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Positronium atom transition - energy of photon

  1. Mar 3, 2010 #1
    1. The problem statement, all variables and given/known data
    Positronium is an atom formed by an electron and a positron. It is similar to the
    hydrogen atom, with the positron replacing the proton. If a positronium atom
    makes a transition from the state n = 3 to a state with n = 1, the energy of the
    photon emitted in this transition is closest to

    3. The attempt at a solution

    what will my proton number Z be in this case?

    E = -13.6eV x Z2 / n2

    but a hydrogen atom's Z = 1, what about the positronium atom? 0?

    state n=3 has -1.511 eV while state 1 has -13.6 eV.

    but the answer is 6 eV? how is that obtained? i have no idea . thanks for help!
     
  2. jcsd
  3. Mar 3, 2010 #2

    ehild

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    Homework Helper
    Gold Member

    Re: positron?

    The positron and electron have about the same mass. The electron does not revolve around the positron, but both revolve around their common centre of mass. This two-body problem can be treated as the motion of a single body with the reduced mass: mp*me/(mp+me) which is half the mass of the electron. The Rydberg constant is proportional to the mass of the electron: Now it is halved.

    ehild
     
  4. Mar 3, 2010 #3
    Re: positron?

    ah isee.. thank you very much ehild!
     
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