d- orbital with maximum electron density along two axes will be

Options

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

Answer

To determine which d-orbital has maximum electron density along two axes, we need to analyze the shapes and orientations of the five d-orbitals: \(d_{xy}\), \(d_{yz}\), \(d_{zx}\), \(d_{x^2-y^2}\), and \(d_{z^2}\).

### Step-by-Step Solution:

1. **Identify the d-orbitals**:
The five d-orbitals are:
- \(d_{xy}\)
- \(d_{yz}\)
- \(d_{zx}\)
- \(d_{x^2-y^2}\)
- \(d_{z^2}\)

2. **Understand the orientation of each orbital**:
- **\(d_{xy}\)**: This orbital has lobes in the xy-plane, oriented between the x and y axes.
- **\(d_{yz}\)**: This orbital has lobes in the yz-plane, oriented between the y and z axes.
- **\(d_{zx}\)**: This orbital has lobes in the zx-plane, oriented between the z and x axes.
- **\(d_{x^2-y^2}\)**: This orbital has lobes along the x and y axes, maximizing electron density along these two axes.
- **\(d_{z^2}\)**: This orbital has a different shape, with a lobular structure along the z-axis and a donut-shaped ring in the xy-plane.

3. **Analyze electron density along two axes**:
- The \(d_{x^2-y^2}\) orbital has lobes that extend along both the x and y axes, indicating maximum electron density along these two axes.
- The \(d_{xy}\), \(d_{yz}\), and \(d_{zx}\) orbitals have lobes that are oriented between axes, thus do not maximize density along two axes.
- The \(d_{z^2}\) orbital does not have significant density along the x and y axes.

4. **Conclusion**:
The d-orbital with maximum electron density along two axes is the \(d_{x^2-y^2}\) orbital.

### Final Answer:
The d-orbital with maximum electron density along two axes is **\(d_{x^2-y^2}\)**.

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