- #1

- 5

- 0

## Homework Statement

If anyone could help me with this classical mechanics exercise I would be very grateful! The exercise is as follows:

The muon (μ) is a particle with mass m

_{μ}=207m

_{e}, with m

_{e}being the electron mass. The pion (∏) has a mass of m

_{∏}=273m

_{e}. The pion can decay into a muon plus a massless neutrino,

*v*, in the reaction ∏ → μ +

*v*.

__Find the kinetic energy of the muon when a pion decays at rest.__

**Hint: Use conservation of both energy and momentum.**

## Homework Equations

The momentum conservation looks like this:

P

_{before}=P

_{after}

Where the momentum is given by:

P=mμγ(u)

The energy conservation is:

E

_{kin, before}=E

_{kin, after}

The kinetic energy is given by:

E

_{kin}=mc^2(γ(u)-1)

quantities we know:

m

_{μ}=207 m

_{e}

m

_{∏}=273 m

_{e}

m

_{v}=0

u

_{∏}=0 (the speed of the pion)

## The Attempt at a Solution

I have tried to write the equations, please correct me if I'm wrong:

E

_{kin, before}= m

_{∏}c^2 (γ(u)-1)

E

_{kin, after}= E

_{kin, μ}+ E

_{kin, v}= m

_{μ}c^2 (γ(u)-1) + m

_{v}c^2 (γ(u)-1)

P

_{before}=P

_{∏}=m

_{∏}u

_{∏}γ(u)=0

P

_{after}=P

_{μ}+P

_{v}=m

_{μ}u

_{μ}γ(u) + m

_{v}u

_{v}γ(u) = m

_{μ}u

_{μ}γ(u) + [itex]\frac{E}{c}[/itex] (because a massless particle can still have momentum)

Now I'm a bit stuck. What is the kinetic energy of the neutrino with zero mass, zero? How do I find the energy,

*E*in the momentum expression, is that the kinetic energy? It seems to me that there are too many unknowns, but I'm pretty sure I'm wrong here!

If anyone could help me, I would I will be very grateful!

Thanks in advance.

mr. bean.