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Measuring the de Broglie wavelength of electrons using Thomson e/m tube

Swarnava Mitra

Published Nov 20, 2021• 0 citations
Publisher

Abstract

The Thomson e/m experiment laid the foundation of the first atomic particle and for once proved the existence of discrete charged particles, now known as electrons. This work aims at studying the wave nature of electrons by measuring their de Broglie wavelengths. The wavelength was obtained from two different facets, namely, the electric field and the magnetic field, and then it has been shown that the two values are in agreement with each other to an order of 10−11 m.

DOI
10.5281/zenodo.6349469

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The Thomson e/m experiment laid the foundation of the first atomic particle and for once proved the existence of discrete charged particles, now known as electrons. This work aims at studying the wave nature of electrons by measuring their de Broglie wavelengths. The wavelength was obtained from two different facets, namely, the electric field and the magnetic field, and then it has been shown that the two values are in agreement with each other to an order of 10−11 m.
Rutherford thought to explore the structure of matter by bombarding thin sheets of metals with alpha particles. According to Bohr, the mechanism of emission of e.m. wave is represented by the downward vertical lines connecting states at different n. The two main successes are: explanation of Rydberg formula and expression of Rydberg empirical constant in terms of fundamental constants and the calculation of the size of the atom in agreement with measurements. The remarkable fact that de Broglie hypothesis of pilot waves, when applied to the hydrogen atom, gives excellent agreement with Bohr's theory seems to give foundation that the matter-wave duality is a characteristic of elementary particles like the electrons. Shortly after de Broglie suggestion an experimental verification of de Broglie ideas was successfully attempted. Davisson and Germer needed to choose a crystal whose spacing was such that, under a reasonable acceleration voltage of the electrons, the de Broglie wavelength would be of the order of the lattice spacing.
As for DE Broglie's hypothesis of matter waves, many experimental physicists have experimentally verified it by using cathode ray tube and proved that matter waves do exist, so there is a mysterious hypothesis of wave-particle duality.In this paper, according to the electric field force of electrons in the cathode ray tube and the continuity equation of electrons, Under assumptions such as inelastic approximation, it is proved that the wave-particle duality is actually the macroscopic motion of real particles in the form of waves.In this paper, it is proved theoretically that the component of electron velocity in the tube satisfies the wave equation, and the wave velocity varies with the change of electric potential in the tube.From the discussion in this paper, it can be seen that there are still some problems to be studied about the motion of electrons in the cathode ray tube, so that the special motion law of electrons in the cathode ray tube can be further explored from both theoretical and experimental aspects.At the same time, it is expected that the theory in this paper can provide theoretical guidance for the manufacture and debugging of electron microscopes and the design of large-scale integrated circuits, and thus influence other related fields...This will involve a vast area of science and technology!This paper is devoted to the in-depth analysis of the objective truth of the wave-particle duality presented by microscopic particles.
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.
The author has worked with high-resolution transmission electron microscope for many years, which provides the most direct evidence of wave-particle duality. This relates to Crookes and J. J. Thomson's cathode rays tubes to determine that electron beams are of particle nature. This also relates to Röntgen's discovery that when an electron beam in the cathode rays tube strikes the glass wall, it produces X-rays with extremely high penetrating power. This behavior is consistent with Maxwell-Lorentz’s electrodynamics that electromagnetic waves must be produced whenever electricity carriers alter their velocity. The wave-particle duality proposed by de Broglie refers to accelerated electron beam, rather than single electron. De Broglie emphasized that the crystallographic diffraction pattern produced by his electron beam was completely consistent with the crystallographic diffraction pattern of von Laue by X-rays, therefore, he proposed that electrons possess wave-particle duality. This is actually the selected area electron diffraction pattern in transmission microscope. It is X-rays, not the waves of the electrons themselves to produce diffraction pattern. He extended this to the wave-particle duality of all matter and light. Schrödinger directly introduced de Broglie's electron beam behavior into electron wave in atoms. It was just at this stage that illogical reasoning occurred, making the quantum theory increasingly difficult to understand.
Einstein assumed duality between radiation and particles. Experiments involving electrons and diffraction effects are described to illustrate such behaviors. Classical physics and Einstein’s findings unmistakably demonstrated that light possessed both wave and particle properties. The responses of electrons in electric and magnetic fields are evidence for their existence as charged particles. The relationship between particle- and wave-like behavior was given by de Broglie in 1924. The dual nature of electrons was demonstrated experimentally by Davisson and Germer, when studying the diffraction of a stream of electrons. The reflection or diffraction of a beam of electromagnetic radiation can be expected to change its intensity, but changes in its wavelength would not ordinarily be anticipated. Photons and electrons may be described in terms of waves, but this approach has inherent limitations. The greater the attempt that is made to study the nature or behavior of a photon or a particle, the greater will be the uncertainty or error of the measurements.