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Orbital Spin and External Magnetic Fields

  1. Nov 12, 2009 #1
    1. The problem statement, all variables and given/known data
    A Hydrogen atom is subjected to a magnetic field strong enough to overwhelm the spin-orbit coupling. Into how many levels would the 2p level split? What would the spacing be in the terms of Bext, e, me, and [tex]\hbar[/tex]


    2. Relevant equations
    I know that I have to use the gLande equation:
    U=gLande[tex]\frac{e}{2(me)}[/tex]mj[tex]\hbar[/tex]Bext


    3. The attempt at a solution
    I have a feeling that the 2p level will split into 3 levels, but I honestly don't know how to show it.

    Any help will be greatly appreciated!
     
  2. jcsd
  3. Nov 12, 2009 #2
    OK... I think I may have got some of it....
    The 2p state of hydrogen has [tex]\ell[/tex]=1 with m[tex]\ell[/tex]=-1,0,1
    So the 2p state splits into three levels by the external B.

    Calculating the gLande factor for the 2p state as [tex]\frac{4}{3}[/tex] and the 1s state as 2, I find that the splitting of the 2p state is only [tex]\frac{2}{3}[/tex] that of the 1s state


    SO... the spacing between the levels is:
    [tex]\frac{e\hbar}{2m}[/tex]Bext[tex]\frac{2}{3}[/tex]

    Does that look right to anybody out there??? Help! :-(
     
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