# Homework Help: Positive pion decay and kinetic energy

1. Feb 22, 2013

### justtram13

1. The problem statement, all variables and given/known data
A nucleus contains Z protons that on average are uniformly distributed throughout a tiny sphere of radiues R.
Suppose that in an accelerator experiment a positive pion is produced at rest at the center of a nucleus containing Z protons. The pion decays into a positive muon (essentially a heavy positron) and a neutrino. The muon has initial kinetic energy Ki.
How much kinetic energy does the muon have by the time it has been repelled very far away from the nucleus? (The muon interacts with the nucleus only through Coulomb's law and is unaffected by nuclear forces. The massive nucleus hardly moves and gets negligible kinetic energy.)

2. Relevant equations
F = k (q1q2/r^2)

3. The attempt at a solution
Neutrino product -> E = pc
Since pion is at rest, its energy equals its mass
E(sub∏) = m(sub∏)

E(sub∏) = E(subμ) + E(subv)
E(sub∏) = E(subμ) + 0
E(sub∏) = E(subμ)

I have no idea where to go from here. As of now, I'm assuming that Ki = Kf, but I don't think that that's right. Any suggestions on where to go from here?

2. Feb 22, 2013

### Staff: Mentor

Only for point-charges, or spherical charge distributions with no overlap. You can use this once the muon left the nucleus.

Do you have to calculate Ki? In that case: Energy and momentum are conserved in the pion decay and you can neglect the neutrino mass. 4-vectors are the quickest way to calculate the muon energy.

The electrostatic repulsion will increase the muon energy.