29.6 The wave nature of matter

Learning objectives

By the end of this section, you will be able to:

• Describe the Davisson-Germer experiment, and explain how it provides evidence for the wave nature of electrons.

The information presented in this section supports the following AP® learning objectives and science practices:

• 1.D.1.1 The student is able to explain why classical mechanics cannot describe all properties of objects by articulating the reasons that classical mechanics must be refined and an alternative explanation developed when classical particles display wave properties. (S.P. 6.3)
• 6.G.1.1 The student is able to make predictions about using the scale of the problem to determine at what regimes a particle or wave model is more appropriate. (S.P. 6.4, 7.1)
• 6.G.2.1 The student is able to articulate the evidence supporting the claim that a wave model of matter is appropriate to explain the diffraction of matter interacting with a crystal, given conditions where a particle of matter has momentum corresponding to a de Broglie wavelength smaller than the separation between adjacent atoms in the crystal. (S.P. 6.1)

De broglie wavelength

In 1923 a French physics graduate student named Prince Louis-Victor de Broglie (1892–1987) made a radical proposal based on the hope that nature is symmetric. If EM radiation has both particle and wave properties, then nature would be symmetric if matter also had both particle and wave properties. If what we once thought of as an unequivocal wave (EM radiation) is also a particle, then what we think of as an unequivocal particle (matter) may also be a wave. De Broglie’s suggestion, made as part of his doctoral thesis, was so radical that it was greeted with some skepticism. A copy of his thesis was sent to Einstein, who said it was not only probably correct, but that it might be of fundamental importance. With the support of Einstein and a few other prominent physicists, de Broglie was awarded his doctorate.

De Broglie took both relativity and quantum mechanics into account to develop the proposal that all particles have a wavelength , given by

where $h$ is Planck’s constant and $p$ is momentum. This is defined to be the de Broglie wavelength    . (Note that we already have this for photons, from the equation $p=h/\lambda$ .) The hallmark of a wave is interference. If matter is a wave, then it must exhibit constructive and destructive interference. Why isn’t this ordinarily observed? The answer is that in order to see significant interference effects, a wave must interact with an object about the same size as its wavelength. Since $h$ is very small, $\lambda$ is also small, especially for macroscopic objects. A 3-kg bowling ball moving at 10 m/s, for example, has