Question

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State the Compton scattering effect of electromagnetic waves and state the formula.

Answer 1

formula of Compton scattering of electromagnetic waves is on the referred attachment

$heya$
WHEN A LIGHT WAVE WHICH IS KNOWN AS PHOTON OF AN ELECTRON THERE IS A DECREASE IN ENERGY OF PHOTON FROM ITS ENERGY AND ENERGY AND IT IS BEING TRANSFERRED AND BEING SCATTERED WHICH IS THE COMPTON SCATTERING EFFECT OF ELECTROMAGNETIC WAVES

Answer 2

Hey friend here is ur query...

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When a high energetic photon
(like the gamma or X ray photon) hit a charged particle like an electron, due to inelastic collision,
the photon loses some energy and the electron get scattered. The energy lost by the photon will be equal to the energy gained by the scattered electron. This process of inelastic scattering of electron by a photon is called Compton scattering and the phenomenon is called Compton effect.
This experiment ensures the particle nature of radiation like the photoelectric effect.

Since the energy of the incident photon is reduced it's wavelength should increase (and frequency should decrease as per the relation:

E=hν =hc/λ

(This is why the yellow photon turned into a red photon in the animation).

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Derivations..
Consider an electron at rest. An X-ray photon is coming from the left and will incident on the electron as shown.


The electron gain some energy by transfer of momentum as expected in particle collisions. So the photon loses some energy and the electron gains some. Let λλbe the wavelength of the incident photon and λ′λ′ be that of the scattered photon. The original energy of the photon will be now equal to the sum of energy gained by the electron and the energy of the scattered photon as required by the conservation of energy. Here θθ represents the scattering angle of photon. Compton also included the possibility that the interaction of photon with electron would sometimes accelerate the electron to speeds sufficiently close to the velocity of light and would require the application of Einstein's special relativity theory to properly describe its energy and momentum. The basic principle used in the derivation of Compton scattering is the conservation of energy and momentum.

Hence

Eγ+Ee=Eγ′+Ee′⟶conservation of energyEγ+Ee=Eγ′+Ee′⟶conservation of energy

where the left hand side indicate the energy of photon and electron before collision an right hand side indicate the energy of photon and electron after collision. (The prime indicates that the parameter is associated with scattering).

Also

pγ→+pe→=pγ′→+pe′→pγ→+pe→=pγ′→+pe′→

Since the initial momentum of electron at rest is zero, we write

pγ→=pγ′→+pe′→⟶conservation of momentumpγ→=pγ′→+pe′→⟶conservation of momentum

Now considering the relativistic effects,

Ee=mec2   (me−rest mass of electron)Ee=mec2   (me−rest mass of electron)

Ee′=(pe′c)2+(mec2)2−−−−−−−−−−−−−√Ee′=(pe′c)2+(mec2)2

Referring to the conservation of energy equation

hc/λ+mec2=hc/λ′+(pe′c)2+(mec2)2−−−−−−−−−−−−−√hcλ+mec2=hcλ′+(pe′c)2+(mec2)2

Rearranging both sides and squaring

(pe′c)2=(hc/λ+mec2−hcλ′)2−m2ec4(pe′c)2=(hcλ+mec2−hcλ′)2−me2c4
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Hope this will help you..