Which of the following is correctly matched ?

Options

A. In HCP unit cell - No of effective atoms =6
B. In ABC ABC type packing - No of effective atoms =12
C. In FCC unit cell - No of effective atoms =12
D. In primitive unit cell - No of effective atoms =1

Answer

To determine which of the statements regarding the number of effective atoms in different types of unit cells is correctly matched, we will analyze each statement step by step.

### Step 1: Analyze HCP Unit Cell
- **Statement**: In HCP unit cell, the number of effective atoms is 6.
- **Explanation**: The Hexagonal Close Packing (HCP) structure has 6 effective atoms per unit cell. This is a well-established fact in solid-state chemistry.
- **Conclusion**: This statement is **true**.

### Step 2: Analyze ABC-ABC Type Packing
- **Statement**: In ABC-ABC type packing, the number of effective atoms is 12.
- **Explanation**: The ABC-ABC type packing refers to Cubic Close Packing (CCP), which is also known as Face-Centered Cubic (FCC). For FCC, the number of effective atoms (Z) is 4, not 12.
- **Conclusion**: This statement is **false**.

### Step 3: Analyze FCC Unit Cell
- **Statement**: In FCC unit cell, the number of effective atoms is 12.
- **Explanation**: As mentioned earlier, the FCC structure has 4 effective atoms per unit cell, not 12.
- **Conclusion**: This statement is **false**.

### Step 4: Analyze Primitive Unit Cell
- **Statement**: In primitive unit cells, the number of effective atoms is 1.
- **Explanation**: A primitive unit cell contains atoms only at the corners. There are 8 corners in a cube, and each corner atom contributes 1/8 to the unit cell. Therefore, the total contribution is \(8 \times \frac{1}{8} = 1\).
- **Conclusion**: This statement is **true**.

### Final Conclusion
- The correctly matched statements are:
1. In HCP unit cell, the number of effective atoms is 6 (True).
2. In primitive unit cells, the number of effective atoms is 1 (True).

Thus, the correct answers are the first and fourth statements.