Quantum Physics

886 Chapter 27 Quantum PhysicsQuick Quiz 27.2A photon of energy E 0 strikes a free electron, with the scattered photon of energyE moving in the direction opposite that of the incident photon. In this Comptoneffect interaction, the resulting kinetic energy of the electron is(a) E 0 (b) E (c) E 0 E (d) E 0 E (e) None of the aboveApplying Physics 27.2The Compton effect involves a change in wavelengthas photons are scattered through different angles.Suppose we illuminate a piece of material with a beamof light and then view the material from different anglesrelative to the beam of light. Will we see a colorchange corresponding to the change in wavelength ofthe scattered light?Explanation There will be a wavelength change for visiblelight scattered by the material, but the change willColor Changes through the Compton Effectbe far too small to detect as a color change. The largestpossible wavelength change, at 180° scattering, will betwice the Compton wavelength, about 0.005 nm. Thisrepresents a change of less than 0.001% of the wavelengthof red light. The Compton effect is only detectablefor wavelengths that are very short to beginwith, so that the Compton wavelength is an appreciablefraction of the incident wavelength. As a result, theusual radiation for observing the Compton effect is inthe x-ray range of the electromagnetic spectrum.INTERACTIVE EXAMPLE 27.6GoalScattering X-RaysUnderstand Compton scattering and its effect on the photon’s energy.Problem X-rays of wavelength 0 0.200 000 nm are scattered from a block of material. The scattered x-rays areobserved at an angle of 45.0° to the incident beam. (a) Calculate the wavelength of the x-rays scattered at this angle.(b) Compute the fractional change in the energy of a photon in the collision.Solution(a) Calculate the wavelength of the x-rays.Substitute into Equation 27.11 to obtain the wavelengthshift:Add this shift to the original wavelength to obtain thewavelength of the scattered photon: hm e c (1 cos )6.63 10 34 Js(9.11 10 31 kg)(3.00 10 8 m/s) 7.11 10 13 m 0.000 711 nm 0 0.200 711 nm(1 cos 45.0)(b) Find the fraction of energy lost by the photon in thecollision.Rewrite the energy E in terms of wavelength, using c f :E hf hcCompute E/E using this expression:EE E f E iE i hc/f hc/ihc/iCancel hc and rearrange terms:EE 1/f 1/i1/iif 1 i ff fSubstitute values from part (a):EE711 nm0.0000.200 711 nm 3.54 10 3Remarks It is also possible to find this answer by substituting into the energy expression at an earlier stage, but thealgebraic derivation is more elegant and instructive.