Electrons in the Schrödinger Atom

For most chemists, the nucleus matters as a positive center to the atom, but the details of the nucleus’ inner workings is left to the physicists. The really interesting stuff, the very heart of chemistry and chemical reactions, is about the electrons. Chemists study where the electrons are and how they interact with each other and with the nuclei of atoms.

That’s why chemistry teachers and professors spend the time delving into Bohr and Schrödinger’s theories. Only by understanding electrons can we really understand what is going on in a chemistry lab or, for that matter, in the world at large.

Remember that Schrödinger’s theory left us with an orbital diagram that looked like this

For the sake of understanding, let's just look at levels 1 and 2. In addition, let's be a little lazy with the spacing. In other words, we'll keep the orbitals in the right order, but we'll condense the distance between them for visual convenience. That will leave us with this diagram to work with.

In order to determine which orbitals are occupied by electrons there are three rules that we follow. They are:

1. The Aufbau Principle
2. The Pauli Exclusion Principle
3. Hund's Rule

The Aufbau Principle

The Aufbau Principle states that electrons occupy the lowest energy level possible. (Aufbau is German for "build up".)

We can see this when we think about a hydrogen atom. Hydrogen has only 1 electron so, according to the Aufbau Principle, that electron will go into the 1s orbital. (We'll use a partial arrow to indicate an electron. We'll explain that choice in the discussion of the Pauli Exclusion Principle)

This diagram is often written in a chemistry short-hand called electron configuration. Electron configuration describes the orbitals of the atom and tells how many electrons are found in each. For hydrogen, the electron configuration is 1s1. In this notation, the large number tells us the energy level, the letter tells us the orbital type and the superscripted number tells the number of electrons present in the orbital.

The Pauli Exclusion Principle

The Pauli Exclusion Principle states that no two electrons in the same atom can have an identical set of quantum numbers. That is actually an easier statement than it sounds. Remember that the first three quantum numbers (n, ℓ and m) describe orbitals. For instance n=3, ℓ=1, m=-1 is the 3px orbital. The fourth quantum number is spin (discussed on this page). 

So, if the first three quantum numbers define a particular orbital, then it follows that each orbital can only hold two electrons, which have opposite spins.

Helium shows this. Helium has two electrons which will be as low as possible (in the 1s orbital) but which will have opposite spins. We show this by "flipping" the arrow symbol.

The electron configuration of helium is 1s2.

Lithium, with three electrons, will have two electrons in the 1s orbital (as above). The third electron will be in the 2s, since the 1s is filled and 2s is then the lowest available orbital.

The electron configuration of lithium is 1s2 2s1.

Beryllium adds another electron to the 2s orbital (with down spin) giving an electron configuration of 1s2 2s2.

Boron puts the 5th electron in to a 2p orbital (since the 1s and 2s are both filled). Although it doesn't really matter which of the p orbitals is occupied (since atoms don't have axes), we generally draw it into the first orbital. Giving the diagram below. The configuration of Boron is 1s2 2s2 2p1. (Note that we don't worry about px, or py or pz)

Hund's Rule

Hund's Rule states that when electrons are added to a set of orbitals with identical energies, they will remain separate as long as possible. In much simpler terms, we add one electron to each before putting 2 electrons in any.

A simple, human analogy of this is when someone gets on a public bus. Assuming that you don't know anyone on the bus, most people tend to sit by themselves rather than sharing a seat with someone if they can. Only when the bus gets crowded will people start to share seats with strangers.

So for carbon, the 6th electron will go into a different p orbital.

The electron configuration is 1s2 2s2 2p2. Note that we do NOT differentiate between the different p orbitals in the electron configuration.

There are, of course, more details about electron configurations.