Quantum Physics

27.5 The Compton Effect 885Exercise 27.5X-rays of wavelength 0.060 0 nm are scattered from a crystal with a grazing angle of 11.7°. Assume m 1 for thisprocess. Calculate the spacing between the crystal planes.Answer0.148 nm27.5 THE COMPTON EFFECTFurther justification for the photon nature of light came from an experimentconducted by Arthur H. Compton in 1923. In his experiment, Compton directed anx-ray beam of wavelength 0 toward a block of graphite. He found that the scatteredx-rays had a slightly longer wavelength than the incident x-rays, and hence the energiesof the scattered rays were lower. The amount of energy reduction dependedon the angle at which the x-rays were scattered. The change in wavelength between a scattered x-ray and an incident x-ray is called the Compton shift.In order to explain this effect, Compton assumed that if a photon behaves like aparticle, its collision with other particles is similar to a collision between two billiardballs. Hence, the x-ray photon carries both measurable energy and momentum,and these two quantities must be conserved in a collision. If the incident photoncollides with an electron initially at rest, as in Figure 27.16, the photon transferssome of its energy and momentum to the electron. As a consequence, the energyand frequency of the scattered photon are lowered and its wavelength increases.Applying relativistic energy and momentum conservation to the collision describedin Figure 27.16, the shift in wavelength of the scattered photon is given by 0 hm e c (1 cos )[27.11]where m e is the mass of the electron and is the angle between the directions ofthe scattered and incident photons. The quantity h/m e c is called the Comptonwavelength and has a value of 0.002 43 nm. The Compton wavelength is very smallrelative to the wavelengths of visible light, so the shift in wavelength would bedifficult to detect if visible light were used. Further, note that the Compton shiftdepends on the scattering angle and not on the wavelength. Experimentalresults for x-rays scattered from various targets obey Equation 27.11 and stronglysupport the photon concept.Quick Quiz 27.1An x-ray photon is scattered by an electron. The frequency of the scattered photonrelative to that of the incident photon (a) increases, (b) decreases, or (c) remainsthe same.Recoiling electronCourtesy of AIP Niels Bohr Library The Compton shift formulaARTHUR HOLLY COMPTON,American Physicist (1892 – 1962)Compton was born in Wooster, Ohio, andhe attended Wooster College and PrincetonUniversity. He became director of the laboratoryat the University of Chicago, whereexperimental work concerned with sustainedchain reactions was conducted. Thiswork was of central importance to theconstruction of the first atomic bomb. Hisdiscovery of the Compton effect and hiswork with cosmic rays led to his sharing the1927 Nobel Prize in physics with CharlesWilson.φf 0 , λ 0θf ′, λ′ λFigure 27.16 Diagram representingCompton scattering of a photonby an electron. The scattered photonhas less energy (or a longer wavelength)than the incident photon.