Answer
$r = 1.59\times 10^{-2}~m$
Work Step by Step
We can find $\gamma$:
$K = (\gamma-1)~mc^2 = 10.0~MeV$
$\gamma-1 = \frac{10.0~MeV}{mc^2}$
$\gamma = 1+\frac{10.0~MeV}{0.511~MeV}$
$\gamma = 20.57$
We can find $\beta$:
$\gamma = \frac{1}{\sqrt{1-\beta^2}}$
$1-\beta^2 = \frac{1}{\gamma^2}$
$\beta^2 = 1-\frac{1}{\gamma^2}$
$\beta = \sqrt{1-\frac{1}{\gamma^2}}$
$\beta = \sqrt{1-\frac{1}{(20.57)^2}}$
$\beta = 0.9988$
We can find the radius:
$r = \frac{\gamma ~mv}{\vert q \vert B}$
$r = \frac{(20.57)(9.109\times 10^{-31}~kg)(0.9988)(3.0\times 10^8~m/s)}{(1.6\times 10^{-19}~C)(2.20~T)}$
$r = 1.59\times 10^{-2}~m$
