Relativistic EnergyThe famous Einstein relationship for energy includes both the kinetic energy and rest mass energy for a particle. The kinetic energy of a high speed particle can be calculated from The relativistic energy of a particle can also be expressed in terms of its momentum in the expression
The relativistic energy expression is the tool used to calculate binding energies of nuclei and the energy yields of nuclear fission and fusion. 
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Rest Mass EnergyThe Einstein equation includes both the kinetic energy of a particle and the energy it has as a result of its mass. If the particle is at rest, then the energy is expressed as which is sometimes called its rest mass energy.

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Conservation of EnergyThe relativistic energy expression is a statement about the energy an object contains as a result of its mass and is not to be construed as an exception to the principle of conservation of energy. Energy can exist in many forms, and mass energy can be considered to be one of those forms.

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Pair ProductionEvery known particle has an antiparticle; if they encounter one another, they will annihilate with the production of two gammarays. The quantum energies of the gamma rays is equal to the sum of the mass energies of the two particles (including their kinetic energies). It is also possible for a photon to give up its quantum energy to the formation of a particleantiparticle pair in its interaction with matter. The rest mass energy of an electron is 0.511 MeV, so the threshold for electronpositron pair production is 1.02 MeV. For xray and gammaray energies well above 1 MeV, this pair production becomes one of the most important kinds of interactions with matter. At even higher energies, many types of particleantiparticle pairs are produced. 
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Relativistic Kinetic EnergyThe relativistic energy expression includes both rest mass energy and the kinetic energy of motion. The kinetic energy is then given by This is essentially defining the kinetic energy of a particle as the excess of the particle energy over its rest mass energy. For low velocities this expression approaches the nonrelativistic kinetic energy expression.

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Kinetic Energy for v/c<<1The relativistic kinetic energy expression can be written asand the square root expression then expanded by use of the binomial theorem : giving Substituting gives: 
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