In carprolactum if 'a' is number of lone pairs of `e^(-)` and 'b' is number of `sp^(3)` hybridised atoms. What is the vlaue of `a+b`?

Answer

To solve the problem, we need to determine the values of 'a' (the number of lone pairs of electrons) and 'b' (the number of sp³ hybridized atoms) in carprolactam and then calculate \( a + b \).

### Step 1: Identify the structure of carprolactam
Carprolactam has a specific molecular structure that includes carbon, nitrogen, and oxygen atoms. We need to analyze this structure to find the lone pairs and hybridization.

### Step 2: Count the lone pairs of electrons (a)
- **Carbon atoms**: In carprolactam, carbon atoms are typically tetrahedral and do not have lone pairs. Therefore, they contribute 0 to 'a'.
- **Oxygen atoms**: Oxygen in carprolactam is generally involved in a double bond (sp² hybridized) and has 2 lone pairs. However, we need to check the specific oxygen in the structure.
- **Nitrogen atom**: The nitrogen atom typically has 1 lone pair of electrons.

Thus, the total number of lone pairs \( a \) is:
- Oxygen: 2 lone pairs
- Nitrogen: 1 lone pair

So, \( a = 2 + 1 = 3 \).

### Step 3: Count the number of sp³ hybridized atoms (b)
- **Carbons**: Most carbon atoms in carprolactam are sp³ hybridized, except for the carbon that is double-bonded (which is sp² hybridized). We can identify the sp³ hybridized carbons:
- Count the sp³ hybridized carbons: 5 carbons are sp³ hybridized.
- **Nitrogen**: The nitrogen atom is sp³ hybridized because it forms three sigma bonds (one with carbon and two with hydrogen) and has one lone pair.

Thus, the total number of sp³ hybridized atoms \( b \) is:
- Carbons: 5
- Nitrogen: 1

So, \( b = 5 + 1 = 6 \).

### Step 4: Calculate \( a + b \)
Now, we can calculate the final value:
\[ a + b = 3 + 6 = 9 \]

### Final Answer
The value of \( a + b \) is **9**.

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