A moving proton has a total relativistic energy of 2 GeV Wha

A moving proton has a total (relativistic) energy of 2 GeV. What is its kinetic energy and What is its momentum?

Solution

Total relativistic energy E = 2 GeV = 2x10 ⁹ x1.6 x10 ^-19 J

                                     = 3.2 x10 ^-10 J

Rest energy of proton Eo = mc ²

Where m = rest mass of proton = 1.67 x10 ^-27 kg

Substitute values you get , Eo = (1.67 x10 ^-27 )(3 x10 ⁸) ²

                                            = 1.503 x10 ^-10 J

(a). Kinetic energy K = E-Eo

                              =( 3.2 x10 ^-10 J)-(1.503 x10 ^-10 J )

                              = 1.697 x10 ^-10 J

(b).Momentum p = ?

We know (pc) 2 = E ² -Eo ²

                       = (3.2 x10 ^-10 ) ² -(1.503 x10 ^-10 ) ²

                       = 7.98 x10 ^-20

               pc = 2.825 x10 ^-10

                 p = (2.825 x10 ^-10 ) /(3x10 ⁸)    Since c = 3 x10 ⁸ m/s

                    = 9.416 x10 ^-19 kgm/s