Question

When an electron and positron collide at the SLAC facility, they each have 50.0GeV kinetic energies. What is the total collision energy available, taking into account the annihilation energy? Note that the annihilation energy is insignificant, because the electrons are highly relativistic.

Short answer

The total collision energy available, taking into account the annihilation energyis 100 GeV.

Step-by-step solution

Definition of Energy

Energy of a particle by virtue of its motion is known as kinetic energy. If the particle is moving at relativistic speeds, then relativistic correction should also be considered to get the accurate value of kinetic energy.

Finding required energy

The total energy of the particle is the sum of the kinetic energy and the rest energy, mc². So, the collision energy, E, equals \({\rm{2}}\left( {{\rm{K}}{\rm{.E + m}}{{\rm{c}}^{\rm{2}}}} \right)\)

\(\begin{align}{}E &= 2\left( {\left( {50\;{\rm{GeV}}} \right) + \left( {5.11 \times {{10}^{ - 4}}\;{\rm{GeV}}} \right)} \right)\\ &= 100\;{\rm{GeV}}\end{align}\)

The total collision energy available, taking into account the annihilation energy is 100 GeV.