Number of formula units in unit cell of MgO (rock salt), ZnS (zinc blende) and Pt (fcc) respectively

Options

A. `4, 3, 2`
B. `4, 3, 4`
C. `4, 4, 4`
D. `4, 3, 1`

Answer

To determine the number of formula units in the unit cell of MgO (rock salt), ZnS (zinc blende), and Pt (face-centered cubic), we can follow these steps:

### Step 1: MgO (Rock Salt Structure)
1. **Identify the structure**: MgO has a rock salt structure, which is similar to NaCl and has a face-centered cubic (FCC) lattice.
2. **Count the O²⁻ ions**: In the FCC lattice, O²⁻ ions are located at:
- 8 corners (each contributing 1/8) = \(8 \times \frac{1}{8} = 1\)
- 6 face centers (each contributing 1/2) = \(6 \times \frac{1}{2} = 3\)
- Total contribution from O²⁻ = \(1 + 3 = 4\)
3. **Count the Mg²⁺ ions**: Mg²⁺ ions occupy the octahedral voids:
- 1 body center = 1
- 12 edge centers (each edge is shared by 4 unit cells) = \(12 \times \frac{1}{4} = 3\)
- Total contribution from Mg²⁺ = \(1 + 3 = 4\)
4. **Total formula units in the unit cell**: Therefore, the number of formula units of MgO in the unit cell is **4**.

### Step 2: ZnS (Zinc Blende Structure)
1. **Identify the structure**: ZnS has a zinc blende structure, which also has a face-centered cubic (FCC) lattice.
2. **Count the S²⁻ ions**: In the FCC lattice, S²⁻ ions are located at:
- 8 corners (each contributing 1/8) = \(8 \times \frac{1}{8} = 1\)
- 6 face centers (each contributing 1/2) = \(6 \times \frac{1}{2} = 3\)
- Total contribution from S²⁻ = \(1 + 3 = 4\)
3. **Count the Zn²⁺ ions**: Zn²⁺ ions occupy the tetrahedral voids:
- There are 8 tetrahedral voids in an FCC lattice, but only 4 are occupied by Zn²⁺ ions.
- Total contribution from Zn²⁺ = 4
4. **Total formula units in the unit cell**: Therefore, the number of formula units of ZnS in the unit cell is **4**.

### Step 3: Pt (Face-Centered Cubic Structure)
1. **Identify the structure**: Platinum (Pt) has a face-centered cubic (FCC) structure.
2. **Count the Pt atoms**: In the FCC lattice, Pt atoms are located at:
- 8 corners (each contributing 1/8) = \(8 \times \frac{1}{8} = 1\)
- 6 face centers (each contributing 1/2) = \(6 \times \frac{1}{2} = 3\)
- Total contribution from Pt = \(1 + 3 = 4\)
3. **Total formula units in the unit cell**: Therefore, the number of formula units of Pt in the unit cell is **4**.

### Final Answer:
The number of formula units in the unit cell of MgO, ZnS, and Pt respectively is **4, 4, and 4**.

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