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?
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!