# Synchroton, number of pairs created

In a synchrotron, a particle and its antiparticle circulate in opposite directions with kinetic energies of 5.63 GeV each. When the two collide one possible outcome is the production of one or more proton-anti proton pairs. What is the maximum possible number of proton-anti proton pairs that could be formed?

The maximum proton-anti proton pairs are formed when all the kinetic energy is transformed into mass .

mass of proton = mass of anti proton $m= 1.00794 amu$

energy of proton-anti proton pair is

$E = 2mc^2 = 2*1.00794*1.66*10^{-27}*9*10^{16} =3.011*10^{-10} J =$

$= 1.88*10^9 eV = 1.88 GeV$

Total number of pairs is

$N = 5.63/1.88 =2.991$

Since the result is less than 3 the total number of pairs is possible formed is 2 the rest of energy being transformed into kinetic energy of pairs.