Speed and rest energy of a particle collision

[arella]

Homework Statement

If I'm given an electron that collides with an anti-electron with momentum in the opposite direction, which produces another particle, P, how to I find the speed of particle P? And how to I find the rest energy?

The initial momentum of the electron is: 9.06GeV/c

Initial momentum of the anti-electron is: 3.1 GeV/c (which would be negative here)

I am given a rest energy of .511 MeV for both electron and anti-electron.

Relevant Equations

K=(gamma-1)mc^2?

Rest energy I know is mc^2.

I honestly have no clue where to start, any help would be great.

 

[jbriggs444]

Homework Statement:: If I'm given an electron that collides with an anti-electron with momentum in the opposite direction, which produces another particle, P, how to I find the speed of particle P? And how to I find the rest energy?

The initial momentum of the electron is: 9.06GeV/c

Initial momentum of the anti-electron is: 3.1 GeV/c (which would be negative here)

I am given a rest energy of .511 MeV for both electron and anti-electron.
Relevant Equations:: K=(gamma-1)mc^2?

Rest energy I know is mc^2.

I honestly have no clue where to start, any help would be great.

What quantities are conserved in this situation? Which of those conserved quantities might be useful?

 

[arella]

What quantities are conserved in this situation? Which of those conserved quantities might be useful?

Energy and momentum are conserved, right? I'm just not sure of the equations I should use to solve for v exactly?

 

[jbriggs444]

Energy and momentum are conserved, right? I'm just not sure of the equations I should use to solve for v exactly?

Yes. Energy is conserved. You can write down an equation for that.
Yes. Momentum is conserved. You can write down an equation for that.

 

[haruspex]

Energy and momentum are conserved, right? I'm just not sure of the equations I should use to solve for v exactly?

That's two equations, so write them. Create variables as necessary for unknowns.

 

[arella]

That's two equations, so write them. Create variables as necessary for unknowns.

My issue is that I am unfamiliar with the equations and have no clue what to put down for them, especially with relativistic circumstances. Could you help show me the equations?

 

[jbriggs444]

My issue is that I am unfamiliar with the equations and have no clue what to put down for them, especially with relativistic circumstances. Could you help show me the equations?

Start with the momentum equation. Starting momentum on the left hand side. Can you figure out what goes there?

 

[arella]

Start with the momentum equation. Starting momentum on the left hand side. Can you figure out what goes there?

mv*gamma is p, yet since I'm approaching this thinking the electron and anti-electron are massless, I'm unsure of how the equations work.

 

[jbriggs444]

mv*gamma is p, yet since I'm approaching this thinking the electron and anti-electron are massless, I'm unsure of how the equations work.

I think you are missing the forest for the trees. The total momentum at the beginning does not require any knowledge of relativity or quantum physics. We are given the initial momenta.

 

[haruspex]

approaching this thinking the electron and anti-electron are massless

Wrong thought. You are given rest energies.

 

[PeroK]

mv*gamma is p, yet since I'm approaching this thinking the electron and anti-electron are massless, I'm unsure of how the equations work.

Well, technically the electron and positron are not massless, but at these energies they are nearly massless.

PS As long as you understand why, you can treat them as effectively massless particles. That should simplify things.