`Si_(2)O_(7)^(6-)` anion is obtained when:

Options

A. no oxygen of a `SiO_(4)` tetrahedron is shared with another `SiO_(4)` tetrahedron
B. one oxygen of a `SiO_(4)` tetrahedron is shared with another `SiO_(4)` tetrahedron
C. two oxytgen of a `SiO_(4)` tetrahedron are shared with another `SiO_(4)` tetrahedron
D. three or all four oxygen of oxygen of a tetrahedron are shared with other `SiO_(4)` tetrahedron

Answer

To determine how the anion \( Si_2O_7^{6-} \) is formed, we need to analyze the structure of the silicate tetrahedron \( SiO_4^{4-} \) and how these tetrahedra can combine.

### Step-by-Step Solution:

1. **Understanding the Silicate Tetrahedron**:
- Each silicon atom in \( SiO_4^{4-} \) is surrounded by four oxygen atoms, forming a tetrahedral shape. This tetrahedron carries a -4 charge due to the four oxygen atoms.

2. **Combining Tetrahedra**:
- When two \( SiO_4^{4-} \) tetrahedra combine, they can share oxygen atoms. The way these tetrahedra share oxygen affects the overall charge of the resulting structure.

3. **Identifying the Anion**:
- The anion \( Si_2O_7^{6-} \) consists of two silicon atoms and seven oxygen atoms. This indicates that some oxygen atoms are shared between the two tetrahedra.

4. **Determining the Sharing of Oxygen**:
- If we consider the possible options:
- **Option 1**: No oxygen is shared.
- **Option 2**: One oxygen is shared.
- **Option 3**: Two oxygens are shared.
- **Option 4**: Three or four oxygens are shared.
- If no oxygen were shared, we would have \( Si_2O_8^{8-} \), which is not the case.

5. **Finding the Correct Option**:
- By sharing one oxygen atom between the two \( SiO_4^{4-} \) tetrahedra, we would have:
- Total oxygen = 8 (from two tetrahedra) - 1 (shared) = 7
- Total charge = -8 (from two tetrahedra) + 2 (from the shared oxygen) = -6
- This matches the structure of \( Si_2O_7^{6-} \).

6. **Conclusion**:
- Therefore, the correct answer is that \( Si_2O_7^{6-} \) is obtained when **one oxygen of \( SiO_4^{4-} \) is shared with another \( SiO_4^{4-} \)**. Thus, the answer is Option 2.