# Positronium atom transition - energy of photon

## 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
Homework Helper

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

ah isee.. thank you very much ehild!