Step 1: Concept Overview:
The electrical conductivity of a solid is dictated by the energy gap between its valence and conduction bands, according to band theory. Metals, being good conductors, possess electrons in the conduction band.
Step 2: Detailed Explanation:
Monovalent Metals (e.g., Sodium): The valence band, which is the highest occupied band, is only half-filled. This partial filling allows it to function as a conduction band, facilitating electron movement and conduction. Band overlap is not required for conductivity.
Divalent Metals (e.g., Magnesium, Beryllium, Zinc): With two valence electrons, a simple model suggests a full valence band. Without band overlap, these would be insulators. However, their conductivity arises from the overlap between the top of the filled valence band and the bottom of the empty conduction band. This overlap provides available energy states for electron movement and thus, conduction.
Trivalent and Tetravalent Metals (e.g., Aluminum): These metals exhibit partially filled valence bands that also serve as conduction bands, enabling conductivity without the need for band overlap.
Step 3: Conclusion:
Band overlap is crucial for explaining metallic conductivity in divalent metals.