You will need a calculator with lots of digits for some parts of this problem. At the Large Hadron Collider at the CERN laboratory in Geneva, Switzerland, protons (with mass of 0.938 GeV/c²) moving in opposite directions are accelerated to energies of 6.5 TeV and then smashed into each other.

1. What is the relativistic factor for these protons?
2. the protons are grouped in moving bunches (each with about 1011 protons) of length in the lab of about 10 cm. How long in cm is a bunch in the rest frame of a proton in the bunch?
3. What would the velocity be in m/s of these largest possible mass particles if created in such a collision?