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Understanding the Mystery of the Avogadro Number and Renaming SI Avogadro Constant as ‘Einstein-Perrin-Loschmidt-Avogadro-Newton’ Ratio

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Preprints.org
DOI
10.20944/preprints202602.1787.v1

The SI Avogadro constant (NA = 6.02214076 ×1023 per mol) bridges microscopic particle counts to macroscopic masses but its specific scale currently has no widely accepted fundamental physical origin. In this context, we show three independent derivations for the natural kilogram-natural scale of 6.02×1026 atoms/kg: (1) Computational nuclear binding energy analysis yielding precise atomic mass units from QCD saturation (~8 MeV/nucleon peak), (2) Empirical validation through kilogram-scale Faraday constant (F = 9.6435 × 107 C/kg) and (3) Atomic mass number (A) based Dulong-Petit specific heat capacity formula, (25000/A J/kg·K). Notably, 1/F ≅ 1.037×10-8 kg/C matches Planck mass (Mpl) modulated by electroweak angle (Mpl sinθW), establishing quantum gravity and charged matter unity. By using the Faraday charge, GN = ℏcF2sin2θW emerges from the “QCD-electroweak-gravity cascade” rather than empirical fitting, yielding a theoretically robust universal gravitational constant. These atom-independent origins reposition the Avogadro scale as emergent feature of unification physics. Considering our 4G model of final unification (through which string theory can be made practical), it is possible to show that, ratio of product of short-range gravitational constants and long-range gravitational constants is, [(Gweak*Gnuclear)/(Gelectrromag*GNewton)] ≅ 6.1088×1023. This ratio plays a crucial role in understanding the hierarchy of fundamental forces. Seeing its fundamental role, we appeal to the science community and concerned authorities to rename SI Avogadro constant (per mole) with ‘Einstein-Perrin-Loschmidt-Avogadro-Newton’ Ratio (EPLAN Ratio).

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