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Renaissance of Bohr's Model Via Derived Alternative Equation

Received: 2 March 2017     Accepted: 11 March 2017     Published: 28 March 2017
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Abstract

The aims of this research were: 1) To derive alternative equation into which can be substituted known experimental data and known physical constants for the calculation of Bohr’s radii of atoms for some elements, 2) respond to some of the objections raised against (or the short coming of Bohr’s theory,) and 3) make a case for the justification of Bohr’s theory. Apart from other elements, Bohr’s radius(a0) for hydrogen was 0.5291 Å; the radii for Na([Ne]3s1) and Na+ ([Ne]3s0) were 2.5844 Å and 0.5675Å respectively which correspond to effective nuclear charges (Zeff) equal to 1.8424 and 3.7291 respectively at the 1st and 2nd principal quantum numbers (n) respectively. The results were obtained based on two definitions: a0αn2/Zeff (from initial Bohr’s equation) and a0αn/(ξn) ½ (from the derived equation, where ξn is the average ionization energy). In conclusion, an alternative equation to Bohr’s equation was successfully derived. No single model should always be a solution to all scientific questions. Both original Bohr’s equation and derived equation can give, after calculation, similar value of any atomic radius. Therefore, Bohr’s theory stands scientifically justified.

Published in American Journal of Modern Physics (Volume 6, Issue 2)
DOI 10.11648/j.ajmp.20170602.11
Page(s) 23-31
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Bohr’s Equation, Heisenberg Principle, Schrödinger-Dirac Formalism, Derived Equation, Effective Nuclear Charge, Radius

References
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  • APA Style

    Ikechukwu Iloh Udema. (2017). Renaissance of Bohr's Model Via Derived Alternative Equation. American Journal of Modern Physics, 6(2), 23-31. https://doi.org/10.11648/j.ajmp.20170602.11

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    ACS Style

    Ikechukwu Iloh Udema. Renaissance of Bohr's Model Via Derived Alternative Equation. Am. J. Mod. Phys. 2017, 6(2), 23-31. doi: 10.11648/j.ajmp.20170602.11

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    AMA Style

    Ikechukwu Iloh Udema. Renaissance of Bohr's Model Via Derived Alternative Equation. Am J Mod Phys. 2017;6(2):23-31. doi: 10.11648/j.ajmp.20170602.11

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  • @article{10.11648/j.ajmp.20170602.11,
      author = {Ikechukwu Iloh Udema},
      title = {Renaissance of Bohr's Model Via Derived Alternative Equation},
      journal = {American Journal of Modern Physics},
      volume = {6},
      number = {2},
      pages = {23-31},
      doi = {10.11648/j.ajmp.20170602.11},
      url = {https://doi.org/10.11648/j.ajmp.20170602.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20170602.11},
      abstract = {The aims of this research were: 1) To derive alternative equation into which can be substituted known experimental data and known physical constants for the calculation of Bohr’s radii of atoms for some elements, 2) respond to some of the objections raised against (or the short coming of Bohr’s theory,) and 3) make a case for the justification of Bohr’s theory. Apart from other elements, Bohr’s radius(a0) for hydrogen was 0.5291 Å; the radii for Na([Ne]3s1) and Na+ ([Ne]3s0) were 2.5844 Å and 0.5675Å respectively which correspond to effective nuclear charges (Zeff) equal to 1.8424 and 3.7291 respectively at the 1st and 2nd principal quantum numbers (n) respectively. The results were obtained based on two definitions: a0αn2/Zeff (from initial Bohr’s equation) and a0αn/(ξn) ½ (from the derived equation, where ξn is the average ionization energy). In conclusion, an alternative equation to Bohr’s equation was successfully derived. No single model should always be a solution to all scientific questions. Both original Bohr’s equation and derived equation can give, after calculation, similar value of any atomic radius. Therefore, Bohr’s theory stands scientifically justified.},
     year = {2017}
    }
    

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  • TY  - JOUR
    T1  - Renaissance of Bohr's Model Via Derived Alternative Equation
    AU  - Ikechukwu Iloh Udema
    Y1  - 2017/03/28
    PY  - 2017
    N1  - https://doi.org/10.11648/j.ajmp.20170602.11
    DO  - 10.11648/j.ajmp.20170602.11
    T2  - American Journal of Modern Physics
    JF  - American Journal of Modern Physics
    JO  - American Journal of Modern Physics
    SP  - 23
    EP  - 31
    PB  - Science Publishing Group
    SN  - 2326-8891
    UR  - https://doi.org/10.11648/j.ajmp.20170602.11
    AB  - The aims of this research were: 1) To derive alternative equation into which can be substituted known experimental data and known physical constants for the calculation of Bohr’s radii of atoms for some elements, 2) respond to some of the objections raised against (or the short coming of Bohr’s theory,) and 3) make a case for the justification of Bohr’s theory. Apart from other elements, Bohr’s radius(a0) for hydrogen was 0.5291 Å; the radii for Na([Ne]3s1) and Na+ ([Ne]3s0) were 2.5844 Å and 0.5675Å respectively which correspond to effective nuclear charges (Zeff) equal to 1.8424 and 3.7291 respectively at the 1st and 2nd principal quantum numbers (n) respectively. The results were obtained based on two definitions: a0αn2/Zeff (from initial Bohr’s equation) and a0αn/(ξn) ½ (from the derived equation, where ξn is the average ionization energy). In conclusion, an alternative equation to Bohr’s equation was successfully derived. No single model should always be a solution to all scientific questions. Both original Bohr’s equation and derived equation can give, after calculation, similar value of any atomic radius. Therefore, Bohr’s theory stands scientifically justified.
    VL  - 6
    IS  - 2
    ER  - 

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