Which of the following pairs of d-orbitals will have electron density along the axes ?

Options

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

Explanation

To determine which pairs of d-orbitals have electron density along the axes, we first need to understand the shapes and orientations of the five d-orbitals. The d-orbitals are:

1. **d_xy**: Lies in the xy-plane, between the x and y axes.
2. **d_yz**: Lies in the yz-plane, between the y and z axes.
3. **d_zx**: Lies in the zx-plane, between the z and x axes.
4. **d_x²-y²**: Lies along the x and y axes, with lobes pointing towards the x and y axes.
5. **d_z²**: Has a lobe along the z-axis and a ring in the xy-plane.

Now, let's analyze the pairs given in the question:

1. **d_xy and d_yz**: Neither of these orbitals has electron density along the axes. They lie in their respective planes.
2. **d_yz and d_zx**: Similar to the first pair, these orbitals lie in their respective planes and do not have electron density along the axes.
3. **d_xy and d_x²-y²**: The d_xy does not have electron density along the axes, while d_x²-y² does.
4. **d_x²-y² and d_z²**: The d_x²-y² has lobes along the x and y axes, and d_z² has a lobe along the z-axis.

From this analysis, we can conclude that the pairs of d-orbitals that have electron density along the axes are:

**Correct Answer: d_x²-y² and d_z².**

### Step-by-Step Solution:
1. **Identify the d-orbitals**: Recognize the five types of d-orbitals: d_xy, d_yz, d_zx, d_x²-y², and d_z².
2. **Analyze the shapes**: Understand the orientation of each d-orbital in three-dimensional space.
3. **Check for electron density along the axes**: Determine which orbitals have lobes that extend along the x, y, or z axes.
4. **Evaluate the pairs**: Compare the pairs given in the question to see which ones contain orbitals with electron density along the axes.
5. **Select the correct pair**: Identify that the pair d_x²-y² and d_z² has electron density along the axes.