Which d-orbitals has its lobes along the axis

Options

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

Answer

To determine which d-orbitals have their lobes along the axis, we can analyze the shapes of the different d-orbitals.

### Step-by-Step Solution:

1. **Understand the d-Orbitals**: The five d-orbitals are designated as \(d_{xy}\), \(d_{xz}\), \(d_{yz}\), \(d_{x^2-y^2}\), and \(d_{z^2}\). Each has a unique shape and orientation in three-dimensional space.

2. **Identify Axial vs. Non-Axial Orbitals**:
- **Axial d-Orbitals**: These orbitals have lobes that are aligned along one of the principal axes (x, y, or z).
- **Non-Axial d-Orbitals**: These orbitals have lobes that are positioned between the axes.

3. **Analyze Each Option**:
- **Option 1: \(d_{xy}\)**: This orbital lies in the xy-plane and does not have lobes along the z-axis. Thus, it is non-axial.
- **Option 2: \(d_{x^2-y^2}\)**: This orbital has lobes along the x and y axes, making it an axial orbital.
- **Option 3: \(d_{z^2}\)**: This orbital has a distinct shape with a lobe along the z-axis, making it an axial orbital.
- **Option 4: \(d_{xz}\)**: This orbital lies in the xz-plane and does not have lobes along the y-axis. Thus, it is non-axial.

4. **Conclusion**: The d-orbitals that have lobes along the axis are \(d_{x^2-y^2}\) and \(d_{z^2}\). Therefore, the correct answer is options 2 and 3.

### Final Answer:
The d-orbitals that have their lobes along the axis are \(d_{x^2-y^2}\) and \(d_{z^2}\).

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