If we combine the expressions relating energy change and frequency of the transition radiation, we get

The corresponding equation for the wavelength is

where R (= 1.0973 ^{7} m^{-1}) is the
Rydberg constant.

If n_{f} = 2, the above expression gives the wavelengths
corresponding to the Balmer series. The first four of these
transitions (n_{i} = 3, 4, 5, and 6) produce lines with
wavelength 656, 486, 434, and 410 nm. These photons are in the
visible range and were the first to be observed from excited hydrogen
atoms. These lines were among the first pieces of evidence of that
pointed toward quantized behavior. The other series produce lines
outside the visible range but have been observed using special
detection systems.

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