Answer
$E=6.69 GeV$
Work Step by Step
To find kinetic energy, the value of gamma must be known. Do this by using a known value of $\beta=0.990$ to get a gamma value of $$\gamma=\frac{1}{\sqrt{1-\beta^2}}=\frac{1}{\sqrt{1-.990^2}}=7.09$$ Substitute this value into the kinetic energy equation $$K=\gamma mc^2$$ along with $m=1.67 \times 10^{-27}kg$ to get a kinetic energy of $$E=(7.09)(1.67 \times 10^{-27}kg)(3.00\times 10^8m/s)^2$$ $$E=1.07\times 10^{-9}J$$ Converting joules to GeV yields $$1.07 \times 10^{-9}J \times \frac{1.00GeV}{1.60\times 10^{-10}J}=6.69 GeV$$
