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The Balmer and Lyman series are series defined by the final position of the electron, after a photon is emitted. The Lyman series involve jumps to or from the ground state (n=1); the Balmer series (in which all the lines are in the visible region) corresponds to n=2.
The grouping has to do with both the wavelength of the emitted photon and the quantum level. The lyman involves jumps to or from the n=1 energy level. Therefore, the change in energy will be greater, causing the emitted photon to have a larger frequency and therefore a smaller wavelength. Thus, the lyman series emits photons in the UV spectrum. In contrast, the balmer series involves jumps to or from the n=2 energy level. Therefore, the change in energy will be slightly smaller, causing the emitted photon to have a smaller frequency and therefore a longer wavelength. Thus, the balmer series emits photons in the visible spectrum.
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