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Energy of different energy levels of hydrogen atom

  1. Nov 22, 2013 #1
    1. The problem statement, all variables and given/known data
    A hydrogen atom is in 2p state, how many different energy levels are there if a magnetic field of 0.10 T is applied to it, and what are their energies? Make sure spin is included.



    2. Relevant equations
    U = -gmsμzB

    g is the Lande-g factor, which is about -2 for electrons
    ms is spin, which is +/- 1/2
    μz is -μbm, which is the Bohr magneton times mass.
    Bohr magneton is equal to about 5.78x10-5
    The mass is, I assume, the mass of the electron, which is about 9.109x10-31

    And the initial energy of the ground state is E0 is -13.6/n^2

    n is 2.

    3. The attempt at a solution
    I get 6 energy levels, because ml has -1,0,1 and each of those has a spin of +/- 1/2.

    So what I did was just make the equation E0 + U, which gives me the initial energy, plus the energy that U provides. But I'm getting extremely small numbers for U. For example, for ml = 1, and the +1/2 spin, I'm getting, for U, 5.27x10-36. Added to E0, that's miniscule. Plus I'm always going to have a negative answer, since E0 is negative.

    So I don't know why it's negative, and I'm not sure if my answers are correct, because they seem extremely small.

    Thanks.
     
  2. jcsd
  3. Nov 22, 2013 #2

    DrClaude

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    Staff: Mentor

    Because of spin-orbit coupling, ##m_l## and ##m_s## are not good quantum numbers. You need to look at the total angular momentum of the electron ##j## and its projection ##m_j##.
     
  4. Nov 22, 2013 #3
    In what way are they not good quantum numbers?

    For total angular momentum of the electron, do I use [tex]\frac{\sqrt{3}}{2}\hbar[/tex]

    Thanks.
     
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