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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(İNÖNÜ ÜNİVERSİTESİ)0000-0003-2642-8462
Pages
417–430
Publication Date
2019-12-30
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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

🎯
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:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Hidrojen benzeri Bohr atomu · Heisenberg belirsizlik ilkesi · Konum belirsizliği

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. (2019). 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://doi.org/10.37094/adyujsci.593724

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