How To Do Orbital Diagrams

Electron orbital diagrams and written configurations tell you which orbitals are filled and which are partially filled for any atom. The number of valence electrons impacts on their chemical properties, and the specific ordering and properties of the orbitals are important in physics, so many students have to get to grips with the basics. The good news is that orbital diagrams, electron configurations (both in shorthand and full form) and dot diagrams for electrons are really easy to understand once you've grasped a few basics.

Electron configurations are expressed through a notation that looks like this: 1s² 2s² 2p¹. Learn the three main parts of this notation to understand how it works. The first number tells you the "energy level," or the principal quantum number (n). The second letter tells you the value of (l), the angular momentum quantum number. For l = 1, the letter is s, for l = 2 it's p, for l = 3 it's d, for l = 4 it's f and for higher numbers it increases alphabetically from this point. Remember that s orbitals contain a maximum of two electrons, p orbitals a maximum of six, d a maximum of 10 and f a maximum of 14.

The Aufbau principle tells you that the lowest-energy orbitals fill first, but the specific order isn't sequential in a way that's easy to memorize. See Resources for a diagram showing the filling order. Note that the n = 1 level only has s orbitals, the n = 2 level only has s and p orbitals, and the n = 3 level only has s, p and d orbitals.

These rules are easy to work with, so the notation for the configuration of scandium is:

1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹

Which shows that the whole n = 1 and n = 2 levels are full, the n = 4 level has been started, but the 3d shell only contains one electron, whereas it has a maximum occupancy of 10. This electron is the valence electron.

Identify an element from the notation by simply counting the electrons and finding the element with a matching atomic number.

Writing out every single orbital for heavier elements is tedious, so physicists often use a shorthand notation. This works by using the noble gases (in the far right column of the periodic table) as a starting point and adding the final orbitals onto them. So scandium has the same configuration as argon, except with electrons in two extra orbitals. The shorthand form is therefore:

[Ar] 4s² 3d¹

Because the configuration of argon is:

[Ar] = 1s² 2s² 2p⁶ 3s² 3p⁶

You can use this with any elements apart from hydrogen and helium.

Orbital diagrams are like the configuration notation just introduced, except with the spins of electrons indicated. Use the Pauli exclusion principle and Hund's rule to work out how to fill shells. The exclusion principle states that no two electrons can share the same four quantum numbers, which basically results in pairs of states containing electrons with opposite spins. Hund's rule states that the most stable configuration is the one with the highest possible number of parallel spins. This means that when writing orbital diagrams for partially full shells, fill in all of the up-spin electrons before adding any down-spin electrons.

This example shows how orbital diagrams work, using argon as an example:

3p ↑ ↓ ↑ ↓ ↑ ↓

3s ↑ ↓

2p ↑ ↓ ↑ ↓ ↑ ↓

2s ↑ ↓

1s ↑ ↓

The electrons are represented by the arrows, which also indicate their spins, and the notation on the left is standard electron configuration notation. Note that the higher-energy orbitals are at the top of the diagram. For a partially full shell, Hund's rule requires that they're filled in this way (using nitrogen as an example).

2p ↑ ↑ ↑

2s ↑ ↓

1s ↑ ↓

Dot diagrams are very different to orbital diagrams, but they're still very easy to understand. They consist of the symbol for the element in the center, surrounded by dots indicating the number of valence electrons. For example, carbon has four valence electrons and the symbol C, so it is represented as:

∙

∙ C ∙

∙

And oxygen (O) has six, so it is represented as:

∙

∙∙ O ∙

∙∙

When electrons are shared between two atoms (in covalent bonding), the atoms share the dot in the diagram in the same way. This makes the approach very useful for understanding chemical bonding.