In a crystalline solid with metallic (valence) bonding, how are the outer (valence) electrons shared among atoms? Provide the best description that reflects the collective behavior of valence electrons in a typical metallic crystal.

Introduction / Context:
Understanding how valence electrons behave inside a solid distinguishes metallic, covalent, and ionic bonding. In metals (often called valence crystals in older texts), outer electrons are not confined to a single atom or a single bond. Instead, they are delocalized over the entire lattice and form an 'electron sea' that enables high electrical and thermal conductivity, ductility, and characteristic metallic luster.

Given Data / Assumptions:

• We are discussing a crystalline solid exhibiting metallic bonding.
• Atoms contribute valence electrons to a common pool.
• No external fields or extreme conditions are assumed.

Concept / Approach:

Metallic bonding arises when metal atoms donate their valence electrons to a shared conduction band. Positive ion cores (atomic nuclei plus inner electrons) are arranged in a regular lattice, while the valence electrons are free to move throughout the crystal. This delocalization explains metallic properties such as conductivity and malleability.

Step-by-Step Solution:

Verification / Alternative check:

Band theory shows that overlapping atomic orbitals form conduction bands that extend over the crystal; electrons occupy these bands and are mobile. This is incompatible with electrons being confined to specific pairs of atoms as in purely covalent bonds.

Why Other Options Are Wrong:

• Are not shared: contradicts metallic bonding.
• Shared only between neighbours: describes localized covalent bonds rather than metallic delocalization.
• Any of the above depending on temperature: temperature affects occupancy and scattering, not the fundamental bonding model.
• Tightly bound to ions only: inconsistent with conductivity of metals.

Common Pitfalls:

Confusing metallic delocalization with covalent sharing or assuming electrons remain localized at low temperature; even at low temperatures, metallic electrons remain delocalized across the lattice.

Final Answer:

Are shared by all atoms (delocalized electron sea)