Onset of relativistic effects When working with particles it is important to know when relativistic effects have to be considered.
A particle of rest mass m0 is moving with speed v. Its classical kinetic energy is Kcl = m0v2/2. Let Krel be the relativistic expression for its kinetic energy.
(a) By expanding Krel/Kcl in powers of v2/c2, estimate the value of v2/c2 for which Krel differs from Kcl by 10 percent.
(b) For this value of v2/c2, what is the kinetic energy in MeV of (1) an electron (m0c2 = 0.51 MeV)? (2) a proton (m0c2 = 930 MeV)?