Electrical conductivity of copper — assertion–reason Assertion (A): Copper is a good conductor of electricity. Reason (R): Copper has a face-centred cubic (FCC) crystal lattice.

Introduction / Context:
This assertion–reason problem tests conceptual understanding of why metals like copper conduct electricity well. It separates a true material fact (copper's good conductivity) from a common but incomplete rationale (crystal structure alone). The goal is to identify the real determinants of conductivity in metals.

Given Data / Assumptions:

• Copper is a metallic conductor with very high electrical conductivity at room temperature.
• Copper crystallizes in a face-centred cubic (FCC) structure.
• Standard solid-state models (Drude/Sommerfeld) apply in the low-field, near-room-temperature regime.

Concept / Approach:
Electrical conductivity σ in metals is governed primarily by mobile electron density n and their scattering (relaxation time τ) according to σ = n * e^2 * τ / m. Band structure sets how many electrons are available at the Fermi level and how they move (effective mass), while phonons, impurities, and defects control scattering. Crystal structure (FCC, BCC, HCP) can influence properties indirectly via packing, slip systems, and phonon spectra, but FCC itself is not the direct cause of copper's superior conductivity. In fact, silver (also FCC) has even higher conductivity, whereas some FCC alloys conduct far worse.

Step-by-Step Solution:
Evaluate A: Copper's room-temperature resistivity is very low (about 1.7 × 10^−8 Ω·m), so A is true.Evaluate R: Copper is FCC; that statement is factually true.Check explanation: High conductivity arises from a nearly free s-electron at the Fermi level, high carrier density, and relatively long τ (low scattering), not simply from FCC geometry; therefore R does not explain A.

Verification / Alternative check:
Silver (FCC) and aluminium (FCC) also conduct well, but pure nickel (FCC) has higher resistivity than copper. Conversely, some BCC metals (e.g., sodium at high temperature) still conduct well. Thus lattice type alone is not the determining factor.

Why Other Options Are Wrong:
(a) claims R explains A, which it does not. (c) incorrectly asserts R is false; copper is FCC. (d) wrongly negates A. (e) is incorrect since both statements are true.

Common Pitfalls:

• Confusing correlation (many good conductors happen to be FCC) with causation.
• Ignoring the role of electron scattering and electron density at the Fermi level.

Final Answer:
Both A and R are true but R is not correct explanation of A