Body -centred cubic lattice has a corrdination number of

Options

A. 4
B. 6
C. 12
D. 8

Answer

To determine the coordination number of a body-centered cubic (BCC) lattice, we can follow these steps:

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

**Hint:** Recall that the coordination number is about how many atoms are in direct contact with a central atom.

### Step 2: Visualize the BCC Structure
In a BCC lattice, there are atoms located at each of the eight corners of a cube and one atom located at the center of the cube.

**Hint:** Draw a simple cube and mark the positions of the corner atoms and the central atom to help visualize the structure.

### Step 3: Identify the Central Atom
In the BCC structure, the central atom is the one located at the body center of the cube.

**Hint:** Focus on the atom at the center and consider how many corner atoms it touches.

### Step 4: Count the Nearest Neighbors
The central atom in the BCC structure touches the corner atoms. Specifically, it touches four corner atoms directly above and below it in the cube. Additionally, each corner atom is shared among adjacent unit cells, but they still contribute to the coordination number of the central atom.

**Hint:** Remember to count all the corner atoms that are in contact with the body-centered atom.

### Step 5: Calculate the Coordination Number
For the body-centered atom, it is surrounded by 8 nearest neighbor atoms (4 from the top layer and 4 from the bottom layer). Therefore, the coordination number for the body-centered atom is 8.

**Hint:** Think about how the arrangement of atoms allows for contact with the central atom.

### Final Answer
The coordination number of a body-centered cubic lattice is **8**.

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