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

Options

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

Answer

To determine the hybridization states of the carbon atoms C2, C3, C5, and C6 in the given hydrocarbon, we will analyze the number of sigma bonds formed by each carbon atom. The hybridization types are as follows:

1. **sp hybridization**: 2 sigma bonds
2. **sp² hybridization**: 3 sigma bonds
3. **sp³ hybridization**: 4 sigma bonds

Now, let's analyze each carbon atom step by step:

### Step 1: Determine the hybridization of C2
- **Analysis**: C2 is bonded to one carbon atom and has one additional bond (likely to another carbon or hydrogen).
- **Sigma Bonds**: C2 has 2 sigma bonds.
- **Conclusion**: Since it has 2 sigma bonds, C2 is **sp hybridized**.

### Step 2: Determine the hybridization of C3
- **Analysis**: C3 is bonded to three other atoms (two carbon atoms and one hydrogen atom).
- **Sigma Bonds**: C3 has 4 sigma bonds.
- **Conclusion**: Since it has 4 sigma bonds, C3 is **sp³ hybridized**.

### Step 3: Determine the hybridization of C5
- **Analysis**: C5 is bonded to two other carbon atoms and one hydrogen atom.
- **Sigma Bonds**: C5 has 3 sigma bonds.
- **Conclusion**: Since it has 3 sigma bonds, C5 is **sp² hybridized**.

### Step 4: Determine the hybridization of C6
- **Analysis**: C6 is bonded to four other atoms (likely three carbon atoms and one hydrogen atom).
- **Sigma Bonds**: C6 has 4 sigma bonds.
- **Conclusion**: Since it has 4 sigma bonds, C6 is **sp³ hybridized**.

### Final Summary of Hybridizations
- C2: sp
- C3: sp³
- C5: sp²
- C6: sp³

### Order of Hybridizations
The order of hybridizations for C2, C3, C5, and C6 is:
- C2: sp
- C3: sp³
- C5: sp²
- C6: sp³

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

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