The correct order of increasing bond length of `F_2, N_2, Cl_2 and O_2` is

Options

A. `O_2 lt N_2 lt Cl_2 lt F_2`
B. `N_2 lt O_2 lt F_2 lt Cl_2`
C. `Cl_2 lt O_2 lt N_2 lt F_2`
D. `F_2 lt Cl_2 lt O_2 lt N_2`

Explanation

To determine the correct order of increasing bond length for the molecules \( F_2, N_2, Cl_2, \) and \( O_2 \), we need to analyze the type of bonds present in each molecule and the factors affecting bond length.

### Step-by-Step Solution:

1. **Identify the Bond Types:**
- \( F_2 \): Contains a single bond (1 sigma bond).
- \( N_2 \): Contains a triple bond (1 sigma bond + 2 pi bonds).
- \( O_2 \): Contains a double bond (1 sigma bond + 1 pi bond).
- \( Cl_2 \): Contains a single bond (1 sigma bond).

2. **Understand Bond Length and Bond Order:**
- The bond length is inversely related to the bond order. This means that as the bond order increases (more bonds between atoms), the bond length decreases.
- Triple bonds are shorter than double bonds, which are shorter than single bonds.

3. **Rank the Bonds:**
- **Triple Bond (N_2)**: Shortest bond length due to the highest bond order.
- **Double Bond (O_2)**: Longer than a triple bond but shorter than single bonds.
- **Single Bond (F_2)**: Longer than double bonds but shorter than other single bonds due to higher electronegativity.
- **Single Bond (Cl_2)**: Longest bond length among the single bonds due to lower electronegativity compared to fluorine.

4. **Establish the Order:**
- Based on the bond types and their lengths, we can establish the following order of increasing bond length:
- \( N_2 < O_2 < F_2 < Cl_2 \)

5. **Final Conclusion:**
- The correct order of increasing bond length is:
\[ N_2 < O_2 < F_2 < Cl_2 \]