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zippideedoda

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## Homework Statement

A pion at rest decays into a muon and an antineutrino. The mass of the antineutrino is zero, find the energies and momenta of the muon and antineutrino. Mass of the pion is 139.57 MeV/c^2 and the mass of the muon is 105.66 MeV/c^2

## Homework Equations

pion -> muon + antineutrino

(1) E=mc^2

(2) E=pc

(3) E^2 = (pc)^2 + (mc^2)^2

## The Attempt at a Solution

Conservation of energy: E(pion) = E(muon) + E(antineutrino)

Using equation 1 and the given masses:

E(pion) = 139.57 MeV

E(muon) = 105.66 MeV (?)

so E(antineutrino) = E(pion) - E(muon) = 33.91 MeV

Use equation 2 for the massless antineutrino and get p = 33.91 MeV/c

since momentum is conserved and p(pion) = 0 (at rest),

p(muon) = -p(antineutrino) = -33.91 MeV/c

I don't think I'm right because if the muon has momentum it is moving and thus I can't find its energy by simply plugging its mass into equation 1.

Thanks for any help.

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