Quantum Physics

27.6 The Dual Nature of Light and Matter 887Exercise 27.6Repeat the exercise for a photon with wavelength 3.00 10 2 nm that scatters at an angle of 60.0°.Answers (a) 3.12 10 2 nm (b) E/ E 3.88 10 2Study Compton scattering for different angles by logging into PhysicsNow at www.cp7e.com andgoing to Interactive Example 27.6.27.6 THE DUAL NATURE OF LIGHT AND MATTERLight and Electromagnetic RadiationPhenomena such as the photoelectric effect and the Compton effect offer evidencethat when light (or other forms of electromagnetic radiation) and matterinteract, the light behaves as if it were composed of particles having energy hf andmomentum h/. In other contexts, however, light acts like a wave, exhibiting interferenceand diffraction effects. Is light a wave or a particle?The answer depends on the phenomenon being observed. Some experimentscan be better explained with the photon concept, whereas others are bestdescribed with a wave model. The end result is that both models are needed.Light has a dual nature, exhibiting both wave and particle characteristics.To understand why photons are compatible with electromagnetic waves, consider2.5-MHz radio waves as an example. The energy of a photon having thisfrequency is only about 10 8 eV, too small to allow the photon to be detected. Asensitive radio receiver might require as many as 10 10 of these photons to producea detectable signal. Such a large number of photons would appear, on the average,as a continuous wave. With so many photons reaching the detector every second,we wouldn’t be able to detect the individual photons striking the antenna.Now consider what happens as we go to higher frequencies. In the visibleregion, it’s possible to observe both the particle characteristics and the wave characteristicsof light. As we mentioned earlier, a light beam shows interference phenomena(thus, it is a wave) and at the same time can produce photoelectrons(thus, it is a particle). At even higher frequencies, the momentum and energy ofthe photons increase. Consequently, the particle nature of light becomes moreevident than its wave nature. For example, the absorption of an x-ray photon iseasily detected as a single event, but wave effects are difficult to observe.The Wave Properties of ParticlesIn his doctoral dissertation in 1924, Louis de Broglie postulated that, becausephotons have wave and particle characteristics, perhaps all forms of matter haveboth properties. This was a highly revolutionary idea with no experimental confirmationat that time. According to de Broglie, electrons, just like light, have a dualparticle–wave nature.In Chapter 26 we found that the relationship between energy and momentumfor a photon, which has a rest energy of zero, is p E/c. We also know from Equation27.5 that the energy of a photon isAIP Niels Bohr LibraryLOUIS DE BROGLIE, FrenchPhysicist, (1892 – 1987)De Broglie was born in Dieppe, France. Atthe Sorbonne in Paris, he studied history inpreparation for what he hoped to be acareer in the diplomatic service. The worldof science is lucky that he changed hiscareer path to become a theoretical physicist.De Broglie was awarded the NobelPrize in 1929 for his discovery of the wavenature of electrons.E hf hc[27.12]Consequently, the momentum of a photon can be expressed asp E c hc[27.13]From this equation, we see that the photon wavelength can be specified by itsmomentum, or h/p. De Broglie suggested that all material particles withmomentum p should have a characteristic wavelength h/p. Because thec h Momentum of a photon