(a) (i) A particle of mass m and charge q is moving with a velocity $\vec{v}$ in a magnetic field $\vec{B}$ as shown in the figure. Show that it follows a helical path. Hence, obtain its frequency of revolution. (ii) In a hydrogen atom, the electron moves in an orbit of radius $2 \text{ \AA}$ making $8 \times 10^{14}$ revolutions per second. Find the magnetic moment associated with the orbital motion of the electron.