The state of hybridization of `C_(2), C_(3),C_(5) and C_(6)` of the hydrocarbon,
`underset(7)(CH_(3)) - underset(CH_(3))underset(|)overset(CH_(3))overset(|)(C)- underset(5)(CH) = underset(4)(CH)-underset(3)overset(CH_(3))overset(|)(CH) - C_(2) equiv underset(1)(CH)`
is in the following sequence

Options

A. sp,`sp^(2), sp^(3) and sp^(2)`
B. `sp, sp^(3), sp^(2) and sp^(3)`
C. `sp^(3), sp^(2), sp^(2) and sp`
D. `sp, sp^(2), sp^(2) and sp^(3)`

Answer

To determine the state of hybridization of the carbon atoms \( C_2, C_3, C_5, \) and \( C_6 \) in the hydrocarbon structure provided, we will follow these steps:

### Step 1: Identify the Carbon Atoms and Their Bonds
- **C2**: This carbon is involved in a double bond with another carbon atom. It forms one sigma bond and two pi bonds.
- **C3**: This carbon is connected to four other atoms (three hydrogens and one carbon). It forms four sigma bonds.
- **C5**: This carbon is involved in a double bond with another carbon atom. It forms one sigma bond and one pi bond, and is also connected to two other atoms (two hydrogens).
- **C6**: This carbon is connected to four other atoms (three hydrogens and one carbon). It forms four sigma bonds.

### Step 2: Count the Sigma and Pi Bonds
- **C2**:
- Sigma bonds = 2
- Pi bonds = 2
- **C3**:
- Sigma bonds = 4
- Pi bonds = 0
- **C5**:
- Sigma bonds = 3
- Pi bonds = 1
- **C6**:
- Sigma bonds = 4
- Pi bonds = 0

### Step 3: Calculate the Steric Number
The steric number is calculated as the sum of sigma bonds and lone pairs. Since there are no lone pairs on these carbon atoms, the steric number equals the number of sigma bonds.

- **C2**: Steric number = 2 (2 sigma bonds)
- **C3**: Steric number = 4 (4 sigma bonds)
- **C5**: Steric number = 3 (3 sigma bonds)
- **C6**: Steric number = 4 (4 sigma bonds)

### Step 4: Determine the Hybridization
The hybridization can be determined from the steric number:
- **Steric Number 2**: Hybridization = sp
- **Steric Number 3**: Hybridization = sp²
- **Steric Number 4**: Hybridization = sp³

Thus, we find:
- **C2**: sp hybridization
- **C3**: sp³ hybridization
- **C5**: sp² hybridization
- **C6**: sp³ hybridization

### Step 5: Write the Sequence of Hybridization
The sequence of hybridization for \( C_2, C_3, C_5, \) and \( C_6 \) is:
- C2: sp
- C3: sp³
- C5: sp²
- C6: sp³

### Final Answer
The sequence of hybridization is: **sp, sp³, sp², sp³**.