Which of the following d-orbital has electron density in all the three axes

Options

A. `3 d_(xy)`
B. `3 d_(x^2 - y^2)`
C. `3 d_(x^2)`
D. `3d_(yz)`

Answer

To solve the question "Which of the following d-orbital has electron density in all the three axes?", we need to analyze the shapes of the d-orbitals and determine which one has electron density distributed across the x, y, and z axes.

### Step-by-Step Solution:

1. **Understanding d-Orbitals**:
- d-orbitals are a set of five orbitals that have different shapes and orientations. The five d-orbitals are: d_xy, d_xz, d_yz, d_x²-y², and d_z².

2. **Analyzing Each d-Orbital**:
- **d_xy**: This orbital lies in the x-y plane. It has no electron density along the z-axis. Therefore, it does not have electron density in all three axes.
- **d_xz**: This orbital lies in the x-z plane. It has no electron density along the y-axis. Thus, it also does not have electron density in all three axes.
- **d_yz**: This orbital lies in the y-z plane. It has no electron density along the x-axis. Hence, it does not have electron density in all three axes.
- **d_x²-y²**: This orbital has lobes along the x and y axes, but it has no electron density along the z-axis. Therefore, it does not have electron density in all three axes.
- **d_z²**: This orbital has a unique shape, often described as a "doughnut" shape. It has lobes along the z-axis and a ring of electron density in the x-y plane. This means it has electron density in all three axes (x, y, and z).

3. **Conclusion**:
- Among the d-orbitals, the **d_z²** orbital is the one that has electron density in all three axes (x, y, and z).

### Final Answer:
The d-orbital that has electron density in all three axes is **d_z²**.