In a previous paper, it was explained that the absorption and emission process (AE-process) of Bohr’s model of the hydrogen atom must involve an electric charge (i.e., electron) transiting between atomic energy levels instead of quantum jumping; otherwise, there is no way to use the AE-process to predict the fine structure constant. In this paper, it is shown that (1) a complete oscillation of the atomic electron (i.e., an electric charge) and of the induced magnetic field must occur for Bohr’s hydrogen atom to emit electromagnetic radiation, and (2) an atomic electron (i.e., electric charge) of Bohr’s hydrogen atom can transit between energy levels without the atom emitting electromagnetic radiation.
In a previous paper, it was explained that the absorption and emission process (AE-process) of Bohr’s model of the hydrogen atom must involve an electric charge (i.e., electron) transiting between atomic energy levels instead of quantum jumping; otherwise, there is no way to use the AE-process to predict the fine structure constant. In this paper, it is shown that (1) a complete oscillation of the atomic electron (i.e., an electric charge) and of the induced magnetic field must occur for Bohr’s hydrogen atom to emit electromagnetic radiation, and (2) an atomic electron (i.e., electric charge) of Bohr’s hydrogen atom can transit between energy levels without the atom emitting electromagnetic radiation.
This paper develops and verifies a physics-first description of the hydrogen-atom transition from the L shell (n = 2) to the K shell (n = 1) by combining the historical Bohr model of atomic structure with classical Maxwell electrodynamics. Beginning with the Coulomb force, centripetal dynamics, and Bohr’s angular-momentum quantization condition, the analysis derives the allowed orbital radii, electron velocities, angular momenta, kinetic energies, electrostatic potential energies, and total bound-state energies of the hydrogen atom. For the n = 2 → n = 1 transition, the calculated energy difference is approximately 10.2 eV, corresponding through the Planck–Einstein relation ΔE = hν to a frequency of approximately 2.47 × 10¹⁵ Hz and a wavelength near 121.6 nm, consistent with the hydrogen Lyman-α transition. The emitted radiation is then examined through Maxwell’s equations and the vacuum constitutive relations. The resulting electromagnetic-wave description yields the transverse electric and magnetic fields together with the associated electromagnetic energy density, Poynting energy flux, momentum density, radiation pressure, and Maxwell stress tensor. In this way, the atomic energy difference obtained from the Bohr model is connected quantitatively to the classical propagation properties of the outgoing electromagnetic radiation. The derivation is mathematically consistent as a historical Bohr–Maxwell reconstruction, but it does not constitute a closed dynamical theory of spontaneous emission. The essential bridge between discrete atomic energy levels and the continuous Maxwell field is supplied by the quantum frequency condition ΔE = hν. Neither classical Maxwell electrodynamics nor Newtonian orbital mechanics independently derives this relation, and classical Maxwell theory does not by itself quantize the emitted radiation energy into individual photons. A complete treatment of spontaneous emission, transition probabilities, radiative lifetimes, and photon-field quantization requires quantum mechanics and ultimately quantum electrodynamics. Accordingly, the framework is presented as a verified correspondence between established limiting descriptions rather than as a replacement for Schrödinger wave mechanics, Dirac theory, or quantum electrodynamics. By clearly separating the atomic bound-state calculation, the quantum energy-frequency bridge, and the classical electromagnetic propagation problem, the analysis provides a rigorous conceptual and mathematical foundation for subsequent Maxwell–Schrödinger, Dirac–Maxwell, quantum-electrodynamic, Maxwell–Scretching, and Scretching Quantum Chain formulations of hydrogenic radiative transitions.
An analysis of applying the property of speed instantaneity to electronic transitions (i.e., transitions of the atomic electron that are not instantaneous), instead of quantum jumps (i.e., instantaneous transitions), during a complete oscillation for the process of Bohr’s model of the atom absorbing and emitting electromagnetic radiation (i.e., photon) reveals a discontinuity that is conserved as an emitted electromagnetic radiation (i.e., photon) discontinuity. The frequency of the oscillations of the atomic electron (i.e., electric charge) and induced magnetic field for the transitions of the atomic electron (i.e., electric charge) during the complete oscillation for the absorption and emission process (of Bohr’s atomic model) is conserved as the frequency of the oscillating electric and magnetic fields of the emitted electromagnetic radiation (i.e., photon). The conserved frequency and discontinuity (based on speed instantaneity and electronic transitions that are not instantaneous) of the atomic absorption and emission process (of Bohr’s atomic model) lead to predicting the need for Planck’s constant (i.e., quantum of action) without the use of probability. Planck claimed the interpretation of reality must change if his method of deriving the radiation law stood on a physical concept. Einstein, whom Planck credited as the first to make an advancement in the quantum field, unknowingly introduced a quantized two-dimensional discontinuum geometry that is one of the foundations on which a table of five realities used in physics was developed for making predictions. Using the table of realities, locality is redefined, and entanglement is demystified.
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.
Introduction The preceding chapters have focused on atomic transitions induced by applied radiation. That is, there is an optical field illuminating the atoms, and their response is calculated. It is implicitly assumed that an excited atom left alone will spontaneously return to the ground state, and conserve energy by emitting light that satisfies E 2 − E 1 = ħ ω 21 in accordance with the Planck and Bohr pictures. But this spontaneous emission process is not addressed quantitatively in these earlier chapters. Spontaneous emission is one of the most pervasive phenomena of atomic physics, and yet its origins remain among the least well-understood. The number of misconceptions is enormous, and they are to be found in textbooks, journal articles, and lecture notes. Because the natural decay of an excited atom adds energy to what is usually an empty mode of the electromagnetic field, the process is fundamentally quantum mechanical. Classical or even semi-classical descriptions cannot be assured to give correct answers. This is not to say that such discussion is to be avoided, but only that caution is needed in interpreting the results. Toward the end of the nineteenth century, many experimental results made it clear that classical mechanics needed to be supplemented by new theories. The first venture into the new physics was Planck's hypothesis that the energy of classical radiating oscillators like those discussed in Chap. 1 would have to be quantized into integer multiples of ħ ω. This notion led to his famous formula for the spectrum of thermal radiation from a non-reflective object (black body), and this formula describes a radiation field in thermodynamic equilibrium with its environment. The result of Planck's hypothesis in the context of thermal equilibrium plays a vital role in the discussion of spontaneous emission. Einstein A - and B -coefficients Soon after Bohr proposed a model of atomic structure consisting of discrete energy levels, connected by radiation whose energy satisfied Δ E = ħω when atoms made transition between them, Einstein published the first serious attempt to connect the absorption and emission processes. Absorption, he reasoned, could occur only in the presence of applied radiation, whereas spontaneous decay occurred without the application of any field.
In the first step, the Joule-Lenz dissipation energy specified for the electron transitions between two neighbouring quantum levels in the hydrogen atom has been compared with the electromagnetic energy of emission from a single level. Both the electric and magnetic vectors entering the Pointing vector of the electromagnetic field are referred to the one-electron motion performed along an orbit in the atom. In the next step, a similar comparison of emission rates is performed for the harmonic oscillator. Formally a full agreement of the Joule-Lenz and electromagnetic expressions for the energy emission rates has been attained. The case of the electron oscillator allowed us to perform a more direct comparison of the quantum approach to the emission rate with the classical electromagnetic theory.
In the first step, the Joule-Lenz dissipation energy specified for the electron transitions between two neighbouring quantum levels in the hydrogen atom has been compared with the electromagnetic energy of emission from a single level. Both the electric and magnetic vectors entering the Pointing vector of the electromagnetic field are referred to the one-electron motion performed along an orbit in the atom. In the next step, a similar comparison of emission rates is performed for the harmonic oscillator. Formally a full agreement of the Joule-Lenz and electromagnetic expressions for the energy emission rates has been attained.