Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems
Author(s)
Stanisław Olszewski*
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 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.
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. Journal of Modern Physics, 5, 2030-2040. doi: 10.4236/jmp.2014.518199.
References
[1] Bohr, N. (1922) The Theory of Spectra and the Atomic Constitution. Cambridge University Press, Cambridge. [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.
[1] Bohr, N. (1922) The Theory of Spectra and the Atomic Constitution. Cambridge University Press, Cambridge. [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.