A Unified Scaling Law for Atomic Radii Based on the 4G Model of Final Unification

Our 4G model of final unification proposes four distinct gravitational constants associated with the fundamental interactions—nuclear, electromagnetic, weak, and classical gravity—offering a comprehensive framework that unifies these forces. By calculating the geometric mean of the nuclear and electromagnetic gravitational constants, a fundamental length scale analogous to a black hole radius for the unified atomic mass unit emerges, closely matching the basic empirical covalent bond length of 33 pm. Extending Rutherford’s nuclear radius law, we propose a generalized atomic radius scaling law as, Atomic radius=[(mass number)1/3 * 33 pm]*f(electronic configuration, quantum corrections, etc). We emphasize the point that, atomic structure is shaped by the combined effect of strong and electromagnetic interactions, not merely electromagnetic interactions. This framework bridges nuclear physics, quantum chemistry, and gravitational theory, providing novel insights into atomic size variations and chemical bonding phenomena grounded in fundamental constants. With reference to our recent publications, in this paper, we are making an attempt to interconnect various atomic radii based on the first principles and advanced 4G concepts. We have presented this in the conference "Integrated Computational and Experimental Methods for Innovation in Chemistry and Interdisciplinary Sciences", ICEMI-CHEMIS 2025, P P Savani University, Surat, Gujarat, India.