Electron-Positron Collision finding Kinetic Energy

[phamula]

Homework Statement

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?

Homework Equations

E=mc²

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

 

[Andrew Mason]

Homework Statement

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?

Homework Equations

E=mc²

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

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

 

[phamula]

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

m_electron=0.51 MeV/c²
m_positron=0.51 MeV/c²
m_pion=140MeV/c²

E_{0 electron} + E_{0 positron} + E_{electron total} + E_{positron total} = E_{0 pion 1} + E_{0 pion 2} + E_{pion 1 total} + E_{pion 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

 

[Andrew Mason]

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

m_electron=0.51 MeV/c²
m_positron=0.51 MeV/c²
m_pion=140MeV/c²

E_{0 electron} + E_{0 positron} + E_{electron total} + E_{positron total} = E_{0 pion 1} + E_{0 pion 2} + E_{pion 1 total} + E_{pion 2 total}

Your equation makes no sense.

$m_ec^2 + m_pc^2 + 2K$ = 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

 

[phamula]

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