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Quantum States and Energy Levels in Hydrogen Atom

Daniele Sasso

Published Feb 1, 2019• 0 citations
OpenAlex

Abstract

In this paper we will calculate energy levels of electron relative to hydrogen atom making use of the four quantum numbers of the deterministic quantum model. Calculations prove in a few situations quantum states with different quantum numbers can have the same value of total energy and a few sub-levels of a more external level can precede sub-levels of more internal levels. Calculations prove also the electron in the fundamental state 1s1, in order to jump to the state 5q10 needs a photon with energy E=13.08 eV= 20.93۰10-19 J, that is in the ultraviolet band.

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In this paper we will calculate energy levels of electron relative to hydrogen atom making use of the four quantum numbers of the deterministic quantum model. Calculations prove in a few situations quantum states with different quantum numbers can have the same value of total energy and a few sub-levels of a more external level can precede sub-levels of more internal levels. Calculations prove also the electron in the fundamental state 1s1, in order to jump to the state 5q10 needs a photon with energy E=13.08 eV= 20.93۰10-19 J, that is in the ultraviolet band.
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.
The concept of quantized energy lies at the heart of quantum physics. It is shown that the visible spectrum of hydrogen consists of five spectral lines, each with a particular energy. These are shown to correspond to transitions or quantum jumps between particular energy levels of the hydrogen atom. The energy-level diagram for hydrogen is particularly simple, with the values of the energy levels from the ground state to the excited states dependent only on the principal quantum number. Spectral lines in the ultraviolet, visible, and infrared are referred to as the Lyman series, the Balmer series, and the Paschen series respectively. Other quantum numbers including the orbital quantum number, the magnetic quantum number, and the spin quantum number are introduced and the rules for combining them are described. Spectroscopic notation to describe quantum states is also explained. The 21 cm radio emission is shown to be a consequence of the spin-flip transition in hydrogen. Other quantum systems, such as molecules, are briefly described.
On the basis of the unconventional concept of the formation of the line spectrum of the hydrogen atom, an equation is obtained that is necessary for computer calculations of the energy emitted by an electron during the transition from a certain current energy level rλ,n to the receiver radius r0. The obtained solution of the energy equation made it possible to derive the formal relations necessary for calculating the values of the radii of the levels of the hydrogen atom and, accordingly, the velocities of the electron in these orbits. The applied aspect of the considered methodology consists in using the results of the performed calculations for the problems of synthesis and analysis of quantum-electronic circuits.
Abstract The energies, kets and wave functions obtained from the Schrödinger equation for the hydrogen atom are examined in Chapter 9. Three quantum numbers are identified. The energies turn out to be the same as in the Bohr model, and an energy-level diagram appropriate to the quantum description is constructed. Graphs of the probability distributions are interpreted as the electron being in a “cloud” around the proton, rather than at a fixed position: the atom is fuzzy, not sharp-edged. The wavelengths of the five photons of the Balmer series are shown to be in the visible range. These photons are emitted when electrons transition from higher-excited states to the second lowest one, which means that electronic-type transitions underlie the presence of colors in our visible environment. The non-collapse of the atom, required by classical physics, is shown to arise from the structure of Schrödinger’s equation.
Recently, spectroscopic and calorimetric observations of hydrogen plasmas and chemical reactions with them have been interpreted as evidence for the existence of electronic states of the hydrogen atom with a binding energy of more than 13.6 eV. The theoretical basis for such states, which have been dubbed hydrinos, is investigated. We discuss both the novel deterministic model of the hydrogen atom, in which the existence of hydrinos was predicted, and standard quantum mechanics. Severe inconsistencies in the deterministic model are pointed out and the incompatibility of hydrino states with quantum mechanics is reviewed.