`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 determine which orbital cannot form a pi bond through lateral overlap with a p_y orbital, we need to analyze each option provided in the question. Let's break down the solution step by step.

### Step 1: Understanding the p_y Orbital
The p_y orbital is oriented along the y-axis. It has a specific shape that allows it to overlap with other orbitals to form bonds. Pi bonds are formed through lateral (side-to-side) overlap of orbitals.

**Hint:** Remember that pi bonds require lateral overlap, while sigma bonds require head-on overlap.

### Step 2: Analyzing Option 1: d_{xz} + p_y
The d_{xz} orbital lies between the x and z axes. When we consider the overlap of d_{xz} with p_y, we find that the p_y orbital overlaps with the node of the d_{xz} orbital. This results in zero overlap, meaning no pi bond can form.

**Hint:** Check the orientation of the orbitals to see if they can overlap effectively.

### Step 3: Analyzing Option 2: d_{x^2 - y^2} + p_y
The d_{x^2 - y^2} orbital is oriented along the x-axis and y-axis. When it approaches the p_y orbital, they can overlap head-on, leading to the formation of a sigma bond, not a pi bond.

**Hint:** Identify if the orbitals can form a sigma bond, which indicates they cannot form a pi bond.

### Step 4: Analyzing Option 3: d_{xy} + p_y
The d_{xy} orbital is situated in the xy-plane. When it overlaps with the p_y orbital, they can achieve lateral overlap, allowing for the formation of a pi bond.

**Hint:** Look for lateral overlaps that can lead to pi bond formation.

### Step 5: Analyzing Option 4: p_z + p_y
The p_z and p_y orbitals are oriented along the z-axis and y-axis, respectively. When they approach each other, they do not overlap effectively, resulting in zero overlap, meaning no pi bond can form.

**Hint:** Consider if the orbitals are oriented in such a way that they can overlap at all.

### Conclusion
Based on the analysis:
- Option 1 (d_{xz} + p_y) cannot form a pi bond due to zero overlap.
- Option 2 (d_{x^2 - y^2} + p_y) forms a sigma bond, not a pi bond.
- Option 3 (d_{xy} + p_y) can form a pi bond.
- Option 4 (p_z + p_y) cannot form a pi bond due to zero overlap.

Thus, the correct options that cannot form a pi bond with p_y are **Option 1 and Option 4**.

### Final Answer
The p_y orbital cannot form a pi bond by lateral overlap with:
- **Option 1: d_{xz}**
- **Option 4: p_z**