Orbitals - 1. Occupancy & Energy

Key properties of orbitals

Orbitals

Three essential features of every orbital

Let's examine how these properties relate to atomic orbitals, or the orbitals of single atoms, by depicting them in orbital diagrams.

Occupancy

Refers to the number of electrons in an orbital, which leads us to the Pauli exclusion principle: according to the Pauli exclusion principle -- a single orbital can contain a maximum of two electrons if they have different spins.

Spins can be pictured as "up" or "down."

Let's show an orbital diagram for a filled 1s orbital with two electrons: one with "up" spin and one with "down."

This corresponds to the electron configuration of helium, "1s2" (recall that an electron configuration refers to how an atom's electrons occupy the atomic orbitals).
Depict the 1s orbital as a horizontal line.

This shows it has a discrete energy level.

Show the first electron with an "up" spin by drawing a half-arrow pointing up.
Denote the second electron with a "down" spin by drawing a half-arrow pointing down next to the first arrow.

Multiple orbitals with different energies on a vertical scale

Now we'll consider how to position multiple orbitals with different energies on a vertical scale.

Under energy, write that energy increases with increasing distance from the nucleus. 1s is the lowest, followed by 2s, followed by 2p, and so on.
Write that electrons occupy the lowest energy orbital first. This is known as the Aufbau principle.
Electrons will fill orbitals in a way that achieves the most stable, lowest-energy configuration. This includes the case of degenerate orbitals, which are orbitals with the same energy level.
Denote that degenerate orbitals are occupied first by single electrons with "up" spin before they are occupied by paired electrons. This is known as Hund's rule.
Since electrons repulse one another, it costs less energy to keep them separated in different orbitals than to have them paired. Having the same spin ensures that the electrons will not pair until all the orbitals have been singly occupied.

Orbital diagram for oxygen

Show the orbital diagram for oxygen; it has the configuration 1s22s22p4.
Draw the 1s orbital as a horizontal line. To the left, draw an up arrow and indicate that this is the direction of increasing energy.
Draw the 2s orbital above the 1s orbital.
Above the 2s orbital, draw the three 2p orbitals as three lines side-by-side.

Now that we have constructed the diagram, we can bring in the electrons.

Add the four 2p electrons one-by-one to the 2p orbitals

First, add one electron with "up" spin to each of the three orbitals.
Finally, add the last electron with "down" spin to pair with one of the other three.

Most orbital diagrams only show occupancy and energy, but the shape of the orbitals can be included for more accuracy.