Answer: Consider Compton scattering of a photon by a

Chapter 38, Problem 38.4

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Consider Compton scattering of a photon by a moving electron. Before the collision the photon has wavelength l 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 l of the scattered photon. Show that if E W mc2 , where m is the rest mass of the electron, your result reduces to l = hc E a1 + m2 c4 l 4hcE b (b) A beam of infrared radiation from a CO2 laser 1l = 10.6 mm2 collides head-on with a beam of electrons, each of total energy E = 10.0 GeV 11 GeV = 109 eV2. Calculate the wavelength l 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?