## Confusion with the conclusion sentence of 1.15 in the solutions manual [ENDORSED]

H-Atom ($E_{n}=-\frac{hR}{n^{2}}$)

Anna De Schutter - 1A
Posts: 66
Joined: Wed Feb 21, 2018 3:01 am

### Confusion with the conclusion sentence of 1.15 in the solutions manual

Hi!

I've been struggling a bit with understanding how the solutions manual presents 1.15.

So the problem states:
"In the ultraviolet spectrum of atomic hydrogen, a line is observed at 102.6nm. 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 understand why the solutions manual converts the wavelength 102.6nm to its frequency 2.922*10^15 s-1 and how it then uses the Rydberg equation:
frequency = R *[ (1/n1^2) - (1/n2^2) ] and says n1=1 and solves for n2 (because I read in previous posts that n1>n2 and we know with the Lyman series n_final=1 so it has to be n1 and n2 will be a higher energy level).

However, it is the conclusion sentence of the solutions manual I'm struggling with. At the end of the solution it states: "the transition is n1=1 to n2=3". I thought that because we had emission (as stated in the problem) that we would go from n2=3 to n1=1 because during emission aren't we emitting a photon? Moreover, in the Lyman series, isn't n_final always equal to 1 and because in this problem we are in the ultraviolet spectrum of atomic hydrogen, the transition should be from n2=3 to n1=1?

I was wondering if someone could explain this to me, am I understanding something the wrong way?

Thank you so much!
Anna De Schutter - section 1A

Tina Wen 1G
Posts: 31
Joined: Fri Apr 06, 2018 11:05 am

### Re: Confusion with the conclusion sentence of 1.15 in the solutions manual

Hi
I think the solution manual is not being precise here. During emission the H-atom should move from higher energy levels to lower ones. So technically it should be a transition from n2=3 to n1=1. Also n1 < n2 because that makes their squared reciprocals 1/n1^2 > 1/n2^2. Correct me if I'm wrong.

Anna De Schutter - 1A
Posts: 66
Joined: Wed Feb 21, 2018 3:01 am

### Re: Confusion with the conclusion sentence of 1.15 in the solutions manual  [ENDORSED]

Thank you! :) And yes you're right, n2>n1, I wrote it the wrong way, my bad!