How this calculator works
The difference of inverse squared principal levels determines the spectral wavenumber. Emission moves from higher to lower n; absorption reverses the same line. This tool uses CODATA 2018 Rinf, the infinite-nuclear-mass constant, consistently with the hydrogen energy-level page. Actual hydrogen wavelengths need a reduced-mass correction and small additional physics. The result is a vacuum wavelength. Inverse calculations accept only positive integer levels and atomic numbers, with a small numerical rounding tolerance.
Formula
1/lambda = Rinf Z² |1/nf² - 1/ni²|; f = c/lambda; Ephoton = hc/lambda. Emission requires ni > nf; absorption requires nf > ni.
Worked example
For Z = 1, n = 2 to n = 1 gives about 121.502273 nm. The n = 3 to n = 2 line gives about 656.112276 nm in the infinite-nuclear-mass approximation.
Advertisement
Frequently asked questions
Why does the result differ from 656.3 nm?
The commonly quoted hydrogen line includes finite nuclear mass and may use an air wavelength. This page uses Rinf and vacuum wavelength.
Can the two levels be equal?
No photon transition is produced when the energy difference is zero.
Can I use this for many-electron atoms?
No. Screening and electron interactions change their level structure.