Positronium Decay: Energy of Photon?

[integrale2]

Hi, i would like about the decay of positronium (a electron and a positron going around the center of mass) in 2 photons: if i suppose the positronium decays at the rest, what is the energy of photons?
I think that the energy of a photon is the same of mass of rest of electron, because the binding energy of positronium is very small with respect to mass of electron at the rest.
If i would like to not neglect the binding energy of positronium, what is the nergy of photon?
Thanks

 

[granpa]

translation:

Hi, i would like [to know?] about the decay of positronium (a[n] electron and a positron [orbiting their] center of mass) in[to] 2 photons: if i suppose the positronium decays [while] at ... rest, what is the energy of [the resulting] photons?
I think that the energy of [each resulting] photon is the same [as the rest] mass ... of [the] electron, because the binding energy of positronium is very small with respect to [the rest] mass of [the] electron...
If i would like to [take into consideration] the binding energy of positronium, what is the energy of [each] photon?
Thanks
http://en.wikipedia.org/wiki/Positronium
Annihilation can proceed via a number of channels each producing one or more gamma rays. The gamma rays are produced with a total energy of 1022 keV (since each of the annihilating particles have mass of 511 keV/c²), the most probable annihilation channels produce two or three photons, depending on the relative spin configuration of the electron and positron. A single photon decay is only possible if another body (e.g. an electron) is in the vicinity of the annihilating positronium to which some of the energy from the annihilation event may be transferred. Up to five annihilation gamma rays have been observed in laboratory experiments[5], confirming the predictions of quantum electrodynamics to very high order.

 

[integrale2]

Hi, thanks for the translation, but I think it is a mistake to eliminate around: "an electron and a positron [orbiting] AROUND their center of mass...
In "http://www.wordreference.com/definition/orbit", i find this example: "The moon orbits AROUND the Earth"...
and what do you think from a physical point of view about:
"If i would like to take into consideration the binding energy of positronium, what is the energy of each photon?"

 

[Redbelly98]

I think that the energy of a photon is the same of mass of rest of electron, because the binding energy of positronium is very small with respect to mass of electron at the rest.
If i would like to not neglect the binding energy of positronium, what is the nergy of photon?
Thanks

Before decay, the energy is

[m c² for electron] + [m c² for positron] + [binding energy]

Afterwards, we have

2 x [energy of one photon]

Since you know all quantities in the equation except the photon energy, it can be solved. If you're still stuck, post again.

 

[integrale2]

Hi, I am in complete agreement upon which you wrote, I still have a little doubt, that is the core of my dilemma: the binding energy of course must be considered negative and then the energy of a photon is slightly lower the rest mass of electronics. E 'right?

 

[Redbelly98]

Yes, that's right.