Positive and negative pions denoted and are antiparticles

Positive and negative pions, denoted + and , are antiparticles of each other.

Each has a rest mass of 139.6 MeV/c2. Suppose a collision between an electron and positron, each with kinetic energy K, produces a +, pair. What is the smallest possible value for K?

Solution

Rest mass energy for electron and positron = 0.511 MeV.

Rest mass energy of pions = 139.6 MeV.

Then, to produce pions, according to conservation of energy, minimum kinectic energy of the electron or positron = 139.6 - 0.511 MeV = 139.089 MeV. That is the minimum value of K.