Question

n the LHC, protons are accelerated to a total energy of 6.90 TeV. The mass of proton is 1.673 × 10−27 kg and Planck’s constant is 6.626 × 10−34 J·s.

1.What is the speed of these protons? ____C

2. 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?___us

3.in the reference frame of the protons, how long does it take the protons to go around the tunnel once?____ns

4. What is the de Broglie wavelength of the protons in Earth's reference frame?___m

5. How fast would a mosquito of mass 1.00 mg be moving if its kinetic energy is 6.90 TeV?______m/s

Answer 1

1) Total energy of a relativistic particle is given by

Also

Hence

2) The time taken by proton to go around the tunnel once in Earth's frame is

3) Proton in its reference frame will experience proper time, hence

4) The momentum of proton is

Hence its de Broglie wavelength is

5) First let us calculate for the mosquito

and its kinetic energy is

Since the kinetic energy is very much less than , therefore mosquito is non-relativistic, hence we can use Newtonian formula for kinetic energy