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Journals / Adıyaman Üniversitesi Fen Bilimleri Dergisi / 2019 / Cilt: 9 - Sayı: 2

Lateral Position Uncertainty of Electrons in Bohr Hydrogen-like Atoms: An Implication of Heisenberg Uncertainty Principle

Bohr Hidrojen Benzeri Atomlarda Elektronların Yanal Konum Belirsizliği: Heisenberg Belirsizlik İlkesinin Uygulanması

Serkan ALAGÖZ
Pages
417–430
Publication Date
2022-10-12
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Afterward, these analyses are extended for relativistic hydrogen-like Bohr atom case.

📌 3 Key Takeaways

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Objective & Hypothesis:This paper presents a theoretical investigation on effects of lateral position uncertainty of captivity electrons within spherical electron shells of Bohr hydrogen-like atoms.
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Key Findings & Data:After deriving uncertainty relation for position and kinetic energy, author theoretically demonstrates that, due to the lateral position uncertainties of electrons in spherical shells, Heisenberg uncertainty principle suggests uncertainty bounds in measurement of kinetic energy states of captivity electrons that orbits non-relativistic hydrogen-like Bohr atom.
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Conclusion & Impact:Afterward, these analyses are extended for relativistic hydrogen-like Bohr atom case.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

This paper presents a theoretical investigation on effects of lateral position uncertainty of captivity electrons within spherical electron shells of Bohr hydrogen-like atoms. A captivity electron, which is spatially confined in Bohr orbits, introduces a lateral position uncertainty that can be determined by considering the area of the electron shell. After deriving uncertainty relation for position and kinetic energy, author theoretically demonstrates that, due to the lateral position uncertainties of electrons in spherical shells, Heisenberg uncertainty principle suggests uncertainty bounds in measurement of kinetic energy states of captivity electrons that orbits non-relativistic hydrogen-like Bohr atom. Afterward, these analyses are extended for relativistic hydrogen-like Bohr atom case.

Özet

Bu makale, Bohr hidrojen benzeri atomların küresel elektron yörüngelerinde bulunan elektronlarının yanal konum belirsizliğinin etkileri üzerine teorik bir araştırma sunmaktadır. Bohr yörüngelerinde uzamsal olarak hapsolmuş bir elektron, elektron kabuğunun alanı göz önüne alınarak belirlenebilecek bir yanal konum belirsizliği sağlar. Konum ve kinetik enerji için belirsizlik ilişkisini türettikten sonra, yazar teorik olarak, küresel kabuklar içindeki elektronların yanal konum belirsizliklerini teorik olarak göstermektedir. Heisenberg belirsizlik ilkesi, göreceli olmayan hidrojen benzeri Bohr atomunun yörüngesinde bulunan esaret elektronlarının kinetik enerji durumlarının ölçümündeki belirsizlik sınırlarını ortaya koymaktadır. Daha sonra, bu analizler göreceli hidrojen benzeri Bohr atomu durumu için genişletilmiştir.

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Cite This Article

ALAGÖZ, S. (2022). Lateral Position Uncertainty of Electrons in Bohr Hydrogen-like Atoms: An Implication of Heisenberg Uncertainty Principle. Adıyaman Üniversitesi Fen Bilimleri Dergisi, Cilt: 9 - Sayı: 2, 417–430. https://ajindex.com/articles/428470

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References (19)

  1. Smith, B., Lecture Notes: Quantum Ideas, Department of Physics University of Oxford, 2012
  2. Shankar, R., Principle of Quantum Mechanics, Plenum Press, New York, 1994
  3. Adler, R.J., Chen, P., Santiago, D.I., The generalized uncertainty principle and black hole remnants, General Relativity and Gravitation, 33(12), 2101-2108, 2001
  4. Beiser, A., Mahajan, S., Choudhary, S.R., Concepts of Modern Physics, McGraw-Hill, New Delhi, 2009
  5. Adler, R. J., Santiago. D.I., On gravity and the uncertainty principle, Modern Physics Letters A, 14(20), 1371-1381, 1999
  6. Harbola, V., Using uncertainty principle to find the ground-state energy of the helium and a helium-like Hookean atom, European Journal of Physics, 32(6), 1607-1615, 2011
  7. Akhoury, R., Yao, Y.P., Minimal length uncertainty relation and the hydrogen spectrum, Physics Letters B, 572, 37-42, 2003
  8. Gill, P.M.W., Johnson, B.G., Pople, J.A., A standard grid for density functional calculations, Chemical Physics Letters, 209, 506-512, 1999
  9. Wilhelm, H.E., Formulation of the uncertainty principle according to the hydrodynamic model of quantum mechanics, Progress of Theoretical Physics, 43(4), 861-869, 1970
  10. Olszewski, S., Bohr’s spectrum of quantum states in the atomic hydrogen deduced from the uncertainty principle for energy and time, Journal of Modern Physics, 5(14), 1264-1271, 2014
  11. Deeney, F.A., O’Leary, J.P., The effects of the Pauli exclusion principle in determining the ionization energies of the helium atom and helium-like ions, European Journal of Physics, 33(3), 667-675, 2012
  12. Kuo, C.D., The uncertainties in radial position and radial momentum of an electron in the non-relativistic hydrogen-like atom, Annals of Physics, 316(2), 431-439, 2005
  13. Bohr, N., On the Constitution of Atoms and Molecules-Part I: The binding of electrons by positive nuclei, Philosophical and Journal of Magazine Science, 26(6), 1-25, 1913
  14. Bohr, N., On the constitution of atoms and molecules - Part II: systems containing only a single nucleus, Philosophical and Journal Of Magazine Science, 26(6), 476-502, 1913
  15. Serway, R.A., Moses, C.J., Moyer, C.A., Modern Physics, Thomson, New York, 1997
  16. Weaver, J.H., The World of Physics, Simon and Schuster, New York, 1987
  17. Wheeler, J.A., Zurek, H., Quantum Theory and Measurement, Princeton Univ. Press, New Jersey, 1983
  18. Schiff, L.I., Quantum Mechanics, McGraw Hill, New York, 1968
  19. Heisenberg, W., Über den anschaulichen