# Electron-Positron Collision finding Kinetic Energy

1. May 15, 2010

### phamula

1. The problem statement, all variables and given/known data
Positive and negative pions, denoted $$\pi$$ + and$$\pi$$ - , are antiparticles of each other.

Each has a rest mass of 140 MeV/c^2. Suppose a collision between an electron and positron, each with kinetic energy K, produces a $$\pi$$+ , $$\pi$$- pair. What is the smallest possible value for K?

2. Relevant equations

E=mc2

3. The attempt at a solution

E(kinetic)=E(total)-E(at rest)

I need to fine Kinetic Energy, but I do not know how to find E(total). E at rest is 140 MeV

2. May 15, 2010

### Andrew Mason

What is the initial rest energy of the electron and the positron? What is the total energy, including kinetic, of the electron and positron? Write that out. That will be the left side of the energy conservation equation.

What is the final rest energy of the two pions? What is the total energy of the pions (including final kinetic energy). What is the minimum value for the kinetic energy of the pions? Use that value for the final kinetic energy. That will be the right side of the equation.

That gives you one unknown (K) which you can now solve.

AM

3. May 16, 2010

### phamula

This is what I came up with, but I don't think I am setting up the variables right.

melectron=0.51 MeV/c2
mpositron=0.51 MeV/c2
mpion=140MeV/c2

E0 electron + E0 positron + Eelectron total + Epositron total = E0 pion 1 + E0 pion 2 + Epion 1 total + Epion 2 total

mc2 + mc2 + (mc2 + (1/2)mv2) +(mc2 + (1/2)mv2) = mc2 + mc2 + (mc2 + (1/2)mv2) +(mc2 + (1/2)mv2)

(.51 MeV) + (.51 MeV) + (1/2)(.51MeV) + (1/2)(.51MeV) = (140 MeV) + (140 MeV) + (1/2)(140MeV)v2 + (1/2)(140MeV)v2

4. May 16, 2010

### Andrew Mason

$m_ec^2 + m_pc^2 + 2K$ = total energy before

Let KE after = 0 (minimum case):

$m_{(\pi^-)}c^2 + m_{(\pi^+)}c^2 + 0$ = total energy AFTER

How is the total energy before related to the total energy after?

AM

5. May 16, 2010

### phamula

Thanks! I found out that mastering physics accepted 3 sig figs specifically and that screwed things up for me.