Question

Choose the FALSE statement from the following.

• A. Generally, in conductors the valence and conducting bands overlap.
• B. The resistivity of a semiconductor increases with increase in temperature.
• C. The conductivity of a semiconductor increases with increase in temperature.
• D. Substances with energy gap of the order of $10\ \text{eV}$ are insulators.

Hint:

Options (B) and (C) are absolute logical opposites of one another. Since both talk about a semiconductor's response to a temperature increase, one of them must be false. Identifying mutually exclusive option pairs right away allows you to hone in on the right choice within seconds!

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We are given four qualitative conceptual statements regarding the energy band theory of solid materials (conductors, semiconductors, and insulators). We must evaluate each statement to identify the single incorrect (FALSE) assertion.

Step 2: Key Formula or Approach:
Recall the behavior of electrical properties under thermal variations:
For semiconductors, as absolute temperature ($T$) increases, thermal energy excites more valence electrons across the forbidden band gap into the conduction band.
This increase in charge carrier density directly elevates electrical conductivity ($\sigma$).
Since resistivity ($\rho$) is the mathematical reciprocal of conductivity ($\rho = \frac{1}{\sigma}$), resistivity must decrease as temperature goes up.

Step 3: Detailed Explanation:
Let's analyze each option systematically:
Option (A): In metallic conductors, the valence and conduction bands overlap or feature no energy gap, allowing valence electrons to drift freely into conduction spaces. This is true.
Option (B): This claims resistivity increases with temperature. However, for semiconductors, the temperature coefficient of resistance is strictly negative. Increased thermal energy lowers resistivity. Thus, this statement is false.
Option (C): This states that conductivity increases with temperature, which is the direct factual converse of Option B and perfectly true.
Option (D): A forbidden energy gap ($E_g$) on the order of $10\ \text{eV}$ is exceptionally wide, making it nearly impossible for thermal excitation to lift electrons to the conduction zone. Such materials are ideal insulators. This is true.

Step 4: Final Answer:
The false statement is option (B).