Calculating Total Energy of Positron and Electron in Quantum Physics Problem

[aurao2003]

Homework Statement

Hi
I am new to this forum and offering quantum physics at A level. Can anybody help with the following problem:

The rest energy of an electron is 0.511MeV. A positron created in a cloud chamber has 0.158MeV of kinetic energy. It collides with an electron at rest, creating two photons of equal energies as a result of annihilation.

1. calculate the total energy of the positron and the electron.
2. show that the energy of each photon is .590MeV.

Thanks
Ben

Homework Equations

The Attempt at a Solution

 

[Fightfish]

Hint: What is the total energy of the positron?

 

[aurao2003]

The total energy should be 0.511 x 2. Since the electrons rest energy is 0.511 any particle colliding with it will have the same energy.

 

[Fightfish]

The total energy should be 0.511 x 2. Since the electrons rest energy is 0.511 any particle colliding with it will have the same energy.

Huh? That does not make any sense to me at all. Why should the energy of any other particle be affected by the rest energy of the electron??
Total energy of the system is simply just the sum of the total energies of the electron and the positron. We know that the total energy of the electron is simply its rest energy, 0.511 MeV. So now all we need to do is get the energy of the positron. What is it?

 

[aurao2003]

The energy of the positron is 0.158MeV. Therefore the total energy of the system is 0.158+0.511=0.669 MeV. However the answer is 1.180 MeV.

 

[Fightfish]

The energy of the positron is 0.158MeV. Therefore the total energy of the system is 0.158+0.511=0.669 MeV. However the answer is 1.180 MeV.

0.158 MeV is the kinetic energy of the positron. The total energy of the positron is the sum of its kinetic and rest energies.

 

[aurao2003]

0.158 MeV is the kinetic energy of the positron. The total energy of the positron is the sum of its kinetic and rest energies.

Thats true. But I wonder how they obtained 1.180 MeV. Please explain. Thanks.

 

[Fightfish]

The total energy of system = energy of electron + energy of positron
= 0.511 MeV + (0.511 MeV + 0.158 MeV)
= 1.180 MeV

 

[aurao2003]

The total energy of system = energy of electron + energy of positron
= 0.511 MeV + (0.511 MeV + 0.158 MeV)
= 1.180 MeV

Thanks a lot. Have a nice day.

Regards
Ben