Consider Compton scattering of a photon by a moving electron. Before the collision the photon has wavelength ? and is moving in the +x-direction, and the electron is moving in the -x-direction with total energy E (including its rest energy mc2). The photon and electron collide head-on. After the collision, both are moving in the -x-direction (that is, the photon has been scattered by 180?). (a) Derive an expression for the wavelength ?' of the scattered photon. Show that if E >> mc2, where m is the rest mass of the electron, your result reduces to (b) A beam of infrared radiation from a CO2 laser (A = 10.6?m) collides head-on with a beam of electrons, each of total energy E = 10.0GeV (1GeV = 109eV). Calculate the wavelength ?' of the scattered photons, assuming a 180? scattering angle. (c) What kind of scattered photons are these (infrared, microwave, ultraviolet, etc.)? Can you think of an application of this effect?

X' - he (1 + E 11 mc^) 4hcE