VelvetRebel
Feb24-10, 12:44 AM
1. The problem statement, all variables and given/known data
A positron with a kinetic energy of 2.000 MeV collides with an electron at rest and the two particles are annihilated. Two photons are produced; one moves in the same direction as the incoming positron and the other movies in the opposite direction. Find the energies of the photons.
2. Relevant equations
Ei=KEpositron+Eo
Ei2=(pic)2+Eo2
Ephoton=pc
3. The attempt at a solution
Ei=2 MeV+2*.511 MeV=3.022 MeV = total energy
3.022 MeV=pphoton-1c+pphoton-2c
pi=pphoton-1-pphoton-2
From here on I don't know what to do. I tried to use Ei2=(pic)2+Eo2 (using 3.022 MeV as Ei and 2*.511 MeV as Eo) to find the pi, which I found to be 2.84 MeV/c, but that does not lead to the correct answer.
The answers should be E1=2.74 MeV and E2=0.282 MeV
A positron with a kinetic energy of 2.000 MeV collides with an electron at rest and the two particles are annihilated. Two photons are produced; one moves in the same direction as the incoming positron and the other movies in the opposite direction. Find the energies of the photons.
2. Relevant equations
Ei=KEpositron+Eo
Ei2=(pic)2+Eo2
Ephoton=pc
3. The attempt at a solution
Ei=2 MeV+2*.511 MeV=3.022 MeV = total energy
3.022 MeV=pphoton-1c+pphoton-2c
pi=pphoton-1-pphoton-2
From here on I don't know what to do. I tried to use Ei2=(pic)2+Eo2 (using 3.022 MeV as Ei and 2*.511 MeV as Eo) to find the pi, which I found to be 2.84 MeV/c, but that does not lead to the correct answer.
The answers should be E1=2.74 MeV and E2=0.282 MeV