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The main difference between the two series is the quantum levels they encompass. The Lyman series includes quantum level one which is why ultraviolet radiation is observed within this series(the leap from n=1 to n=2 realeses more energy than any other quantum jump that is why the radiation is uv.) On the other hand, the Balmer series includes n=2 to n=infinity which is why visible slight can be measured through this series.
That would be based on which energy level the electron is currently at and where it's going to go. The Lyman series is based on Ultraviolet light which entitles a larger change in energy from level 1. On the other hand, the Balmer series are frequency and wavelengths relevant to Visible light and level 2.
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