Considering the state of hybridization of carbon atoms, find out the molecule among the following which is linear?

Options

A. `CH_3-C-=C-CH_3`
B. `CH_2=CH-CH_2-C-=CH`
C. `CH_3-CH_2-CH_2-CH_3`
D. `CH_3-CH=CH-CH_3`

Explanation

To determine which molecule among the given options has a linear geometry based on the hybridization of carbon atoms, we can follow these steps:

### Step 1: Understand Hybridization Types
- **SP Hybridization**: Involves one s orbital and one p orbital, resulting in two hybrid orbitals. The bond angle is 180 degrees, leading to a linear geometry. This occurs in molecules with a triple bond or two double bonds.
- **SP2 Hybridization**: Involves one s orbital and two p orbitals, resulting in three hybrid orbitals. The bond angle is 120 degrees, leading to a trigonal planar geometry. This occurs in molecules with one double bond.
- **SP3 Hybridization**: Involves one s orbital and three p orbitals, resulting in four hybrid orbitals. The bond angle is approximately 109.5 degrees, leading to a tetrahedral geometry. This occurs in molecules with only single bonds.

### Step 2: Analyze Each Option
1. **Option 1: CH3-C≡C-CH3**
- The central carbon atoms are involved in a triple bond (C≡C), which means they are SP hybridized. The bond angle is 180 degrees, indicating a linear geometry.

2. **Option 2: CH2=CH-CH2-C≡CH**
- The carbon atoms involved in the triple bond (C≡CH) are SP hybridized, but the presence of double bonds (C=C) means that some carbon atoms will be SP2 hybridized. Therefore, this molecule is not entirely linear.

3. **Option 3: CH3-CH2-CH2-CH3**
- All carbon atoms are connected by single bonds, leading to SP3 hybridization. This results in a tetrahedral geometry, so this molecule is not linear.

4. **Option 4: CH3-CH=CH-CH3**
- The carbon atoms connected by the double bond (C=C) are SP2 hybridized, while the others are SP3 hybridized. This does not yield a linear structure.

### Step 3: Conclusion
From the analysis, **Option 1 (CH3-C≡C-CH3)** is the only molecule that exhibits linear geometry due to the SP hybridization of the carbon atoms involved in the triple bond.

### Final Answer
The molecule that is linear among the given options is **CH3-C≡C-CH3**.

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