Sum of the number of oxygen shared in between two silicon atoms in `Si_(3)O_(9)^(6-)` and `Si_(3)O_(10)^(8-)` is:

Answer

To solve the problem, we need to determine the number of oxygen atoms shared between silicon atoms in the two given silicate compounds: \( \text{Si}_3\text{O}_9^{6-} \) and \( \text{Si}_3\text{O}_{10}^{8-} \).

### Step-by-Step Solution:

1. **Identify the Type of Silicate**:
- The compound \( \text{Si}_3\text{O}_9^{6-} \) is a cyclic silicate. In cyclic silicates, each silicon atom shares two oxygen atoms with adjacent silicon atoms.
- The compound \( \text{Si}_3\text{O}_{10}^{8-} \) is a mica mineral, which is a type of two-dimensional silicate. In two-dimensional silicates, each tetrahedral unit shares three oxygen atoms.

2. **Calculate the Shared Oxygen Atoms**:
- For \( \text{Si}_3\text{O}_9^{6-} \):
- Since it is a cyclic silicate, the number of oxygen atoms shared between two silicon atoms is **2**.
- For \( \text{Si}_3\text{O}_{10}^{8-} \):
- As it is a two-dimensional silicate, the number of oxygen atoms shared between two silicon atoms is **3**.

3. **Sum the Shared Oxygen Atoms**:
- Now, we add the number of shared oxygen atoms from both compounds:
\[ \text{Total Shared Oxygen} = 2 + 3 = 5 \]

### Final Answer:
The sum of the number of oxygen atoms shared between two silicon atoms in \( \text{Si}_3\text{O}_9^{6-} \) and \( \text{Si}_3\text{O}_{10}^{8-} \) is **5**.

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