Abstract A fundamental unresolved problem persists in atomic physics: why electron-shell occupation follows the numerical sequence , and why the periodic table is structured into exactly seven periods. It remains an open issue whether these empirical numerical rules are inherently correlated with the core constants of the 14-Order Unified Field Theory (14FT), namely , , and . Within the theoretical framework of 14FT, this study clarifies the order-state essence of atomic microstructure: the orbital arrangement of extranuclear electrons is confined by the 14-order potential field derived from fundamental regular tetrakaidecahedron units, such that electron shell layering, energy-level splitting and piecewise periodic regulation all comply strictly with intrinsic 14-order topological rules. Specifically, the principal quantum number corresponds to the hierarchical projection of 14-fold symmetric topology; the maximum electron accommodation of each atomic shell is expressed as items of a 14-order harmonic series; the seven-period structure of the periodic table originates from the numerator of the stable projection constant ; the theoretical upper bound of total element species stems from quadratic geometric saturation of tetrakaidecahedron topology. This work establishes a first-principle geometric interpretation for the periodic law of chemical elements and deepens the atomic-scale demonstration of the cross-scale verification system (V8) proposed previously in 14FT.