Whenever a hydrogen atom emits a photon in the Balmer series,
it may emit another photon in the Balmer series
it must emit another photon in the Paschen series
the second photon, if emitted will have a wavelength of about 122 nm
it may emit a second photon, but the wavelength of this photon cannot be predicted
Any transition causing a photon to be emitted in the Balmer series must end at n = 2. This must be followed by the transition from n = 2 to n = 1, emitting a photon of energy 10.2 eV, which corresponds to a wavelength of about 122 nm. This belongs to the Lyman series.
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