To understand the derivation of the Compton scattering formula. In 1923, Arthur H. Compton conducted a series of experiments that demonstrated the particle-like nature of electromagnetic radiation. Compton studied the collision of photons from a uniform wavelength beam with a stationary target. He observed that the radiation that exited from the target showed two characteristic wavelengths, one at the original wavelength λ and another at a new wavelength λ′ shifted by an amount Δλ from the original.
In this problem we will use the principles of conservation of energy and conservation of momentum, coupled with some basic ideas in quantum physics and relativity, to derive a statement for the shifted wavelength λ′.
1. Consider a photon with initial momentum pi on a collision course with a stationary electron of mass m. What is the total energy Ei of these two particles before the collision?
Don't forget to include the rest mass energy of the electron. Express your answer in terms of the pi, the speed of light c, and m.