What question did this study set out to answer?

The aim is to derive Planck's constant using the geometric properties of the hydrogen atom.

January 18, 2026Open Access

Deriving Planck's Constant from Hydrogen Atom Geometry

Key Points

The aim is to derive Planck's constant using the geometric properties of the hydrogen atom.
Derivation based on a single postulate related to natural energy quantum in hydrogen's ground state.
Utilization of telescoping series to analyze atomic transitions.
Geometric interpretation of the fine structure constant to refine results.
Achieved 0.018% agreement with CODATA values for Planck's constant.
Demonstrated that Planck's constant is a geometric consequence of atomic structure rather than an independent constant.

Abstract

I derive Planck’s constant from the geometry of the hydrogen atom, achieving 0.018%agreement with CODATA. The derivation rests on a single postulate—that the hydrogenground state is one radian of a natural energy quantum—motivated by the telescoping seriesover atomic transitions. A geometric interpretation of the fine structure constant refines theresult but does not affect the principle. The result demonstrates that h is not an independentfundamental constant but a geometric consequence of atomic structure.

Deriving Planck's Constant from Hydrogen Atom Geometry

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Abstract

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