Question

Pick out the correct statement from the following:

• A. The maximum energy required to shift an electron from the conduction band to valence band is called the energy band gap
• B. In a semiconductor, no free electrons are found in the conduction band at $0\text{ K}$
• C. The number density of free electrons in the valence band decides the strength of the electric current
• D. Valence band is always completely filled, while conduction band is always partially filled

Hint:

Remember that absolute zero ($0\text{ K}$) means zero thermal movement. Without any heat energy to liberate electrons from their atomic bonds, the conduction band remains entirely empty, causing the semiconductor to act as a perfect insulator.

Answer 1

The Correct Option is B

Concept: Solid-state materials are classified electrically based on energy band theory definitions.
• The valence band contains lower-energy bound state electrons, while the conduction band contains high-energy states where electrons can migrate freely to conduct current.
• At absolute zero temperature ($0\text{ K}$), electrons do not possess any thermal kinetic energy to break out of covalent atomic bounds.

Step 1: Evaluate each statement critically.

• Statement (A) is incorrect: The band gap measures the minimum energy needed to shift an electron from the lower valence band up into the conduction band.
• Statement (B) is correct: At $0\text{ K}$, a semiconductor behaves as a perfect electrical insulator. Because thermal excitation energy is entirely absent, every single valence electron remains bound, leaving the conduction band completely empty.
• Statement (C) is incorrect: The electrical current capacity is determined by the number density of free electrons active within the conduction band, not bound states.
• Statement (D) is incorrect: In insulators or semiconductors at low temperatures, the conduction band can be completely empty.