The Large Hadron Collider $($LHC$)$ situated at the German Swiss border, routinely accelerates protons to $7\mathrm{.}0$ TeV $.$

a$)$ Calculate the rest energy of a proton.

b$)$ Using the relativistic expression for kinetic energy,

$K=(-1)m{c}^2$

Calculate the speeds to which the protons are accelerated.

$($Hint: You can neglect the rest energy of the proton, which is the second term in the expression for $K$ above.

$(1$ TeV $={10}^{12}eV,$ and $m_p=1\mathrm{.}67{10}^{-27}kg)$