Rydberg Equation Calculator

Rydberg Equation

Calculate the wavelength of light emitted or absorbed during an electron transition in a hydrogen atom.

Last updated: March 2026 | By ForgeCalc Engineering

Common Series
Lyman: n₁ = 1
Balmer: n₁ = 2
Paschen: n₁ = 3
Brackett: n₁ = 4
Wavelength (λ)
656.11
Nanometers (nm)
Photon Energy
1.890 eV

What is the Rydberg Equation?

The Rydberg equation is a mathematical formula used to predict the wavelengths of photons emitted or absorbed during electron transitions between energy levels in a hydrogen atom. It was the first successful attempt to explain the discrete spectral lines observed in atomic spectra.

When an electron jumps from a higher energy level (n₂) to a lower energy level (n₁), it emits a photon with energy equal to the difference between the levels. The equation relates this wavelength to the principal quantum numbers of the levels involved.

The Formula

1/λ = R_H × (1/n₁² - 1/n₂²)

Where:
λ (lambda) is the wavelength of the photon (m)
R_H is the Rydberg constant (1.097 × 10⁷ m⁻¹)
n₁ is the lower energy level (integer)
n₂ is the higher energy level (integer)

Frequently Asked Questions

What is the Lyman series?

The Lyman series corresponds to transitions where the electron ends at the n=1 level. These photons are in the ultraviolet (UV) range.

Why is the Balmer series famous?

The Balmer series (n₁=2) is famous because its spectral lines fall within the visible spectrum, meaning they can be seen by the human eye as distinct colors.

Does this work for other atoms?

The standard Rydberg equation only works for hydrogen. For 'hydrogen-like' ions (like He⁺ or Li²⁺), you must multiply the result by Z², where Z is the atomic number.

What happens when n₂ is infinity?

When n₂ approaches infinity, it represents the ionization energy—the energy required to completely remove the electron from the atom.

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