To determine the correct order of bond lengths for the halogen diatomic molecules (I2, Br2, Cl2, F2), we need to consider the factors affecting bond length, which include atomic size and bond strength.
### Step-by-Step Solution:
1. **Understanding Bond Length**:
- Bond length is inversely proportional to bond strength. This means that as bond strength increases, bond length decreases, and vice versa.
2. **Atomic Size**:
- The atomic size of halogens increases as we move down the group in the periodic table. The order of atomic sizes is:
- Iodine (I) > Bromine (Br) > Chlorine (Cl) > Fluorine (F)
3. **Bond Strength and Overlapping**:
- Smaller atoms have better overlap of their atomic orbitals, leading to stronger bonds. As we go down the group, the size increases, resulting in poorer overlap and thus weaker bonds.
4. **Analyzing Each Halogen**:
- For I2, Br2, Cl2, and F2:
- I2 has the largest bond length due to the largest atomic size and weakest bond strength.
- Br2 has a smaller bond length than I2.
- Cl2 has a smaller bond length than Br2.
- F2, despite being the smallest atom, experiences significant electron-electron repulsion due to its small size, which affects its bond length.
5. **Considering Exceptions**:
- The repulsion between the electrons in F2 leads to an increase in bond length compared to what would be expected based solely on size. Therefore, F2 has a bond length that is longer than Cl2 and Br2.
6. **Final Order of Bond Length**:
- Taking into account the atomic sizes and the effects of electron repulsion, the correct order of bond lengths from longest to shortest is:
- I2 > Br2 > F2 > Cl2
### Conclusion:
Thus, the correct order of bond lengths is **I2 > Br2 > F2 > Cl2**.
