- #1
lee_sarah76
- 18
- 0
Homework Statement
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.
Homework Equations
Conservation of Momentum
Conservation of Energy
E2 = (pc)2 + (mc)2
E = mc2
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?