Question

Electrical conductivity in metals primarily depends on

• A. Number of free electrons
• B. Atomic mass
• C. Grain size
• D. Lattice defects

Hint:

The electrical conductivity equation is \(\sigma = n e \mu_e\). While lattice defects and grain boundaries can lower the mobility (\(\mu_e\)) through electron scattering, the baseline conductivity of a metal is fundamentally determined by its high density of free conduction electrons (\(n\)).

Answer 1

The Correct Option is A

Concept: According to the classical Drude free-electron model and modern quantum solid-state physics, a metallic crystal lattice consists of an organized array of positive ion cores surrounded by a highly mobile "gas" or "sea" of delocalized valence electrons. The intrinsic electrical conductivity (\(\sigma\)) of a material is mathematically defined as: \[ \sigma = n e \mu_e \] Where:
• \(n\) is the number density of free conduction electrons per unit volume.
• \(e\) is the fundamental charge of an electron (\(1.602 \times 10^{-19} \text{ C}\)).
• \(\mu_e\) represents the electron mobility, which describes how easily electrons can move through the lattice when driven by an electric field.

Step 1: Identifying the primary factor for conductivity.
Let us analyze the terms in our conductivity equation:
• The presence of a large, dense population of free conduction electrons (\(n\)) is the fundamental requirement for metallic electrical conduction.
• Metals possess exceptionally high electrical conductivity because their valence electron shells overlap, allowing these electrons to detach easily from individual atom cores and move freely through the entire crystal lattice. Without this large population of mobile charge carriers, electrical conduction cannot occur, regardless of how clean the lattice is.

Step 2: Evaluating the influence of alternative options.

• Lattice defects Grain size: These structural features introduce internal boundaries and disorder that cause electrons to scatter, reducing electron mobility (\(\mu_e\)) and slightly lowering conductivity. However, these are secondary scattering parameters that modify conductivity rather than defining its baseline magnitude.
• Number of free electrons: This parameter determines whether a material acts as a high-performance conductor, a semiconductor, or an insulator, making it the primary factor governing electrical conductivity. Thus, metallic electrical conductivity depends primarily on the number of free electrons, matching option (A).