Assuming the bond direction to the z-axis, which of the overlapping of atomic orbitals of two atom (A) and (B) will result in bonding ?
(I) s-orbital of A and `p_(x)` orbital of B (II) s-orbital of A and `p_(z)` orbital of B
(III) `p_(y)`-orbital of A and `p_(z)` orbital of B (IV) s-orbital of both (A) and (B)

Options

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

Answer

To determine which overlapping of atomic orbitals between two atoms (A and B) will result in bonding, we need to analyze each case based on the orientation of the orbitals and the direction of the bond, which is assumed to be along the z-axis.

### Step-by-Step Solution:

1. **Identify the Orbitals in Each Case**:
- (I) s-orbital of A and p_x orbital of B
- (II) s-orbital of A and p_z orbital of B
- (III) p_y orbital of A and p_z orbital of B
- (IV) s-orbital of both A and B

2. **Analyze Case (I)**:
- **s-orbital of A and p_x orbital of B**:
- The s-orbital is spherical and can overlap with the p_x orbital, but since the p_x orbital is oriented along the x-axis and the bond is along the z-axis, there is no effective overlap.
- **Conclusion**: This will not result in bonding.

3. **Analyze Case (II)**:
- **s-orbital of A and p_z orbital of B**:
- The s-orbital can overlap head-on with the p_z orbital, which is oriented along the z-axis.
- **Conclusion**: This will result in bonding, as there is effective overlap.

4. **Analyze Case (III)**:
- **p_y orbital of A and p_z orbital of B**:
- The p_y orbital is oriented along the y-axis, while the p_z orbital is along the z-axis. Since these orbitals are perpendicular to each other, they cannot overlap effectively.
- **Conclusion**: This will not result in bonding.

5. **Analyze Case (IV)**:
- **s-orbital of both A and B**:
- Both s-orbitals can overlap head-on along the z-axis.
- **Conclusion**: This will result in bonding, as there is effective overlap.

6. **Final Conclusion**:
- The cases that result in bonding are (II) s-orbital of A and p_z orbital of B, and (IV) s-orbital of both A and B. Therefore, the answer is options (II) and (IV).

### Summary of Results:
- **Bonding Interactions**:
- (II) s-orbital of A and p_z orbital of B
- (IV) s-orbital of both A and B

### Final Answer:
The overlapping of atomic orbitals that will result in bonding are (II) and (IV).