The five d-orbitals are designated as `d_(xy), d_(yz), d_(xz), d_(x^(2) - y^(2))` and `d_(z^(2))` . Choose the correct statement.

Options

A. The shapes of the first three orbitals are similar but that of the fourth and fifth orbitals are different
B. The shapes of all five d-orbitals are similar.
C. The shapes of the first four orbitals are similar but that of the fifth orbital is different.
D. The shapes of all five d-orbitals are different

Explanation

To solve the question regarding the five d-orbitals and identify the correct statement, we will analyze the shapes and characteristics of each d-orbital.

### Step-by-Step Solution:

1. **Identify the d-orbitals**: The five d-orbitals are:
- \(d_{xy}\)
- \(d_{yz}\)
- \(d_{xz}\)
- \(d_{x^2 - y^2}\)
- \(d_{z^2}\)

2. **Understand the shapes of the d-orbitals**:
- The \(d_{xy}\), \(d_{yz}\), \(d_{xz}\), and \(d_{x^2 - y^2}\) orbitals have a **double-dumbbell shape**. This means they have lobes that are oriented between the axes.
- The \(d_{z^2}\) orbital has a different shape. It has a **dumbbell shape** along the z-axis with a ring around the center. This is distinct from the other four orbitals.

3. **Compare the shapes**:
- The first four orbitals (\(d_{xy}\), \(d_{yz}\), \(d_{xz}\), and \(d_{x^2 - y^2}\)) are similar in that they all exhibit the double-dumbbell shape.
- The \(d_{z^2}\) orbital is different due to its unique shape, which includes a ring.

4. **Conclusion**: Based on the shapes, we can conclude that:
- The first four d-orbitals are similar in shape, while the \(d_{z^2}\) orbital is different.

5. **Select the correct statement**: The correct statement is that the first four d-orbitals are similar, but the fifth one (\(d_{z^2}\)) is different.

### Final Answer:
The correct statement is that the first four d-orbitals are similar in shape, while the \(d_{z^2}\) orbital is different.