Which of the following orbital is with the four lobes present on the axis ?

Options

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

Answer

To determine which orbital has four lobes present on the axis, we need to analyze the characteristics of the different d orbitals. The options we will consider are: \(d_{z^2}\), \(d_{xy}\), \(d_{yz}\), and \(d_{x^2 - y^2}\).

### Step-by-Step Solution:

1. **Understanding Orbital Shapes**:
- The d orbitals have specific shapes and orientations in three-dimensional space. Each type of d orbital has a unique arrangement of lobes.

2. **Analyzing \(d_{z^2}\)**:
- The \(d_{z^2}\) orbital has a distinct shape that consists of a lobe along the z-axis and a donut-shaped region around the xy-plane. This does not have four lobes aligned on the axes.

3. **Analyzing \(d_{xy}\)**:
- The \(d_{xy}\) orbital has lobes that lie between the x and y axes. It does not have lobes directly on the axes, so this option is also not correct.

4. **Analyzing \(d_{yz}\)**:
- The \(d_{yz}\) orbital has lobes that lie between the y and z axes. Similar to \(d_{xy}\), it does not have lobes on the axes, making this option incorrect as well.

5. **Analyzing \(d_{x^2 - y^2}\)**:
- The \(d_{x^2 - y^2}\) orbital has four lobes that are oriented along the x and y axes. This means that two lobes are aligned along the x-axis and two lobes are aligned along the y-axis, fulfilling the requirement of having four lobes present on the axes.

6. **Conclusion**:
- Based on the analysis, the orbital with four lobes present on the axis is \(d_{x^2 - y^2}\). Therefore, the correct answer is **Option 4: \(d_{x^2 - y^2}\)**.