Effect of impurity alloying on metallic resistivity — Cu added to Ni A small amount of copper is added to a nickel conductor. Which statement best describes the change in resistivity and why?

Introduction / Context:
Alloying modifies electron scattering in metals. Even small amounts of substitutional impurities introduce lattice disorder, which affects the electrical resistivity. This question focuses on how adding copper to nickel influences low-temperature (residual) resistivity and the general behavior explained by Matthiessen’s rule.

Given Data / Assumptions:

• Dilute substitutional alloy: Cu atoms replace some Ni sites.
• Phonon spectrum and carrier density remain broadly similar for small additions.
• We distinguish residual resistivity (impurity-limited, low T) from temperature-dependent phonon scattering.

Concept / Approach:
Matthiessen’s rule states that total resistivity ρ(T) ≈ ρ_residual + ρ_phonon(T). Impurity atoms break translational symmetry and act as scattering centers even at T → 0, giving a finite ρ_residual. Therefore, adding Cu increases ρ_residual. At ordinary temperatures, total resistivity typically increases as well because the added residual term adds to the phonon term.

Step-by-Step Solution:
Introduce impurities → enhanced electron scattering independent of temperature.This raises ρ_residual (T → 0 limit).Therefore, compared with pure Ni, Ni-Cu alloy exhibits higher resistivity, with the clearest signature at low temperature.

Verification / Alternative check:
Experimental curves of ρ(T) for dilute Ni-Cu alloys show an upward shift of the entire ρ(T) curve and a finite intercept at T = 0 proportional to impurity concentration.

Why Other Options Are Wrong:
“Resistivity decreases” ignores defect scattering. “Remains the same” contradicts alloy scattering physics. “Thermal resistivity decreases” is unsupported. “Becomes zero” is impossible in normal metals.

Common Pitfalls:

• Assuming a purer element always conducts better; alloy disorder can dominate scattering.
• Confusing mobility changes with carrier concentration changes; small alloying mainly alters scattering, not electron count.

Final Answer:
Residual (low-temperature) resistivity increases because Cu atoms act as defect scatterers