The Holland Atom II: Atomic Radius Variation and Shell-Band Geometry

Atomic radius is one of the most widely used quantities in chemistry and atomic physics, yet no universally accepted atomic boundary exists. Multiple accepted radius definitions coexist, including empirical, calculated, covalent, metallic, ionic, and van der Waals radii, often assigning substantially different values to the same element.

This paper performs a comprehensive audit of atomic radius variation across the periodic table and investigates whether the long-recognised differences between accepted radius systems contain physical information rather than representing measurement disagreement alone.

Using published radius datasets spanning empirical, theoretical, bonding, crystalline, and interaction-derived radius families, the study demonstrates that atomic radius variation is highly structured. Radius systems occupy reproducible relative positions, exhibit systematic scaling relationships, and display statistically significant organisation across groups, periods, and blocks of the periodic table. The analysis reveals that radius variation behaves as a genuine physical observable rather than random measurement uncertainty.

As a practical outcome, Empirical Atomic Radius is selected as the standard geometric reference radius for future Holland Atom investigations. More significantly, the results support the hypothesis that accepted atomic radius definitions may be sampling different regions within a finite shell envelope rather than representing competing descriptions of atomic size.

Within the Holland Atom framework, developed from General Expanse Tension Theory (GETT), atomic charge shells are interpreted as resonance-locked standing modes possessing finite radial extent. The observed variation between accepted radius systems is therefore proposed to represent measurable shell-band structure and standing-mode amplitude. No empirical result obtained in this study was found to contradict this interpretation, while multiple non-trivial findings—including strong periodic-table organisation, statistically distinct block populations, and shell-band behaviour independent of atomic size within the full observable envelope—provide support for the shell-band hypothesis.

This work forms the second paper in the Holland Atom research programme. It follows The Holland Atom I: Atomic Reconstruction and establishes the geometric reference framework required for The Holland Atom III: Charge Density and Atomic Scaling. In doing so, it provides both a practical standard for future Holland Atom development and a new perspective on one of the oldest unresolved questions in atomic structure: why multiple accepted atomic radius definitions exist.