Metals – order of magnitude of electrical conductivity (units: Ω⁻¹·m⁻¹) What is the typical order of magnitude for the electrical conductivity of common metals (e.g., copper, aluminum) expressed in Ω⁻¹·m⁻¹ at room temperature?

Introduction / Context:
Electrical conductivity quantifies how readily a material allows electric current to pass. Metals are among the best conductors due to their high density of free electrons. This question tests recognition of the correct order of magnitude for metallic conductivity in SI units (Ω⁻¹·m⁻¹, also written S/m).

Given Data / Assumptions:

• Room temperature conditions (around 20–25 °C).
• Common, commercially pure metals such as copper and aluminum.
• Macroscopic, bulk samples (no nanostructure or extreme purity effects).

Concept / Approach:

For metals, conductivity sigma is the reciprocal of resistivity rho. Typical metallic resistivities lie near 10^-8 Ω·m (copper ~1.7×10^-8 Ω·m; aluminum ~2.8×10^-8 Ω·m). Therefore sigma ≈ 1 / (a few ×10^-8) ≈ a few ×10^7 Ω⁻¹·m⁻¹. Orders of magnitude capture the scale rather than precise values, so 10^7 Ω⁻¹·m⁻¹ is the correct benchmark for “good” metals at room temperature.

Step-by-Step Solution:

Verification / Alternative check:

Aluminum provides a cross-check: rho_al ≈ 2.8×10^-8 Ω·m → sigma ≈ 3.6×10^7 Ω⁻¹·m⁻¹, consistent with the same order of magnitude.

Why Other Options Are Wrong:

10^5 is two orders too low (would be poor semimetal). 10^-4 and 10^-6 are absurdly small conductivities (insulating regime). 10^10 is too high even for ultrapure cryogenic metals at room temperature it is unrealistic.

Common Pitfalls:

Confusing resistivity and conductivity units or mixing cgs and SI. Also, forgetting that order-of-magnitude answers ignore precise material-to-material variation but keep the correct power of ten.

Final Answer:

10^7