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What is the Aufbau principle?

The Aufbau principle , also known as the rain rule or construction principle, is a practical rule that allows predicting the electronic configuration of the vast majority of the elements in the periodic table, as well as that of their ions.

This principle establishes that, as protons are added to the nucleus, one by one to build each chemical element successively, the electrons are also successively added to the lowest-energy atomic orbitals that are available.

In other words, Aufbau established that there is a specific order according to which the atomic orbitals can be filled. This order is explained below.

The order of filling the orbitals according to the Aufbau principle

The order in which the atomic orbitals are filled depends on their energy level. The golden rule is that these energy levels are filled from lowest to highest, as if it were a building in which the apartments on the lower floors must be filled in order to access the higher floors.

The following graph shows schematically the energy levels of the first atomic orbitals ordered from lowest to highest energy.

In this image, each square represents a particular orbital in which only 2 electrons fit. Each group of squares of the same color represents a sublevel of energy.

These sublevels are identified by a number and a letter (1s, 3p, 3d, etc.). The number indicates the main energy level, while the letter indicates the type of orbital that the group forms.

According to this scheme, the first sublevel to be filled is the 1s (the one with the lowest energy of all), then comes the 2s, the 2p, the 3s, the 3p, the 4s, the 3d and so on.

Despite how easy it is to establish the order of filling if you have a graph like the previous one, it is difficult to remember the particular order in which the different sublevels go. For this, what some call “the rule of rain” is used.

This rule consists of two simple steps:

Step 1

A list is made in which each line corresponds to an energy level, and contains one after another, all the sublevels available at that energy level.

For example, the first line corresponds to level 1 (n = 1) and only contains the sublevel 1s; the second line corresponds to level n = 2 and contains sublevels 2s and 2p; the third contains the sublevels 3s, 3p and 3d, and so on.

The full list looks like this:

Step 2

Descending diagonals are drawn from right to left, one below the other, as shown below.

These lines resemble the path of water droplets during a windy rain, which is why this graph is often called “the rain method”. The order of filling is determined by the order in which these diagonals touch the sublevels in the list.

Based on the previous figure, the energy order of the orbitals and, therefore, the order in which they must be filled is:

This order of filling is the only one that really matters when writing the electron configuration of an atom. A filling these sublevels, one must remember that in the sublevels s only fit 2 electrons, where p fit 6, the d holds 10 and the f fit 14.

Exceptions to the Aufbau principle

The Aufbau principle clearly states that you cannot start filling a sublevel until you have completely filled all previous sublevels. However, there are some exceptions to this rule.

In some cases, the atom prefers to have an energy sublevel that is just half full than to have an incomplete one that is not half full. In those cases, the actual electron configuration of the atom does not agree with the order predicted by the rain method.

For example, according to the Aufbau principle, the chromium atom should have an electron configuration ending in 4s 2 3d 4 . However, its actual configuration is 4s 1 3d 5 since the sublevels 4s and 3d are half full while in the other configuration they are not.

The same happens with copper whose configuration ends in 4s 1 3d 10 , instead of 4s 2 3d 9 , since this fills the sublevel d and the s is half full.

Examples of the application of the Aufbau principle

Here are 5 examples of elements that comply with the Aufbau principle:

Example 1: Electron configuration of sodium

Sodium is element 11, so it has 11 protons and 11 electrons. Its electron configuration is 1s 2 2s 2 2p 6 3s 1 .

Example 2: Electronic configuration of argon

Argon (Ar) is element 18, so it has 18 protons and 18 electrons. Its electron configuration is therefore 1s 2 2s 2 2p 6 3s 2 3p 6 . It can be seen that it completely filled its sublevels s and p.

Example 3: Electron configuration of gallium

Gallium (Ga) is element 31, so it has 31 protons and 31 electrons. Its electron configuration is 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 1 .

This can be written in brief as [Ar] 4s 2 3d 10 4p 1 , where [Ar] represents the electron configuration of argon presented in the previous example.

Example 4: Electronic configuration of carbon

Carbon (C) is element 6, so it has 6 protons and 6 electrons. Its electron configuration is 1s 2 2s 2 2p 2 .

Example 5: Electronic configuration of chlorine

Chlorine (Cl) is element 17. Its 17 electrons are distributed according to the following electronic configuration: 1s 2 2s 2 2p 6 3s 2 3p 5 or [Ne] 3s 2 3p 5 .

Additional examples of exceptions to the Aufbau principle

Here are 2 additional examples of items that violate the Aufbau principle:

Example 6: Electronic configuration of Molybdenum

Molybdenum (Mo) is element 42. The first 36 electrons are distributed in the same way as in krypton, but their valence electrons do not follow the normal order. Instead of having the electron configuration [Kr] 5s 2 4d 4 , its configuration is [Kr] 5s 1 4d 5 , similar to what happens with chromium.

Example 7: Electronic configuration of Silver

Silver (Ag, element 47) exhibits a violation of the Aufbau principle similar to that of copper. Its electron configuration is [Kr] 5s 1 4d 10 instead of [Kr] 5s 2 4d 9.

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