Question

A proton moves with a speed of 0.955c.

(a)

Calculate its rest energy.

MeV

(b)

Calculate its total energy.

GeV

(c)

Calculate its kinetic energy.

GeV

Answer 1

Part A.

rest energy of proton is given by:

E = m0*c^2

E = 1.67*10^-27*(3*10^8)^2 = 1.503*10^-10 J

E = (1.503*10^-10)/(1.6*10^-19) eV = 939.4*10^6 eV

E = 939.4 MeV

Part B.

total energy of proton is given by:

E_net = *m*c^2

= lorentz factor = 1/sqrt (1 - (v/c)^2)

E_net = 1.67*10^-27*(3*10^8)^2/sqrt (1 - (0.955c/c)^2)

E_net = 5.067*10^-10 eV

E_net = (5.067*10^-10)/(1.6*10^-19) eV = 3.17*10^9 eV

E_net = 3.17 GeV

Part C.

kinetic energy is given by:

Kinetic energy = total energy - rest energy

Kinetic energy = 3.17*10^-9 - 939.4*10^6 = 2.23*10^9 eV

KE = 2.23 GeV

Please Upvote.