Radial distribution of a 3d orbital

[Dethrone]

How do I sketch the radial distribution of a $3d_{x^2-y^2}$ orbital? :D

 

[I like Serena]

How do I sketch the radial distribution of a $3d_{x^2-y^2}$ orbital? :D

Hey Rido!

Check out for instance Atomic orbitals on wiki?
It has some nice and different types of representations for the $3d_{x^2-y^2}$ orbital. (Mmm)

 

[jacobi1]

Also, try The Orbitron: a gallery of atomic orbitals and molecular orbitals.
It has many different images of all different kinds of orbitals and their equations, but more importantly, it has explanations of how the shapes and equations arise.

 

[Dethrone]

Thanks ILS and jacobi! (Cool)

I was able to find this image, which I'm pretty sure is the radial distribution of the 3D orbital.

View attachment 3854

In general, an orbital has $n-l-1$ radial nodes, and in this case, $n=3$, $l=2$, so there are $0$ radial nodes. This agrees with the image because there are no roots on the graph. There are however, two angular nodes / nodal planes that are perpendicular to the axis, but does not need to be reflected in the graph.

 

[CellCoree]

To sketch the radial distribution of a $3d_{x^2-y^2}$ orbital, you will need to follow these steps:

1. Start by drawing a Cartesian coordinate system with the origin at the center. This will represent the nucleus of the atom.

2. Next, draw three perpendicular axes (x, y, and z) that intersect at the origin. These axes will help you visualize the orientation of the orbital.

3. The $3d_{x^2-y^2}$ orbital is a complex orbital with two nodal planes, one along the x-axis and one along the y-axis. These nodal planes divide the orbital into four lobes, with two lobes along the x-axis and two lobes along the y-axis.

4. To sketch the radial distribution, start by drawing the four lobes as four elongated ovals, two along the x-axis and two along the y-axis. These lobes represent the regions where the electron density is highest.

5. Next, draw the nodal plane along the x-axis as a flat line passing through the center of the x-axis. This plane represents the region where the electron density is zero.

6. Similarly, draw the nodal plane along the y-axis as a flat line passing through the center of the y-axis.

7. The electron density in the lobes decreases as you move away from the nucleus, so make sure to draw the lobes with decreasing size as you move away from the origin.

8. Finally, add shading or color to the lobes to represent the different phases of the orbital. The lobes along the x-axis will have a different phase than the lobes along the y-axis.

This sketch will give you a visual representation of the radial distribution of a $3d_{x^2-y^2}$ orbital. Remember, the shape and orientation of an orbital can vary depending on the atom and its electronic configuration, so this sketch is just a general representation.