= Solution
The <reciprocal lattice> is generated by
$$
\boxed{\mathbf b_1=\frac{2\pi}{a}\hat{\mathbf x},\qquad
\mathbf b_2=\frac{2\pi}{a}\hat{\mathbf y},\qquad
\mathbf G_{hk}=h\mathbf b_1+k\mathbf b_2.}
$$
Its points are spaced by $2\pi/a$ along both reciprocal axes. Perpendicular bisectors between the origin and its four nearest reciprocal neighbours enclose the <first Brillouin zone>,
$$
\boxed{-\frac\pi a\le k_x\le\frac\pi a,\qquad
-\frac\pi a\le k_y\le\frac\pi a.}
$$
The original drawing labels both the reciprocal-lattice spacing and the nearer zone boundaries. Its shaded disk is the occupied region for one <electron> per real-space cell.
\Image[/past-exam-of-the-chemistry-a-course-of-the-university-of-cambridge/2021/paper-2-fermi-circle.png]
{title=Original square reciprocal lattice, first Brillouin zone and half-filled spin-degenerate Fermi disk}
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