Which of the following d-orbitals has dough-nut shape ?

Options

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

Answer

To determine which of the d-orbitals has a doughnut shape, we can follow these steps:

### Step 1: Understand the d-Orbitals
The d-orbitals consist of five different types: d_xy, d_xz, d_yz, d_x²-y², and d_z². Each of these orbitals has a unique shape and orientation in three-dimensional space.

### Step 2: Visualize the Shapes
- **d_xy**: This orbital has four lobes arranged in a cloverleaf shape, lying in the xy-plane.
- **d_xz**: Similar to d_xy, this orbital has four lobes but is oriented in the xz-plane.
- **d_yz**: This orbital also has four lobes, oriented in the yz-plane.
- **d_x²-y²**: This orbital has four lobes aligned along the x and y axes.
- **d_z²**: This orbital has a different structure. It consists of a lobular shape along the z-axis and a ring (or doughnut) around the equatorial plane.

### Step 3: Identify the Donut Shape
Among the d-orbitals, the d_z² orbital is characterized by its unique shape that includes a toroidal (doughnut-like) region around the center, along with two lobes extending along the z-axis.

### Conclusion
The d-orbital that has a doughnut shape is the **d_z² orbital**.

### Final Answer
The d-orbital with a doughnut shape is **d_z²**.

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