# Initial and final states of hydrogen atom

## Homework Statement

A hydrogen atom in an excited state emits a photon of wavelength 95nm. What are the initial and final states of the hydrogen atom? [Hint: you will need to make a reasonable guess of what is the final state. look at the energy of the photon and compare this energy with all the possible transitions in the hydrogen atom.]

## Homework Equations

En=-E0/n^2
lambda=hc/(Ei-Ef)

## The Attempt at a Solution

For the initial state, I set 95 = 1240/ (13.6-(-13.6/n^2)) and solved for n. I got 4.985, so I said it was 5th order initially. However, I think I may be doing this entirely wrong, as I cannot figure out how to get the final state.

Dick
Homework Helper
The equation you solved is assuming the final state of the hydrogen atom was the ground state, n=1. Could the final state have been any other n?

Does that change my equation for finding the initial state, or just for the final state? And for the final state, I tried to find E with E=hc/lambda, and then plug that in as the final energy, but that didn't work. I got something less then one.

Dick
Homework Helper
In general, the energy is 13.606*(1/nf^2-1/ni^2) where nf is the final state and ni is the intial state. What you did in your first attempt is basically the same as putting nf=1 and finding ni. And ni=5 looks good to me. Why couldn't nf be 2 or larger?

Okay, so what I did now was set 95 = 1240 / [(-13.6/n^2)-(-13.6/25)] and solved for n, but I am getting something between 1 and 2, and not really very definitively either one. You can't be between energy states, so I know I must still be doing something wrong.

Thank you for all your help so far!

Dick