# How were the shapes of s, p, d, and f orbitals determined? How did they get their names of s, p, d, and f?

##### 1 Answer

The orbital shapes are actually representation of **contour**

Orbitals are actually bounded regions which describe an area where the electron can be .Probability density of an electron is the same as

**The wave function**

where

harmonic.

**nodes**.And it is not surprising that the radial wave function and the angular wave function plot is different for each orbital because the wavefunction is different for each orbital.

For the hydrogen atom wavefunctions for different quantum values(which can be assigned to different orbitals are )

We know that for a 1s orbital in the hydrogen atom

Therefore the the wavefunction is given by

The wavefunction of the 1s orbital doesn't has a angular component and that can be easily figured out by the equation describing it.

Because angular component Y is dependent on

For some equations you may see the angular part like

If you want a single function to describe all orbitals for the hydrogen atom then

If r here approaches

Different **quantum numbers**

I'll not go into this but all this can be deviated from the Schrodinger equation for the hydrogen atom (for **this** image)

Now when we know *why* the wavefunction is different for each orbital you can now analyze the plots

Now there are some ups and down in the plot which are caused by nodes

**What are nodes?**

Wavefunctions are the solutions to the TISE. Mathematically these differential equations create the nodes in the bound state wave functions, or orbitals. Nodes are the region where the electron probability density is 0.The two types of nodes are angular and radial.

Radial nodes occur where the radial component is 0

Angular nodes are either x, y, and z planes where electrons aren’t present while radial nodes are sections of these axes that are closed off to electrons.

As total number of nodes =

Apart from this there is another method to calculate it but then you have the separate the TISE for hydrogen atom in angular and radial component which is very useful while proving this statement

.

**Dotted clouds**

It is easier to visualize an orbital with dotted clouds

Sometimes negative and positive signs are used to describe the probability density of an electron in a pi orbital

**Naming of the orbitals**

They are derived from the description by early spectroscopists of certain series of alkali metal spectroscopic lines as **sharp,
principal, diffuse, and fundamental**. It has nothing to do with the orbitals.