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For this problem, the question is "In the spectrum of atomic hydrogen, several lines are generally classified together as belonging to a series (For example, Balmer series or Lyman series). What is common to the lines within a series that makes grouping them together logical?". Can anyone please explain to me why the lower energy level is n =1 for the Lyman series and n = 2 for the Balmer series (according to the solutions manual)? thank you!
I believe the Lyman series is the ultraviolet one, which is the part of the electromagnetic spectrum with the highest energy/frequency. Since n=1 has the farthest gap from the other levels, an electron requires a lot more energy to jump up or has to emit a lot more energy to drop down, so it corresponds to the Lyman series.
The gaps between energy levels get larger the further from the nucleus you go, so the jumps (or emissions) with the largest energy will have to do with the largest gap because it would require the most energy to jump. Since the largest gap will always involve n=1, it is said to be associated with the Lyman series. The Lyman series is the set of emissions with the highest energy and therefore smallest wavelength (they're classified as uv radiation). As for the Balmer series, it's the grouping of emissions with the second shortest wavelength (and second highest energy) and it's associated with the second largest jump an electron can make. The second largest gap is from n=3 to n=2, so this series involves the energy level of n=2.
The lines close to each other are absorbed/emitted at similar frequencies, meaning they correspond to similar wavelengths. These wavelength ranges correspond to categories we named for them. In these cases, the wavelengths will either correspond to what we've defined as the visible light or UV spectra.
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