# Initial and final state of a hydrogen atom

• Jun 6th 2013, 01:19 PM
Cesc1
Initial and final state of a hydrogen atom
Hi dudes! I hope you can help me with this problem; it was on my modern physics exam but I got it wrong; however, the teacher didn't tell me what the right answer was. Anyway, here is the problem:

In a hydrogen atom a photon of wavelength 95 nm is emitted. What are the initial and final states of the hydrogen atom?

My solution:

The energy of the photon is hc/λ = 1240 eV*nm / 95 nm = 13.05 eV, which is the energy difference between the final and initial states. So I get

E = 13.05 eV = Ei - Ef = -E0/ni^2 - (-E0 /nf^2) = -13.6 eV(1/ni^2 - 1/nf^2)

So I get this equation with 2 unknowns, and after a few guesses I came to the conclusion that the initial state must be ni=5 and the final state is nf=1, because after substituting those values I get 13.056 eV, which is a close approximation to the value of 13.05 eV I got earlier.

Where is the mistake? Thanks in advance!
• Jun 6th 2013, 01:30 PM
topsquark
Re: Initial and final state of a hydrogen atom
Quote:

Originally Posted by Cesc1
Hi dudes! I hope you can help me with this problem; it was on my modern physics exam but I got it wrong; however, the teacher didn't tell me what the right answer was. Anyway, here is the problem:

In a hydrogen atom a photon of wavelength 95 nm is emitted. What are the initial and final states of the hydrogen atom?

My solution:

The energy of the photon is hc/λ = 1240 eV*nm / 95 nm = 13.05 eV, which is the energy difference between the final and initial states. So I get

E = 13.05 eV = Ei - Ef = -E0/ni^2 - (-E0 /nf^2) = -13.6 eV(1/ni^2 - 1/nf^2)

So I get this equation with 2 unknowns, and after a few guesses I came to the conclusion that the initial state must be ni=5 and the final state is nf=1, because after substituting those values I get 13.056 eV, which is a close approximation to the value of 13.05 eV I got earlier.

Where is the mistake? Thanks in advance!

Looks good to me. What is the given correct answer?

-Dan
• Jun 6th 2013, 01:47 PM
Cesc1
Re: Initial and final state of a hydrogen atom
Quote:

Originally Posted by topsquark
Looks good to me. What is the given correct answer?

-Dan