$($b$)$ The first Brillouin zone of a two dimensional rectangular lattice is shown in Figure $1.$

Figure $1$: First Brillouin zone of a rectangular lattice.

i$.$ Give the relationship between the kinetic energy and wavevector $k$ for a free electron.

$[1]$

ii$.$ Show that the kinetic energy of a free electron at a corner of the first Brillouin zone $($point M in Figure $1)$ is higher by a factor of $3\mathrm{.}25$ than that of an electron at the midpoint of a side face of the zone $($point X$),$ where $a=\frac{3b}{2}$