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 will analyze the given options one by one.

### Step-by-Step Solution:

1. **Identify the orbitals**: The question provides four options:
- A) dz²
- B) dxy
- C) dyz
- D) dx²y²

2. **Analyze the dz² orbital**:
- The dz² orbital has a shape that consists of two lobes along the z-axis and a donut-shaped region around the xy-plane.
- **Conclusion**: This orbital has only 2 lobes on the z-axis, so it does not meet the criteria.

3. **Analyze the dxy orbital**:
- The dxy orbital is oriented in the xy-plane and has lobes that lie between the x and y axes.
- **Conclusion**: This orbital does not have lobes on the axes themselves, so it does not meet the criteria.

4. **Analyze the dyz orbital**:
- The dyz orbital is oriented in the yz-plane and has lobes that lie between the y and z axes.
- **Conclusion**: Similar to the previous ones, this orbital does not have lobes on the axes, so it does not meet the criteria.

5. **Analyze the dx²y² orbital**:
- The dx²y² orbital has four lobes that are oriented along the x and y axes. Specifically, it has lobes that extend outwards along the x-axis and y-axis.
- **Conclusion**: This orbital has four lobes present on the axes, which meets the criteria stated in the question.

### Final Answer:
The correct answer is **D) dx²y²**.

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