Question About Relativistic Energy

Factual Questions
#1

Hey there this is my first post so I thought I would ask a question about some issues i’ve been having with a relativity problem.
(note this is not for homework its just a question in my textbook i’m extremely curious about)

The question is:

A pion at rest decays into a muon and an antineutrino. Find (a) the kinetic energy of the muon and (b) the energy of the antineutrino in electron volts.
Pion mass = 139.503 MeV/c^2
Muon mass = 105.777 MeV/c^2
Antineutrino mass = 0 (approximately 0 apparantly)

I figured out that the rest energy of the pion subtracted by the rest energy of the muon is 33.726 MeV but i can’t figure out how to determine how much of this leftover energy is distributed between the muon (kinetic energy) and the antineutrino.

(answers)
(a) 4.08 MeV
(b) 29.6 MeV

the answers add up to 33.68 MeV so I think i’m at least on the right track

#2

Since the pion starts at rest, the momentum of the muon must be equal and opposite to the momentum of the antineutrino. Now you have two equations (one for energy and one for momentum) so you can solve for two unknowns.

#3

Thanks for the help! I figured it out right away when i read this. It never even occured to me to apply conservation of momentum.

#4

No problem. Glad to help.