which of the following statements are true about metals ?
(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

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 determinted
D. Valence band may ramain partially filled

Explanation

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

### Step 1: Analyze Statement (a)
**Statement (a): Valence band overlaps with conduction band.**

In metals, the valence band and conduction band can overlap. This overlap allows electrons to move freely between the two bands, which is a characteristic property of metals. Therefore, this statement is **true**.

### Step 2: Analyze Statement (b)
**Statement (b): The gap between valence band and conduction band is negligible.**

In metals, the energy gap between the valence band and conduction band is indeed very small or negligible. This allows for easy electron transition, contributing to the electrical conductivity of metals. Thus, this statement is also **true**.

### Step 3: Analyze Statement (c)
**Statement (c): The gap between valence band and conduction band cannot be determined.**

This statement is misleading. While the gap is very small or negligible in metals, it can still be measured or determined. Therefore, this statement is **false**.

### Step 4: Analyze Statement (d)
**Statement (d): Valence band may remain partially filled.**

In metals, the valence band can indeed be partially filled with electrons. This characteristic is what allows metals to conduct electricity. Therefore, this statement is **true**.

### Conclusion
Based on the analysis:
- Statement (a) is true.
- Statement (b) is true.
- Statement (c) is false.
- Statement (d) is true.

Thus, the correct statements about metals are (a), (b), and (d).

### Final Answer
The true statements about metals are:
- (a) Valence band overlaps with conduction band.
- (b) The gap between valence band and conduction band is negligible.
- (d) Valence band may remain partially filled.