Which d-orbital does not have four lobes?

Options

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

Explanation

To determine which d-orbital does not have four lobes, we will analyze the shapes of the different d-orbitals.

### Step-by-Step Solution:

1. **Understanding d-Orbitals**:
- d-orbitals are a set of five orbitals in the electron configuration of atoms. They are designated as \(d_{xy}\), \(d_{xz}\), \(d_{yz}\), \(d_{x^2-y^2}\), and \(d_{z^2}\).

2. **Analyzing \(d_{x^2-y^2}\)**:
- The \(d_{x^2-y^2}\) orbital has four lobes. The lobes are oriented along the x and y axes.
- **Conclusion**: This orbital has four lobes.

3. **Analyzing \(d_{xy}\)**:
- The \(d_{xy}\) orbital also has four lobes. These lobes are positioned between the x and y axes.
- **Conclusion**: This orbital has four lobes.

4. **Analyzing \(d_{xz}\)**:
- The \(d_{xz}\) orbital has four lobes as well, with lobes situated between the x and z axes.
- **Conclusion**: This orbital has four lobes.

5. **Analyzing \(d_{yz}\)**:
- The \(d_{yz}\) orbital has four lobes, with lobes located between the y and z axes.
- **Conclusion**: This orbital has four lobes.

6. **Analyzing \(d_{z^2}\)**:
- The \(d_{z^2}\) orbital is different. It has a unique shape with only two lobes, resembling a "lower leaf" structure. The lobes are oriented along the z-axis, and there is a spherical region around the nucleus.
- **Conclusion**: This orbital does not have four lobes.

### Final Answer:
The d-orbital that does not have four lobes is **\(d_{z^2}\)**.