Statement-1: In fluorite structure, `r^(+)/r^(-) gt 1`
Statement-2: There are 4 unoccupied octahedral positions in a unit cell of `CaF_2`
Statement-3:There are 4 unoccupied tetrahedral positions in a unit cell of `CaF_2`.

Options

A. T F F
B. T F T
C. F F F
D. T T F

Answer

To analyze the statements regarding the fluorite structure of calcium fluoride (CaF₂), we will evaluate each statement step by step.

### Step 1: Evaluate Statement-1
**Statement-1:** In fluorite structure, \( r^{(+)} / r^{(-)} > 1 \)

- In the fluorite structure, the cation is \( Ca^{2+} \) and the anion is \( F^{-} \).
- The ionic radius of \( Ca^{2+} \) is larger than that of \( F^{-} \).
- Therefore, the ratio \( r^{(+)} / r^{(-)} \) (which is \( r_{Ca^{2+}} / r_{F^{-}} \)) is indeed greater than 1.

**Conclusion:** Statement-1 is true.

### Step 2: Evaluate Statement-2
**Statement-2:** There are 4 unoccupied octahedral positions in a unit cell of \( CaF_2 \).

- In the fluorite structure, \( Ca^{2+} \) ions occupy the face-centered cubic (FCC) lattice points.
- The \( F^{-} \) ions occupy the tetrahedral voids.
- In a face-centered cubic unit cell, there are a total of 4 octahedral voids.
- Since all tetrahedral voids are occupied by \( F^{-} \) ions, the octahedral voids remain unoccupied.

**Conclusion:** Statement-2 is true.

### Step 3: Evaluate Statement-3
**Statement-3:** There are 4 unoccupied tetrahedral positions in a unit cell of \( CaF_2 \).

- As established, the \( F^{-} \) ions occupy all the tetrahedral voids in the unit cell.
- Since all tetrahedral voids are occupied, there are no unoccupied tetrahedral positions.

**Conclusion:** Statement-3 is false.

### Final Conclusion
- Statement-1 is true.
- Statement-2 is true.
- Statement-3 is false.