Correctly match is:

Options

A. `d_(x^(2)-y^(2))` atomic orbital -one nodal plane
B. `p_(y)` atomic orbital -Two nodal planes
C. `sigma_(p_(x))` -`psi`(gerade)
D. `P_(p_(y))` -`psi`(ungerade)

Explanation

To solve the question of correctly matching the statements about atomic orbitals and their properties, we will analyze each option step by step.

### Step 1: Analyze the first option
**Statement:** "d x square minus y square atomic orbital have one nodal plane."

- **Explanation:** The \(d_{x^2-y^2}\) orbital has a specific shape that resembles a four-leaf clover oriented along the x and y axes. In this orbital, the electron density is distributed in the lobes along the x and y axes, and there is a plane (the xy-plane) where the electron density is zero. Therefore, this orbital does indeed have one nodal plane.

**Conclusion:** This statement is **correct**.

### Step 2: Analyze the second option
**Statement:** "PY atomic orbital have two nodal planes."

- **Explanation:** The \(p_y\) orbital has a dumbbell shape oriented along the y-axis. It has no nodal planes, as the electron density exists in the lobes on either side of the nucleus. The only nodal plane present is the plane that bisects the orbital along the x-axis, which is one nodal plane, not two.

**Conclusion:** This statement is **incorrect**.

### Step 3: Analyze the third option
**Statement:** "sigma p x is g-rayed."

- **Explanation:** The term "gerade" refers to orbitals that have a center of symmetry. The \( \sigma_{p_x} \) orbital is symmetric with respect to the origin, meaning that if you were to draw a plane through the center, the left side would mirror the right side. Thus, it is indeed a gerade orbital.

**Conclusion:** This statement is **correct**.

### Step 4: Analyze the fourth option
**Statement:** "structure of py orbital is like this and when we pass center of symmetry from here then the left part is equals to the right part that means it is also a gerade molecule."

- **Explanation:** The \(p_y\) orbital is also symmetric about the origin, similar to the \(p_x\) orbital. Therefore, it is also a gerade orbital. However, if this statement claims it is ungerade, then it is incorrect.

**Conclusion:** This statement is **incorrect**.

### Final Matching
From the analysis:
1. \(d_{x^2-y^2}\) atomic orbital has one nodal plane - **Correct**
2. \(p_y\) atomic orbital has two nodal planes - **Incorrect**
3. \(\sigma_{p_x}\) is gerade - **Correct**
4. \(p_y\) structure is ungerade - **Incorrect**

### Summary of Correct Matches
- Correct matches are:
- \(d_{x^2-y^2}\) has one nodal plane.
- \(\sigma_{p_x}\) is gerade.