If `'Z'` is the number of atoms in the unit cell that represents the closet packing sequence……`ABCABC`….. The number of tetrahedral voids in the unit cell is equal

Options

A. n
B. n/2
C. n/4
D. 2n

Explanation

To solve the question regarding the number of tetrahedral voids in a unit cell that represents the closest packing sequence (ABCABC), we will follow these steps:

### Step-by-Step Solution:

1. **Understanding the Closest Packing Arrangement**:
- The closest packing arrangement in three dimensions is known as cubic close packing (CCP), which follows the ABCABC sequence. In this arrangement, the atoms are packed tightly together.

2. **Determining the Number of Atoms in the Unit Cell (Z)**:
- In a cubic close-packed structure, the number of atoms per unit cell (Z) can be calculated. For a cubic unit cell, there are atoms located at the corners and the face centers.
- The formula for calculating the number of atoms in the unit cell is:
\[ Z = \text{Number of corner atoms} + \text{Number of face-centered atoms} \]
- Each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell, and there are 8 corners. The face-centered atom contributes \( 1 \) atom, and there are 6 faces.
- Therefore, the total number of atoms in the unit cell is:
\[ Z = 8 \times \frac{1}{8} + 6 \times \frac{1}{2} = 1 + 3 = 4 \]
- Thus, \( Z = 4 \).

3. **Calculating the Number of Tetrahedral Voids**:
- In a cubic close-packed structure, the number of tetrahedral voids is related to the number of atoms in the unit cell. The relationship is given by:
\[ \text{Number of tetrahedral voids} = 2 \times n \]
- Here, \( n \) represents the number of atoms in the unit cell, which we found to be \( Z = 4 \).
- Therefore, the number of tetrahedral voids is:
\[ \text{Number of tetrahedral voids} = 2 \times 4 = 8 \]

4. **Final Answer**:
- The number of tetrahedral voids in the unit cell is equal to \( 2n \), where \( n \) is the number of atoms in the unit cell. Hence, the answer is:
\[ \text{Number of tetrahedral voids} = 2Z = 8 \]