Answer
At such high speeds, we use the relativistic formulas for momentum and kinetic energy.
$p=1.26\times10^{-18}kg \cdot m/s$
$KE=3.63\times10^{-10}J$
Work Step by Step
The value of $\gamma$ is $\frac{1}{\sqrt{1-v^{2}/c^{2}}}=22.366$.
$$p=\gamma mv=22.366(207)(9.11\times10^{-31}kg)(0.999)(3.00\times10^8m/s)$$
$$p=1.26\times10^{-18}kg \cdot m/s$$
The relativistic kinetic energy is $(\gamma-1)mc^2$.
$$KE=(22.366-1)(207)(9.11\times10^{-31}kg)(3.00\times10^8m/s)^2$$
$$KE=3.63\times10^{-10}J$$
