A photon of wavelength λ is scattered from an electron , which was at rest The wavelength shift △λ - Physics - Dual Nature Of Radiation And Matter

Question

A photon of wavelength λ is scattered from an electron ,
which was at rest The wavelength shift △λ is three
times of λ and the angle of scattering θ is 600 The
angle at which the electron recoiled is ϕ The value of
tanϕ is (electron speed is much smaller than the speed of
light)

Aarushi Mishra · Accepted Answer

<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_5ac668e8690ab%20png"
style=
"width: 677px; height: 456px;">∆λ=3λλ'-λ=3λλ'=4λFinal momentum of photonP=h4λP→=Pcos 60°+Psin 60°=P12i^+32j^Initial momentum of photonPi=hλ=4PP→i=4P i^Initially we can assume electron to be at rest as speed of light >> speed of electron
Let final momentum of electron be p→'By law of conservation of momentumP→i=P→+p→'4P i^=P12i^+32j^+p→'p→'=4P i^-P12i^+32j^p→'=P72i^-32j^clearly tan ϕ=-3272=37=0
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A photon of wavelength λ is scattered from an electron , which was at rest .The wavelength shift △λ is three times of λ and the angle of scattering θ is 600 . The angle at which the electron recoiled is ϕ .The value of tanϕ is (electron speed is much smaller than the speed of light)