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Homework Help: Hydrogen Emission Spectrum

  1. Nov 26, 2012 #1
    1. The problem statement, all variables and given/known data
    What wavelengths emitted from a hydrogen gas discharge tube are associated with transitions from higher levels down to the n = 1 level?
    [a] infrared
    [c] mixture of infrared and visible
    [d] ultraviolet

    2. Relevant equations
    1/λ = Rh[1/(m^2)-1/(n^2)] Rh = 1.09 x 10^7 m^-1.

    3. The attempt at a solution
    Can someone explain hydrogen gas electron transition to me? This stuff is a little over my head.

    I obtained various wavelengths with arbitrary quantum numbers greater than 1. I took +infinity as a bound since higher quantum numbers reaches the series limit.
    1/λ*(1 m/10^ 9 nm) = (1.097e-7 m^-1)[1/(1^2)-1/(infinity)]
    λ (+infinity ,1)= 91.6 nm

    1/λ*(1 m/10^ 9 nm) = (1.097e-7 m^-1)[1/(1^2)-1/(4^2)]
    λ (4 ,1)= 4.86 nm

    The level transitions yield a photon with wavelengths corresponding to UV light.

    I’m confused though because taking bounds of the 1.01 type down to 1 allows the photon to be associated with different lights. Do I have to keep m and n whole when doing this problem? With m & n being non-integral values n can be taken arbitrarily closer and closer to 1 (with n>1) pushing the wavelength to positive infinity. Non-integral values possess a different number of points in a dimensional space corresponding to different emissions.
  2. jcsd
  3. Nov 26, 2012 #2


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    Science Advisor
    Homework Helper

    Yes, you have to keep m and n whole numbers. That's quantization. There are only discrete states for bound electrons.
  4. Nov 26, 2012 #3
    Okay I understand this now. Thanks a lot!!
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