Rydberg Equation Calculator

How it is calculated

The tool uses the Rydberg equation for hydrogen: 1/λ = R × (1/n₁² − 1/n₂²) with R = 1.0973731568×10⁷ m⁻¹, n₁ the lower energy level and n₂ the higher one. Both levels are whole numbers (decimals are cut off), n₁ must be at least 1 and n₂ must be strictly larger than n₁; otherwise no result is shown. The wavelength is λ = 1/(1/λ), converted from metres to nanometres and shown with two decimals, together with the wavenumber 1/λ in m⁻¹ in scientific notation. It describes hydrogen only; ions with one electron need a Z² factor, and heavier atoms need other methods. The value is the wavelength in vacuum.

Common mistakes

• Entering the higher level as n₁ and the lower as n₂: the tool needs n₂ greater than n₁ and returns nothing otherwise.
• Typing a decimal such as 2.5; levels are whole numbers and the fraction is simply dropped.
• Using the result for helium, lithium or any atom with several electrons; the formula is for hydrogen.
• Expecting a visible colour for every pair: n₁ = 1 gives ultraviolet lines and n₁ = 3 gives infrared lines.
• Comparing the vacuum wavelength with a value measured in air without noting the small difference.