Which d-orbital has its four lobes along the axis?

Options

A. `d_(xy)`
B. `d_(yz)`
C. `d_(zx)`
D. `d_(x^(2)-y^(2))`

Answer

To determine which d-orbital has its four lobes along the axis, we need to analyze the shapes of the five types of d-orbitals. Here’s a step-by-step solution:

### Step 1: Identify the Types of d-Orbitals
The five types of d-orbitals are:
1. \(d_{xy}\)
2. \(d_{yz}\)
3. \(d_{zx}\)
4. \(d_{x^2-y^2}\)
5. \(d_{z^2}\)

### Step 2: Analyze the Shapes of Each d-Orbital
- **\(d_{xy}\)**: The lobes of this orbital lie between the x and y axes. They do not lie along the axes.
- **\(d_{yz}\)**: Similar to \(d_{xy}\), the lobes lie between the y and z axes.
- **\(d_{zx}\)**: The lobes of this orbital lie between the z and x axes.
- **\(d_{x^2-y^2}\)**: This orbital has lobes that lie along the x and y axes. Specifically, it has four lobes positioned along the x and y axes.
- **\(d_{z^2}\)**: This orbital has a different shape, with a lobe along the z-axis and a torus around the xy-plane.

### Step 3: Identify the Correct Orbital
From the analysis:
- The \(d_{x^2-y^2}\) orbital has its four lobes aligned along the x and y axes. Therefore, it is the d-orbital that has its four lobes along the axes.

### Conclusion
The d-orbital that has its four lobes along the axis is **\(d_{x^2-y^2}\)**.

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