Past exam of the chemistry A course of the University of Cambridge / 2022 / Paper 2 / A9 / a / iii / Solution

The energy-band widths are the difference between their extrema:For the separated bands, the top of the $s$ band and bottom of the $p$ band are both at $k=\pi /a$. HenceIt is a direct band gap at the zone boundary, because both limiting states have the same wavevector. This result uses the opposite signs of the $s$ and axial-$p$ hoppings.