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Hydrogen Spectrum (Rydberg) Calculator

Work out hydrogen spectrum (rydberg) instantly with clear inputs, formula shown and shareable results.

About Hydrogen Spectrum (Rydberg) Calculator

The Rydberg formula gives 1/lambda = R(1/n1^2 - 1/n2^2), using the hydrogen value R = 1.09678e7 per metre. The 3 to 2 transition yields 656.5 nm - the red H-alpha line that dominates emission nebulae. Transitions ending at n = 1 land in the ultraviolet Lyman series, at n = 2 in the visible Balmer series.

Formulas

Rydberg formula

1 / lambda = R(H) (1/n1^2 - 1/n2^2), R(H) = 1.09678e7 /m

Photon energy

E = h c / lambda

Worked example

With the default values below, Hydrogen Spectrum (Rydberg) Calculator returns Emitted Wavelength of 656.470. Change any input above and every figure here is recalculated in your browser.

Inputs used

Lower level n1minimum 1
2
Upper level n2minimum 2
3

Results

Emitted Wavelength
656.470 nm
Photon Energy
1.8887 eV
Frequency
4.5667 × 10¹⁴ Hz
Spectral Series
Balmer series (visible)

Step by step

  1. 1Values used
  2. 2Rydberg formula
  3. 3Photon energy
  4. 4Emitted Wavelength= 656.470 nm
  5. 5Photon Energy= 1.8887 eV
  6. 6Frequency= 456,674,000,000,000.0000 Hz
  7. 7Spectral Series= Balmer series (visible)

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Which line is H-alpha?

The 3 to 2 Balmer transition at 656.3 nm. It is the strongest visible hydrogen line and gives nebulae their red colour.

Why is the Lyman series invisible?

Because dropping to n = 1 releases at least 10.2 eV, which corresponds to 121.6 nm - deep ultraviolet, absorbed by the atmosphere.

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