A mineral `MX_(2)` crystallizes in ccp of `M^(2+)` ions whereas `X^(-)` ions occupy the tetrahedral voids. The number of cations and anions per unit cell, the coordination number of cation and percent of tetrahedral voids occupied are :

Options

A. `4, 8, 8, 100%`
B. `4, 8, 8, 50%`
C. `8, 4, 8, 50%`
D. `8, 4, 8, 100%`

Explanation

To solve the problem step-by-step, we will analyze the given information about the mineral \( MX_2 \) that crystallizes in a cubic close-packed (CCP) structure.

### Step 1: Determine the number of cations and anions per unit cell

1. In a cubic close-packed (CCP) structure, the number of atoms (or ions) per unit cell is 4.
2. Since the mineral is represented as \( MX_2 \), it contains 1 cation \( M^{2+} \) and 2 anions \( X^{-} \).
3. Therefore, for every unit cell, we have:
- Number of cations \( M^{2+} = 4 \)
- Number of anions \( X^{-} = 8 \) (since there are 2 \( X^{-} \) ions for each \( M^{2+} \) ion).

### Step 2: Calculate the coordination number of the cation

1. In a CCP structure, the coordination number of the cation (which is \( M^{2+} \)) is 8. This means each cation is surrounded by 8 anions.

### Step 3: Determine the coordination number of the anion

1. The \( X^{-} \) ions occupy the tetrahedral voids in the CCP structure.
2. The coordination number of the tetrahedral voids is 4. This means each \( X^{-} \) ion is surrounded by 4 \( M^{2+} \) ions.

### Step 4: Calculate the percentage of tetrahedral voids occupied

1. In a CCP structure, there are 8 tetrahedral voids per unit cell.
2. Since all \( X^{-} \) ions occupy these tetrahedral voids, we have:
- Number of tetrahedral voids occupied = 8 (as there are 8 \( X^{-} \) ions).
3. Therefore, the percentage of tetrahedral voids occupied is:
\[ \text{Percentage of tetrahedral voids occupied} = \left( \frac{\text{Number of voids occupied}}{\text{Total number of voids}} \right) \times 100 = \left( \frac{8}{8} \right) \times 100 = 100\% \]

### Summary of Results

- Number of cations per unit cell: 4
- Number of anions per unit cell: 8
- Coordination number of cation: 8
- Coordination number of anion: 4
- Percentage of tetrahedral voids occupied: 100%

### Final Answer

- Number of cations: 4
- Number of anions: 8
- Coordination number of cation: 8
- Coordination number of anion: 4
- Percentage of tetrahedral voids occupied: 100%