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:

λs−λ0=hm0c(1−cosΘ)

Where,

Ө: 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+pecosϕ(1) (conservation of momentum in x direction)

0=−pfsinΘ+pesinϕ(2) (conservation of momentum in y direction)

p2e=p2e(cos2ϕ+sin2ϕ)

=(pi−pfcosΘ)2+p2fsin2Θ

=p2i+p2f−2pipfcosΘ

hν0+m0c2=hν+(√m20c4+p2ec2)

m20c4+p2ec2=(hν0−hν+m0c2)2

=(hν0−hν)2+m20c4+2m0c2(hν0−hν)

p2ec2=(hν0−hν)2+2m0c2(hν0−hν)

p2ic2+p2fc2−2pipfcosΘc2=(hν0−hν)2+2m0c2(hν0−hν)

hνν0(1−cosΘ)=m0c2(ν0−ν)

∴λs−λ0=hm0c(1−cosΘ)

Therefore, above is the Compton effect equation andhm0c≡λc 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.

Hey guys!

Here you can find all types notes by handwritten.

Here,we are providing physics compton effect,which is most useful in your semester exam.This topic is totally designed according to our syllabus.

#This all topic will be covered in video lecture form on my youtube chanel.

Youtube Link:-

https://www.youtube.com/channel/UCNWq6u9VWAeJS1JgLpHGNEg