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 determine the values of \(X\) and \(Y\) in the compound Borax \((Na_2B_4O_7 \cdot 10H_2O)\), we need to analyze the hybridization of the boron atoms in the structure of Borax.

### Step-by-Step Solution:

1. **Identify the Structure of Borax**:
- Borax has the formula \(Na_2B_4O_7 \cdot 10H_2O\). It consists of four boron atoms, which are part of a borate ion structure.

2. **Determine the Hybridization of Boron Atoms**:
- In the borate structure, we typically have two types of boron atoms: those that are bonded to three oxygen atoms (trigonal planar) and those that are bonded to four oxygen atoms (tetrahedral).

3. **Analyze the Hybridization**:
- **sp² Hybridization**: This occurs when a boron atom is bonded to three other atoms (like in a trigonal planar arrangement). In Borax, there are two boron atoms that exhibit this hybridization.
- **sp³ Hybridization**: This occurs when a boron atom is bonded to four other atoms (like in a tetrahedral arrangement). In Borax, there are also two boron atoms that exhibit this hybridization.

4. **Count the Hybridized Boron Atoms**:
- Let \(X\) be the number of boron atoms that are sp² hybridized, and \(Y\) be the number of boron atoms that are sp³ hybridized.
- From our analysis, we find:
- \(X = 2\) (for the two sp² hybridized boron atoms)
- \(Y = 2\) (for the two sp³ hybridized boron atoms)

5. **Calculate \(X + Y\)**:
- Now, we can find \(X + Y\):
\[ X + Y = 2 + 2 = 4 \]

### Final Answer:
Thus, the value of \(X + Y\) is \(4\).

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