Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems

ABSTRACT

The mechanical angular momentum and magnetic moment of the electron and proton spin have been calculated semiclassically with the aid of the uncertainty principle for energy and time. The spin effects of both kinds of the elementary particles can be expressed in terms of similar formulae. The quantization of the spin motion has been done on the basis of the old quantum theory. It gives a quantum number*n* = 1/2 as the index of the
spin state acceptable for both the electron and proton particle. In effect of
the spin existence the electron motion in the hydrogen atom can be represented
as a drift motion accomplished in a combined electric and magnetic field. More
than 18,000 spin oscillations accompany one drift circulation performed along
the lowest orbit of the Bohr atom. The semiclassical theory developed in the
paper has been applied to calculate the doublet separation of the
experimentally well-examined *D* line
entering the spectrum of the sodium atom. This separation is found to be much
similar to that obtained according to the relativistic old quantum theory.

The mechanical angular momentum and magnetic moment of the electron and proton spin have been calculated semiclassically with the aid of the uncertainty principle for energy and time. The spin effects of both kinds of the elementary particles can be expressed in terms of similar formulae. The quantization of the spin motion has been done on the basis of the old quantum theory. It gives a quantum number

KEYWORDS

Spin Effect and Its Semiclassical Quantization, Electron and Proton Elementary Particles, Electron Drift in the Hydrogen Atom, Separation of the Doublet Spectral Lines

Spin Effect and Its Semiclassical Quantization, Electron and Proton Elementary Particles, Electron Drift in the Hydrogen Atom, Separation of the Doublet Spectral Lines

Cite this paper

Olszewski, S. (2014) Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems.*Journal of Modern Physics*, **5**, 2030-2040. doi: 10.4236/jmp.2014.518199.

Olszewski, S. (2014) Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems.

References

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[2] Landau, L.D. and Lifshitz, E.M. (1972) Quantum Mechanics (in Russian). Izd. Nauka, Moscow.

[3] Olszewski, S. (2011) Journal of Modern Physics, 2, 1305.

http://dx.doi.org/10.4236/jmp.2011.211161

[4] Olszewski, S. (2012) Journal of Modern Physics, 3, 217.

http://dx.doi.org/10.4236/jmp.2012.33030

[5] Olszewski, S. (2012) Quantum Matter, 1, 127.

http://dx.doi.org/10.1166/qm.2012.1010

[6] Olszewski, S. (2014) Journal of Modern Physics, 5, 1264.

http://dx.doi.org/10.4236/jmp.2014.514127

[7] Tolansky, S. (1948) Hyperfine Structure in Line Spectra and Nuclear Spin. 2nd Edition, Methuen, London.

[8] Ruark, A.E. (1928) Proceedings of the National Academy of Sciences of the United States of America, 14, 322.

http://dx.doi.org/10.1073/pnas.14.4.322

[9] Flint, H.E. (1928) Proceedings of the Royal Society A, London, 117, 630. http://dx.doi.org/10.1098/rspa.1928.0025

[10] Flint, H.E. and Richardson, O.W. (1928) Proceedings of the Royal Society A, London, 117, 637.

http://dx.doi.org/10.1098/rspa.1928.0026

[11] Jammer, M. (1966) The Conceptual Development of Quantum Mechanics. McGraw-Hill, New York.

[12] Slater, J.C. (1967) Quantum Theory of Molecules and Solids. Vol. 3, McGraw-Hill, New York.

[13] Landau, L.D. and Lifshitz, E.M. (1969) Mechanics. Electrodynamics (in Russian). Izd. Nauka, Moscow.

[14] Kittel, C. (1987) Quantum Theory of Solids. 2nd Edition, Wiley, New York.

[15] Onsager, L. (1952) The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 43, 1006-1008.

http://dx.doi.org/10.1080/14786440908521019

[16] Beck, E. (1919) Annalen der Physik, 305, 109-148.

http://dx.doi.org/10.1002/andp.19193651802

[17] Uhlenbeck, G.E. and Goudsmit, S.A. (1925) Die Naturwissenschaften, 13, 953-954.

http://dx.doi.org/10.1007/BF01558878

[18] Matveev, A.N. (1964) Electrodynamics and the Theory of Relativity (in Russian). Izd. Wyzszaja Szkola, Moscow.

[19] Schiff, L.I. (1968) Quantum Mechanics. 3rd Edition, McGraw-Hill, New York.

[20] White, H.E. (1934) Introduction to Atomic Spectra. McGraw-Hill, New York.

[21] Millikan, R.A. and Bowen, I. (1924) Physical Review, 23, 1.

[22] Rubinowicz, A. (1933) Handbuch der Physik. In: Geiger, H. and Scheel, K., Eds., Vol. 24, Part 1, Springer, Berlin.

[23] Rose, M.E. (1961) Relativistic Electron Theory. Wiley, New York.

[24] Avery, J. (1976) Creation and Annihilation Operators. McGraw-Hill, New York.

[25] Kobos, A.M. (2013) Postepy Fizyki, 64, 86.