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Institute of Physics eBooks

The Davisson–Germer experiment

V. Granata

Published Aug 1, 2020• 0 citations
Publisher

Abstract

In this chapter, we discuss the well celebrated Davisson-Germer experiment, that demonstrates the wave nature of the electron. Then, we present the table-top apparatus that reproduces the original experiment. We point out that such experimental set-up is easily usable by students, and it allows to measure the electron wavelength, thus confirming de Broglie’s hypothesis.

DOI
10.1088/978-0-7503-2678-0ch15

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•Jun 23, 2021•0 citations
In this chapter, we discuss the well celebrated Davisson-Germer experiment, that demonstrates the wave nature of the electron. Then, we present the table-top apparatus that reproduces the original experiment. We point out that such experimental set-up is easily usable by students, and it allows to measure the electron wavelength, thus confirming de Broglie’s hypothesis.
A primary electron beam of a transmission electron microscope is scattered into secondary beams by the planes of atoms of a single crystal. These secondary beams are focused to form a diffraction pattern on the final screen. This experiment is similar to the Thompson one which, independently by Davisson and Germer, demonstrated the de Broglie hypothesis of the existence of electron waves. Without changing the experimental apparatus, it is possible to realize an interference experiment with electrons coming from two spatially separated sources in analogy with the optical Young set-up. Both experiments are clear evidence of the electron wave-like behaviour. By varying the conditions of illumination, changes of the fringe visibility which reveal the spatial coherence properties of the electron beam, are displayed.
We tried to introduce the idea of quantization in Chapter 9 as a completion of a one semester course. However, we skipped over some really interesting events in the history of Science between 1900 and 1913 when Bohr derived the quantized energy of the H atom. First we want to carry out the 1901 Planck derivation of the formula for blackbody radiation [1]. Many texts just show the curve, write e¼ hn, and move on. As a student, this author found that limited explanation very frustrating since energy quantization is a fundamental concept. Even among graduate texts in quantum mechanics, we are aware of only one that does the complete treatment which we will draw upon for the mathematics [2] but supplement with a narrative that we have found helpful to students over the years. Then in 1905, Albert Einstein (1879-1955), one of the most influential scientists of all time, gave an explanation of the photoelectric effect [3] for which he received the Nobel Prize in 1921. Even reducing our list to essential topics, we need to discuss the Davisson-Germer experiment [4]. The photoelectric effect introduces the idea that light waves can act as particles while the Davisson-Germer experiment showed that particles can act like waves and confirmed the De Broglie equation [5]. However, you can be assured that it will not be as difficult as you might have anticipated and if you can absorb the meaning of just these three key experiments you should be able to begin thinking in terms of quantum mechanics! Despite our slow historical development, this is 2010 and we have to get to the twenty-first century somehow!
Davisson and Germer performed an experiment, in which electrons were reflected from parallel layers of atoms in a crystal. The electrons showed interference, thus demonstrating the wave nature of the electron. Louis de Broglie postulated a wave model of the electron, in which an electron orbit was represented by a group of in-phase waves. The model predicted that the angular momentum of an electron could take on only a limited number of values, a concept that Neils Bohr had introduced some years earlier as an ad hoc assumption. In an electron microscope, electrons stream off a hot filament and are accelerated to high velocity by passing between two electrically charged plates. The electrons' wavelength is related to their velocity and it is easy to obtain electrons with wavelengths near 0.1 nm, which suggests the possibility of obtaining resolution of about the same magnitude.
This chapter describes the dual nature of electron/de Broglie waves. de Broglie suggested that like light, an electron also behaves as both a particle and a wave. Based on this hypothesis, a relationship between wavelength of electrons (a particle) and momentum was developed. It opines that ‘wavelength of the particle is inversely proportional to momentum’. This is called the de Broglie relation. On the basis of the above facts, we have developed a relationship between wavelength and voltage applied and this relation may be stated as ‘the wavelength of a particle is inversely proportional to the square root of the voltage applied to the system’. This chapter also uses the Davisson and Germer experiment to show the wave nature of the particle, i.e., diffraction of electrons by crystal lattice. The experimental results were the same as found in the case of the diffraction of X-ray by crystals. This chapter also provides an idea on quantisation of angular momentum. It also discusses Heisenberg’s uncertainty principle, phase velocity, group velocity, and uncertainty relation between energy and time. The chapter comprises the experimental evidence of Heisenberg’s uncertainty principle, such as by diffraction of electrons through a slit and gamma ray microscope thought experiment, which is shows the physical significance of the uncertainty principle. Sufficient references, solved problems, and questions on concepts have been provided at the end of chapter.
We discuss the breakdown of classical theory in relation to phenomena on the nanoscale. The historical discovery of the wave nature of electrons in the Davisson–Germer Experiment is reviewed. We present the puzzling experimental data and its explanation in terms of particle diffraction, which contradicts classical mechanics. The quantitative success of de Broglie’s formula in associating particle momenta with a wavelength is demonstrated. Analyzing the conditions in which the wave nature of particles becomes apparent, namely, the condition for correspondence between the de Broglie wavelength and the lattice from which the particles are diffracted, we draw some general conclusions. Particularly, by translating to de Broglie wavelengths the particle masses and energy values that are typical to materials and processes on the nanoscales, one immediately realizes that wave properties are expected to be dominant. Quantum mechanics is therefore essential for a proper description of nanoscale phenomena.