In diamond, the coordination number of carbon is:

Options

A. four and its unit cell has eight carbon atoms
B. four and its unit cell has six carbon atoms
C. six and its unit cell has four carbon atoms
D. four and its unit cell has four carbon atoms

Answer

To determine the coordination number of carbon in diamond, we can follow these steps:

### Step 1: Understand the Definition of Coordination Number
The coordination number of an atom in a crystal structure is defined as the number of nearest neighboring atoms surrounding that atom.

**Hint:** Recall that the coordination number is related to how many atoms are directly adjacent to a given atom in a crystal lattice.

### Step 2: Analyze the Structure of Diamond
Diamond has a unique structure where each carbon atom is tetrahedrally coordinated. In diamond, the carbon atoms are arranged in a three-dimensional network.

**Hint:** Think about how the arrangement of atoms in a tetrahedral shape influences the number of nearest neighbors.

### Step 3: Identify the Lattice Type
Diamond is formed from two interpenetrating face-centered cubic (FCC) lattices. In this structure, there are a total of 8 carbon atoms in the unit cell.

**Hint:** Remember that FCC lattices have atoms at the corners and the centers of the faces.

### Step 4: Determine the Position of Carbon Atoms
In diamond, 4 of the carbon atoms form the FCC lattice, while the other 4 occupy half of the tetrahedral voids created by the arrangement of the first 4 atoms.

**Hint:** Visualize the tetrahedral voids and how many atoms surround a single atom in these voids.

### Step 5: Calculate the Coordination Number
Each carbon atom that occupies a tetrahedral void is surrounded by 4 other carbon atoms. Therefore, the coordination number of carbon in diamond is 4.

**Hint:** Consider how many neighboring atoms are in contact with the carbon atom in the tetrahedral void.

### Final Answer
The coordination number of carbon in diamond is **4**.

### Summary of Steps:
1. Define coordination number.
2. Analyze diamond's structure.
3. Identify the lattice type (FCC).
4. Determine the position of carbon atoms.
5. Calculate the coordination number based on neighboring atoms.