The correct increasing order of bond dissociation energy for `N_2, O_2, F_2, Cl_2` is

Options

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

Explanation

To determine the correct increasing order of bond dissociation energy for \( N_2, O_2, F_2, \) and \( Cl_2 \), we will analyze the bond types and their corresponding energies.

### Step-by-Step Solution:

1. **Understanding Bond Dissociation Energy**:
- Bond dissociation energy is the energy required to break a bond between two atoms in a molecule. Higher bond dissociation energy indicates a stronger bond.

2. **Identify the Bond Types**:
- \( N_2 \) (Nitrogen) has a triple bond: \( N \equiv N \)
- \( O_2 \) (Oxygen) has a double bond: \( O = O \)
- \( F_2 \) (Fluorine) has a single bond: \( F - F \)
- \( Cl_2 \) (Chlorine) has a single bond: \( Cl - Cl \)

3. **Comparing Bond Strengths**:
- Triple bonds (like in \( N_2 \)) are stronger than double bonds (like in \( O_2 \)), which in turn are stronger than single bonds (like in \( F_2 \) and \( Cl_2 \)).
- Among the single bonds, \( F_2 \) has a lower bond dissociation energy than \( Cl_2 \) due to the smaller size of fluorine atoms leading to greater electron-electron repulsion.

4. **Ranking the Bond Dissociation Energies**:
- From the above analysis, we can rank the bond dissociation energies as follows:
- Lowest: \( F_2 \)
- Next: \( Cl_2 \)
- Then: \( O_2 \)
- Highest: \( N_2 \)

5. **Final Order**:
- Therefore, the correct increasing order of bond dissociation energy is:
\[ F_2 < Cl_2 < O_2 < N_2 \]