton shift Δ λ

 .λ is the initial wavelength

. λ’ is the wavelength after scattering 

h is the planks constant

m_e  is the rest mass of electrons

c is the speed of light

θ is the angle of scattering

Term  is the Compton wavelength of the electron. And λ′ - λ is the least zero when scattering angle is zero (θ = 0) and twice the Compton wavelength when (θ = 180). 

Compton Effect was observed in 1923 and verified by one of the students of the Compton the years following and Compton earned Nobel Prize in year 1927. Compton scattering is important in radiobiology as it is the interaction between the gamma rays or x-rays and the electrons of the atoms, it applied in radio therapy. Inverse Compton scattering has applications in astronomy as well. Compton Effect is also important because it demonstrate that light cannot be explained only as waves.