Show for a two dimensional rectangular lattice that the kinetic energy of a free electron at a corner of the first Brillouin zone $($point $M$ in Figure below$)$ is higher by a factor of $1\mathrm{.}25$ than that of an electron at the midpoint of a side face of the zone $($point $x),$ where $a=2b.$

First Brillouin zone of a rectangular lattice.

Sketch using the empty lattice approximation the lowest energy band structure of the rectangular lattice relation for $($:$G_{hk}=0\}$ along $xM.$ Use information obtained above.