General Formula for atomic emission spectra

[rayclan]

hi everyone!

does a general Rydberg-like formula exist to predict the emission spectrum wavelengths of any atom?

if not, why?

 

[cgk]

No. Apart from hydrogen, atoms are non-trivial quantum many-body systems. Calculating their properties requires an actual numerical calculation of their wave functions, taking all the electron-electron and electron-nucleus interactions into account. Of course, one could maybe get an approximate or fitted formula for transitions of some atoms, which might or might not work well enough for a given application.

It is really just luck that there is a simple formula for hydrogen. It works because the H system is a two-body system (nucleus and one electron, nothing else) and such systems can be integrated exactly.