Answer
$p = 2.46~MeV/c$
Work Step by Step
We can find $\gamma$:
$K = mc^2(\gamma-1)$
$\frac{K}{mc^2} = \gamma-1$
$\gamma = \frac{K}{mc^2}+1$
$\gamma = \frac{2.00~MeV}{0.511~MeV}+1$
$\gamma = 4.914$
We can find $\beta$:
$\gamma = \frac{1}{\sqrt{1-\beta^2}}$
$\sqrt{1-\beta^2} = \frac{1}{\gamma}$
$1-\beta^2 = \frac{1}{\gamma^2}$
$\beta^2 = 1-\frac{1}{\gamma^2}$
$\beta = \sqrt{1-\frac{1}{\gamma^2}}$
$\beta = \sqrt{1-\frac{1}{4.914^2}}$
$\beta = 0.979$
We can find the momentum:
$p = \gamma mv$
$p = (\gamma)(E_0/c^2) (v)$
$p = (4.914)(511~keV/c^2) (0.979~c)$
$p = 2.46~MeV/c$
