The number of carbon atoms per unit cell of diamond unit cell is

Options

A. 1
B. 4
C. 8
D. 12

Explanation

To determine the number of carbon atoms per unit cell in a diamond unit cell, we can follow these steps:

### Step 1: Understand the Structure of Diamond
Diamond has a face-centered cubic (FCC) structure with additional carbon atoms located in the tetrahedral voids.

### Step 2: Count the Atoms at the Corners
In a cubic unit cell, there are 8 corners. Each corner atom contributes \( \frac{1}{8} \) of its volume to the unit cell. Therefore, the contribution from the corner atoms is:
\[ \text{Contribution from corners} = 8 \times \frac{1}{8} = 1 \text{ atom} \]

### Step 3: Count the Atoms at the Face Centers
In the diamond structure, there are 6 face centers, and each face-centered atom contributes \( \frac{1}{2} \) of its volume to the unit cell. Thus, the contribution from the face-centered atoms is:
\[ \text{Contribution from face centers} = 6 \times \frac{1}{2} = 3 \text{ atoms} \]

### Step 4: Count the Atoms in the Tetrahedral Voids
In the diamond structure, there are 8 tetrahedral voids in the FCC unit cell, but only half of them (4) are occupied by carbon atoms in the diamond structure. Each of these contributes 1 atom:
\[ \text{Contribution from tetrahedral voids} = 4 \text{ atoms} \]

### Step 5: Calculate the Total Number of Carbon Atoms
Now, we can add the contributions from all the sources:
\[ \text{Total number of carbon atoms} = \text{Contribution from corners} + \text{Contribution from face centers} + \text{Contribution from tetrahedral voids} \]
\[ \text{Total number of carbon atoms} = 1 + 3 + 4 = 8 \text{ atoms} \]

### Conclusion
The number of carbon atoms per unit cell of diamond is **8**.