To solve this problem it is necessary to apply the concepts related to Kinetic Energy in Protons as well as mass-energy equivalence.
By definition the energy in a proton would be given by
The mass-energy equivalence is given as,
[tex]E = mc^2[/tex]
Here,
[tex]m = mass(1.67*10^{-27} kg)[/tex]
c = Speed of light [tex](3*10^8m/s)[/tex]
The energy of the photon is given by,
[tex]E = 2*E_0 = 2*(m c^2)[/tex]
Replacing with our values,
[tex]E = 2 (1.67*10^{-27}kg) (3*10^8m/s)^2[/tex]
[tex]E = 3.006*10^{-10} J[/tex]
[tex]E = 3.006*10^{-10} J(\frac{6.242*10^{12}MeV}{1J})[/tex]
[tex]E = 1876.34MeV[/tex]
Therefore we can calculate the kinetic energy of an anti-proton through the energy total, that is,
[tex]Etotal = E + KE_{proton} + KE_{antiproton}[/tex]
[tex](2200 MeV) = (1876.6 MeV) + (161.9 MeV) + KE_{antiproton}[/tex]
[tex](2200 MeV) = (2038.5 MeV) + KE_{antiproton}[/tex]
[tex]KE_{antiproton} = (2200 MeV) - (2038.5 MeV)[/tex]
[tex]KE_{antiproton} = 161.5 MeV[/tex]
Therefore the kinetic energy of the antiproton if the kinetic energy of the proton is 161.90 MeV would be 161.5MeV
