`d_(z^(2))`-orbital has:

Options

A. Two lobes along z-axis
B. Ring along yz-plane
C. Ring along xy-plane
D. Ring along x axis

Answer

To determine the characteristics of the \(d_{z^2}\) orbital, we can analyze its structure step by step.

### Step 1: Understanding the \(d_{z^2}\) Orbital
The \(d_{z^2}\) orbital is one of the five \(d\) orbitals found in the d-subshell. It has a unique shape compared to the other \(d\) orbitals.

### Step 2: Visualizing the Orbital
To visualize the \(d_{z^2}\) orbital, we can start by noting its features:
- It has two lobes that extend along the z-axis.
- There is a ring (or a torus) that lies in the xy-plane.

### Step 3: Drawing the Orbital
1. **Lobes**: Draw two elongated lobes pointing upwards and downwards along the z-axis.
2. **Ring**: Draw a circular ring in the xy-plane, centered at the origin. This ring represents the area where the electron density is present in the xy-plane.

### Step 4: Identifying Characteristics
Based on the visualization:
- The lobes are indeed aligned along the z-axis.
- The ring is present in the xy-plane.

### Step 5: Conclusion
From the analysis, we can conclude that:
- The \(d_{z^2}\) orbital has two lobes along the z-axis and a ring in the xy-plane.

### Final Answer
The correct characteristics of the \(d_{z^2}\) orbital are:
- A: Two lobes along the z-axis (Correct)
- C: A ring in the xy-plane (Correct)

Thus, the correct options are A and C.

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