# Pion decaying energy

The question is:

A pion decays into a muon and a neutrino (which is almost massless, so we’ll take it to have a mass of zero). If the pion is initially at rest, find the energy of the outgoing muon.

Final Answer: $$E_μ=(m_π^2+m_μ^2)c^2/2m_π$$

I used conservation of energy and so the initial energy is just the rest energy of the pion which equals $$m_πc^2$$ and this should equal the final energy.

Getting the final energy is what I am having trouble with, the mass of the neutrino is approx. 0 so I used the $$E=\sqrt{p^2c^2 + m^2c^4}$$ and crossed out the term with m leaving $$E_\nu=pc$$. Then, for the muon there is rest energy and kinetic energy I eventually get $$E_μ=m_μc^2/\sqrt{1-u_μ^2/c^2}.$$

However, the final answer neither includes a $$p$$ nor a $$u$$, so I think that the problem is in finding the final energy and isolating for the $$E_μ$$.

• Hi and welcome to physics SE. Please, use laTex notation for formulae. It's about writing them in between of dollar symbols, and laTex commands inside. See here: math.meta.stackexchange.com/questions/5020/… – FGSUZ Jan 29 at 0:44
• You are simply forgetting an equation: conservation of momentum – Gabriel Golfetti Jan 29 at 0:48
• @GabrielGolfetti That's more like an answer than like a comment. – rob Jan 29 at 1:24

• note that $-p_{\mu} = p_{\nu} = E_{\nu} = m_{\pi} - E_{\mu}$ – JEB Jan 29 at 3:27