Rydberg Hydrogen Wavelength Calculator
When an electron in a hydrogen atom jumps between energy levels it emits or absorbs light of a precise wavelength, producing the sharp spectral lines that built quantum theory. The Rydberg formula predicts every one of those wavelengths from just two integers, the lower and upper energy levels. This calculator takes those two levels and returns the emitted wavelength in nanometres and metres along with its frequency. It covers the Lyman, Balmer, Paschen and higher series and is a staple of atomic physics and astronomy coursework.
Rydberg formula
1 / lambda = R_H * (1/n1^2 - 1/n2^2)
R_H = 1.0967758e7 per metre (hydrogen)
n1 = lower level, n2 = upper level (n2 > n1)
frequency = c / lambda, c = 299,792,458 m/s
Take the reciprocal of the right-hand side to get the wavelength in metres, then multiply by ten to the ninth for nanometres. The frequency follows from the speed of light divided by wavelength.
Hydrogen spectrum context
- The Rydberg constant for hydrogen is about 1.0967758 times ten to the seventh per metre.
- Series n1 = 1 (Lyman) lies in the ultraviolet; n1 = 2 (Balmer) is visible.
- The Balmer alpha line, n2 = 3 to n1 = 2, sits at about 656 nanometres in the red.
- Series n1 = 3 (Paschen) and higher fall in the infrared.
- The same formula, scaled by the square of nuclear charge, applies to other one-electron ions.
Rydberg wavelength: frequently asked questions
What is the Rydberg formula?
The Rydberg formula gives the wavelength of light emitted or absorbed when an electron in a hydrogen atom moves between energy levels: 1/lambda = R_H * (1/n1^2 - 1/n2^2), where n1 is the lower level, n2 is the upper level and R_H is the Rydberg constant for hydrogen.
What is the Rydberg constant?
The Rydberg constant for hydrogen, R_H, is approximately 1.0967758 times ten to the seventh per metre. It is one of the most precisely measured constants in physics. Multiplying it by the difference of the inverse squares of the two levels gives the inverse wavelength of the spectral line.
What are the hydrogen spectral series?
Each lower level n1 names a series: n1 = 1 is the Lyman series in the ultraviolet, n1 = 2 is the Balmer series in the visible, n1 = 3 is the Paschen series in the infrared, and higher levels give Brackett and Pfund series further into the infrared.
Why must the upper level exceed the lower level?
For emission the electron falls from a higher level n2 to a lower level n1, so n2 must be greater than n1 for a positive, physical wavelength. If you enter n2 equal to or below n1 the calculator returns n/a because that transition does not produce an emission line.
What is the wavelength of the Balmer alpha line?
The Balmer alpha line, from n2 = 3 down to n1 = 2, has a wavelength of about 656 nanometres, the deep red light that gives glowing hydrogen and many nebulae their characteristic colour. It is one of the most studied lines in all of astronomy.
Official sources
- U.S. National Institute of Standards and Technology: Rydberg constant.
- NIST Atomic Spectra Database: Atomic spectra reference.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.