Foundations of solid-state physics: What is meant by a “free electron” in materials and electrical engineering contexts?

Introduction / Context:
Understanding charge carriers is essential to explain conductivity. In metals and doped semiconductors, electrons may become mobile and contribute to current. This question clarifies the term “free electron,” commonly used in band theory and conduction models.

Given Data / Assumptions:

• We are discussing electrons within solids.
• Standard definitions from basic electricity and materials science apply.
• Charge of an electron is constant and negative.

Concept / Approach:
A “free electron” is not charge-neutral or cost-related; it is an electron that is not bound to a specific atom and can move through the crystal lattice under an electric field. In metals, many valence electrons are delocalized; in semiconductors, doping and thermal energy can liberate electrons to the conduction band.

Step-by-Step Solution:
Recall electron charge: q = −1.602e−19 C; this never changes.Bound electrons remain associated with atoms and cannot conduct easily.A free electron is liberated (delocalized), able to drift through the material.Therefore, the precise definition matches an electron freed from its parent atom.

Verification / Alternative check:
In band theory, free electrons occupy the conduction band and have effective mass and mobility parameters that determine conductivity.

Why Other Options Are Wrong:
(b) Relates to cost, not physics; (c) electrons always carry negative charge; (d) no electron has “double charge” in normal circumstances.

Common Pitfalls:
Confusing “free” with “neutral,” or assuming free electrons are a different particle type. They are simply unbound/mobile electrons within the material.

Final Answer:
An electron that has been freed from its parent atom.