In F.C.C. arrangement of identical spheres, distance between two nearest octahedral void is `8.51 A`. The distance between two nearest tetrahedral voids would be ?

Options

A. `6A`
B. `9A`
C. `12 A`
D. `30 A`

Explanation

To solve the problem, we need to find the distance between two nearest tetrahedral voids in a face-centered cubic (FCC) arrangement given that the distance between two nearest octahedral voids is 8.51 Å.

### Step-by-Step Solution:

1. **Understanding FCC Structure**:
- In a face-centered cubic (FCC) structure, atoms are located at the corners and the centers of each face of the cube.

2. **Finding the Distance Between Octahedral Voids**:
- The distance between two nearest octahedral voids in an FCC structure is given by the formula:
\[ \text{Distance between octahedral voids} = \frac{A}{\sqrt{2}} \]
- We are given that this distance is 8.51 Å.

3. **Calculating the Edge Length (A)**:
- Rearranging the formula to find A:
\[ A = \text{Distance} \times \sqrt{2} \]
- Substituting the given distance:
\[ A = 8.51 \times \sqrt{2} \approx 8.51 \times 1.414 \approx 12.0 \, \text{Å} \]

4. **Finding the Distance Between Tetrahedral Voids**:
- The distance between two nearest tetrahedral voids in an FCC structure is given by the formula:
\[ \text{Distance between tetrahedral voids} = \frac{A}{2} \]
- Now substituting the value of A:
\[ \text{Distance} = \frac{12.0}{2} = 6.0 \, \text{Å} \]

5. **Final Answer**:
- The distance between two nearest tetrahedral voids is 6.0 Å.

### Summary:
- The distance between two nearest tetrahedral voids is **6.0 Å**.