Rydberg Equation Calculator
Wavelength, frequency and photon energy of a hydrogen emission line from the two energy levels involved.
Results
What this tool does
Johannes Rydberg found in 1888 that every spectral line of hydrogen fitted a single formula built from two whole numbers, long before anyone knew why. Bohr explained it in 1913: the numbers are the electron's energy levels, and the light carries away exactly the difference. The red 656 nm line of the Balmer series, from level 3 down to level 2, is the one that makes hydrogen nebulae glow pink in astrophotographs.
Formula
1/lambda = RH (1/n1² - 1/n2²)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
n1 | Lower energy level | — |
n2 | Upper energy level | — |
LN | Wavelength | nm |
WN | Wavenumber | 1/cm |
FR | Frequency | THz |
PE | Photon energy | eV |
Worked example
- Lower energy level2
- Upper energy level3
- Wavelength656.4696 nm
- Wavenumber15,232.998 1/cm
- Frequency456.6738 THz
- Photon energy1.888651 eV
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.
Frequently asked questions
Which series is which?
The lower level names the series. n1 = 1 is Lyman, all in the ultraviolet; n1 = 2 is Balmer, the four lines visible in a hydrogen discharge tube and in the spectra of stars; n1 = 3 is Paschen, in the infrared, followed by Brackett and Pfund. The wavelengths here are for vacuum, so they differ slightly from the air values often tabulated.