A mineral having the formula `AB_(2)` crystallizes in the `ccp` lattice, with `A` atoms occupying the lattice points. Select the correct statement(s).

Options

A. The coordination number `(CN)` for `A` atoms `= 8`.
B. The `CN` for `B` atom `= 4`
C. `100%` of `TV_(s)` are occupied by `B` atoms
D. `50%` of `TV_(s)` are occupied by `B` atoms.

Explanation

To solve the problem regarding the mineral with the formula \( AB_2 \) that crystallizes in a cubic close-packed (ccp) lattice, we will follow these steps:

### Step-by-Step Solution:

1. **Understanding the ccp Lattice**:
- The cubic close-packed (ccp) structure is also known as face-centered cubic (fcc). In an fcc lattice, there are 4 atoms per unit cell.

2. **Identifying the Atoms**:
- In the given formula \( AB_2 \), \( A \) occupies the lattice points, and \( B \) occupies the voids. Since \( A \) occupies the lattice points, the number of \( A \) atoms in the unit cell is 4 (as there are 4 atoms per fcc unit cell).

3. **Calculating the Number of \( B \) Atoms**:
- The formula \( AB_2 \) indicates that for every 1 atom of \( A \), there are 2 atoms of \( B \). Therefore, if there are 4 atoms of \( A \), the number of \( B \) atoms will be:
\[ \text{Number of } B = 2 \times \text{Number of } A = 2 \times 4 = 8 \]

4. **Coordination Numbers**:
- In a ccp lattice, the coordination number of \( A \) atoms (which are at the lattice points) is 8. This means each \( A \) atom is surrounded by 8 other atoms.
- The coordination number of \( B \) atoms, which occupy tetrahedral voids, is 4. Each \( B \) atom is surrounded by 4 \( A \) atoms.

5. **Tetrahedral Voids**:
- In a ccp lattice, there are 8 tetrahedral voids per unit cell. Since we have 8 \( B \) atoms, it means that all the tetrahedral voids are occupied by \( B \) atoms.
- Therefore, 100% of the tetrahedral voids are occupied by \( B \) atoms.

### Summary of Findings:
- Coordination number for \( A \) atoms = 8 (Option A is correct).
- Coordination number for \( B \) atoms = 4 (Option B is correct).
- 100% of tetrahedral voids are occupied by \( B \) atoms (Option C is correct).
- Option D (50% of tetrahedral voids occupied) is incorrect.

### Final Answer:
- Options A, B, and C are correct.