Question

In band theory, metals have

• A. \( \text{Completely filled valence band and empty conduction band} \)
• B. \( \text{Partially filled conduction band} \)
• C. \( \text{Large band gap} \)
• D. \( \text{No electrons} \)

Hint:

Metals do not possess a band gap (\( E_g = 0 \)). Their extreme electrical conductivity is enabled by either overlapping bands or a partially filled conduction band where electrons can freely maneuver.

Answer 1

The Correct Option is B

Concept: According to the energy band theory of solids, electrical conductivity is determined by the electron configuration within the highest occupied bands and the energy gap (\( E_g \)) between them:
• Insulators/Semiconductors: Have a completely filled valence band and an empty conduction band separated by an energy gap.
• Metals (Conductors): Characterized by either a partially filled energy band (conduction band) or overlapping valence and conduction bands.

Step 1: Analyzing Metallic Band Configurations
In a metal, because the highest occupied band (the conduction band) is only partially filled, there are numerous empty, easily accessible electronic quantum states located directly above the Fermi energy level. When an external electric field is applied, electrons can easily gain kinetic energy and transition to these adjacent empty states, facilitating free charge transport.

Step 2: Eliminating Incorrect Statements
- Option (1) defines an insulator at \( 0 \text{ K} \) or a semiconductor. - Option (3) is characteristic of wide-bandgap insulators. - Option (4) is completely physically incorrect as metals contain large numbers of free conduction electrons.