Alloy scattering and resistivity change — adding a small percentage of Cu to Ni Copper has lower resistivity than nickel. When a small percentage of Cu is alloyed into Ni, how does the resistivity of the resulting Ni–Cu alloy change and why?

Introduction / Context:Electrical resistivity in metals is governed by scattering of conduction electrons from phonons, impurities, and lattice defects. Alloying even small amounts of a second element modifies scattering and therefore resistivity. Understanding this is central to materials engineering and the design of resistive alloys.

Given Data / Assumptions:

• Base metal: nickel; solute: copper (small percentage).
• Crystal lattice remains metallic and substitutional.
• No phase transformation is assumed for dilute additions.

Concept / Approach:Matthiessen’s rule states ρ(T) ≈ ρ_residual + ρ_phonon(T). Impurity atoms (Cu in Ni) create local potential variations and strain fields that scatter electrons, increasing ρ_residual. Even though pure Cu has lower resistivity than pure Ni, adding Cu to Ni breaks lattice periodicity and increases total resistivity of the alloy compared with pure Ni.

Step-by-Step Solution:Introduce impurity → new scattering centers.Residual resistivity rises even at low temperature (phonon contribution minimal).Total resistivity therefore increases across the temperature range relative to pure Ni.

Verification / Alternative check:Empirical ρ–composition curves for Ni–Cu alloys show monotonic increases in ρ with solute content in the dilute regime, consistent with alloy scattering theories.

Why Other Options Are Wrong:

• Decrease: contradicts alloy-scattering physics.
• No trend or no change: inconsistent with well-established data.
• Zero resistivity at room temperature: impossible for ordinary alloys; superconductivity requires cryogenic conditions and specific compounds.

Common Pitfalls:

• Equating base-metal conductivity with alloy behavior; disorder dominates.
• Ignoring that impurity scattering is temperature-independent and persists at low T.

Final Answer:It increases due to impurity (defect) scattering of electrons