Answer
$K=3.12 MeV$
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 $m=9.11 \times 10^{-31}kg$ to get a kinetic energy of $$K=(7.09-1.00)(9.11 \times 10^{-31}kg)(3.00\times 10^8m/s)^2$$ $$K=4.99\times 10^{-13}J$$ Converting joules to MeV yields $$4.99 \times 10^{-13}J \times \frac{1.00GeV}{1.60\times 10^{-13}J}=3.12 MeV$$
