The largest void is

Options

A. Octahedral void
B. Tetrahedral void
C. Triangular void
D. All have similar radius

Answer

To determine which void is the largest among octahedral voids, tetrahedral voids, and triangular voids, we need to calculate the radius of each type of void in relation to the radius of the anion (denoted as R) and the radius of the cation (denoted as r).

### Step-by-Step Solution:

1. **Understanding the Types of Voids**:
- **Octahedral Void**: Formed when an atom is located at the center of an octahedron formed by six surrounding atoms.
- **Tetrahedral Void**: Formed when an atom is located at the center of a tetrahedron formed by four surrounding atoms.
- **Triangular Void**: Formed by three atoms at the corners of an equilateral triangle.

2. **Calculating the Radius of the Octahedral Void**:
- In an octahedral void, the radius of the void (r) can be derived from the geometry of the arrangement.
- The radius of the octahedral void is given by the formula:
\[ r = 0.414R \]

3. **Calculating the Radius of the Tetrahedral Void**:
- In a tetrahedral arrangement, the radius of the void is calculated using the angle bisector and trigonometric relationships.
- The radius of the tetrahedral void is given by the formula:
\[ r = 0.225R \]

4. **Calculating the Radius of the Triangular Void**:
- In a triangular arrangement, the void is formed by three atoms at the corners of an equilateral triangle.
- The radius of the triangular void is given by the formula:
\[ r = 0.155R \]

5. **Comparing the Radii**:
- Now we compare the calculated radii:
- Octahedral void: \( r = 0.414R \)
- Tetrahedral void: \( r = 0.225R \)
- Triangular void: \( r = 0.155R \)

6. **Conclusion**:
- The largest void is the octahedral void since \( 0.414R > 0.225R > 0.155R \).

### Final Answer:
The largest void is the **octahedral void**.

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