1.15 Homework Question

[Isabella Sanzi 2E]

Hey guys,
The question for chapter 1 number 15 is:
In the ultraviolet spectrum of atomic hydrogen, a line is observed at 102.6 nm. Determine the values of n for the initial and final energy levels of the electron during the emission of energy that leads to this spectral line.
I already found the frequency, but when I tried to use Rydberg's equation to solve for n, I was confused because there are 2 different values for n (n1 and n2) and I was just wondering how you were supposed to solve this when you do not have either n1 or n2 to start with. When I checked the solutions manual, they assigned n1 to be 1, and I am confused on how they got to that conclusion.
Thanks!

[Ryan Sydney Beyer 2B]

The question states that the emission given off is in the ultraviolet so we know that it is in the Lyman Series.
From this we know that n1 = 1. I think any problem has to give us some clue as to which energy level it is referring to or else we would have to resort to guess and check methods.

From there we use and to solve for the energy of the ultraviolet light and the energy of the final energy state. Then we subtract the two and rearrange to look like and then we can solve for n2.

[Rita Dang 3D]

Since the question tells us that the line is observed in the ultraviolet spectrum of atomic hydrogen, we can infer the line being observed belong to the Lyman series (by the definition of Lyman series). In Lyman series, we always have n_1=1.