H atom parameters: how Classical Physics gives new/clear results

In our recent paper [A. Bacchieri, Phys. Essays 36 , 61 (2023)], we had found that the total escape speed from all the masses in the universe, u = (‐2 u ) 1/2 , where u is the total gravitational potential energy, (whose value depends on the location of the masses with respect to the considered point), equals the speed of light; hence, c = u , which, as known, implies the light to be composed of massive particles. The neutrinos also have a speed equal to c (hence they have a mass), but, contrary to the light, they interact very rarely with the matter, whereas the light interacts with the circling electrons; therefore, the impacts of light-matter, to surely happen, require the particles of light to be provided with a positive charge on their front, and a negative one on their tail, like an electrical massive dipole (photon): In particular, each photon turns out to be a longitudinal (elastic) particle, ( λ being the length of one of them), while their continuous sequence (they are connected to each other through their tail-front electrical bond) is known as a ray of light ; its frequency ν = n /1s becomes the number of photons (of the same ray), passing in the unit of time, and since photons may be considered as indivisible entities, the frequency of light and other related quantities may vary, at the atomic scale, by discrete values. Moreover, if the electron should have its proper electric charge uniformly distributed, a contrary direction incident photon ‐ circling electron , during their impact, could cause the electron to fall into its nucleus; this event does not happen, hence we inferred that the electron charge is like a point-particle, fixed on the electron surface and facing, during the electron revolution, the related nucleus (hence the orbit of this charge differs from the electron orbit by the electron radius). This structure implies the electron charge to be the photon‐electron impact point, while these impacts are the origin of the electron radial velocity w directed toward higher orbits. On these bases, it turns out that, in a given location (where u has a certain value), during the photon‐electron interaction, because of the electron velocity w and the related Doppler effect (causing the decrease in the re-emitted photon's frequency as well as the increase in their length (or vice versa), the speed of light becomes invariant nevertheless of any relative motion source (of light)-observer . On these bases, regarding the H atom (observed from the electron‐proton common center of gravity orbited by the electron reduced mass <mml:math display="inline"> <mml:msub> <mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:math> , we found n = 1, 2, …, 137 (instead of the claimed n = 1, 2, …, ∞), as the number of progressive circular orbits of its electron; <mml:math display="inline"> <mml:msubsup> <mml:mrow> <mml:mi>v</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mo> </mml:mo> </mml:mrow> </mml:msubsup> </mml:math> = <mml:math display="inline"> <mml:mi>c</mml:mi> <mml:mo>/</mml:mo> <mml:mn>137</mml:mn> <mml:mo>,</mml:mo> </mml:math> as the electron ground-state (g-s) orbital speed; <mml:math display="inline"> <mml:msubsup> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mo> </mml:mo> </mml:mrow> </mml:msubsup> </mml:math> = r 0 <mml:math display="inline"> <mml:mo>/</mml:mo> <mml:mn>137</mml:mn> </mml:math> α, being α the fine-structure constant, as the electron g-s orbit; <mml:math display="inline"> <mml:mo> </mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>v</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo> </mml:mo> </mml:mrow> </mml:msubsup> </mml:math> = αc , as the electron charge g-s orbital speed, different from the one ( <mml:math display="inline"> <mml:msubsup> <mml:mrow> <mml:mi>v</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mo> </mml:mo> </mml:mrow> </mml:msubsup> </mml:math> = <mml:math display="inline"> <mml:mi>c</mml:mi> <mml:mo>/</mml:mo> <mml:mn>137</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:math> of the circling electron; <mml:math display="inline"> <mml:msub> <mml:mrow> <mml:mo> </mml:mo> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>137</mml:mn> <mml:mo>·</mml:mo> <mml:mo> </mml:mo> <mml:mn>4</mml:mn> <mml:mi>π</mml:mi> <mml:msub> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>∞</mml:mi> </mml:mrow> </mml:msub> </mml:math> , being <mml:math display="inline"> <mml:msub> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>∞</mml:mi> </mml:mrow> </mml:msub> </mml:math> the Rydberg constant, as the g-s orbit of the electron charge; in particular, being <mml:math display="inline"> <mml:mo> </mml:mo> <mml:mi>γ</mml:mi> </mml:math> the mass of one photon related to its transit time T , we found <mml:math display="inline"> <mml:msub> <mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> </mml:msub> <mml:mo>/</mml:mo> <mml:mi>γ</mml:mi> <mml:mi>c</mml:mi> <mml:msub> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>∞</mml:mi> </mml:mrow> </mml:msub> <mml:mo> </mml:mo> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>e</mml:mi> </mml:mrow> </mml:msub> <mml:mo>/</mml:mo> <mml:mi>γ</mml:mi> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo> </mml:mo> </mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> <mml:msup> <mml:mrow> <mml:mn>137</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo> </mml:mo> </mml:mrow> </mml:msup> </mml:math> , where <mml:math display="inline"> <mml:msub> <mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>e</mml:mi> </mml:mrow> </mml:msub> </mml:math> is the electron mass, while <mml:math display="inline"> <mml:msubsup> <mml:mrow> <mml:mi>γ</mml:mi> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo> </mml:mo> </mml:mrow> </mml:msubsup> </mml:math> is the mass of the incident photon flowing during the unit of time, absorbed by the electron along its g-s orbit. Finally, the massiveness of light leads to a new meaning of the famous E = mc 2 (involving photons and neutrinos).