Atomic and Ionic Radii of Elements and Bohr Radii from Ionization Potentials are Linked Through the Golden Ratio

Atomic and Ionic Radii of Elements and Bohr Radii from Ionization Potentials are Linked Through the Golden Ratio

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Author(s): Raji Heyrovska

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804 1404 82-92 Volume 2 - Mar 2013


In an earlier article, Bohr radius of hydrogen was shown to be the sum of two Golden sections pertaining to the electron and proton. This led to discovering that all bond lengths between same two atoms are sums of two Golden sections representing the radii of the anion and cation, and that the radii of adjacent atoms and or ions in chemical bonds are additive. Subsequently, atomic radii were shown to vary linearly with their Bohr radii obtained from the first ionization potentials. Reported here is a new finding mentioned in the title, for elements of Groups 1A - 8A. The electron is found to occupy a space of its own in the atoms, in support of works on solvated electrons and electrides.


Bond lengths, Covalent Radii, Ionic radii, Bohr radii, Golden sections, Main group elements, radii of electrons, Nuclear radii, Golden ratio


  1. Heyrovska, R. The Golden ratio, ionic and atomic radii and bond lengths. Molecular Physics, 103, 877 - 882 (2005); and the literature therein
  2. Livio, M. The Golden Ratio: The Story of PHI, the World's Most Astonishing Number, Broadway Books, NY, (2002)
  3. Heyrovska, R. The Golden ratio in the creations of Nature arises in the architecture of atoms and ions. Chapter 12 in Book: Innovations in Chemical Biology, Editor: Bilge Sener,, (2009)
  4. Pauling, L. The Nature of the Chemical Bond, Cornell Univ. Press, NY, (1960) Bragg, W. L., Philos. Mag., 40, 169 (1920)
  5. Heyrovska, R. a) 2004 International Joint meeting of ECS, USA and Japanese, Korean and Australian Societies, Honolulu, Hawaii, October 2004, Vol. 2004 - 2, Extended. Abs.C2-0551. ; b) Golden sections of inter-atomic distances as exact ionic radii of atoms
  6. (See figures, data and the literature therein)
  7. Heyrovska, R., Dependence of the length of the hydrogen bond on the covalent and cationic radii of hydrogen, and additivity of bonding distances. Chem. Phys. Letts., 432, 348 - 351 (2006)
  8. Yu, D., Xue, D., Ratajczak, H. Golden ratio and bond-valence parameters of hydrogen bonds of hydrated borates, Journal of Molecular Structure, 783, 210-214 (2006)
  9. Heyrovska, R., Narayan, S. Atomic structures of molecules based on additivity of atomic and/or ionic radii. AIP Conference Proceedings, 216, 1119 (2009); Editor(s): Beverly Karplus Hartline, Renee K. Horton, Catherine M. Kaicher.
  10. Heyrovska, R., Dependences of molar volumes in solids, partial molal and hydrated ionic volumes of alkali halides on covalent and ionic radii and the Golden ratio. Chem. Phys. Letts., 436, 287 - 293 (2007)
  11. Heyrovska, R., Dependence of ion-water distances on covalent radii, ionic radii in water and distances of oxygen and hydrogen of water from ion/water boundaries, Chem. Phys. Letts., 429, 600 - 605 (2006)
  12. Heyrovska, R. Absolute Potentials of the Hydrogen Electrode and of Aqueous Redox Couples, Electrochemical and Solid-State Letters, 12(10), F29-F30 (2009);
  13. Heyrovska, R., Aqueous Redox Potentials Found to be Inversely Proportional to the Bohr Radius, Electrochem.Soc. Trans., 25, 159-163 (2010)
  14. Heyrovska, R., Radii of redox components from absolute redox potentials compared with covalent and aqueous ionic radii, Electroanalysis, 22, 903 - 907 (2010)
  15. Heyrovska, R. a) Direct dependence of covalent, van der Waals and valence shell radii of atoms on their Bohr radii for elements of Groups 1A - 8A. Ohtaki Memorial Lecture, 10th Eurasia Conference on Chemical Sciences, Manila, Philippines, 2008. Philippine J. Sci. 137, 133-139, (2008); b)
  16. a.; b.
  18. Abel, B., Buck, U., Sobolewskic, A. L. and Domcke, W. On the nature and signatures of the solvated electron in water, Phys. Chem. Chem. Phys., 14, 22–34 (2012)
  19. Lee, K., Kim, S. W., Toda, Y., Matsuishi, S., Hosono, H., Dicalcium nitride as a two-dimensional electride with an anionic electron layer, Nature, 494. 336-341 (2013)
  20. Shechtman, D., Quasi-Periodic Materials – A Paradigm Shift in Crystallography.
  21. Coldea, R., et al, Quantum criticality in an Ising chain: experimental evidence for emergent E8 symmetry, Science, 327, 177-180 (2010)
  22. Heyrovska, R., Structures at the atomic level of cobalt, zinc and lead niobates (with an Appendix: Atomic structure of cobalt niobate crystal)

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This article is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) License.
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