The state of hybridization of `C_2, C_3, C_5`, and `C_6` of the hydrocarbon
`CH_3-overset(CH_3)overset(|)underset(CH_3)underset(|6)C-underset(5)CH=overset(CH_3)overset(|)underset(4)CH-underset(3)CH-underset(2)C-=underset(1)CH`
is in the following sequence:

Options

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

Explanation

To determine the hybridization states of the carbon atoms C2, C3, C5, and C6 in the given hydrocarbon structure, we will follow these steps:

### Step 1: Identify the structure and the carbon atoms
The hydrocarbon structure provided is CH3-CH(CH3)-C(CH3)=C(CH3)-C(CH3)-C(CH3)-C(CH3). We need to analyze the hybridization of C2, C3, C5, and C6.

### Step 2: Determine the hybridization of C2
- **C2** is connected to 2 other carbon atoms and has 0 lone pairs.
- **Steric Number** = Number of bonded atoms + Lone pairs = 2 (C) + 0 (lone pairs) = 2.
- A steric number of 2 corresponds to **sp hybridization**.

### Step 3: Determine the hybridization of C3
- **C3** is connected to 2 carbon atoms and 1 hydrogen atom, with 0 lone pairs.
- **Steric Number** = 2 (C) + 1 (H) + 0 (lone pairs) = 3.
- A steric number of 3 corresponds to **sp² hybridization**.

### Step 4: Determine the hybridization of C5
- **C5** is connected to 2 carbon atoms and 1 hydrogen atom, with 0 lone pairs.
- **Steric Number** = 2 (C) + 1 (H) + 0 (lone pairs) = 3.
- A steric number of 3 corresponds to **sp² hybridization**.

### Step 5: Determine the hybridization of C6
- **C6** is connected to 4 carbon atoms and has 0 lone pairs.
- **Steric Number** = 4 (C) + 0 (lone pairs) = 4.
- A steric number of 4 corresponds to **sp³ hybridization**.

### Summary of Hybridization States
- C2: sp
- C3: sp²
- C5: sp²
- C6: sp³

### Final Answer
The sequence of hybridization states for C2, C3, C5, and C6 is: **sp, sp², sp², sp³**.

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