The Rydberg Equation's Structure
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The Rydberg equation relates hydrogen's line-spectrum wavelengths to two whole numbers marking the electron's starting and ending energy levels.
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Plugging different whole-number pairs into the Rydberg equation's structure reproduces each of hydrogen's observed spectral lines in turn.
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The Rydberg equation was found empirically, by fitting hydrogen's measured lines, years before any model explained why it worked.