Matematiska och systemtekniska institutionen

Janne Rydberg


Fysik och Skolteknik

Rydberg-Ritz combination principle

The Rydberg-Ritz combination principle (Rydberg 1890, Ritz 1908) states that it is possible to find pairs of spectral lines, which have the property that the sum of their wavenumbers is also an observed spectral line.

This principle becomes is obvious when we know that spectra are due to transitions between energy levels. An atom can decay from a state 2 to a ground state 0 either directly, or in two steps 2→1 and 1→0. Energy is conserved, E=hf, so the two frequencies (wavenumbers) of the latter route add to the frequency of the first route.

In 1913, Niels Bohr showed this for the hydrogen atom,

E=13.6 eV/n2

We have

fnm = 13.6(1/n2 − 1/m2)

Similarly,

fml = 13.6(1/m2 − 1/l2)

Hence

fnm+fml = 13.6(1/n2 − 1/m2) +13.6(1/m2 − 1/l2) = 13.6(1/n2 − 1/l2) =fnl

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