`p_(y)`-orbital can not form `pi` -bond by lateral overlap with :

Options

A. `d_(xz)`- orbital
B. `d_(x^(2)-y^(2))`-orbitals
C. `d_(xy)`-orbital
D. `p_(z)` -orbital

Answer

To solve the question regarding which orbital cannot form a pi bond by lateral overlap with the \( p_y \) orbital, we will analyze each option step by step.

### Step-by-Step Solution:

1. **Understanding Pi Bonds**:
- A pi bond is formed by the lateral (sideways) overlap of orbitals. This is crucial for determining which orbitals can interact with the \( p_y \) orbital.

2. **Analyzing Option A: \( d_{xz} + p_y \)**:
- The \( d_{xz} \) orbital lies in the x-z plane, while the \( p_y \) orbital is oriented along the y-axis.
- Since the \( p_y \) orbital is perpendicular to the x-z plane, when they approach each other, they overlap at a node (where the probability of finding an electron is zero).
- This results in zero overlap, meaning no pi bond can be formed.
- **Conclusion**: \( p_y \) cannot form a pi bond with \( d_{xz} \).

3. **Analyzing Option B: \( d_{x^2 - y^2} + p_y \)**:
- The \( d_{x^2 - y^2} \) orbital is oriented along the x and y axes.
- When \( p_y \) (along the y-axis) approaches \( d_{x^2 - y^2} \), they can only overlap head-on, leading to the formation of a sigma bond rather than a pi bond.
- **Conclusion**: \( p_y \) cannot form a pi bond with \( d_{x^2 - y^2} \).

4. **Analyzing Option C: \( d_{xy} + p_y \)**:
- The \( d_{xy} \) orbital lies in the x-y plane, which is the same plane as the \( p_y \) orbital.
- When these orbitals approach each other, they can overlap laterally, allowing for the formation of a pi bond.
- **Conclusion**: \( p_y \) can form a pi bond with \( d_{xy} \).

5. **Analyzing Option D: \( p_z + p_y \)**:
- The \( p_z \) orbital is oriented along the z-axis, while \( p_y \) is along the y-axis.
- When these orbitals approach each other, they also have a node where they do not overlap, resulting in zero overlap.
- **Conclusion**: \( p_y \) cannot form a pi bond with \( p_z \).

### Final Answer:
The \( p_y \) orbital cannot form a pi bond by lateral overlap with:
- **Option A**: \( d_{xz} \)
- **Option B**: \( d_{x^2 - y^2} \)
- **Option D**: \( p_z \)