Solid-state materials and band theory — match each item to its band-structure characteristic List I (Material / dopant) A. Copper (a good conductor) B. Rubber (an electrical insulator) C. Antimony doped into Si/Ge (Group V donor) D. Boron doped into Si/Ge (Group III acceptor) List II (Band-structure effect) 1. Produces a discrete energy level just above the valence band (acceptor level) 2. Produces a discrete energy level just below the conduction band (donor level) 3. Large forbidden energy gap (typical of insulators) 4. Valence and conduction bands overlap (typical of good conductors)

Introduction / Context:
This matching question tests fundamental solid-state physics as used in electronics: how intrinsic materials and dopants shape band structures and hence conductivity. Conductors, insulators, and doped semiconductors can be recognized by simple band diagrams and the placement of donor/acceptor energy levels relative to the conduction and valence bands.

Given Data / Assumptions:

• Copper represents a metallic conductor.
• Rubber represents an insulating polymer with a large band gap.
• Antimony (Sb, Group V) acts as a donor in Si/Ge.
• Boron (B, Group III) acts as an acceptor in Si/Ge.

Concept / Approach:
In metals, the valence and conduction bands overlap or a partially filled band exists, so electrons move freely. Insulators show a large forbidden gap between valence and conduction bands, limiting carrier excitation. In semiconductors, doping introduces discrete energy levels: donors (Group V) add levels just below the conduction band; acceptors (Group III) add levels just above the valence band, easing promotion of carriers with modest thermal energy.

Step-by-Step Solution:

Verification / Alternative check:
Introductory band diagrams for metals, insulators, and doped semiconductors consistently show these placements. Device physics texts use the same donor/acceptor level locations to explain n-type and p-type behavior and the ease of thermal ionization at room temperature.

Why Other Options Are Wrong:

• Assigning rubber to donor/acceptor levels confuses intrinsic insulation with doped semiconductor behavior.
• Placing “overlap” on rubber or dopants contradicts their basic roles.
• Swapping donor/acceptor positions in energy band diagrams reverses n-type vs p-type physics.

Common Pitfalls:
Mixing up “discrete level near E_c” (donor) and “near E_v” (acceptor); assuming all good conductors simply have tiny gaps rather than true band overlap; forgetting that polymers like rubber are wide-gap insulators.

Final Answer:
A-4, B-3, C-2, D-1