Gorgon decay into photon and Lexicon using energy-momentum conservation

[rei]

I've been trying to use energy and momentum conservation in this problem but it didn't work out or I got a quadratic equation and got 3 different answers. Can anyone help me please. Here is the problem

The Gorgon ( rest mass of 3000 MeV/c^2) decays into a photon (i.e, a particle of light) and Lexicon (rest mass of 1800 MeV/c^2).

The Gorgon was initially at rest. The photon is emitted in the -x direction and the Lexicon is in the +x direction. Find the energy of the photon and the final velocity of the Lexicon.

Thanks a lot

 

[Astronuc]

Please show what you have done.

Think - Conservation of energy and conservation of momentum.

The momentum of a photon, p = E/c

Remember there is rest energy and kinetic energy, so total energy must be conserved, and momentum.

 

[rei]

I have Eg = Ep + El and the same thing for p

also E = square root of [(pc)^2 + (mc^2)^2]

and pc of photon will be equal -pc of elicon.

Substitute both of the above into the conservation of energy equation. I only have one unknow which is p of photon. But then I got a quandratic equation with 3 different answers. I don't know what to do next.

Thanks