Question 1.A.15

[Yuri Lin 4H]

In the solutions manual, it looks like it's assumed that the first n in 1/n^2 of the Rydberg equation (the n^2 with a 1 subscript) is 1. Can you always assume that the smaller n is always 1 for the Rydberg equation? How did they arrive at this conclusion, and how do we know it's not some other energy level?

[SGonzales_3L]

No, we cannot always assume that the initial state is n=1. The reason why they use n₁=1 is because the spectral line is observed at 102.6 nm. This wavelength falls within the UV region, suggesting that the spectral line is a part of the Lyman series which, by definition, transitions where the n₁=1. Had the frequency of the spectral line been anywhere from 420-700 nm, we would use the Balmer series and n₁=2.

[Yuri Lin 4H]

No, we cannot always assume that the initial state is n=1. The reason why they use n₁=1 is because the spectral line is observed at 102.6 nm. This wavelength falls within the UV region, suggesting that the spectral line is a part of the Lyman series which, by definition, transitions where the n₁=1. Had the frequency of the spectral line been anywhere from 420-700 nm, we would use the Balmer series and n₁=2.

Ok, thank you so much for the clarification! That makes sense.