Chapter 32, Problem 56GP

To determine

To find: The kinetic energy of each pion.

Explanation of Solution

A proton and an antiproton initially at rest. So, there is no initial momentum, the final momentum must add to zero.

From the energy conservation equation,

  $2m_{\text{p}}{c}^2=2{\text{KE}}_{\pi }+2m_{\pi }{c}^2$

After rearranging the above equation,

The kinetic energy of each pion

  $\begin{array}{l}{\text{KE}}_{\pi }=m_{\text{p}}{c}^2-m_{\pi }{c}^2\\ =938.3\text{MeV}-139.6\text{MeV}\\ =798.7\text{MeV}\end{array}$

Therefore, the kinetic energy of each pion $798.7\text{MeV}$