Question

Because of energy loss due to synchrotron radiation in the LHC at CERN, only 5.00 MeV is added to the energy of each proton during each revolution around the main ring. How many revolutions are needed to produce 7.00 TeV (7000 GeV) protons, if they are injected with an initial energy of 8.00 GeV?

Short answer

The total number of revolutions required is\(1.39 \times {10^6}{\rm{ revolutions}}\).

Step-by-step solution

Definition of Energy

Particle accelerators are huge machines that are used to accelerate the elementary particles to relativistic speeds and then collide them in the collision chamber. Due to the collision at very high speeds the elementary particles break into several fundamental particles, whose path data is recorded in the chamber.

Finding required revolutions

Total energy of the proton is given as-

\(8\;{\rm{GeV}} + N\left( {5 \times {{10}^{ - 3}}\;{\rm{GeV}}} \right) = 7000\;{\rm{GeV}}\)

solving the above equation for\({\rm{N}}\)we will get the number of revolutions as:

\(\begin{align}{}N &= \frac{{7000\;{\rm{GeV}} - 8\;{\rm{GeV}}}}{{5 \times {{10}^{ - 3}}\;{\rm{GeV }}}}\\& = 1.39 \times {10^6}{\rm{ revolutions}}\end{align}\)

The total number of revolutions required is\(1.39 \times {10^6}{\rm{ revolutions}}\).