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 atoms A and B will result in bonding, we need to analyze each case based on the orientation of the orbitals and the type of overlap that occurs. We are assuming the bond direction is along the z-axis.

### Step-by-Step Solution:

1. **Case (I): s-orbital of A and pₓ orbital of B**
- The s-orbital is spherical and can overlap in any direction. However, the pₓ orbital is oriented along the x-axis.
- Since the bond direction is along the z-axis, there will be no effective overlap between the s-orbital and the pₓ orbital.
- **Conclusion**: No bonding occurs.

2. **Case (II): s-orbital of A and pᶻ orbital of B**
- The s-orbital is spherical and can overlap in any direction, while the pᶻ orbital is oriented along the z-axis.
- This results in a head-on overlap, which is symmetrical.
- **Conclusion**: Bonding occurs, forming a sigma bond.

3. **Case (III): pᵧ orbital of A and pᶻ orbital of B**
- The pᵧ orbital is oriented along the y-axis, while the pᶻ orbital is oriented along the z-axis.
- Since these orbitals are perpendicular to each other, there will be no effective overlap.
- **Conclusion**: No bonding occurs.

4. **Case (IV): s-orbital of both A and B**
- Both s-orbitals are spherical and can overlap effectively.
- This results in a symmetrical overlap along the z-axis.
- **Conclusion**: Bonding occurs, forming a sigma bond.

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