which of the following statemets is not true about the hexagonal close packing ?

Options

A. the coordination number is 12
B. it has 74 % packing efficiency
C. Tetrahedral voids of the second layer are covered by the sphere of the third layer
D. in this arrangment spheres of the fouth layer are exactly alingened with those of the first layer

Explanation

To determine which statement is not true about hexagonal close packing (HCP), we need to analyze the structure and properties of HCP.

### Step-by-Step Solution:

1. **Understanding Hexagonal Close Packing (HCP)**:
- HCP is a type of crystal structure that maximizes the packing efficiency of spheres. It consists of layers of atoms arranged in a hexagonal pattern.
- The arrangement can be described as having three layers: A, B, and C, which repeat in the sequence ABC.

2. **Layer Arrangement**:
- In HCP, the first layer (A) has spheres arranged in a hexagonal pattern.
- The second layer (B) is placed such that it covers the triangular voids of the first layer.
- The third layer (C) is placed over the second layer, again covering the voids.

3. **Types of Voids**:
- In HCP, two types of voids are formed: tetrahedral voids and octahedral voids.
- Tetrahedral voids are formed when one atom is placed above the triangular voids of the first layer, while octahedral voids are formed between two layers of atoms.

4. **Coordination Number**:
- The coordination number for HCP is 12, meaning each atom is in contact with 12 other atoms.

5. **Packing Efficiency**:
- HCP has a packing efficiency of approximately 74%, which is the maximum for spheres.

6. **Identifying the False Statement**:
- Now, we need to evaluate the given statements about HCP to find the one that is not true. Common statements might include:
- HCP has a coordination number of 12.
- HCP consists of layers arranged in an ABC pattern.
- HCP has a packing efficiency of 74%.
- HCP has only tetrahedral voids and no octahedral voids.

- Among these, the last statement is false because HCP contains both tetrahedral and octahedral voids.

### Conclusion:
The statement that is not true about hexagonal close packing is that HCP has only tetrahedral voids and no octahedral voids.