`e_(g)` orbitals include

Options

A. `d_(xy) and d_(yz)`
B. `d_(yz) and d_(xz)`
C. `d_(yz) and d_(xz)`
D. `d_(x_(2)-y_(2)) and d_(z_(2))`

Answer

To solve the question regarding which orbitals are included in the \( e_g \) set, we can follow these steps:

### Step 1: Understand the d-Orbitals
The d-orbitals consist of five different types: \( d_{xy} \), \( d_{xz} \), \( d_{yz} \), \( d_{x^2-y^2} \), and \( d_{z^2} \). These orbitals can be grouped based on their energy levels when a metal ion is surrounded by ligands.

**Hint:** Remember that the d-orbitals are split into two groups when ligands approach a metal ion.

### Step 2: Identify the Splitting of d-Orbitals
When ligands approach a transition metal ion, the d-orbitals split into two sets due to the crystal field effect. These sets are:
- \( t_{2g} \): This set includes \( d_{xy} \), \( d_{xz} \), and \( d_{yz} \).
- \( e_g \): This set includes \( d_{x^2-y^2} \) and \( d_{z^2} \).

**Hint:** Focus on the orientation of the orbitals with respect to the axes to understand their splitting.

### Step 3: Identify the \( e_g \) Orbitals
From the splitting, we can identify the \( e_g \) orbitals specifically. The \( e_g \) orbitals are:
- \( d_{x^2-y^2} \)
- \( d_{z^2} \)

These orbitals are oriented along the axes (x, y, and z) and experience greater repulsion from the ligands, leading to higher energy.

**Hint:** Visualize the shapes of the orbitals to see how they align with the axes.

### Step 4: Conclusion
Thus, the \( e_g \) orbitals include:
- \( d_{x^2-y^2} \)
- \( d_{z^2} \)

**Final Answer:** The \( e_g \) orbitals include \( d_{x^2-y^2} \) and \( d_{z^2} \).