Question

A proton and an antiproton collide head-on, with each having a kinetic energy of 7.00TeV (such as in the LHC at CERN). How much collision energy is available, taking into account the annihilation of the two masses? (Note that this is not significantly greater than the extremely relativistic kinetic energy.)

Short answer

The total collision energy of the annihilation of the two masses is \(14\;{\rm{TeV}}\).

Step-by-step solution

Definition of Energy

Law of conservation of energy states that the energy content of the universe remains constant. Energy can neither be created nor destroyed, it just changes its form from one to another.

Finding required energy

The total energy of the particle is the sum of the kinetic energy and the rest energy, mc². Thecollision energy,

\({\rm{E}}\)=\({\rm{2}}\left( {{\rm{K}}{\rm{.E + m}}{{\rm{c}}^{\rm{2}}}} \right)\)

\(\begin{array}{}E = 2\left( {7\;{\rm{TeV}} + \left( {9.38 \times {{10}^{ - 4}}\;{\rm{TeV}}} \right)} \right)\\ = 14\;{\rm{TeV}}\end{array}\)

The total collision energy of the annihilation of the two massesis\(14\;{\rm{TeV}}\).