Arrange the following in the decreasing order of their thermal stability of `Cl_(2), F_(2), I_(2), Br_(2)`.

Options

A. `F_(2)gt Cl_(2)gt Br_(2)gt I_(2)`
B. `Cl_(2)gt Br_(2)gt F_(2)gt I_(2)`
C. `Cl_(2)gt F_(2)gt Br_(2)gt I_(2)`
D. `F_(2)gt Br_(2)gt Cl_(2)gt I_(2)`

Explanation

To arrange the halogen molecules \( Cl_2, F_2, I_2, \) and \( Br_2 \) in decreasing order of their thermal stability, we need to consider the bond lengths and bond dissociation enthalpies of these molecules. Here’s the step-by-step solution:

### Step 1: Understand the Concept of Thermal Stability
Thermal stability of a molecule is related to the strength of the bond holding the atoms together. Stronger bonds (higher bond dissociation enthalpy) correspond to greater thermal stability.

### Step 2: Analyze the Halogens
The halogens in question are \( Cl_2, F_2, I_2, \) and \( Br_2 \). As we move down the group in the periodic table from fluorine to iodine, the size of the atoms increases due to the addition of electron shells.

### Step 3: Compare Bond Lengths
- **Fluorine (\( F_2 \))**: The bond length is relatively short due to the small size of the fluorine atom. However, \( F_2 \) has significant lone pair repulsion, which affects its bond strength.
- **Chlorine (\( Cl_2 \))**: The bond length is longer than that of \( F_2 \) but shorter than \( Br_2 \) and \( I_2 \).
- **Bromine (\( Br_2 \))**: The bond length is longer than \( Cl_2 \) but shorter than \( I_2 \).
- **Iodine (\( I_2 \))**: The bond length is the longest among these molecules.

### Step 4: Relate Bond Length to Bond Strength
- Shorter bond lengths generally indicate stronger bonds and thus higher bond dissociation enthalpy.
- Therefore, the order of bond lengths from shortest to longest is:
\( F_2 < Cl_2 < Br_2 < I_2 \)

### Step 5: Determine Bond Dissociation Enthalpy
- The bond dissociation enthalpy is highest for \( Cl_2 \), followed by \( Br_2 \), then \( F_2 \), and finally \( I_2 \).
- This means the order of thermal stability (decreasing) is:
\( Cl_2 > Br_2 > F_2 > I_2 \)

### Final Answer
Thus, the decreasing order of thermal stability is:
\[ Cl_2 > Br_2 > F_2 > I_2 \]

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