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CRC Press eBooks

Quantized Energy

A. J. Norton

Published Mar 16, 2021• 0 citations
Publisher

Abstract

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.

DOI
10.1201/9781003164661-4

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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.
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.
Based on the open-loop and closed-loop theory of Daojing, a novel physical mechanism and calculation formula for electronic transitions are proposed. The Bohr radius and the hydrogen atom energy level formula are derived. For a total of 26 hydrogen spectral lines across the Lyman, Balmer, Paschen, Brackett, and Pfund series, the theoretical calculation results are consistent with public experimental data within four significant figures. This demonstrates that quantization is an inevitable result of closed-loop stability, rather than an artificial hypothesis, and that electronic transitions are a continuous transition of closed-loop dynamic periodic modes, rather than an instantaneous quantum jump.
Transition of hydrogen electron through S-orbits has been studied.Energy levels and frequencies of the emitted spectral lines were computed through new simple atomic model.The equations assume that, the energy and frequency of the emitted lines of six known series are related to enclosed areas of successive orbits and proportionality constants.These constants are strongly related to all spectral lines in all series.The results found from this model will give abroad understanding of quantum mechanics principles.
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.
Introduction Series of atomic spectral lines had been studied by emission from excited vapors even before Balmer described the regularity of the visible lines of hydrogen in 1884. However, direct excitation had been restricted to the few lowest-lying levels, particularly those accessible by electric dipole transitions from the ground state using classical light sources. The advent of tunable lasers in the 1970s changed such spectroscopic limitations enormonsly, allowing excitation to a very much larger number of states. Atoms in highly excited states, typically with principal quantum numbers n ≥ 10, are called Rydberg atoms. They are oversize, fragile states of significant intrinsic interest. They are very rare in nature because of their size and fragility, but they are found in interstellar space (H I regions). One of the best sources for comprehensive descriptions of Rydberg atoms and references to the literature describing their exploration is Ref. [120]. It describes their characteristic properties and behavior both classically and quantum mechanically, and especially their strongly enhanced interactions with external fields. The first thing to note is that Rydberg atoms are usually characterized by a single, highly excited electron while all the other electrons remain in their original states. Thus their properties are very nearly classical, and the atoms are much closer to the ideal hydrogen-like model of Chap. 7, along with appropriate quantum defects (see Chap. 10). The spectroscopy of such states is especially interesting because the active electron is much less perturbed by the other electrons in the atom than when it is in lower states. Moreover, there are some special circumstances in which the energy of a Rydberg state is degenerate with an atomic state having two electrons excited to lower levels, and such configurations yield further new information. Second, Rydberg atoms do not usually decay back to the ground state by emission of characteristic radiation, so their study is mediated by other techniques that reveal new and interesting properties. Such properties arise because Rydberg atoms have a huge dipole moment and very low binding energy resulting from the large average distance between the excited electron and the nucleus-plus-core of the rest of the atom with net charge e . Third, transitions between Rydberg states are quite different from those connecting to the ground state for at least three reasons.
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.