Assertion–Reason: magnetic susceptibility of copper and diamagnetism Assertion (A): The magnetic susceptibility of copper is approximately −0.5 × 10^−5. Reason (R): Copper is a diamagnetic material.

Introduction / Context:Magnetic susceptibility χ indicates how a material responds to an applied magnetic field. Diamagnets develop a small magnetization opposite to the applied field, yielding negative susceptibility values. Copper is a canonical example used in basic magnetism courses.

Given Data / Assumptions:

• SI convention for volume magnetic susceptibility (dimensionless).
• Weak-field, room-temperature conditions.
• Isotropic bulk copper sample.

Concept / Approach:Diamagnetism arises from induced orbital currents that oppose the change in magnetic flux (Lenz-like behavior at the electronic level). For diamagnetic materials, χ < 0, typically with small magnitude (10^−6 to 10^−5). Copper, although a good electrical conductor, exhibits net diamagnetism after accounting for the contributions of conduction and core electrons, with χ around −10^−5.

Step-by-Step Solution:Assess Assertion: χ(Cu) ≈ −0.5 × 10^−5 → a small negative number → consistent with diamagnetism.Assess Reason: “Copper is diamagnetic” correctly describes its sign of χ.Causality: Being diamagnetic explains why the susceptibility is negative and small → R explains A.

Verification / Alternative check:Handbooks list copper’s susceptibility close to −10^−5. Sign and magnitude agree with the assertion and the rationale of diamagnetism.

Why Other Options Are Wrong:(b) claims no explanatory link, but diamagnetism directly accounts for negative χ. (c) and (d) contradict established data. (e) is incorrect because both statements are true.

Common Pitfalls:

• Confusing diamagnetism (negative χ) with paramagnetism (positive χ).
• Mixing volume and molar susceptibility units; the sign remains negative.

Final Answer:Both A and R are true and R is correct explanation of A