A Find the momentum in MeVc for a proton with a kinetic ener

A) Find the momentum in MeV/c for a proton with a kinetic energy of 10MeV B) Find the energy in MeV for a photon with the same momentum as the proton in part A

Solution

(A) The momentum in MeV/c for a proton with a kinetic energy of 10MeV with mass   938.3 MeV/c^2

Use eV units where c = 1, E = m + K , E^2 = p^ 2 + m^ 2

p = (m + K)^ 2 m^ 2 = m^ 2 + 2mK + K^2 m^ 2 = K^2 + 2mK

Note that in c = 1 units, momentum is always larger than kinetic energy.

K = 10 MeV p =sqrt (10^2 + 2 * 938.3*10) = 137.35 MeV/c

(B) for photon where c = 1, E = m + K now rest mass of photon is zero i.e m=0

E= K=137.35  MeV/c