In Borax `(Na_(2)B_(4)O_(7).10H_(2)O)` if number of `sp^(2)` hybridised B- atoms are X and number of `sp^(3)` hybridised B- atom are Y. What is the value of `X+Y`?

Answer

To solve the problem, we need to determine the number of boron atoms in borax (Na₂B₄O₇·10H₂O) that are hybridized as sp² and sp³.

### Step-by-Step Solution:

1. **Identify the Structure of Borax**:
- Borax has the formula Na₂B₄O₇·10H₂O. This indicates that it contains 4 boron (B) atoms, 7 oxygen (O) atoms, and is associated with water molecules.

2. **Analyze the Hybridization of Boron Atoms**:
- Boron can exhibit different hybridizations depending on its bonding environment. In borax, we need to analyze how each boron atom is bonded to oxygen atoms.
- The boron atoms can be categorized based on their bonding:
- **sp³ Hybridization**: This occurs when a boron atom forms four bonds (tetrahedral geometry).
- **sp² Hybridization**: This occurs when a boron atom forms three bonds (trigonal planar geometry).

3. **Determine the Hybridization of Each Boron Atom**:
- In the structure of borax:
- Two boron atoms are connected to four oxygen atoms (including bridging oxygens and hydroxyl groups). These boron atoms are sp³ hybridized.
- The other two boron atoms are connected to three oxygen atoms. These boron atoms are sp² hybridized.

4. **Count the Number of Hybridized Boron Atoms**:
- From the analysis:
- Number of sp² hybridized boron atoms (X) = 2
- Number of sp³ hybridized boron atoms (Y) = 2

5. **Calculate X + Y**:
- Now we can find the total number of hybridized boron atoms:
\[ X + Y = 2 + 2 = 4 \]

### Final Answer:
The value of \( X + Y \) is 4.

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