Select the correct statement(s) related to hexagonal close packing of identical spheres in three dimensions :

Options

A. In one unit cell there are 12 octahedral voids and all are completely inside the unit cell.
B. In one unit cell there are six octahedral voids and all are completely inside the unit cell
C. In one unit cell there are six octahedral void and of which three are completely inside the unit cell and other three are partially inside the unit cell
D. Co-ordination number of every sphere is 12 in hcp lattice.

Explanation

To solve the question regarding the hexagonal close packing (HCP) of identical spheres in three dimensions, let's analyze the statements provided and determine their correctness step by step.

### Step 1: Understand the structure of HCP
Hexagonal close packing (HCP) is a way of arranging spheres in three dimensions. In this arrangement, the spheres are packed closely together, maximizing the use of space.

### Step 2: Analyze the statements
1. **Statement A**: "In one unit cell, there are 12 octahedral voids and are all completely inside the unit cell."
- **Analysis**: This statement is incorrect. In a hexagonal close-packed structure, there are actually 6 octahedral voids per unit cell, not 12. Therefore, this statement is false.

2. **Statement B**: "In one unit cell, there are 6 octahedral voids and all are completely inside the unit cell."
- **Analysis**: This statement is correct. As mentioned, there are 6 octahedral voids in the HCP unit cell, and they are indeed completely inside the unit cell.

3. **Statement C**: "In one unit cell, there are six octahedral voids and of which three are completely inside the unit cell and the other three partial inside the unit cell."
- **Analysis**: This statement is incorrect. All 6 octahedral voids are completely inside the unit cell; there are no partial voids.

4. **Statement D**: "The coordination number of every sphere is 12 in HCP."
- **Analysis**: This statement is correct. In HCP, each sphere is surrounded by 12 other spheres, giving it a coordination number of 12.

### Conclusion
Based on the analysis:
- **Correct Statements**: B and D
- **Incorrect Statements**: A and C

### Final Answer
The correct statements related to hexagonal close packing of identical spheres in three dimensions are:
- Statement B: "In one unit cell, there are 6 octahedral voids and all are completely inside the unit cell."
- Statement D: "The coordination number of every sphere is 12 in HCP."

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