Question

The principle that explains the variation of electrical conductivity in metals and semiconductors with temperature is:

• A. Ohm's law
• B. Coulomb's law
• C. Free electron theory
• D. Band theory of solids

Hint:

Remember: metals have no gap, semiconductors have a small one. Temperature helps electrons jump the gap — that’s band theory in action!

Answer 1

The Correct Option is D

Step 1: Understand the key terms.

• Electrical conductivity refers to a material's ability to conduct electric current.
• Temperature affects how easily electrons can move in a material.
• To explain this behavior in metals and semiconductors, we need a theory that describes how electrons are arranged and how they gain energy.

Step 2: What is Band Theory?

• Band theory explains the behavior of electrons in solids by describing energy levels as bands.
• There are mainly two important bands:
  • Valence band: Occupied by electrons.
  • Conduction band: Where electrons must go to conduct electricity.
• The gap between these bands (called the band gap) determines whether a material is a conductor, semiconductor, or insulator.

Step 3: Temperature dependence.

• In metals: The conduction band is already filled with free electrons. Increasing temperature increases lattice vibrations, which scatter electrons and reduce conductivity.
• In semiconductors: The conduction band is mostly empty. As temperature increases, more electrons gain energy to jump across the band gap. So, conductivity increases.

Step 4: Why the other options are incorrect.

• (A) Ohm's law: Describes the relationship between voltage, current, and resistance — does not explain temperature effects.
• (B) Coulomb’s law: Relates to force between charged particles — not relevant here.
• (C) Free electron theory: Explains metallic conduction at basic level but cannot accurately describe semiconductors.

Thus, the principle that best explains the variation of electrical conductivity with temperature is the Band theory of solids.