Though the five d-orbitals are degenerate, the first four d-orbitals are similar to each other in shape whereas the fifth d-orbital is different from others. What is the name of the fifth orbital?

Options

A. (a) `d_(x^(2)-y^(2))`
B. (b) `d_(z^(2))`
C. (c) `d_(xz)`
D. (d) `d_(xy)`

Answer

To solve the question regarding the fifth d-orbital that is different in shape from the other four d-orbitals, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding d-Orbitals**:
- There are five d-orbitals in total: \(d_{xy}\), \(d_{yz}\), \(d_{zx}\), \(d_{x^2-y^2}\), and \(d_{z^2}\).

2. **Identifying Similarities**:
- The first four d-orbitals (\(d_{xy}\), \(d_{yz}\), \(d_{zx}\), and \(d_{x^2-y^2}\)) have a similar shape. They are often described as having a "double-lobed" structure, which means they have two regions of electron density.

3. **Analyzing the Fifth d-Orbital**:
- The fifth d-orbital, \(d_{z^2}\), has a different shape compared to the other four. Its structure is often described as having a "doughnut" shape around the nucleus with a lobe extending along the z-axis.

4. **Naming the Fifth d-Orbital**:
- Based on the analysis, the fifth d-orbital that is different in shape from the others is called \(d_{z^2}\).

### Final Answer:
The name of the fifth d-orbital is \(d_{z^2}\).

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