Question

A π meson of rest energy 139.6 MeV moving at a speed of 0.921c collides with and sticks to a proton of rest energy 938.3 MeV that is at rest. (a) Find the total relativistic energy of the resulting composite particle. (b) Find the total linear momentum of the composite particle. (c) Using the results of (a) and (b), find the rest energy of the composite particle.

Answer 1

Answer:

A) 1268 MeV

B)  299MeV/c

C) 1268 MeV

Explanation:

Given :

π meson rest energy = 139.6 MeV

Speed = 0.921c

proton at rest energy = 938.3 MeV

a) Find the total relativistic energy of resulting composite particle

E = E(meson) + E(proton)

  = $\frac{(mc^2)_{meson} }{\sqrt{1-\frac{v^2}{c^2} } } + (mc^2)_{proton}$

  = $\frac{139.6MeV}{\sqrt{1-\frac{(0.906c)^2}{c^2} } } + 938.3$

E = 1268 MeV

B) determine the total linear momentum of the composite particle

= 299MeV/c

attached below is the detailed solution

C) Determine the rest energy of the composite particle

E = 1268 MeV