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Balmer: an empirical integer formula for the hydrogen spectral series

Contribution grade

Atomic spectroscopy and empirical laws · Reusable scientific method, experimental result or historical framework

Reference score300,000Provisional editorial estimate of this exact contribution; its grade is assessed separately.

What changed

Four measured lines in the hydrogen spectrum fit a surprisingly compact number pattern. Balmer expressed their wavelengths using a common scale b times m^2/(m^2-4), with integer m=3,4,5,6. He then compared the extension of that pattern with additional violet and ultraviolet observations. This was a useful empirical rule before an atomic theory explained why those numbers appeared.

Scientific scope

Four measured lines in the hydrogen spectrum fit a surprisingly compact number pattern. Balmer expressed their wavelengths using a common scale b times m^2/(m^2-4), with integer m=3,4,5,6. He then compared the extension of that pattern with additional violet and ultraviolet observations. This was a useful empirical rule before an atomic theory explained why those numbers appeared. The contribution is the hydrogen-series pattern and its historical comparisons, not new wavelength measurements or a quantum-mechanical derivation. The original scale 3645.6 in 10^-7 mm is a wavelength parameter, not Planck constant; these historical values are not modern vacuum or isotope-corrected wavelengths. A speculative extension to other integer families is not the later general Rydberg law. Angstrom supplied the principal measurements; Hagenbach encouragement and communication and Vogel/Huggins observations keep separate roles.

Evidence

The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. The contribution is the hydrogen-series pattern and its historical comparisons, not new wavelength measurements or a quantum-mechanical derivation. The original scale 3645.6 in 10^-7 mm is a wavelength parameter, not Planck constant; these historical values are not modern vacuum or isotope-corrected wavelengths. A speculative extension to other integer families is not the later general Rydberg law. Angstrom supplied the principal measurements; Hagenbach encouragement and communication and Vogel/Huggins observations keep separate roles.

Contributors

Provisional WRS assessment, edition 2026-10-23.5. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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