What is the momentum of the muon in a pi-meson decay?

[Abdul.119]

Homework Statement

pi-meson's rest energy is 139.57MeV, it decays into a muon and a neutrino. The muon has a rest energy of 105.45MeV, and a proper lifetime of 2.197*10^-6. The neutrino's mass can be treated as massless in the process.

1) Assuming the pi-meson decays at rest, what is the momentum of the muon?

Homework Equations

E_muon + E_neutrino = E_pi-meson
E_muon = c^2* ((m_pi-meson)^2 - (m_muon)^2)) / (2m_pi-meson)
E_muon = sqrt((P_muon^2 c^2) + (m_muon c^2)^2)

The Attempt at a Solution

Ok I used used the second equation and it gives about 9.866*10^18, then, use this value in the 3rd equation and solving for the momentum, I get a negative value under the square root, which doesn't make sense. In the 2nd equation, the values I plugged in for m_pi-meson and m_muon are just 139.57 and 105.47, and used 3*10^8 for c. Where did I go wrong?

 

[mfb]

E_muon = c^2* ((m_pi-meson)^2 - (m_muon)^2)) / (2m_pi-meson)
E_muon = sqrt((P_muon^2 c^2) + (m_muon c^2)^2)

Where do those equations come from?

Ok I used used the second equation and it gives about 9.866*10^18

9.866*10¹⁸ what? Kilometers, apples, ...? Units are important.

 

[Abdul.119]

Where do those equations come from?
9.866*10¹⁸ what? Kilometers, apples, ...? Units are important.

The first equation is based on the conservation laws, you can see from here https://teachers.web.cern.ch/teache...h/mbitu/energy_and_momentum_conservation1.htm I used equation (2.5)
For the second equation, I used the fact that E^2 = p^2 c^2 + m^2 c^4 , squared both sides to get E, and tried to solve for the momentum from here

 

[Abdul.119]

Oh never mind, I solved it. Thanks for the help.