Answer
$v=0.866c$
$p=4.73\times10^{-22}kg \cdot m/s$
Work Step by Step
Use equation 26–5b.
$$KE=(\gamma-1)mc^2=mc^2$$
$$\frac{1}{\sqrt{1-v^2/c^2}}-1=1$$
$$v=c\sqrt{1-\frac{1}{(2^2)}}=0.866c$$
Find the momentum using equation 26–4.
$$p=\gamma mv$$
$$p=\frac{(9.11\times10^{-31}kg)(0.866)(3.00\times10^8m/s)}{\sqrt{1-0.866^2}}$$
$$p=4.73\times10^{-22}kg \cdot m/s$$
