Which two orbitals are located along the axis, and not between the axis?

Options

A. (a) `d_(xy),d_(z^2)`
B. (b) `d_(xy),d_(yz)`
C. (c) `d_(yz),d_(zx)`
D. (d) `d_(z^2),d_(x^2-y^(2))`

Answer

To solve the question of which two orbitals are located along the axis and not between the axis, we need to analyze the given d orbitals. Let's go through the solution step by step.

### Step-by-Step Solution:

1. **Understand the d Orbitals**:
The d orbitals consist of five types: \(d_{xy}\), \(d_{yz}\), \(d_{zx}\), \(d_{x^2-y^2}\), and \(d_{z^2}\). Each of these orbitals has a distinct shape and orientation in three-dimensional space.

2. **Identify Axial vs. Non-Axial Orbitals**:
- **Axial Orbitals**: These are the orbitals that are aligned along the axes of the coordinate system (x, y, or z).
- **Non-Axial Orbitals**: These orbitals are positioned in between the axes and do not align directly with any of the coordinate axes.

3. **Analyze Each Option**:
- **Option A: \(d_{xy}\) and \(d_{z^2}\)**:
- \(d_{xy}\) is located in the xy-plane and does not align with the z-axis, hence it is non-axial.
- \(d_{z^2}\) has a lobular shape along the z-axis, making it axial.
- **Conclusion**: This option is incorrect.

- **Option B: \(d_{xy}\) and \(d_{yz}\)**:
- Both \(d_{xy}\) and \(d_{yz}\) are located in their respective planes and do not align with the z-axis or x-axis directly.
- **Conclusion**: This option is incorrect.

- **Option C: \(d_{yz}\) and \(d_{zx}\)**:
- Similar to the previous options, both \(d_{yz}\) and \(d_{zx}\) are also located in their respective planes and do not align directly with the axes.
- **Conclusion**: This option is incorrect.

- **Option D: \(d_{x^2-y^2}\) and \(d_{z^2}\)**:
- \(d_{x^2-y^2}\) is oriented along the x and y axes, making it axial.
- \(d_{z^2}\) is also aligned along the z-axis, making it axial as well.
- **Conclusion**: This option is correct.

4. **Final Answer**:
The two orbitals that are located along the axis and not between the axis are \(d_{x^2-y^2}\) and \(d_{z^2}\).