The number of atoms contained in one face -centred cubic unit cell of monoatomic substance is :

Options

A. 1
B. 2
C. 4
D. 6

Answer

To find the number of atoms contained in one face-centered cubic (FCC) unit cell of a monoatomic substance, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Structure of FCC:**
- In a face-centered cubic unit cell, atoms are located at each of the eight corners of the cube and at the center of each of the six faces.

2. **Contribution of Corner Atoms:**
- Each corner atom is shared among eight adjacent unit cells. Therefore, the contribution of one corner atom to the unit cell is:
\[ \text{Contribution from one corner atom} = \frac{1}{8} \]
- Since there are 8 corners in a cube, the total contribution from all corner atoms is:
\[ \text{Total contribution from corners} = 8 \times \frac{1}{8} = 1 \]

3. **Contribution of Face Atoms:**
- Each face atom is shared between two adjacent unit cells. Therefore, the contribution of one face atom to the unit cell is:
\[ \text{Contribution from one face atom} = \frac{1}{2} \]
- Since there are 6 faces in a cube, the total contribution from all face atoms is:
\[ \text{Total contribution from faces} = 6 \times \frac{1}{2} = 3 \]

4. **Calculating the Total Number of Atoms:**
- Now, we can calculate the total number of atoms (Z) in the FCC unit cell by adding the contributions from the corners and faces:
\[ Z = \text{Total contribution from corners} + \text{Total contribution from faces} = 1 + 3 = 4 \]

5. **Conclusion:**
- Therefore, the number of atoms contained in one face-centered cubic unit cell of a monoatomic substance is **4**.

### Final Answer:
The number of atoms in one face-centered cubic unit cell of a monoatomic substance is **4**.

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