Assertion:Face centred cubic cell has 4 atoms per unit cell.
Reason:In fcc unit cell , there are 8 atoms at the corners and 6 atoms at face centres .

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false
D. If both assertion and reason are false

Answer

To solve the question regarding the face-centered cubic (FCC) unit cell, we will analyze both the assertion and the reason step by step.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that a face-centered cubic (FCC) cell has 4 atoms per unit cell.

2. **Understanding the Reason**:
- The reason provided states that in an FCC unit cell, there are 8 atoms at the corners and 6 atoms at the face centers.

3. **Counting Atoms in FCC**:
- In an FCC unit cell, there are 8 corner atoms. Each corner atom is shared by 8 adjacent unit cells, so the contribution of each corner atom to the unit cell is \( \frac{1}{8} \).
- Therefore, the total contribution from the 8 corner atoms is:
\[ 8 \times \frac{1}{8} = 1 \text{ atom} \]

4. **Counting Face Center Atoms**:
- In addition to the corner atoms, there are 6 face-centered atoms in an FCC unit cell. Each face-centered atom is shared by 2 unit cells, so the contribution of each face-centered atom is \( \frac{1}{2} \).
- Therefore, the total contribution from the 6 face-centered atoms is:
\[ 6 \times \frac{1}{2} = 3 \text{ atoms} \]

5. **Calculating Total Atoms**:
- Now, we add the contributions from the corner atoms and the face-centered atoms:
\[ 1 \text{ (from corners)} + 3 \text{ (from faces)} = 4 \text{ atoms} \]

6. **Conclusion**:
- Since we have determined that there are indeed 4 atoms per FCC unit cell, the assertion is true.
- The reason is also true as it correctly describes the arrangement of atoms in the FCC unit cell.

7. **Final Answer**:
- Both the assertion and the reason are true, and the reason correctly explains the assertion. Therefore, the correct option is that both the assertion and reason are true, and the reason is the correct explanation of the assertion.