Rydberg Formula Calculator: Wavelength, Frequency and Energy of Hydrogen Spectral Lines
The colours of hydrogen from the Rydberg formula.
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How this calculator works
Enter the atomic number and the two levels.
The calculator uses the Rydberg formula.
It gives the wavelength, frequency, energy and series.
Formulas used
- \frac{1}{\lambda} = RZ^2\left(\frac{1}{n_l^2} - \frac{1}{n_u^2}\right)
- E = \frac{hc}{\lambda}
- R_H = 1.0968\times10^7\ \mathrm{m^{-1}}
Worked example
With the default numbers in the calculator above:
- Wavelength in a vacuum: 656.4696 nm
- Frequency: 456.674 THz
- Photon energy: 1.88865 eV
- Spectral series: Balmer series, visible region
Change the numbers in the calculator to see the full working, every step, for your own case.
A second worked example
A different case, with these numbers: Lower level n (the electron lands here) 1; Higher level n (the electron starts here) 2.
- Wavelength in a vacuum: 121.5684 nm
- Frequency: 2466.04 THz
- Photon energy: 10.1987 eV
- Spectral series: Lyman series, ultraviolet region
Common questions
What are the Balmer lines?
The visible lines of hydrogen, from electrons falling to level 2. The red line, H-alpha, is at 656 nm.
Why are there different series?
Each series is a group of lines that end on the same lower level: Lyman on 1 (ultraviolet), Balmer on 2 (visible), Paschen on 3 (IR).
Does the formula work for other atoms?
Only for atoms with one electron, such as He+ and Li2+, using the nuclear charge Z.
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Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: Any physics or chemistry text (the Rydberg formula and atomic spectra).
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