An electron and a positron,each having kinetic energy 1.843 GeV, 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

In the annihilation process, the total energy and momentum before and after the annihilation must be conserved. Since the kinetic energy of the electron-positron pair is 1.843 GeV each, the total initial energy is 2 x 1.843 GeV = 3.686 GeV.

After annihilation, a proton-antiproton pair is produced. The mass of the proton-antiproton pair (M) is given as 938.3 MeV/c^2. The total energy of the final state particles is the sum of their rest masses and kinetic energies.

Let the final kinetic energy of the antiproton be K. Then, the total final energy is:

E = 2M + K

Since energy is conserved, we can equate the initial and final energies:

3.686 GeV = 2 x 938.3 MeV/c^2 + K

Solving for K, we get:

K = 0.905 GeV

Therefore, the kinetic energy of the antiproton produced in the annihilation is 0.905 GeV.

An Electron and a Positron,each Having Kinetic Energy 1