Answer
$K=5.72GeV$
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 $$K=(\gamma-1)mc^2$$ along with $m=1.67 \times 10^{-27}kg$ to get a kinetic energy of $$K=(7.09-1.00)(1.67 \times 10^{-27}kg)(3.00\times 10^8m/s)^2$$ $$K=9.15\times 10^{-10}J$$ Converting joules to GeV yields $$9.15 \times 10^{-10}J \times \frac{1.00GeV}{1.60\times 10^{-10}J}=5.72 GeV$$
