Particle energies are usually given in electronvolts. One electronvolt is the energy transferred when an electron moves through a p.d. of 1 V:1 eV = 1.6 × 10-19 J Larger units: 1 MeV = 106 eV = 1.6 × 10-13 J, and 1 GeV = 109 eV = 1.6 × 10-10 J. Modern accelerators reach GeV and even TeV energies.At these energies, particles move at a significant fraction of the speed of light and relativistic effects must be considered. The equations Ek = ½mv2 and p = mv no longer hold. As more energy is supplied, a particle's speed gets closer to c but never reaches it; its energy and momentum keep increasing even though its speed hardly changes.A useful test: relativistic effects matter when the kinetic energy is comparable to or bigger than the particle's rest energy (0.511 MeV for an electron, 938 MeV for a proton).Relativity also affects unstable particles. A fast-moving unstable particle is observed to have a longer lifetime than when it is at rest, so it travels further before decaying. For example, muons made high in the atmosphere by cosmic rays reach the Earth's surface, which would be impossible without this effect.Worked example: an electron has 2.0 GeV of kinetic energy.
E = 2.0 × 109 × 1.6 × 10-19 = 3.2 × 10-10 J.
This is thousands of times its rest energy of 0.511 MeV, so it must be treated relativistically: ½mv2 would give a speed far greater than c.
E = 2.0 × 109 × 1.6 × 10-19 = 3.2 × 10-10 J.
This is thousands of times its rest energy of 0.511 MeV, so it must be treated relativistically: ½mv2 would give a speed far greater than c.