Skip to content
Research Article Open access CC BY 4.0

Calculation of the Radius for Any Atom Based on the Planck Constant-free Equation, Mathematical Complexity, and Atomism

Ikechukwu Iloh Udema

Asian Journal of Advanced Research and Reports · pp. 149–159 · Published 27 Dec 2022

10.9734/ajarr/2022/v16i12458

Abstract

Concern has been expressed against the new theories, Heisenberg uncertainty principle (HUP) and Schrödinger wave/quantum mechanics (SE) that are purported to have replaced Bohr’s theory and equation. The research was undertaken with the following objectives: 1) to review concerns about atomism; 2) appraise the issues of mathematical complexities in HUP and SE; 3) review criticism against SE and HUP; 4) most importantly derive a Planck constant invariant equation for the calculation of any atomic radii; and 5) re-calculate the radii of selected elements chosen for their biological importance. The theoretical research with calculations, showed that the opposing theories are criticised because, they are obsessed with mathematical complexities with ambiguities without common ground that should usher alternative solution to the problem of the size of atom and thus, they cannot be considered as a valid description of reality. Bohr’s equation and variants of it and the Planck constant invariant equation (Eq. (15)) derived in this research are regarded as deterministic in nature and were capable of reproducing Bohr’s radii for any atom; the radii were also capable of reproducing the average ionisation energies of hydrogen and oxygen atoms, chosen for illustration only, when substituted into derived preliminary equation (Eq. (10)).

Atomism Bohr’s radii of any element criticism of Heisenberg and Schrödinger mathematical complexities deterministic Planck constant free equation ionisation energy

References (16)

  1. 1 CODATA recommended values of the fundamental physical constants: 2010 [DOI]
  2. 2 CODATA recommended values of the fundamental physical constants: 2018 [DOI]
  3. 3 Heisenberg's uncertainty principle [DOI]
  4. 4 Theoretical Calculation of Absolute Radii of Atoms and Ions. Part 1. The Atomic Radii [DOI]
  5. 5 Mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysis [DOI]
  6. 6 Experimental violation and reformulation of the Heisenberg's error-disturbance uncertainty relation [DOI]
  7. 7 Measurement breaking the standard quantum limit for free-mass position [DOI]
  8. 8 Quantization as an Eigenvalue Problem [DOI]
  9. 9 The nature of free electrons in superfluid helium—a test of quantum mechanics and a basis to review its foundations and make a comparison to classical theory [DOI]
  10. 10 ESTIMATION OF THE ATOMIC RADII OF PERIODIC ELEMENTS USING SUPPORT VECTOR MACHINE [DOI]
  11. 11 Fine Structure Constant is Related to Effective Nuclear Charge and Bohr’s Radius for Any Atom [DOI]
  12. 12 Chemistry: Facts, Patterns and Principles
  13. 13 Revisiting Bohr’s Theory via a Relationship between Magnetic Constant and Bohr Radius of Any Element [DOI]
  14. 14 A Mathematical Relationship between Hydrogenic Periodic Property and Nuclear Properties in Furtherance of Bohr’s Theory [DOI]
  15. 15 A Procedure to Obtain the Effective Nuclear Charge from the Atomic Spectrum of Sodium [DOI]
  16. 16 COMPARISON BETWEEN TWO DIFFERENT APPROACHES TOWARD ATOMIC RADII

Cited by 3

Desirability of Reduced Mass Concept, Conflicting CODATA Values of Some Constants: Variants of Fine Structure Constant and Rydberg Constant Equations

Ikechukwu Iloh Udema · Asian Journal of Research and Reviews in Physics · 2025

The question of Heisenberg uncertainty principle: Inevitable alternative interpretations and applications

Ikechukwu Iloh Udema · World Journal of Advanced Research and Reviews · 2025

Showing 2 of 3 known citations — external sources report more than can currently be individually listed.

Article metrics

Real usage data collected on this platform.

44

Page views

0

PDF downloads

13

Outbound clicks

3

Citations

Views over time

Views by country

Approximate, from request IP at view time — not citizenship or institution. Countries with fewer than 5 views are grouped as "Other".

Traffic sources

Referring site, by host.

Views and downloads exclude known bots/crawlers. Citations combines this platform's own DOI-resolved index with each external source's own reported total — see Cited by above for individually listed citing works. Last refreshed 0 seconds ago.