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

Yıl 2019, Cilt: 9 Sayı: 2, 417 - 430, 30.12.2019

Serkan Alagöz

https://doi.org/10.37094/adyujsci.593724

Öz

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.

Anahtar Kelimeler

Hydrogen-like Bohr atom, Heisenberg uncertainty principle, position uncertainty, kinetic energy uncertainty

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

Öz

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.

Anahtar Kelimeler

Hidrojen benzeri Bohr atomu, Heisenberg belirsizlik ilkesi, Konum belirsizliği, Kinetik enerji belirsizliği

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