# Solving for Momentum in Pion Decay

1. Jan 17, 2014

### lee_sarah76

1. The problem statement, all variables and given/known data

We are the given the rare decay:

π+ → e+ + ve

Also, we are given mπ = 139.6 MeV/c2, mv ≈ 0, me+ = 0.511 MeV/c2

And we are given that the decay starts with the pion at rest, so I took that to mean that pπ = 0

Solve for the momentum of the positron.

2. Relevant equations

Conservation of Momentum
Conservation of Energy
E2 = (pc)2 + (mc)2
E = mc2

3. The attempt at a solution

I started with the fact that since the pion was at rest before decay, pπ = 0 so pe + pv = 0.

Then, also using the fact that the pion was at rest before decay I solved for its energy using the formula E = mc2, substituting mπ = 139.6 MeV/c2 getting that Ebefore = 139.6 MeV.

Ebefore = Eafter = Ee + Ev

(Ee)2 = (pec)2 + (mec2)2

And because the neutrino is massless:
Ev = pv*c

From before, since Ee + Ev = 139.6 MeV, I solved for Ee to get Ee =139.6 MeV - Ev.

Then I substituted pvc for Ev to get the equation:

(139.6 MeV - pvc)2 = (pec)2 + (mec2)2

The (pc)2 would cancel each other out, leaving:

-279.2pvc = -19487.8 MeV

So, pv = 69.799 MeV/c leaving pe = -69.799 MeV/c

My question is, is this right, or have I made some glaring mistakes in my method?

2. Jan 17, 2014

### TSny

Looks good to me.