Assertion : The electron gain enthalpy of chlorine is less negative than that of fluorine.
Reason : The fluorine atom is much smaller in size than that of chlorine.

Answer

To solve the question, we need to analyze the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that "The electron gain enthalpy of chlorine is less negative than that of fluorine." This means that when chlorine gains an electron, it releases less energy compared to fluorine.

### Step 2: Understand the Reason
The reason given is "The fluorine atom is much smaller in size than that of chlorine." This suggests that the smaller size of fluorine affects its ability to gain an electron.

### Step 3: Analyze Electron Gain Enthalpy
Electron gain enthalpy (or electron affinity) is the amount of energy released when an electron is added to a neutral gaseous atom. A more negative value indicates that more energy is released when the atom gains an electron.

### Step 4: Compare Electron Gain Enthalpy Values
- The electron gain enthalpy of fluorine is approximately -333 kJ/mol.
- The electron gain enthalpy of chlorine is approximately -349 kJ/mol.

Since -349 kJ/mol (chlorine) is more negative than -333 kJ/mol (fluorine), this means chlorine releases more energy when gaining an electron compared to fluorine.

### Step 5: Conclusion on Assertion and Reason
- The assertion is **incorrect** because it states that chlorine's electron gain enthalpy is less negative than fluorine's, which is not true.
- The reason is **correct** because it correctly identifies that fluorine is smaller than chlorine, which contributes to the differences in their electron gain enthalpy.

### Final Answer
- Assertion: Incorrect
- Reason: Correct