All Problems Relativistic Mechanics
Problem 1.387
A stationary particle of rest mass \(m_{0}\) disintegrates into three particles with rest masses \(m_{1}, m_{2},\) and \(m_{3} .\) Find the maximum total energy that, for example, the particle \(m_{1}\) may possess.
1.387. \(E_{1 \max }=\frac{m_{0}^{2}+m_{1}^{2}-\left(m_{2}+m_{3}\right)^{2}}{2 m_{0}} c^{2} .\) The particle \(m_{1}\) has the highest energy when the energy of the system of the remaining two particles \(m_{2}\) and \(m_{3}\) is the lowest, i.e. when they move as a single whole.