Maxwell’s Equations as the Basis for Model of Atoms


A century ago the classical physics couldn’t explain many atomic physical phenomena. Now the situation has changed. It’s because within the framework of classical physics with the help of Maxwell’s equations we can derive Schrödinger’s equation, which is the foundation of quantum physics. The equations for energy, momentum, frequency and wavelength of the electromagnetic wave in the atom are derived using the model of atom by analogy with the transmission line. The action constant A0 = (μ0/ε0)1/2s02e2 is a key term in the above mentioned equations. Besides the other well-known constants, the only unknown constant in the last expression is a structural constant of the atom s0. We have found that the value of this constant is 8.277 56 and that it shows up as a link between macroscopic and atomic world. After calculating this constant we get the theory of atoms based on Maxwell’s and Lorentz equations only. This theory does not require knowledge of Planck’s constant h, which is replaced with theoretically derived action constant A0, while the replacement for the fine structure constant α-1 is theoretically derived expression 2s02 = 137.036. So, the structural constant s0 replaces both constants h and α. This paper also defines the stationary states of atoms and shows that the maximal atomic number is equal to Zmax = 137. The presented model of the atoms covers three of the four fundamental interactions, namely the electromagnetic, weak and strong interactions.

Share and Cite:

Perkovac, M. (2014) Maxwell’s Equations as the Basis for Model of Atoms. Journal of Applied Mathematics and Physics, 2, 235-251. doi: 10.4236/jamp.2014.25029.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Wheeler, J.A. and Feynman, R.P. (1945) Interaction with the Absorber as the Mechanism of Radiation. Reviews of Modern Physics, 17, 157-181.
[2] Wheeler, J.A. and Feynman, R.P. (1949) Classical Electrodynamics in Terms of Direct Interparticle Action. Reviews of Modern Physics, 21, 425-433.
[3] Perkovac, M. (2002) Quantization in Classical Electrodynamics. Physics Essays, 15, 41-60.
[4] Perkovac, M. (2003) Absorption and Emission of Radiation by an Atomic Oscillator. Physics Essays, 16, 162-173.
[5] Frankl, D.R. (1986) Electromagnetic Theory. Prentice-Hall, Inc., Englewood Cliffs, New Jersey.
[6] Jackson, J.D. (1999) Classical Electrodynamics. 3rd Edition, John Wiley & Sons Inc., New York.
[7] Bosanac, T. (1973) Teoretska elektrotehnika 1. Tehnicka knjiga, Zagreb.
[8] Haznadar, Z. and Stih, Z. (1997) Elektromagnetizam. Skolska knjiga, Zagreb.
[9] Hänsel, H. and Neumann, W. (1995) Physik. Spektrum Akademischer Verlag, Heidelberg.
[10] Perkovac, M. (2012) Maxwell Equations for Nanotechnology. Proceedings of the 35th International Convention of the IEEE MIPRO, Opatija, 21-25 May 2012, 429-436.
[11] Rüdenberg, R. (1923) Elektrische Schaltvorgänge. Verlag von Julius Springer, Berlin.
[12] Czichos and Association Hütte (1989) Die Grundlagen der Ingenieurwissenschaften. Springer-Verlag, Berlin.
[13] Surutka, J. (1971) Elektromagnetika. Gradjevinska knjiga, Beograd.
[14] Perkovac, M. (2013) Model of an Atom by Analogy with the Transmission Line. Journal of Modern Physics, 4, 899- 903.
[15] Giancolli, D.C. (1988) Physics for Scientists and Engineers. Prentice Hall, Englewood Cliffs.
[16] Page, L. and Adams, N.I. (1940) Electrodynamics. D. Van Nostrand Company, Inc., New York.
[17] Perkovac, M. (2010) Statistical Test of Duane-Hunt’s Law and Its Comparison with an Alternative Law.
[18] Perkovac, M. (2014) Determination of the Structural Constant of the Atom. Journal of Applied Mathematics and Physics, 2, 11-21.
[19] Benguria, R.D., Loss, M. and Siedentop, H. (2007) Stability of Atoms and Molecules in an Ultrarelativistic Thomas-Fermi-Weizsäcker Model, 1-11.
[22] Bellotti, G. (2012) The Hydrogen Atomic Model Based on the Electromagnetic Standing Waves and the Periodic Classification of the Elements. Applied Physics Research, 4, 141-151.
[23] Bellotti, G. (2012) The Ideas Behind the Electromagnetic Atomic Theory. Advances in Natural Science, 5, 7-11.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.