Bohr postulates derived from the toroidal electron model


  • C. A. M. dos Santos Escola de Engenharia de Lorena - University of São Paulo
  • M. S. da Luz Universidade Federal do Triângulo Mineiro



Toroidal Electron Model, Schwinger Electromagnetic Wave, Bohr Postulates


The quantization of the electron orbits in the Bohr atom is revisited. The toroidal electron model, in which electron charge is described by Schwinger electromagnetic wave orbiting the electron mass, offers a natural explanation for the orbit quantization. As a consequence, the four Bohr postulates can be directly derived from the toroidal electron structure. A physical meaning for the Rydberg constant is also proposed.


N. Bohr, On the constitution of atoms and molecules, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 26 (1913) 326, 1.

J. R. Rydberg, On the structure of the line-spectra of the chemical elements, Philosophical Magazine, 5th series, 29 (1890), 331.

R. Eisberg and R. Resnick, Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles, 2nd edition (John Wiley & Sons, 1985)

O. Consa, Helical Solenoid Model of the Electron, Prog. in Phys. 14 (2018) 80.

A. O. Di Tommaso and G. Vassallo, Electron Structure, Ultra-dense Hydrogen and Low Energy Nuclear Reactions, J. Cond. Matt. Nucl. Sci. 29 (2019) 525.

F. Celani, A. O. Di Tommaso, and G. Vassallo, Maxwell’s Equations and Occam’s Razor, J. Condensed Matter Nucl. Sci. 25 (2017) 100.

G. Vassallo and A. Kovacs, The Proton and Occam’s Razor, J. Phys.: Conf. Ser. 2482 (2023) 012020. https://doi/10.1088/1742-6596/2482/1/012020

D. Hestenes, The zitterbewegung interpretation of quantum mechanics, Found. Phys. 20 (1990) 1213.

D. Hestenes, Zitterbewegung structure in electrons and photons, (2020).

C. A. M. dos Santos, The Structure of the Electron Revealed by Schwinger Limits. Preprint available on (under review)

M. Rivas, The atomic hypothesis: physical consequences, J. Phys. A: Math. Theor. 41 (2008) 304022, https://DOI10.1088/1751-8113/41/30/304022

M. Rivas, Kinematical Theory of elementary spinning particles, Bilbao, March 2024. Available on

C. A. M. dos Santos, F. S. Oliveira, L. M. S. Alves, and M. S. da Luz, On the Fermi gas, the Sommerfeld fine structure constant, and the electron-electron scattering in conductors. Preprint available on (under review)

Another possibility is electron mass to be distributed in the toroidal structure, as pointed out previously [10]

2018 CODATA Value: Fine-structure constant. The NIST Reference on Constants, Units, and Uncertainty. NIST. Retrieved on October 22, 2023

λe is defined in agreement with the well-known relationship between λB , λC , and λe , given by λB = λC /α = λe/α2 (rB = rc/α = re/α2 ), where λe = 2πre and re is the classical electron radius

A. Sommerfeld, Atombau und Spektrallinien (in German), Braunschweig, DE: Friedr. Viewe & Sohn, 2nd edition, (1921) 42

R. A. Serway and J. W. Jewett, Physics for Scientists and Engineers with Modern Physic 6th edition, Cengage Learning, (2004) 553




How to Cite

dos S. Carlos A. M. and M. da Luz, “Bohr postulates derived from the toroidal electron model”, Rev. Mex. Fís., vol. 70, no. 4 Jul-Aug, pp. 040201 1–, Jul. 2024.