Question

A proton moves with a speed of 0.875c. (a) Calculate its rest energy. MeV (b) Calculate its total energy. GeV (c) Calculate its kinetic energy. GeV

Answer 1

here,

the mass of proton , m0 = 1.67 * 10^-27 kg

the speed of proton , v = 0.875 c = 2.625 * 10^8 m/s

a)

the rest energy , RE = m0 * c^2

RE = 1.67 * 10^-27 * (3 * 10^8)^2 J

RE = 1.5 * 10^-10 J = 1.5 * 10^-10 /( 1.6 * 10^-19) eV

Re = 937.5 MeV

b)

the total energy , TE = m * c^2 = m * c^2 /sqrt(1 - (v/c)^2)

TE = 1.67 * 10^-27 * (3 * 10^8)^2 /sqrt(1 - (0.875 c/c)^2)

TE = 3.1 * 10^-10 J = 3.1 * 10^-10 /( 1.6 * 10^-19) eV

TE = 1.94 GeV

c)

the kinetic energy , KE = TE - RE

KE = 1.94 GeV - 937.5 MeV = 1 GeV