An electron and a positron, each having kinetic energy 1.843 GeV, collide head-on and annihilate, producing a proton and antiproton pair (M = 938.3 MeV/c²). What is the kinetic energy of the antiproton produced in this way? A) 0.938 GeV. B) 0.905 GeV. C) 1.586 GeV. D) 1.843 GeV.

Question

Quizplus · Accepted Answer

The total energy in the electron-positron system is 1.843 GeV + 1.843 GeV = 3.686 GeV. 
Since the electron and positron annihilate and produce a proton and antiproton pair, we know that the total energy of the final state is the same as in the initial state, i.e. 3.686 GeV. 
Since the masses of the proton and antiproton add up to 2M = 1876.6 MeV/c², their combined energy is 3.686 GeV - 1.8766 GeV = 1.8094 GeV. 
Since the proton and antiproton are produced at rest, their energies are equal and each one has an energy of 1.8094/2 = 0.9047 GeV. 
Therefore, the kinetic energy of the antiproton produced is 0.9047 GeV.

An Electron and a Positron, Each Having Kinetic Energy 1