# Aufbau Principle

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## What is the Aufbau Principle?

The Aufbau principle dictates the manner in which electrons are filled in the atomic orbitals of an atom in its ground state. It states that electrons are filled into atomic orbitals in the increasing order of orbital energy level. According to the Aufbau principle, the available atomic orbitals with the lowest energy levels are occupied before those with higher energy levels.

The word ‘Aufbau’ has German roots and can be roughly translated as ‘construct’ or ‘build up’. A diagram illustrating the order in which atomic orbitals are filled is provided below. Here, ‘n’ refers to the principal quantum number and ‘l’ is the azimuthal quantum number.

The Aufbau principle can be used to understand the location of electrons in an atom and their corresponding energy levels. For example, carbon has 6 electrons and its electronic configuration is 1s22s22p2.

It is important to note that each orbital can hold a maximum of two electrons (as per the Pauli exclusion principle). Also, the manner in which electrons are filled into orbitals in a single subshell must follow Hund’s rule, i.e. every orbital in a given subshell must be singly occupied by electrons before any two electrons pair up in an orbital.

### Salient Features of the Aufbau Principle

• According to the Aufbau principle, electrons first occupy those orbitals whose energy is the lowest. This implies that the electrons enter the orbitals having higher energies only when orbitals with lower energies have been completely filled.
• The order in which the energy of orbitals increases can be determined with the help of the (n+l) rule, where the sum of the principal and azimuthal quantum numbers determines the energy level of the orbital.
• Lower (n+l) values correspond to lower orbital energies. If two orbitals share equal (n+l) values, the orbital with the lower n value is said to have lower energy associated with it.
• The order in which the orbitals are filled with electrons is: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, and so on.

Exceptions

The electron configuration of chromium is [Ar]3d54s1 and not [Ar]3d44s2 (as suggested by the Aufbau principle). This exception is attributed to several factors such as the increased stability provided by half-filled subshells and the relatively low energy gap between the 3d and the 4s subshells.

The energy gap between the different subshells is illustrated below.

Half filled subshells feature lower electron-electron repulsions in the orbitals, thereby increasing the stability. Similarly, completely filled subshells also increase the stability of the atom. Therefore, the electron configurations of some atoms disobey the Aufbau principle (depending on the energy gap between the orbitals).

For example, copper is another exception to this principle with an electronic configuration corresponding to [Ar]3d104s1. This can be explained by the stability provided by a completely filled 3d subshell.

## Electronic Configuration using the Aufbau Principle

### Writing the Electron Configuration of Sulphur

• The atomic number of sulphur is 16, implying that it holds a total of 16 electrons.
• As per the Aufbau principle, two of these electrons are present in the 1s subshell, eight of them are present in the 2s and 2p subshell, and the remaining are distributed into the 3s and 3p subshells.
• Therefore, the electron configuration of sulphur can be written as 1s22s22p63s23p4.

### Writing the Electron Configuration of Nitrogen

• The element nitrogen has 7 electrons (since its atomic number is 7).
• The electrons are filled into the 1s, 2s, and 2p orbitals.
• The electron configuration of nitrogen can be written as 1s22s22p3

### How are buildings constructed?

Construction of a building begins at the bottom. The foundation is laid, and the building goes up step by step. You obviously cannot start with the roof, since there is no place to hang it. The building goes from the lowest level to the highest level in a systematic way.

## Aufbau Principle

In order to create ground state electron configurations for any element, it is necessary to know the way in which the atomic sublevels are organized in order of increasing energy. Figure 5.15.2 shows the order of increasing energy of the sublevels.

Figure 5.15.2: Electrons are added to atomic orbitals in order from low energy (bottom of the graph) to high (top of the graph), according to the Aufbau principle. Principle energy levels are color coded, while sublevels are grouped together, and each circle represents an orbital capable of holding two electrons. (Credit: Christopher Auyeung; Source: CK-12 Foundation; License: CC BY-NC 3.0)

The lowest energy sublevel is always the 1s sublevel, which consists of one orbital. The single electron of the hydrogen atom will occupy the 1s orbital when the atom is in its ground state. As we proceed to atoms with multiple electrons, those electrons are added to the next lowest sublevel: 2s, 2p, 3s

, and so on. The Aufbau principle states that an electron occupies orbitals in order from lowest energy to highest. The Aufbau (German for building up, construction) principle is sometimes referred to as the “building up” principle. It is worth noting that in reality, atoms are not built by adding protons and electrons one at a time, and that this method is merely an aid to understand the end result.

As seen in the figure above, the energies of the sublevels in different principal energy levels eventually begin to overlap. After the 3p sublevel, it would seem logical that the 3d sublevel should be the next lowest in energy. However, the 4s sublevel is slightly lower in energy than the 3d sublevel and thus fills first. Following the filling of the 3d sublevel is the 4p, then the 5s and the 4d. Note that the 4f sublevel does not fill until just after the 6s sublevel. Figure 5.15.2 is a useful and simple aid for keeping track of the order of fill of the atomic sublevels.

Figure 5.15.3: The Aufbau principle is illustrated in the diagram by following each red arrow in order from top to bottom: 1s, 2s, 2p, 3s, etc. (Credit: Christopher Auyeung; Source: CK-12 Foundation; License: CC BY-NC 3.0)

Summary

• The Aufbau principle gives the order of electron filling in an atom.
• It can be used to describe the locations and energy levels of every electron in a given atom.

Review

1. What is the Aufbau principle?
2. Which orbital is filled after the 2p

? Which orbital is filled after 4s? Which orbital is filled after 6s?

### Trends in Expected Electron Configuration

The four “rules” above can be used as guidelines to predict the ground state electron configuration of atoms, the filling of subshells, and the configuration of electrons in degenerate orbitals. However, the utility of these guidelines for predicting actual electron configurations requires more nuanced knowledge of the relative energy levels of orbitals.

Generally, orbital energy levels directly correspond to their shell number. Additionally, orbitals within a shell generally follow the energetic trend where s<p<d<f. Although these general trends for relative orbital energy levels hold true for most of the main block elements (the s – and p-blocks), there are important exceptions in the orbital energy levels of transition metal atoms and ions of the d- and f-blocks.

Figure 2.2.3.5. This is a depiction of the periodic table that highlights the s-, p-, d-, and f- blocks in different colors. Violations of the expected trend in electron configurations are outlined in a heavy black line. Several elements of the d block and f block violate the general trends in electron configuration because their orbital energy levels do not follow general trends. (CC-BY-NC-SA; Kathryn Haas)

Elements that violate general trends in electron configuration are outlined with a dark line in Figure 2.2.3.5

. All of the exceptions are within the d- and f- blocks, and the violations are caused by an unexpected order of the orbital energy levels.

In the next section you will learn why the orbital energy levels correlate with shell number and why subshells within a shell usually follow the trend that s<p<d<f. You will also learn why there are occasional exceptions to this trend and how these exceptions influence elemental properties.

### Silicon Electron Configuration Example Problem

This is a worked example problem showing the steps necessary to determine the electron configuration of an element using the principles learned in the previous sections

### Problem

Determine the electron configuration of silicon.

### Solution

Silicon is element No. 14. It has 14 protons and 14 electrons. The lowest energy level of an atom is filled first. The arrows in the graphic show the s quantum numbers, spin up and spin down.

• Step A shows the first two electrons filling the 1s orbital and leaving 12 electrons.
• Step B shows the next two electrons filling the 2s orbital leaving 10 electrons. (The 2p orbital is the next available energy level and can hold six electrons.)
• Step C shows these six electrons and leaves four electrons.
• Step D fills the next lowest energy level, 3s with two electrons.
• Step E shows the remaining two electrons starting to fill the 3p orbital.

One of the rules of the Aufbau principle is that the orbitals are filled by one type of spin before the opposite spin starts to appear. In this case, the two spin-up electrons are placed in the first two empty slots, but the actual order is arbitrary. It could have been the second and third slot or the first and third.

The electron configuration of silicon is:

1s22s2p63s23p2

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## Notation and Exceptions to the Aufbau Principal

The notation seen on period tables for electron configurations uses the form:

nOe

• n is the energy level
• O is the orbital type (s, p, d, or f)
• e is the number of electrons in that orbital shell.

For example, oxygen has eight protons and eight electrons. The Aufbau principle says the first two electrons would fill the 1s orbital. The next two would fill the 2s orbital leaving the remaining four electrons to take spots in the 2p orbital. This would be written as:

1s22s2p4

The noble gases are the elements that fill their largest orbital completely with no leftover electrons. Neon fills the 2p orbital with its last six electrons and would be written as:

1s22s2p6

The next element, sodium would be the same with one additional electron in the 3s orbital. Rather than writing:

1s22s2p43s1

and taking up a long row of repeating text, a shorthand notation is used:

[Ne]3s1

Each period will use the notation of the previous period’s noble gas. The Aufbau principle works for nearly every element tested. There are two exceptions to this principle, chromium, and copper.

Chromium is element No. 24, and according to the Aufbau principle, the electron configuration should be [Ar]3d4s2. Actual experimental data shows the value to be [Ar]3d5s1. Copper is element No. 29 and should be [Ar]3d92s2, but it has been to be determined to be [Ar]3d104s1.

The graphic shows the trends of the periodic table and the highest energy orbital of that element. It is a great way to check your calculations. Another method of checking is to use a periodic table, which includes this information.

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