Metallic bonding and electron sharing In a crystalline metal, how are the valence electrons shared among atoms according to the metallic-bonding model?

Introduction / Context:
Metallic bonding explains the high electrical and thermal conductivity and malleability of metals. In this model, valence electrons are delocalized and move freely throughout the crystal, forming an “electron sea.”

Given Data / Assumptions:

• Crystalline metallic solid with overlapping atomic orbitals forming bands.
• Valence electrons are not confined to individual atoms.
• Periodic potential of the lattice leads to energy bands and mobile carriers.

Concept / Approach:
In metals, the conduction band overlaps or is partially filled, allowing electrons to move throughout the entire crystal. This delocalization means electrons are effectively shared by all atoms, not just near neighbors. The model accounts for conductivity (mobile carriers), ductility (non-directional bonding), and reflectivity (free-electron response to electromagnetic waves).

Step-by-Step Solution:
Consider band structure: partially filled band permits mobile electrons.Electron wavefunctions extend over many lattice sites → delocalization.Therefore, valence electrons are shared collectively by the entire lattice.

Verification / Alternative check:
Hall effect, specific heat, and optical reflectivity measurements support the free-electron-like behavior and collective sharing of valence electrons in metals.

Why Other Options Are Wrong:
Localization to single atoms (a) contradicts metallic conduction. Sharing only between neighbors (b) resembles covalent bonding. Option (d) incorrectly ties the bonding mode solely to temperature. Option (e) is physically incorrect.

Common Pitfalls:

• Misapplying covalent bonding concepts to metals.
• Assuming electron sharing changes fundamentally with moderate temperature changes; it does not.

Final Answer:
They are shared collectively by all atoms (delocalized electron gas)