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Physics Essays

Double-slit interference and single-slit diffraction experiments on electrons

Huawang Li

Published Sep 3, 2022• 0 citations
Publisher

Abstract

De Broglie proposed the matter wave in 1924. The de Broglie wave is neither a mechanical wave nor an electromagnetic wave and has a very short wavelength. The Davisson-Germer electron diffraction experiment performed in 1925 involved bombarding the surface of a nickel crystal with a narrow beam of electrons. When the accelerating voltage V was maintained at 54 V, the wavelength of the incident electron was λ=h/ 2 m e V = 0.167 nm [Y. S. Chen and Z. Z. Li, College Physics (Tianjin University, Tianjin, 1999)] demonstrating the existence of the matter wave. We introduce a type of electron wave with a very long wavelength in this study that is different from the matter wave. For example, the wavelength of the electron wave can reach 0.43 mm in the double-slit interference of electrons. Experiments demonstrate that this long-wavelength electron wave can produce both double-slit interference and electron diffraction. A comparative analysis of matter and electron waves reveals the physical natures of these waves and wave‐particle duality.

DOI
10.4006/0836-1398-35.3.313

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De Broglie proposed the matter wave in 1924. The de Broglie wave is neither a mechanical wave nor an electromagnetic wave and has a very short wavelength. The Davisson-Germer electron diffraction experiment performed in 1925 involved bombarding the surface of a nickel crystal with a narrow beam of electrons. When the accelerating voltage V was maintained at 54 V, the wavelength of the incident electron was λ=h/ 2 m e V = 0.167 nm [Y. S. Chen and Z. Z. Li, College Physics (Tianjin University, Tianjin, 1999)] demonstrating the existence of the matter wave. We introduce a type of electron wave with a very long wavelength in this study that is different from the matter wave. For example, the wavelength of the electron wave can reach 0.43 mm in the double-slit interference of electrons. Experiments demonstrate that this long-wavelength electron wave can produce both double-slit interference and electron diffraction. A comparative analysis of matter and electron waves reveals the physical natures of these waves and wave‐particle duality.
Abstract The contributions of Otto Stern to the discovery of wave-particle duality of matter particles predicted by de Broglie are reviewed. After a short introduction to the early matter-vs-wave ideas about light, the events are highlighted which lead to de Broglie’s idea that all particles, also massive particles, should exhibit wave behavior with a wavelength inversely proportional to their mass. The first confirming experimental evidence came for electrons from the diffraction experiments of Davisson and Germer and those of Thomson. The first demonstration for atoms, with three orders of magnitude smaller wave lengths, came from Otto Stern’s laboratory shortly afterwards in 1929 in a remarkabletour de forceexperiment. After Stern’s forced departure from Hamburg in 1933 it took more than 40 years to reach a similar level of experimental perfection as achieved then in Stern’s laboratory. Today He atom diffraction is a powerful tool for studying the atomic and electronic structure and dynamics of surfaces. With the advent of nanotechnology nanoscopic transmission gratings have led to many new applications of matter waves in chemistry and physics, which are illustrated with a few examples and described in more detail in the following chapters.
The evolution of light theories began with Isaac Newton's corpuscular model, which explained reflection and refraction but could not account for diffraction and interference. In contrast, Christiaan Huygens proposed a wave theory, explaining light's behavior through an ether-based medium, supported by his principle that each point in a wavefront acts as a secondary source. This idea was experimentally supported in the early nineteenth century when Thomas Young's double-slit experiment revealed an interference pattern, affirming light's wave nature. Later, James Clerk Maxwell unified electricity and magnetism, establishing light as an electromagnetic wave and extending the electromagnetic spectrum beyond visible light. In the twentieth century, Einstein's photoelectric effect introduced the concept of wave-particle duality, demonstrating that light behaves as discrete photons. Soon after, Louis de Broglie extended the idea of wave-particle duality to matter, a prediction confirmed in 1927 when Clinton Davisson and Lester Germer observed electron diffraction from a crystal and, independently, G.P. Thomson demonstrated electron diffraction through thin films, both proving that electrons also exhibit wave-like properties. This concept was dramatically visualized by Claus Jonsson's 1961 electron double-slit experiment. Recently, the ALICE collaboration observed quantum interference patterns at the femtometer scale in ultra-relativistic nuclear collisions, pushing quantum interference studies to new frontiers.
In 1924 Louis de Broglie introduced the concept of wave-particle duality: the Planck constant hhh relates the momentum ppp of a massive particle to its de Broglie wavelength λ=h/pλ=h/pλ=h/p. The superposition principle is one of the main postulates of quantum mechanics; diffraction and interference phenomena are therefore predicted and have been observed on objects of increasing complexity, from electrons to neutrons and molecules. Beyond the early electron diffraction experiments, the demonstration of single-electron double-slit-like interference was a highly sought-after result. Initially proposed by Richard Feynman as a thought experiment it was finally carried out in 1976. A few years later, positron diffraction was first observed. However, an analog of the double-slit experiment has not been performed to date on any system containing antimatter. Here we present the first observation of matter wave interference of single positrons, by using a period-magnifying Talbot-Lau interferometer based on material diffraction gratings. Individual positrons in the 8-14 keV energy range from a monochromatic beam were detected by high-resolution nuclear emulsions. The observed energy dependence of fringe contrast proves the quantum-mechanical origin of the detected periodic pattern and excludes classical projective effects. Talbot-Lau interferometers are well-suited to the experimental challenges posed by low intensity antimatter beams and represent a promising option for measuring the gravitational acceleration of neutral antimatter.
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.
Classical physics identified matter with particles and radiation with waves. Although these descriptions accounted for a large number of very important facts, it became apparent at the beginning of the twentieth century that other phenomena, such as blackbody radiation and photoelectric effect, are satisfactorily explained only if radiation is described in terms of particles. Louis de Broglie developed a theory according to which, conversely, matter has wave properties. As an outcome of this theory, he was able to write down a formula relating the corresponding wavelength with the momentum of the particle. Diffraction patterns characterize waves, and the basic fact that corroborated the validity of the notion of matter waves was that the Davisson and Germer experiment proved electrons can be diffracted. In classical optics the simplest experiment displaying this phenomenon is the well-known Young two-slit experiment, in which a beam of light is passed through a diaphragm with two slits.