The ratio of the number of sp, `sp^(2)`, and `sp^(3)` orbitals in the compound is
`CH_(3)-CH=C=CH-C-=C-CH_(3)`

Options

A. `1:1:1`
B. `2:2:1`
C. `3:2:1`
D. `3:3:4`

Answer

To determine the ratio of the number of sp, sp², and sp³ orbitals in the compound CH₃-CH=CH-CH≡C-CH₃, we will analyze the hybridization of each carbon atom in the compound step by step.

### Step 1: Identify the Structure
The compound can be represented as follows:
- CH₃ (C1) - CH (C2) = CH (C3) - C≡C (C4 and C5) - CH (C6) - CH₃ (C7)

### Step 2: Analyze Each Carbon Atom
1. **C1 (CH₃)**:
- Forms 4 sigma bonds (3 with H and 1 with C2).
- **Hybridization**: sp³ (steric number = 4).

2. **C2 (CH)**:
- Forms 3 sigma bonds (1 with C1, 1 with C3, and 1 with H).
- **Hybridization**: sp² (steric number = 3).

3. **C3 (CH)**:
- Forms 3 sigma bonds (1 with C2, 1 with C4, and 1 with H).
- **Hybridization**: sp² (steric number = 3).

4. **C4 (C≡C)**:
- Forms 2 sigma bonds (1 with C3 and 1 with C5) and has 2 pi bonds (due to the triple bond).
- **Hybridization**: sp (steric number = 2).

5. **C5 (C≡C)**:
- Similar to C4, it forms 2 sigma bonds (1 with C4 and 1 with C6) and has 2 pi bonds.
- **Hybridization**: sp (steric number = 2).

6. **C6 (CH)**:
- Forms 3 sigma bonds (1 with C5, 1 with C7, and 1 with H).
- **Hybridization**: sp² (steric number = 3).

7. **C7 (CH₃)**:
- Forms 4 sigma bonds (3 with H and 1 with C6).
- **Hybridization**: sp³ (steric number = 4).

### Step 3: Count the Number of Each Hybridization Type
- **sp³**: C1 (1) + C7 (1) = 2
- **sp²**: C2 (1) + C3 (1) + C6 (1) = 3
- **sp**: C4 (1) + C5 (1) = 2

### Step 4: Calculate the Total Orbitals
- **Total sp³ orbitals**: 2 carbon atoms × 4 orbitals = 8 orbitals
- **Total sp² orbitals**: 3 carbon atoms × 3 orbitals = 9 orbitals
- **Total sp orbitals**: 2 carbon atoms × 2 orbitals = 4 orbitals

### Step 5: Determine the Ratio
The ratio of the number of sp, sp², and sp³ orbitals is:
- sp : sp² : sp³ = 4 : 9 : 8

### Final Answer
The ratio of the number of sp, sp², and sp³ orbitals in the compound CH₃-CH=CH-CH≡C-CH₃ is **4 : 9 : 8**.

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