Which of the following statements is not correct ?

Options

A. The fraction of the total volume unoccupied by the atoms in a primitive cell is 0.48
B. Molecular solids are generally volatile
C. The number of carbon atoms in a unit cell of Diamond is 4
D. The number of Bravais lattices in which a crystal can be categorized is 14.

Explanation

To determine which of the statements is not correct, we will analyze each statement provided in the question.

### Step-by-Step Solution:

1. **Understanding the First Statement:**
- The first statement claims that "the fraction of the total volume unoccupied by the items in a primitive cell is 0.48."
- In a simple cubic cell (SCC), the packing fraction is known to be 0.52. This means that 52% of the volume is occupied by the particles, and therefore, the void fraction (unoccupied volume) is 1 - 0.52 = 0.48.
- **Conclusion:** This statement is correct.

2. **Understanding the Second Statement:**
- The second statement claims that "the number of carbon atoms in a unit cell of diamond is 4."
- Diamond has a face-centered cubic (FCC) lattice structure. In an FCC unit cell, the number of atoms is calculated as 4 (1/8 from each of the 8 corners and 1/2 from each of the 6 faces).
- However, the statement suggests that the number of carbon atoms is 4, which is correct. But the explanation provided in the video indicates a misunderstanding regarding the void spaces.
- **Conclusion:** This statement is also correct.

3. **Understanding the Third Statement:**
- The third statement claims that "the number of primitive lattices in which a crystal can be categorized is 14."
- It is a well-established fact in crystallography that there are indeed 14 distinct Bravais lattices that categorize crystals based on their symmetry and structure.
- **Conclusion:** This statement is correct.

4. **Final Analysis:**
- After analyzing all three statements, we find that the second statement regarding the number of carbon atoms in a diamond unit cell has a misleading explanation. While the number of carbon atoms is indeed 4, the context provided in the video suggests a misunderstanding of the voids in the FCC structure.
- Therefore, the statement that is not correct based on the context provided is the one regarding the number of carbon atoms in diamond, as the explanation leads to confusion.

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