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We talked about this in my discussion yesterday and my TA told us that for each series grouped together, the energy levels where the electrons start is always the same. For example, for the Lyman series, the electrons always either start at or return to (depending on if the light is absorbed or emitted) the energy level n=1. For the Balmer series, the electrons always start at or return to n=2. The other series in that question are the same with n=3 and n=4, respectively. So their principal quantum levels are always the same for each series!
This would be important in other problems where they give you the energy difference or only the wavelength and ask you to find the n positions of both energy levels. For example, if they only gave you a wavelength of light of 500nm, you would know at least it is visible light, and therefore a Balmer series. You would then know, depending on whether energy is absorbed or emitted, that the base energy level is n=2. Now you can isolate the other n and solve for it to be able to solve for it.
The principal quantum number is an integer that describes the energy level of the electron. As n increases, the number of electronic shells increases and the electron is further from the nucleus and therefore has a higher energy. To compute n, we can utilize Rydberg's equation given the energy: En=-hR/n^2.
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