For `AB_(2)` type molecule which statement (s) si (are) correct about bond angle `(B-A-B)`
(I) Bond angel `prop EN` of the central atom `A`
(II) Bond angle `prop 1//EN` of the central atom `A`
(III) Bond angle `prop` Size of central atom
(IV) Bond angle prop 1/Size of central atom .

Options

A. I,III,III
B. II,IV
C. I,IV
D. II,III

Answer

To solve the question regarding the bond angle \( B-A-B \) in an \( AB_2 \) type molecule, we will analyze the statements provided based on the relationship between bond angle, electronegativity, and size of the central atom \( A \).

### Step-by-Step Solution:

1. **Understanding the Molecule Structure**:
- In an \( AB_2 \) molecule, \( A \) is the central atom and \( B \) atoms are bonded to it. The geometry is typically bent or V-shaped.

2. **Effect of Electronegativity on Bond Angle**:
- When the electronegativity (EN) of the central atom \( A \) is high, it attracts the bonding electrons more strongly. This results in increased repulsion between the bond pairs, which tends to increase the bond angle \( B-A-B \).
- Therefore, we can conclude that the bond angle is proportional to the electronegativity of the central atom \( A \).
- **Conclusion**: Statement (I) is correct.

3. **Inverse Relationship with Electronegativity**:
- If the electronegativity of \( A \) is low, the bond pair-bond pair repulsion decreases, leading to a smaller bond angle. Thus, we can say that the bond angle is inversely proportional to the electronegativity of the central atom \( A \).
- **Conclusion**: Statement (II) is incorrect.

4. **Effect of Size of Central Atom**:
- The size of the central atom \( A \) affects the bond angle. A larger central atom has a lower ability to attract bonding electrons due to an increased distance from the nucleus to the bonding electrons. This results in decreased bond pair-bond pair repulsion and a smaller bond angle.
- Therefore, the bond angle is inversely proportional to the size of the central atom \( A \).
- **Conclusion**: Statement (III) is incorrect.

5. **Inverse Relationship with Size**:
- Since we established that as the size of the central atom increases, the bond angle decreases, we can say that the bond angle is proportional to \( \frac{1}{\text{Size of central atom}} \).
- **Conclusion**: Statement (IV) is correct.

### Final Answer:
The correct statements regarding the bond angle \( B-A-B \) in an \( AB_2 \) type molecule are:
- (I) Bond angle is proportional to EN of the central atom \( A \).
- (IV) Bond angle is proportional to \( \frac{1}{\text{Size of central atom}} \).

Thus, the correct options are (I) and (IV).