Which of the following has the smallest bond length ?

Options

A. `O_(2)`
B. `N_(2)`
C. `Cl_(2)`
D. `HCl`

Explanation

To determine which of the given molecules has the smallest bond length, we need to analyze the bond multiplicity of each molecule. Bond multiplicity refers to the number of bonds between two atoms; the higher the multiplicity, the shorter the bond length.

### Step-by-Step Solution:

1. **Identify the Molecules**: The molecules we need to consider are O2, N2, Cl2, and HCl.

2. **Determine Bond Types**:
- **O2 (Oxygen)**: The bond between the two oxygen atoms is a double bond (O=O). Thus, the bond multiplicity (Bm) is 2.
- **N2 (Nitrogen)**: The bond between the two nitrogen atoms is a triple bond (N≡N). Thus, the bond multiplicity (Bm) is 3.
- **Cl2 (Chlorine)**: The bond between the two chlorine atoms is a single bond (Cl-Cl). Thus, the bond multiplicity (Bm) is 1.
- **HCl (Hydrochloric Acid)**: The bond between hydrogen and chlorine is also a single bond (H-Cl). Thus, the bond multiplicity (Bm) is 1.

3. **Compare Bond Multiplicities**:
- O2: Bm = 2
- N2: Bm = 3
- Cl2: Bm = 1
- HCl: Bm = 1

4. **Analyze Bond Length**: According to the principle that bond length is inversely proportional to bond multiplicity:
- Higher bond multiplicity means shorter bond length.
- Therefore, since N2 has the highest bond multiplicity (3), it will have the shortest bond length.

5. **Conclusion**: The molecule with the smallest bond length among the given options is **N2**.

### Final Answer: N2

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