Which of the following statements is//are correct about `TVs` in an fcc unit cell?
Given: Edge length `= a`
Body diagonai `= b`

Options

A. Each `TV` lies at a diastance b//4 from the nearest corner.
B. Each `TV` lies at a distance `3b//4` from the farthest corner.
C. Each `TV` lies at a distance of `sqrt3a//4` from the nearest corner.
D. The distance between two `TV_(s)` is `b//2`.

Explanation

To solve the question regarding the tetrahedral voids in a face-centered cubic (FCC) unit cell, we will analyze the given statements one by one based on the properties of FCC lattices.

### Step-by-Step Solution:

1. **Understanding FCC Unit Cell**:
- In an FCC unit cell, atoms are located at each of the corners and the centers of each face of the cube.
- The edge length of the cube is given as `a`, and the body diagonal is given as `b`.

2. **Finding the Body Diagonal**:
- The body diagonal `b` of a cube can be calculated using the formula:
\[ b = \sqrt{a^2 + a^2 + a^2} = a\sqrt{3} \]
- Therefore, \( b = a\sqrt{3} \).

3. **Position of Tetrahedral Voids**:
- In an FCC unit cell, there are 8 tetrahedral voids. The positions of these voids can be determined based on the arrangement of the atoms.
- The tetrahedral voids are located at specific fractional coordinates within the unit cell.

4. **Analyzing Each Statement**:
- **Option 1**: Each tetrahedral void lies at a distance of \( \frac{b}{4} \) from the nearest corner.
- The distance from the corner to the tetrahedral void is indeed \( \frac{b}{4} \). This statement is **correct**.

- **Option 2**: Each tetrahedral void lies at a distance of \( \frac{3b}{4} \) from the farthest corner.
- The distance from the farthest corner can be calculated as \( b - \frac{b}{4} = \frac{3b}{4} \). This statement is **correct**.

- **Option 3**: Each tetrahedral void lies at a distance of \( \frac{\sqrt{3}a}{4} \) from the nearest corner.
- Since \( b = a\sqrt{3} \), we have \( \frac{b}{4} = \frac{a\sqrt{3}}{4} \), which is equivalent to \( \frac{\sqrt{3}a}{4} \). This statement is **correct**.

- **Option 4**: The distance between two tetrahedral voids is \( \frac{b}{2} \).
- The distance between two tetrahedral voids can be calculated based on their positions. It is found to be \( \frac{b}{2} \). This statement is **correct**.

5. **Conclusion**:
- All the statements regarding the tetrahedral voids in an FCC unit cell are correct.

### Final Answer:
All options are correct regarding the tetrahedral voids in an FCC unit cell.

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