Answer
$r = 4.85~mm$
Work Step by Step
We can express the kinetic energy in units of joules:
$K = (10.0\times 10^6~eV)(\frac{1.6\times 10^{-19}~J}{1~eV}) = 1.6\times 10^{-12}~J$
We can find an expression for the speed:
$K = \frac{1}{2}mv^2$
$v^2 = \frac{2K}{m}$
$v = \sqrt{\frac{2K}{m}}$
We can find the radius according to Chapter 28:
$r = \frac{mv}{\vert q \vert B}$
$r = \frac{m\sqrt{\frac{2K}{m}}}{\vert q \vert B}$
$r = \frac{\sqrt{2Km}}{\vert q \vert B}$
$r = \frac{\sqrt{(2)(1.6\times 10^{-12}~J)(9.109\times 10^{-31}~kg)}}{(1.6\times 10^{-19}~C)(2.20~T)}$
$r = 4.85\times 10^{-3}~m$
$r = 4.85~mm$
