Among the following, the molecule with linear geometry is

Options

A. `C_(2)H_(4)`
B. `CO_(2)`
C. `NH_(3)`
D. `H_(2)O`

Explanation

To determine which molecule among the given options has a linear geometry, we will follow these steps:

### Step 1: Understand Linear Geometry
Linear geometry is associated with molecules that have sp hybridization. This means that the central atom must have a steric number of 2.

### Step 2: Use the Steric Number Formula
The steric number can be calculated using the formula:
\[ \text{Steric Number} = \frac{1}{2} \left( \text{Valence Electrons of Central Atom} + \text{Number of Monovalent Atoms} - \text{Cationic Charge} + \text{Anionic Charge} \right) \]
This formula helps us determine the hybridization of the central atom.

### Step 3: Analyze Each Molecule
1. **C2H4 (Ethylene)**:
- There are two carbon atoms, so we cannot directly apply the steric number formula to a single central atom.
- Each carbon in C2H4 forms three sigma bonds (two with hydrogen and one with another carbon), leading to sp² hybridization.
- **Conclusion**: Not linear.

2. **CO2 (Carbon Dioxide)**:
- Carbon has 4 valence electrons, and there are no monovalent atoms or charges.
- Steric Number = \( \frac{1}{2} (4 + 0) = 2 \)
- This corresponds to sp hybridization.
- **Conclusion**: Linear.

3. **NH3 (Ammonia)**:
- Nitrogen has 5 valence electrons and there are three hydrogen atoms (monovalent).
- Steric Number = \( \frac{1}{2} (5 + 3) = 4 \)
- This corresponds to sp³ hybridization.
- **Conclusion**: Not linear.

4. **H2O (Water)**:
- Oxygen has 6 valence electrons and there are two hydrogen atoms.
- Steric Number = \( \frac{1}{2} (6 + 2) = 4 \)
- This corresponds to sp³ hybridization.
- **Conclusion**: Not linear.

### Final Conclusion
After analyzing all the given molecules, the only molecule with linear geometry is **CO2**.

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