Energy of the photon before scattering:
E=λhc. Energy of the photon after scattering:
Es=λshc. According to the law of conservation of energy, the energy of the photon before scattering and the rest energy of the particle are spent to give kinetic energy to the particle and to change the photon's energy to E2:
E+E0=K+Es,K=E+Eo−Es= =ch(λ1−λs1)+E0. We know that in Compton scattering, the wavelength can be expressed as
λs=λ+mech(1−cosθ). The scattered wavelength is maximum when cosine theta is -1:
λs=λ+mec2h. Substitute this to the equation for kinetic energy:
K=E−Ehc+mec2hhc+E0= =E0+E(1−hc2me+2Emec2).
Comments
Dear Sk Rizwan, thank you for comment. This is typo, there should be "hc"
How I common h/c in equation no 3??
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