Rydberg Equation Calculator

By Dominik Czernia, PhD candidate
Last updated: Jul 07, 2018

Our Rydberg equation calculator is a tool which helps you compute and understand the hydrogen emission spectrum. You can use our calculator for other chemical elements too, provided they have only one electron (so-called hydrogen-like atom, e.g., He⁺, Li²⁺ or Be³⁺). Read on to learn more about different spectral lines series found in hydrogen and about a technique which makes use of the emission spectrum. In the below text you will also find out what Rydberg formula is. Check our hydrogen energy levels calculator if you want to compute the exact energy levels of a hydrogen-like atom.

Hydrogen emission spectrum

We know from the Bohr model that electron orbits around nucleus only at specific distances, called energy levels n (n > 0 and is an integer). When an electron drops to a lower orbit (n decreases), it emits an electromagnetic wave (photon) of a certain wavelength which corresponds to the change of electron's energy. There are many possible electron transitions in an atom, and the collection of those transitions make up an emission spectrum, which is unique for each element. In hydrogen, we obtain different series:

  • Lyman series, when an electron goes from n ≥ 2 to n = 1 energy level,
  • Balmer series, when an electron goes from n ≥ 3 to n = 2 energy level,
  • Paschen series, when an electron goes from n ≥ 4 to n = 3 energy level,
  • Brackett series, when an electron goes from n ≥ 5 to n = 4 energy level,
  • Pfund series, when an electron goes from n ≥ 6 to n = 5 energy level,
  • Humphreys series, when an electron goes from n ≥ 7 to n = 6 energy level.

Rydberg formula

The specific wavelengths of emitted light could be predicted with the following Rydberg formula:

1/λ = R * Z² * (1/n₂² - 1/n₁²)


  • λ is the wavelength of emitted light,
  • Z is the atomic number (for hydrogen Z = 1),
  • n₁ is the principal quantum number of the initial state (initial energy level),
  • n₂ is the principal quantum number of the final state (final energy level),
  • R is the Rydberg constant for hydrogen R ≈ 1.0973 * 10^7 1/m.

In the advanced mode of our Rydberg equation calculator, you can compute the frequency and energy of the emitted electromagnetic wave. If you want to know how to convert wavelength to energy or frequency, check our photon energy calculator.


The study of the interaction between matter and an electromagnetic wave is called spectroscopy. It is a very helpful technique which is currently used in many areas of science. We can distinguish three main types of spectroscopy:

  • emission spectroscopy in which we measure the energy of photons released by the material. Emission can also be induced by other sources, e.g., flames, sparks or electromagnetic wave. Our Rydberg equation calculator is dedicated to this type of spectroscopy.
  • absorption spectroscopy occurs when we pass photons through the material and observe which photons energies were absorbed.
  • reflection spectroscopy in which we determine how incident photons are reflected or scattered by the material.
Dominik Czernia, PhD candidate
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