Statement-1:In a hexagonal close packing , third layer is identical to first layer.
Statement-2: In a primitive unit-cell, the third nearest neighbours of an atom located at a corner are at the other end of face-diagonal.
Statement-3: If the radius of cation is nearly equal to radius of anions, then most favourable arrangement is BCC.

Options

A. T T T
B. F F T
C. T F T
D. T T F

Answer

To analyze the statements given in the question, we will evaluate each statement one by one.

### Step-by-Step Solution:

**Statement 1: In a hexagonal close packing, the third layer is identical to the first layer.**

1. **Understanding Hexagonal Close Packing (HCP):**
- In HCP, the arrangement of atoms is such that the first layer (let's denote it as Layer A) is arranged in a hexagonal pattern.
- The second layer (Layer B) is placed in the voids of the first layer.
- The third layer (Layer C) is placed directly above the first layer.

2. **Identifying Layers:**
- The first layer (A) has atoms arranged in a hexagonal shape.
- The second layer (B) fits into the voids of Layer A.
- The third layer (C) is aligned directly above Layer A, meaning it has the same arrangement as Layer A.

3. **Conclusion:**
- Since the third layer is directly above the first layer and has the same orientation, Statement 1 is **True**.

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**Statement 2: In a primitive unit cell, the third nearest neighbors of an atom located at a corner are at the other end of the face-diagonal.**

1. **Understanding Primitive Unit Cell:**
- In a primitive unit cell, consider an atom located at one of the corners.
- The nearest neighbors (1st nearest) are located at the adjacent corners of the unit cell.

2. **Identifying Neighbors:**
- The second nearest neighbors are located at the face centers.
- The third nearest neighbors are not at the face diagonal but rather at the body diagonal of the cube.

3. **Conclusion:**
- Since the third nearest neighbors are located at the body diagonal and not at the face diagonal, Statement 2 is **False**.

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**Statement 3: If the radius of cation is nearly equal to the radius of anion, then the most favorable arrangement is BCC.**

1. **Understanding Ionic Radii:**
- When the radius of cation (r+) is nearly equal to the radius of anion (r-), the radius ratio (r+/r-) approaches 1.
- The coordination number for a radius ratio of approximately 1 is typically associated with a body-centered cubic (BCC) structure.

2. **Conclusion:**
- Since the radius ratio being nearly equal to 1 suggests a BCC arrangement, Statement 3 is **True**.

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### Final Conclusion:
- Statement 1: True
- Statement 2: False
- Statement 3: True

Thus, the overall evaluation is **True, False, True**.

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