Answer
$T = \frac{2\pi~\gamma~m}{\vert q \vert ~B}$
Work Step by Step
$r = \frac{\gamma~m~v}{\vert q \vert ~B}$
We can find an expression for the period:
$T = \frac{2\pi~r}{v}$
$T = \frac{(2\pi)~\frac{\gamma~m~v}{\vert q \vert ~B}}{v}$
$T = \frac{2\pi~\gamma~m}{\vert q \vert ~B}$
