Number of atoms per unit cell in fcc and bcc unit cells are 4 and 2 respectively. Given statement wrong or right?

Answer

To determine whether the statement regarding the number of atoms per unit cell in face-centered cubic (FCC) and body-centered cubic (BCC) unit cells is correct, we will analyze the contributions of atoms in each type of unit cell.

### Step-by-Step Solution:

1. **Understanding FCC (Face-Centered Cubic) Structure**:
- In an FCC unit cell, there are atoms located at each of the corners and at the centers of each face.
- **Corner Atoms**: There are 8 corner atoms in the FCC unit cell. Each corner atom is shared by 8 adjacent unit cells, contributing \( \frac{1}{8} \) of an atom to the unit cell.
- Contribution from corner atoms:
\[ 8 \text{ corners} \times \frac{1}{8} = 1 \text{ atom} \]
- **Face-Centered Atoms**: There are 6 face-centered atoms. Each face-centered atom is shared by 2 unit cells, contributing \( \frac{1}{2} \) of an atom to the unit cell.
- Contribution from face-centered atoms:
\[ 6 \text{ faces} \times \frac{1}{2} = 3 \text{ atoms} \]
- **Total Atoms in FCC**:
\[ \text{Total} = 1 \text{ (from corners)} + 3 \text{ (from faces)} = 4 \text{ atoms} \]

2. **Understanding BCC (Body-Centered Cubic) Structure**:
- In a BCC unit cell, there is one atom at the center of the cube and atoms at each of the corners.
- **Corner Atoms**: Again, there are 8 corner atoms, each contributing \( \frac{1}{8} \) of an atom to the unit cell.
- Contribution from corner atoms:
\[ 8 \text{ corners} \times \frac{1}{8} = 1 \text{ atom} \]
- **Body-Centered Atom**: There is 1 atom at the center of the cube, which is not shared with any other unit cell.
- Contribution from the body-centered atom:
\[ 1 \text{ atom} \]
- **Total Atoms in BCC**:
\[ \text{Total} = 1 \text{ (from corners)} + 1 \text{ (from body center)} = 2 \text{ atoms} \]

3. **Conclusion**:
- For FCC, the number of atoms per unit cell is **4**.
- For BCC, the number of atoms per unit cell is **2**.
- Therefore, the statement "the number of atoms per unit cell in FCC and BCC is 4 and 2 respectively" is **correct**.

### Final Answer:
The statement is **right**.