A stationary particle decays into two particles and , which move off with equal but oppositely directed momenta. We have to show that the kinetic energy of is given by

where , and are masses and are the corresponding rest energies.

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Let the magnitude of momentum of the final particles be p. From conservation of energy, we note that the sum of relativistic energies of the final particles and has to be equal to the rest mass energy of the initial particle .

We thus have the equation

.

Or,

We square the above equation and carry out algebraic simplifications. We get

The kinetic energy of the particle will therefore be given by