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 the molecules \( N_2, O_2, F_2, \) and \( Cl_2 \), we can analyze the types of bonds present in each molecule and the factors affecting bond strength.

### Step-by-Step Solution:

1. **Identify the Type of Bonds**:
- \( N_2 \) has a triple bond (N≡N).
- \( O_2 \) has a double bond (O=O).
- \( F_2 \) has a single bond (F-F).
- \( Cl_2 \) also has a single bond (Cl-Cl).

2. **Understand Bond Strength**:
- The bond dissociation energy generally increases with the number of bonds between two atoms. A triple bond is stronger than a double bond, which is stronger than a single bond.
- Therefore, we can rank the bonds based on their types:
- Triple bond (N≡N) > Double bond (O=O) > Single bond (Cl-Cl) and (F-F).

3. **Consider the Effect of Atomic Size and Electronegativity**:
- Although \( Cl_2 \) and \( F_2 \) both have single bonds, \( F_2 \) has a lower bond dissociation energy than \( Cl_2 \). This is due to the high electronegativity of fluorine, which leads to greater electron-electron repulsion in the \( F-F \) bond, making it weaker than the \( Cl-Cl \) bond.

4. **Rank the Bond Dissociation Energies**:
- Based on the above analysis, we can rank the bond dissociation energies from lowest to highest:
- \( F_2 \) (weakest single bond) < \( Cl_2 \) (stronger single bond) < \( O_2 \) (double bond) < \( N_2 \) (strongest triple bond).

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