Positronium atom transition - energy of photon

[quietrain]

Homework Statement

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

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!

 

[ehild]

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

 

[quietrain]

ah isee.. thank you very much ehild!