Bohr’s Spectrum of Quantum States in the Atomic Hydrogen Deduced from the Uncertainty Principle for Energy and Time

Stanisław Olszewski

Institute of Physical Chemistry, Polish Academy of Sciences, Warsaw, Poland.

DOI: 10.4236/jmp.2014.514127                

Abstract

A modified uncertainty principle coupling the intervals of energy and time can lead to the shortest distance attained in course of the excitation process, as well as the shortest possible time interval for that process. These lower bounds are much similar to the interval limits deduced on both the experimental and theoretical footing in the era when the Heisenberg uncertainty principle has been developed. In effect of the bounds existence, a maximal nuclear charge Ze acceptable for the Bohr atomic ion could be calculated. In the next step the velocity of electron transitions between the Bohr orbits is found to be close to the speed of light. This result provides us with the energy spectrum of transitions similar to that obtained in the Bohr’s model. A momentary force acting on the electrons in course of their transitions is estimated to be by many orders larger than a steady electrostatic force existent between the atomic electron and the nucleus.

Keywords

Uncertainty Principle for Energy and Time, Bohr’s Spectrum of Quantum levels in the Hydrogen Atom

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Bohr, N. (1913) Philosophical Magazine, 26, 1. de Boer, J., Dal, E. and Ulfbeck, O. (1986) The Lesson on Quantum Theory—Niels Bohr Centenary Symposium. North-Holland, Amsterdam.
[2]	Schrodinger, E. (1926) Annalen der Physik, 79, 361-376. http://dx.doi.org/10.1002/andp.19263840404
[3]	Bohr, N. (1961) Proceedings of the Physical Society, 78, 1083. http://dx.doi.org/10.1088/0370-1328/78/6/301
[4]	Tarasov, L.V. (1978) Foundations of Quantum Mechanics. Vyzszaja Szkola Moscow. (in Russian)
[5]	Heisenberg, W. (1927) Zeitschrift fur Physik, 43, 172-198. http://dx.doi.org/10.1007/BF01397280
[6]	Schommers, W. (1989) Space-Time and Quantum Phenomena. In: Schommers, W., Ed., Quantum Theory and Pictures of Reality, Springer, Berlin. http://dx.doi.org/10.1007/978-3-642-95570-9_5
[7]	Allcock, G.R. (1969) Annals of Physics, 53, 253-285. http://dx.doi.org/10.1016/0003-4916(69)90251-6
[8]	Bunge, M. (1970) Canadian Journal of Physics, 48, 1410-1411. http://dx.doi.org/10.1139/p70-172
[9]	Isaacs, A. (1990) Concise Dictionary of Physics. Oxford University Press, Oxford.
[10]	Olszewski, S. (2011) Journal of Modern Physics, 2, 1305-1309. http://dx.doi.org/10.4236/jmp.2011.211161
[11]	Olszewski, S. (2012) Journal of Modern Physics, 3, 217-220. http://dx.doi.org/10.4236/jmp.2012.33030
[12]	Olszewski, S. (2012) Quantum Matter, 1, 127-133. http://dx.doi.org/10.1166/qm.2012.1010
[13]	Landau, L.D. and Lifshitz, E.M. (1969) Mechanics. Electrodynamics. Nauka, Moscow. (in Russian)
[14]	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
[15]	Flint, H.E. (1928) Proceedings of the Royal Society A, London, 117, 630. http://dx.doi.org/10.1098/rspa.1928.0025
[16]	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
[17]	Jammer, M. (1966) The Conceptual Development of Quantum Mechanics. McGraw-Hill, New York.
[18]	Arbab, A.I. and Yassein, F.A. (2012) Journal of Modern Physics, 3, 163-169. http://dx.doi.org/10.4236/jmp.2012.32022
[19]	Olszewski, S. (2013) Quantum Matter, 2, 408-411. http://dx.doi.org/10.1166/qm.2013.1072
[20]	Sommerfeld, A. (1931) Atombau und Spektrallinien. Vol. 1, 5th Edition, Vieweg, Braunschweig.
[21]	Slater, J.C. (1960) Quantum Theory of the Atomic Structure. Vol. 1, McGraw-Hill, New York.