Which of the following statement is false ?

Options

A. Two tetrahedral voids are formed on each of the four body diagonals of the cube
B. When body centre of the cube is surrounded by six atoms of face centres , an octahedral voids is formed .
C. Tetrahedral void is present at the centre of each of the 12 edges
D. The shortest distance between two octahedral a voids is `a/sqrt2` ( a is the edge length of the unit cell).

Answer

To determine which statement is false, we need to analyze each of the provided options regarding tetrahedral voids (THV) and octahedral voids (OHV) in a cubic lattice structure.

### Step-by-Step Solution:

1. **Analyze Statement 1**:
- "Two tetrahedral voids are formed on each of the four body diagonals of the cube."
- In a cubic structure, there are indeed two tetrahedral voids located along each body diagonal. Since there are four body diagonals in a cube, the total number of tetrahedral voids is \(2 \times 4 = 8\).
- **Conclusion**: This statement is **true**.

2. **Analyze Statement 2**:
- "The center of the cube is surrounded by six atoms of the face center and an octahedral void is formed."
- The center of a cube is indeed surrounded by the six face-centered atoms, which creates an octahedral void at the center of the cube.
- **Conclusion**: This statement is **true**.

3. **Analyze Statement 3**:
- "Tetrahedral void is present at the center of each of the 12 edges."
- This statement is incorrect. Tetrahedral voids are not located at the center of the edges; instead, octahedral voids are found at the center of the edges. Tetrahedral voids are located at specific positions, primarily along the body diagonals or at other defined locations within the cubic structure.
- **Conclusion**: This statement is **false**.

4. **Analyze Statement 4**:
- "The shortest distance between the two octahedral voids is A by root 2."
- The distance between two octahedral voids located at the centers of edges can be calculated using the Pythagorean theorem. If we consider two voids at the edge centers, the distance between them is indeed \(A/\sqrt{2}\).
- **Conclusion**: This statement is **true**.

### Final Conclusion:
Based on the analysis, the false statement is **Statement 3**: "Tetrahedral void is present at the center of each of the 12 edges."