Renaissance of Bohr's Model Via Derived Alternative Equation

Ikechukwu Iloh Udema

doi:doi:10.11648/j.ajmp.20170602.11

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Renaissance of Bohr's Model Via Derived Alternative Equation

Ikechukwu Iloh Udema

Published in American Journal of Modern Physics (Volume 6, Issue 2)

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 (Z_eff) equal to 1.8424 and 3.7291 respectively at the 1^st and 2^nd principal quantum numbers (n) respectively. The results were obtained based on two definitions: a₀αn²/Z_eff (from initial Bohr’s equation) and a₀αn/(ξ_n) ^½ (from the derived equation, where ξ_n 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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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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Ikechukwu Iloh Udema

Ude International Concepts Ltd., Agbor, Nigeria

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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

Copy | Download

@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}
}

Copy | Download

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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