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Zeeman splitting.

  1. May 4, 2009 #1
    1. The problem statement, all variables and given/known data

    (Q1) Which transition will produce a normal zeeman triplet in a weak applied field?


    (Q2) The sodium resonance line is a doublet. What is the total number of components that appear when the line is split by a weak applied field?


    3. The attempt at a solution

    (Q1) 1D2 --> 1P1 or 2P(3/2) ---> 2S(1/2) ?
     
  2. jcsd
  3. May 5, 2009 #2
    q1. Seems correct - remember you can't shift between states with the same l-number.
     
  4. May 5, 2009 #3
    The visual effect above is awful, sorry.

    1. Sufficient and neccesary conditions for normal Zeeman triplet is:

    The total number of electrons is even, and the electrons form the state with S=0, 2S+1=1.

    2. As to the famous sodium doublet, the 589.6nm line will split into four lines, with frequency difference 2/3 Lorentz unit (LU), 3/4 LU, 2/3 LU, respectively; the 589.0nm line splits into six ones, with identical frequency difference of 2/3 LU. No line exists at the initial location any more.

    Comments:

    1. Sodium Doublet: 589.6nm: 2P_(3/2) ----->2S_(1/2), 589.0nm: 2P_(1/2) ----->2S_(1/2).

    2. Transition Rule: \Delta m = +1, 0, -1.

    589.0nm: 2P_(1/2) ----->2S_(1/2), m, mg

    ---|----------------------------------------------------- 3/2, 2
    ---|---------|----|-------------------------------------- 1/2, 2/3
    ---|---------|----|---------|----|---------------------- -1/2, -2/3
    ---|---------|----|---------|----|----------|----------- -3/2, -2
    1 1 1 1 1 1
    1 1 1 1 1 1
    1 1 1 1 1 1
    ---|---------|----|---------|----|----------|----------- 1/2, 1
    ------------------|--------------|----------|----------- -1/2, -1



    589.6nm: 2P_(1/2) ----->2S_(1/2), m, mg

    ---|---------------------------------------------------- 1/2, 2/3
    ---|---|-----------------|----|------------------------- -1/2, -2/3
    1 1 1 1
    1 1 1 1
    1 1 1 1
    ---|---|-----------------|----|-------------------------- 1/2, 1
    -------|----------------------|-------------------------- -1/2, -1


    where $g$ above is Lande g fractor, and for effectively mono-electron atoms, such as 1H, 3Li, 11Na, 19K, 29Cu, 47Ag, 79Au,

    3 1 S * (S+1) -- L * (L+1)
    g = --- + --- (---------------------------------)
    2 2 J * (J+1)
     
    Last edited: May 5, 2009
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