As far as my understanding of solid state physics goes, I can't see a clear connection between binding energy and band gap. But our teacher asked us the question as an assignment but i really can't move ahead with anything on this.
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$\begingroup$ Note that the binding energy depends on what the pieces are that are bound together. Do you mean the binding energy of a single electron to the solid minus one electron? Or do you consider an electron free if it is in the conduction band? $\endgroup$ – my2cts Dec 2 '18 at 12:44
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$\begingroup$ B.E. of a single electron to the solid minus one. $\endgroup$ – Soban Bakhtiyar Dec 2 '18 at 12:46
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$\begingroup$ Assignment, so I will only give pointers. Look at the tight-binding approximation, look up books by Walter Harrison. $\endgroup$ – Pieter Dec 2 '18 at 16:11
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Insulators and semiconductors have a band gap. It takes at least this energy to free an electron from a binding valence orbital. In a metal valence electrons are already mobile. To remove an electron altogether from the solid requires an addition energy, the work function. Both quantities are hard to calculate.
