Paper 4, Section I, C

Dynamics and Relativity | Part IA, 2015

Write down the 4-momentum of a particle with energy EE and 3-momentum p. State the relationship between the energy EE and wavelength λ\lambda of a photon.

An electron of mass mm is at rest at the origin of the laboratory frame: write down its 4 -momentum. The electron is scattered by a photon of wavelength λ1\lambda_{1} travelling along the xx-axis: write down the initial 4-momentum of the photon. Afterwards, the photon has wavelength λ2\lambda_{2} and has been deflected through an angle θ\theta. Show that

λ2λ1=2hmcsin2(12θ)\lambda_{2}-\lambda_{1}=\frac{2 h}{m c} \sin ^{2}\left(\frac{1}{2} \theta\right)

where cc is the speed of light and hh is Planck's constant.

Typos? Please submit corrections to this page on GitHub.