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Japan Journal of Research

A Rydberg-Bohr-de Broglie Algebraic Model of Hydrogen Atoms

Xiao En Wang

Published Sep 30, 2024• 0 citations
Publisher

Abstract

Bohr ignored the electromagnetic interaction of moving charges in atoms and only considered Coulomb forces, thus encountering half frequency difficulties. This article considers the Lorentz force to make the classical Bohr model consistent with modern quantum theory, uses de Broglie's standing wave principle instead of Bohr's quantization assumption, derives the energy level formula for hydrogen atoms, and explains the radiation mechanism of hydrogen atomic spectra. The hydrogen atom in a spectral tube emits a photon wave train during one free path, and the wavelength of the photon is the eigen wavelength of its wave train. The head wavelength of the wave train is four thirds of its eigen wavelength, and the tail wavelength of the wave train is two-thirds of its eigen wavelength.

DOI
10.33425/2690-8077.1139

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Abstract Only Coulomb force is considered in Bohr model. It is found that electron in ground state hydrogen atom is also affected by Lorentz force of the same magnitude. Under the combined action of Coulomb force and Lorentz force, the radius of hydrogen atom is twice that of Bohr, and the rotation frequency of electron is half that of Bohr. The "half frequency" problem of Bohr's theory is solved, and the quantization result of the energy level of hydrogen atom is obtained by using the standing wave condition of quantum mechanics. The mechanism and details of photon absorption by hydrogen atom are analyzed and explained, and the physical meaning of Planck constant is explained.
Abstract Only Coulomb force is considered in Bohr model. It is found that electron in ground state hydrogen atom is also affected by Lorentz force of the same magnitude. Under the combined action of Coulomb force and Lorentz force, the radius of hydrogen atom is twice that of Bohr, and the rotation frequency of electron is half that of Bohr. The "half frequency" problem of Bohr's theory is solved, and the quantization result of the energy level of hydrogen atom is obtained by using the standing wave condition of quantum mechanics. The mechanism and details of photon absorption by hydrogen atom are analyzed and explained, and the physical meaning of Planck constant is explained.
Balmer equation for the atomic spectral lines was generalized by Rydberg. Here it is shown that 1) while Bohr's theory explains the Rydberg constant in terms of the ground state energy of the hydrogen atom, quantizing the angular momentum does not explain the Rydberg equation, 2) on reformulating Rydberg's equation, the principal quantum numbers are found to correspond to integral numbers of de Broglie waves and 3) the ground state energy of hydrogen is electromagnetic like that of photons and the frequency of the emitted or absorbed light is the difference in the frequencies of the electromagnetic energy levels.
In his doctoral thesis in 1911, Bohr reached the conclusion that at thermal equilibrium metal atom has no magnetic effect. Therefore, when establishing the hydrogen atom model in 1913, he did not consider the Lorentz force, but only the Coulomb force. The radius of the hydrogen atom he obtained is half smaller, and the orbital rotation frequency is twice larger. It must be multiplied by 1/2 to be consistent with the value of the Rydberg experiment. He proposed to calculate the photon frequency by using the average value of the zero frequency of infinite quantum number and the basic frequency, but it is not applicable to the energy levels for the ordinary quantum numbers, and later he called it the correspondence principle. In our modified Bohr model, we eliminate and solve Bohr's half frequency problem; The photon energy is equal to the difference between the two energy levels, and the photon frequency is equal to the difference between the two rotation frequencies of the electron; All excited states of hydrogen atom are elliptical orbits, and the nucleus is located in the center of the ellipse; The microscopic model of photonic structure is established, and the microscopic mechanism of atomic luminescence and quantum entanglement is given.
In 1913, Niels Bohr developed an accurate model for the hydrogen atom. The mathematics involved and the simplicity of this model is easily understood. The intention of the paper is not to replace Bohr's model, but to find a similar model for all atoms. The model discussed, which was developed on the same basis as Bohr's model for the hydrogen atom, calculates the radii and the energies of the orbits. The wavelength of an emitted photon when an electron makes a ‘jump’ from a higher state to a lower state can also be calculated from the model. Finally, the paper demonstrates that the model obeys the de Broglie's hypothesis that the moving electron exhibits both wave and particle properties.
In recent years, it has been recognized that treatment of the spectral problem should be associated with closed orbits. This paper proves that the closed orbit obtained by Bohr using numerical algebraic equation is reasonable both mathematically and physically and that the de Broglie wavelength of the electron in the hydrogen atom is equal to the circumference of its orbit. By Bohr model and de Broglie’s matter-wave thought, some quantization conditions, electronic transition formulae, a mechanism and details of emitting photon wave train, a filling order of electrons in the periodic table, and Madelung rule have been deduced theoretically. We solve the Löwdin’s challenge problem.