Question

In the LHC, protons are accelerated to a total energy of 7.40 TeV. The mass of proton is 1.673 × 10⁻²⁷ kg and Planck’s constant is 6.626 × 10⁻³⁴ J·s.

The LHC tunnel is 27.0 km in circumference. As measured by an Earth observer, how long does it take the protons to go around the tunnel once?

Answer 1

The total energy of a particle of mass m moving a speed v is given by

Squaring both sides

According to an Earth observer, the proton covered 27km distance at speed v. The time taken by the proton is

Substituting

We get

This is the same time as light would take to travel 27km distance, the reason is the speed of the proton in LHC is almost equal to the speed of light.