Which of the following statements are true about metals ?

Options

A. Valence band overlaps with conduction band
B. The gap between valence band and conduction band is negligible
C. The gap between valence band and conduction band cannot be determined
D. Valence band may remain partially filled.

Explanation

To determine which statements about metals are true, let's analyze each statement step by step.

### Step 1: Understand the concept of valence band and conduction band in metals
In metals, the valence band (the highest energy band that is filled with electrons) and the conduction band (the band where electrons can move freely and conduct electricity) have a unique relationship.

### Step 2: Analyze the statements
1. **Valence band overlaps with conduction band.**
- In metals, the valence band and conduction band do overlap. This means that electrons can easily move from the valence band to the conduction band, allowing metals to conduct electricity efficiently.
- **Conclusion:** This statement is **true**.

2. **The gap between valence band and conduction band is negligible.**
- In metals, the energy gap between the valence band and conduction band is indeed negligible or non-existent due to the overlap. This allows for easy electron movement.
- **Conclusion:** This statement is **true**.

3. **The gap between valence band and conduction band cannot be determined.**
- This statement is misleading. While the gap is very small or negligible, it can still be determined in terms of its characteristics (i.e., it is effectively zero in metals).
- **Conclusion:** This statement is **false**.

4. **Valence band may remain partially filled.**
- In metals, the valence band can indeed be partially filled, which contributes to their ability to conduct electricity.
- **Conclusion:** This statement is **true**.

### Final Evaluation of Statements
- **True Statements:** 1, 2, and 4.
- **False Statement:** 3.

### Answer
The true statements about metals are:
1. Valence band overlaps with conduction band.
2. The gap between valence band and conduction band is negligible.
4. Valence band may remain partially filled.