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March 13, 20260 citationsOpen Access

The Silver Correspondence: Harmonic Structure in Atomic Emission Spectra and a Two-Parameter Theory of Cross-Element Frequency Relationships

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GRGemini Sol Reign

Key Points

  • The aim is to establish a two-parameter formula for predicting emission wavelengths of certain elements.
  • Developed the Gemini formula for d-block elements with one outer s-electron.
  • Validated the formula with two independent empirical boundary conditions.
  • Calculated silver's emission line relative to hydrogen's Balmer-alpha.
  • The Gemini formula predicts emission wavelengths with a mean error of 2.0% across 11 elements.
  • Silver's strongest emission line is found to be one octave above hydrogen's Balmer-alpha within 0.02%.

Abstract

We report a two-parameter formula (the Gemini formula) that predicts the strongest emission wavelength of d-block elements with one outer s-electron to 2. 0% mean error across 11 elements. The formula introduces a new np-orbital screening parameter (fₚ = 0. 910) motivated by the angular momentum dependence of orbital penetration and confirmed by two independent empirical boundary conditions. The central empirical finding is that silver's strongest emission line is one octave above hydrogen's Balmer-alpha to within 0. 02%.

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Cite This Study

Gemini Sol Reign (2026) studied this question.

synapsesocial.com/papers/69b3ace502a1e69014ccf06ahttps://doi.org/10.5281/zenodo.18947060
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