Help with 1A.11?

[Alice Chang 2H]

I'm not sure if this is the correct topic to post this under, but can anyone help me understand question 1A.11? I read through the answer from the solutions manual, but I don't understand how they got to that conclusion.

Here's the question:

In the spectrum of atomic hydrogen, several lines are generally classified together as belonging to a series (for example, Balmer series or Lyman series, as shown in Fig. 1A.10). What is common to the lines within a series that makes grouping them together logical?

[Anisha Chandra 1K]

Just checked out the solution and I think what they're trying to say is that each series measures the wavelength emitted by an electron going down from a higher energy level to a lower energy level. The difference between each series is what energy level the electron goes down to at time of measurement. So for the Balmer series, the spectral lines come from electrons going down to n = 2 (higher wavelength, lower frequency) and for the Lyman series, the spectral lines come from electrons going down to n = 1 (smaller wavelength, higher frequency).

Follow up question for anyone else who sees this: Does the Lyman series emit light of higher frequency because the electron goes down one more energy level and thus, loses more energy in the form of light?

[Gerald Bernal1I]

I believe the light emitted is just the difference between the frequency that displaced the atom and the threshold energy, so I don't know if its a higher frequency each time since sometimes it can be zero when it matches the threshold energy.