Explain conduction in solids in terms of the movement of free (delocalised) electrons in metallic conductors

2.3.1 Conduction in Solids

What is Conduction?

Conduction is the transfer of heat energy through a material without the material itself moving. Think of it like a line of people passing a hot cup of tea down a row of friends – the cup (heat) moves, but the friends (material) stay in place.

Free (Delocalised) Electrons in Metals

In metallic solids, some electrons are not bound to any particular atom. They roam freely through the lattice of metal ions, forming a “sea” of electrons. When one part of the metal is heated, these free electrons gain energy and start moving faster, carrying heat to cooler regions.

How Electrons Carry Heat

When a free electron collides with a metal ion, it transfers some of its kinetic energy. This energy is then passed on to the next electron in line. The process repeats, creating a chain reaction that moves heat from hot to cold.

Mathematically, the heat current density \$J_q\$ is proportional to the temperature gradient:

\$ J_q = -k \nabla T \$

where \$k\$ is the thermal conductivity of the metal.

Factors Affecting Conduction

  • Temperature: Higher temperatures give electrons more energy, increasing conduction.
  • Material: Metals with more free electrons (e.g., copper) conduct better than those with fewer (e.g., aluminium).
  • Purity: Impurities scatter electrons, reducing conduction.
  • Cross‑section: Larger cross‑section allows more electrons to flow.

Metal vs. Insulator vs. Semiconductor

Material TypeFree ElectronsConductivity
MetalManyHigh
InsulatorFewLow
SemiconductorModerate (can be increased by doping)Variable

Exam Tip: When answering questions about conduction, always mention the role of free electrons and how they transfer energy through collisions. Use the analogy of a “crowd” of electrons moving through the metal lattice.

Key Formula: Thermal conductivity \$k\$ is a property of the material and can be found in tables. Remember that higher \$k\$ means better conduction.

Fun Fact: ⚡️ Copper is the best conductor of electricity, but aluminium is often used in power cables because it’s lighter and cheaper, even though its conductivity is slightly lower.

Practical Example

When you touch a metal spoon that’s been in a hot pot, the heat travels along the spoon via free electrons, warming your hand. That’s conduction in action!

Quick Review Questions

  1. What type of electrons are responsible for heat conduction in metals?
  2. Why does increasing the temperature of a metal increase its thermal conductivity?
  3. How does impurity affect the conduction process?