16. Consider the Compton scattering of a photon of wavelength 2 by a free electron moving with a momentum of magnitude P in the same direction as that of the incident photon. (a) Show that in this case the Compton equation (1.42) becomes (Po+P)c Δλ = 20ο sin² E-Pc where po =h/20 is the magnitude of the incident photon momentum, op is the photon scattering angle and E = (m² c4 + P2 c2)1/2 is the initial electron energy. (b) What is the maximum value of the electron momentum after the collision? Compare with the case P=0 considered in the text. (c) Show that if the free electron initially moves with a momentum of magnitude P in a direction opposite to that of the incident photon, the Compton shift becomes Αλ = 20ο (Po-P)c E + Pc sin² 17. Consider a photon of energy of energy E₁ = 2 eV which is scattered through an angle op. From an electron having a kinetic energy T = 10 GeV (1GeV = 10⁹ eV) and moving initially in a direction opposite to that of the photon. What is the energy E₁of the scattered photon? (Hint: use the result (c) of Problem 16.)