What is the number of atoms per unit cell in a body centred cubic structure ?

Options

A. 9
B. 4
C. 2
D. 1

Answer

To determine the number of atoms per unit cell in a body-centered cubic (BCC) structure, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Structure**: In a body-centered cubic (BCC) structure, there are atoms located at the corners of the cube and one atom at the center of the cube.

2. **Count the Corner Atoms**: There are 8 corners in a cube, and each corner atom is shared by 8 adjacent unit cells. Therefore, the contribution of each corner atom to the unit cell is:
\[ \text{Contribution of each corner atom} = \frac{1}{8} \]
Since there are 8 corner atoms, the total contribution from the corner atoms is:
\[ \text{Total contribution from corner atoms} = 8 \times \frac{1}{8} = 1 \]

3. **Count the Body-Centered Atom**: There is 1 atom located at the center of the cube. This atom is entirely within the unit cell, so its contribution is:
\[ \text{Contribution of body-centered atom} = 1 \]

4. **Calculate Total Atoms per Unit Cell**: Now, we can sum the contributions from the corner atoms and the body-centered atom to find the total number of atoms per unit cell:
\[ \text{Total atoms per unit cell} = \text{Contribution from corner atoms} + \text{Contribution from body-centered atom} = 1 + 1 = 2 \]

5. **Final Answer**: Therefore, the number of atoms per unit cell in a body-centered cubic structure is:
\[ \boxed{2} \]