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Compton Effect

Compton effect is defined as the effect that is observed when x-rays or gamma rays are scattered on a material with an increase in wavelength. Arthur Compton studied this effect in the year 1922. During the study, Compton found that wavelength is not dependent on the intensity of incident radiation. It is dependent on the angle of scattering and on the wavelength of the incident beam. It is given in the following mathematical form:
λsλ0=hm0c(1cosΘ)
Where,
Ó¨: angle at which radiation scattered
m0: rest mass of an electron
hm0c : Compton wavelength of the electron
λs and λ0: radiation spectrum peaks.

Derivation of Compton effect equation

Considering the elastic collide between a photon and an electron, following is the derivation:
hν0 : energy of photon
pi=hν0c :momentum of the photon
pi=pfcosΘ+pecosÏ•(1) (conservation of momentum in x direction)
0=pfsinΘ+pesinÏ•(2) (conservation of momentum in y direction)
p2e=p2e(cos2Ï•+sin2Ï•)
=(pipfcosΘ)2+p2fsin2Θ
=p2i+p2f2pipfcosΘ
hν0+m0c2=hν+(m20c4+p2ec2)
m20c4+p2ec2=(hν0hν+m0c2)2
=(hν0hν)2+m20c4+2m0c2(hν0hν)
p2ec2=(hν0hν)2+2m0c2(hν0hν)
p2ic2+p2fc22pipfcosΘc2=(hν0hν)2+2m0c2(hν0hν)
hνν0(1cosΘ)=m0c2(ν0ν)
λsλ0=hm0c(1cosΘ)
Therefore, above is the Compton effect equation andhm0cλc is Compton wavelength of an electron.
This was a step by step explanation on the derivation of Compton effect equation derivation. Stay tuned with PHYSICS ADDA to know more other related Physics ,Maths.

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