The maximum number of carbon atoms arranged linearly in the molecule,
`CH_(3)-C-=C-CH=CH_(2)` is

Options

A. 5
B. 4
C. 2
D. 3

Answer

To determine the maximum number of carbon atoms arranged linearly in the molecule \( CH_3-C \equiv C-CH=CH_2 \), we will analyze the structure and hybridization of each carbon atom.

### Step-by-Step Solution:

1. **Identify the Structure**:
The given molecule can be represented as follows:
\[ CH_3 - C \equiv C - CH = CH_2 \]
This shows a chain of carbon atoms with various types of bonds (single, double, and triple).

2. **Count the Carbon Atoms**:
The molecule contains a total of 5 carbon atoms:
- \( C_1 \) (from \( CH_3 \))
- \( C_2 \) (the first carbon in the chain)
- \( C_3 \) (the second carbon in the chain, involved in a triple bond)
- \( C_4 \) (the carbon with a double bond)
- \( C_5 \) (the terminal carbon with two hydrogens)

3. **Determine Hybridization**:
- **Carbon 1 (\( C_1 \))**:
- Bonds: 3 (with H) + 1 (with \( C_2 \)) = 4 sigma bonds
- Hybridization: \( sp^3 \) (tetrahedral geometry)

- **Carbon 2 (\( C_2 \))**:
- Bonds: 1 (with \( C_1 \)) + 1 (with \( C_3 \)) + 2 (from triple bond) = 2 sigma bonds
- Hybridization: \( sp \) (linear geometry)

- **Carbon 3 (\( C_3 \))**:
- Bonds: 1 (with \( C_2 \)) + 1 (with \( C_4 \)) + 2 (from triple bond) = 2 sigma bonds
- Hybridization: \( sp \) (linear geometry)

- **Carbon 4 (\( C_4 \))**:
- Bonds: 1 (with \( C_3 \)) + 1 (with \( C_5 \)) + 1 (from double bond) = 3 sigma bonds
- Hybridization: \( sp^2 \) (trigonal planar geometry)

- **Carbon 5 (\( C_5 \))**:
- Bonds: 1 (with \( C_4 \)) + 2 (with H) = 3 sigma bonds
- Hybridization: \( sp^2 \) (trigonal planar geometry)

4. **Identify Linear Arrangement**:
- The carbons \( C_2 \) and \( C_3 \) are both \( sp \) hybridized, which means they are linear and can be arranged in a straight line.
- The other carbons (\( C_1 \), \( C_4 \), and \( C_5 \)) are not linear due to their \( sp^3 \) and \( sp^2 \) hybridizations.

5. **Conclusion**:
The maximum number of carbon atoms that can be arranged linearly in the given molecule is **2** (the \( C_2 \) and \( C_3 \) carbons).

### Final Answer:
The maximum number of carbon atoms arranged linearly in the molecule \( CH_3-C \equiv C-CH=CH_2 \) is **2**.