Visualization of a potassium atom with electron configuration

Question

Say we have a normal potassium atom. It is understood that its electron configuration is

$$1s^{2}\,2s^{2}\,2p^{6}\,3s^{2}\,3p^{6}\,4s^{1}.$$

This configuration contains the energy levels, orbital types and electron orientations of a potassium atom. However, even though it is clear in numbers and words, would it be possible to visualize a realistic potassium atom? Upon research online, I found that currently used education models are all Bohr models, which aren't accurate in the depiction of electron orbitals (they are actually electron clouds with varying density). This is especially true when visualizing different electron orbital levels and the spins of individual electrons.

I understand that the Bohr model is clearer for educational purposes. However, it can be very misleading when you get into the nooks and crannies of quantum configuration.

Thanks a lot!

Answer 1

As you mention in the question, the $1s$, $2s$, etc orbitals can be thought of as fuzzy clouds where the density of the cloud represents the electron density. To get the total electron density of the atom you simply add together all the clouds.

This sounds complicated, but the sum of all the three $p$ orbitals or all the five $d$ orbitals, or all the seven $f$ orbitals, and so on, has spherical symmetry. The $s$ orbitals also have spherical symmetry, so for the potassium atom we have:

• $1s$ looks like a fuzzy sphere

• $2s$ looks like a fuzzy sphere

• the sum of the three $2p$ looks like a fuzzy sphere

• $3s$ looks like a fuzzy sphere

• the sum of the three $3p$ looks like a fuzzy sphere

• $4s$ looks like a fuzzy sphere

and the slightly disappointing result is that if you could see a potassium atom it would just look like a fuzzy sphere. The only way you would get a non-spherical atom is if you have a partially filled $p$, $d$, etc orbital. For example aluminium is $1s^22s^22p^63s^23p^1$ and the filled $1s^22s^22p^63s^2$ orbitals form a fuzzy sphere with a single non-spherical $3p$ electron added on, so it looks like a very slightly prolate sphere. However the emphasis is on slightly. The single $3p$ electron makes little difference to the fuzzy sphere formed by the other twelve electrons and at a first glance the atom still looks like a fuzzy sphere.

As an undergraduate project I spent a happy few weeks computing the electron density of atoms using the Hartree-Fock method and the results were uniformly boring as they were all fuzzy spheres!