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In 1A.11, it asks "what is common to the lines within a series that makes grouping them together logical?" and I was wondering what they're looking for. Is the fact that the lower energy level is always n=1 for Lyman and n=2 for Balmer what groups them together?
Yes, I think the question is trying to convey the concept that when an electron is moving between energy levels, mainly falling from a higher energy level to n=1(Lyman series) and from a higher energy level to a n=2(Balmer series), EMR is emitted in different forms, from visible light to ultraviolet radiation and that results in certain 'lines' which are grouped based on which energy level the electron falls to. I'm not exactly sure where the 'lines' come from but I think it's from some experiment.
The grouping of the lines in the Lyman and Balmer Series corresponds to the states that hydrogen starts and ends in as well as the type of electromagnetic radiation is emitted. The Balmer Series are the energy transitions that involve the n=2 state of hydrogen and are all part of the visible light spectrum. The Lyman Series are the energy transitions that begin with or end with the n=1 state, which is the ground state of hydrogen.
It makes sense to group them in this way because as you already saw during Dr. Lavelle's lecture, the energy difference between n=1 and any other level is the largest while the energy difference between n=2 and any other level is relatively smaller. This is the reason why a gap is observed on the emission spectrum(energy given off in the form of electromagnetic radiation as an electron "fall" from a higher energy level to a lower one in a hydrogen atom). This also applies to the gap you would see to the left of Balmer series, which involves the energy difference between n=3 and any other higher energy level. These gaps, or distinct energy difference between difference series(different final energy levels that the electron drops to), makes grouping them in terms of Lyman series and Balmer series reasonable. This is also the reason why Lyman series release UV light and Balmer series emits visible light since the energy difference in Lyman series is significantly larger.
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