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Homework Help: Splitting of Balmer Spectrum

  1. Mar 4, 2006 #1
    I need to show the splitting of the [itex]H_{\alpha}[/itex] line of the Balmer series of a Hydrogen atom using the spin hypothesis.

    Here is my work on this.
    [itex]H_{\alpha}[/itex] is obtained from the transition of the electron from the third orbit to the second i.e. from n=3 to n=2.
    Seletion rule for Hydrogen atom is: [itex]\Delta l = \pm 1[/itex] & [itex]\Delta m_l = \pm 1 , 0[/itex].
    This implies transition from 3s to 2s is forbidden but transition from 3p to 2s is allowed. How do I explain the splitting of the spectral line?
  2. jcsd
  3. Mar 4, 2006 #2


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    You need to do perturbation theory to the H atom using the spin-orbit coupling hamiltonian which should be assumed to be a time independent perturbation. One more thing: is the energy level involved in a H_alpha degenerate or not ?

  4. Mar 5, 2006 #3
    I haven't studied perturbation theory. I cannot say whether the energy level of Halpha is degenerate. They can involve transition from 3 2P1/2 or 3 2P3/2.

    However, since the Hydrogen atom consists of only 1 electron, so s = +1/2 or -1/2. Is it possible to show the splitting using spin hypothesis?
    Last edited: Mar 5, 2006
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