If the total number of atoms per unit cell is 2, the unit cell is

Options

A. primitive cubic.
B. Body centred cubic
C. face-centred cubic.
D. end face-centred.

Answer

To determine the type of unit cell based on the total number of atoms per unit cell being 2, we will analyze each type of cubic unit cell: Primitive Cubic, Body-Centered Cubic (BCC), Face-Centered Cubic (FCC), and End Face Centered.

### Step-by-Step Solution:

1. **Primitive Cubic Unit Cell**:
- In a primitive cubic unit cell, there is one atom located at each of the 8 corners of the cube.
- Contribution of each corner atom = \( \frac{1}{8} \).
- Total number of atoms per unit cell = \( 8 \times \frac{1}{8} = 1 \).
- Since we need 2 atoms per unit cell, this option is incorrect.

2. **Body-Centered Cubic (BCC) Unit Cell**:
- In a BCC unit cell, there are atoms at each of the 8 corners and one atom at the center of the cube.
- Contribution of each corner atom = \( \frac{1}{8} \) (8 corners).
- Contribution of the center atom = 1 (since it is entirely inside the unit cell).
- Total number of atoms per unit cell = \( 8 \times \frac{1}{8} + 1 = 1 + 1 = 2 \).
- This matches our requirement of 2 atoms per unit cell, so this option is correct.

3. **Face-Centered Cubic (FCC) Unit Cell**:
- In an FCC unit cell, there are atoms at each of the 8 corners and at the centers of each of the 6 faces.
- Contribution of each corner atom = \( \frac{1}{8} \) (8 corners).
- Contribution of each face atom = \( \frac{1}{2} \) (6 faces).
- Total number of atoms per unit cell = \( 8 \times \frac{1}{8} + 6 \times \frac{1}{2} = 1 + 3 = 4 \).
- Since we need 2 atoms per unit cell, this option is incorrect.

4. **End Face Centered Unit Cell**:
- In an end face centered unit cell, there are atoms at the corners and at the centers of the two end faces.
- Contribution of each corner atom = \( \frac{1}{8} \) (8 corners).
- Contribution of each face atom = \( \frac{1}{2} \) (2 faces).
- Total number of atoms per unit cell = \( 8 \times \frac{1}{8} + 2 \times \frac{1}{2} = 1 + 1 = 2 \).
- This matches our requirement of 2 atoms per unit cell, so this option is also correct.

### Conclusion:
The unit cell that has a total of 2 atoms per unit cell can be either Body-Centered Cubic (BCC) or End Face Centered. However, since BCC is the most commonly referenced structure for this condition, we can conclude:

**The unit cell is Body-Centered Cubic (BCC).**