Which of the following statements is not correct ?

Options

A. The number of Bravais lattices in which a crystal can be categorized is 14
B. The fraction of the total volume occupied by the atoms in a primitive cell is 0.52
C. Molecular solids are generally volatile
D. The number of carbon atoms in a unit cell of diamond is 4

Answer

To determine which statement is not correct, we need to analyze the provided statements regarding crystal lattices and molecular solids.

### Step-by-Step Solution:

1. **Identify the Statements**:
We have several statements to evaluate:
- The number of Bravais lattices is 14.
- The fraction of the total volume occupied by atoms in a primitive cell is 0.52.
- Molecular solids are generally volatile.
- The number of carbon atoms in a unit cell of diamond is 4.

2. **Evaluate Each Statement**:
- **Statement 1**: The number of Bravais lattices is 14.
- This statement is **correct**. There are indeed 14 distinct Bravais lattices in three-dimensional space.

- **Statement 2**: The fraction of the total volume occupied by atoms in a primitive cell is 0.52.
- This statement needs to be evaluated mathematically. The fraction of volume occupied in a primitive cell is calculated using the formula for the volume of a sphere and the volume of the cube. The calculation shows that the fraction of volume occupied is actually \( \frac{5}{6} \) which is approximately 0.8333, not 0.52. Therefore, this statement is **incorrect**.

- **Statement 3**: Molecular solids are generally volatile.
- This statement is **correct**. Molecular solids typically consist of molecules held together by weak intermolecular forces, making them more volatile compared to ionic or covalent solids.

- **Statement 4**: The number of carbon atoms in a unit cell of diamond is 4.
- This statement is **incorrect**. The diamond structure has 8 carbon atoms per unit cell, as each unit cell contains 4 lattice points, and each lattice point contributes 2 carbon atoms. Thus, the total is \( 4 \times 2 = 8 \).

3. **Conclusion**:
The statements that are not correct are:
- The fraction of the total volume occupied by atoms in a primitive cell is 0.52 (this is incorrect).
- The number of carbon atoms in a unit cell of diamond is 4 (this is also incorrect; it should be 8).

### Final Answer:
The statement that is not correct is: "The number of carbon atoms in a unit cell of diamond is 4."