What question did this study set out to answer?

The study aims to create a simplified arithmetic model to aid in learning periodic table elements efficiently.

April 14, 2026Open Access

Reducing Cognitive Load in Periodic Table Learning: An Arithmetic Heuristic Based on Atomic Triads

Key Points

The study aims to create a simplified arithmetic model to aid in learning periodic table elements efficiently.
Developed a deterministic arithmetic model for homologous elements in the periodic table.
Derived a relationship for consecutive elements based on electron subshell capacities.
Validated the model with 77 consecutive atomic triads from hydrogen to oganesson.
Introduced an interactive calculator tool for classroom use.
Achieved perfect agreement with predictions from the Madelung rule.
Successfully reduced cognitive load by linking period lengths to subshell capacities.
Facilitated learning without the need for full electronic configurations.

Abstract

Version 3 - April 2026 This educational work presents a deterministic arithmetic model for consecutive homologous elements (Z₁ < Z₂ < Z₃) in the periodic table. The relationship Z₂ = (Z₁ + Z₃)/2 − K is derived, where the correction parameter K = (Δ₂ − Δ₁)/2 assumes only four integer values: 0, 3, 5, and 7. These correspond to half the electron capacities of the s, p, d, and f subshells newly introduced between Z₂ and Z₃. The model is validated across all 77 consecutive triads from hydrogen (Z=1) to oganesson (Z=118) and demonstrates perfect agreement with period-length predictions based on the Madelung rule. Intended strictly as a pedagogical scaffold, the work reduces cognitive load by linking observable period lengths to subshell capacities without requiring full electronic configurations. An interactive calculator tool is provided as supplementary material to facilitate classroom exploration.*

Reducing Cognitive Load in Periodic Table Learning: An Arithmetic Heuristic Based on Atomic Triads

Key Points

Abstract

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