The AUFBAU principle

To get the most from this page you should already know the meaning of the following terms: principal quantum number, sub-levels (s, p, d and f) and orbitals. If you need to refresh your memory then click here for some help.

Energy levels within atoms

One crucial concept to consider when working out the electron configurations of atoms is the splitting of sub-levels within each principal energy level. In hydrogen atoms and other one-electron ions such as helium ions (He+) the sub-levels present within any particular principal energy level are degenerate, this simply means they have the same energy. However, in multi-electron atoms electron-electron repulsion breaks this degeneracy, causing the sub-levels within the atoms to have different energies. For example in multi-electron atoms; the 2s sub-level has lower energy compared to the 2p sub-level.

Additionally, there can be energy crossovers between electron shells; for example the 3d sub-level has a higher energy than the 4s sub-level in some atoms. This energy splitting of the sub-levels arises from two main factors: electron-electron repulsions and the effective nuclear charge experienced by each electron in the atom. Furthermore, as the principal quantum number increases, the energy differences between electron shells decrease dramatically. This is outlined in the diagram below:

image to show how the energy sub-levels in multi-electron atoms are split

Working out electron configurations

Now as you likely already know the electrons in atoms occupy various energy levels or electron shells that are further split into various sub-levels (s, p, d, and f) and these sub-levels contain orbitals, which are regions in 3d space where there is a very high probability of finding the electrons. The electrons are placed into the various s, p, d and f orbitals in the atom according to certain rules:

The aufbau principle

Rules for working out electron configurations

The AUFBAU principle (from the German for building up) is a set of basic rules devised by Niels Bohr to predict the electron configurations in atoms. The rules are easy to apply:

  1. Lower energy levels fill before higher energy levels. So the first principal energy level, that is the first electron shell fills before moving onto the second electron shell and this of course fills before moving onto the next principal energy level or electron shell.
  2. All orbitals can hold a maximum of 2 electrons and they are paired up with opposite spins-the Pauli Exclusion Principle.
  3. When filling degenerate orbitals, that is orbitals with the same energy we use Hund's rule of maximum multiplicity. For example considering filling the p-orbitals. There are three degenerate p-orbitals so they can hold a maximum of 6 electrons. According to Hund's rule if we have a set of degenerate orbitals then the electrons will fill them up singularly and with parallel spins before pairing up any electrons. When the electrons do start to pair up they pair up with opposite spins; this is outlined below:
The three degenerate p-orbits are shown below and here each contains one electron all with parallel spins, this is allowed as it follows Hund's rule.

↑ ↑ ↑

The arrangement below is not allowed, the p-orbitals are all occupied singularly but the electrons do not have parallel spins.

↓ ↑ ↑

The arrangement below is also not allowed since this time the electrons are paired up in one of the p-orbitals when an empty degenerate orbital is available.

↑ ↓ ↑

Filling the electron shells

orbital energy level diagram for a multi-electron atom

The electron energy levels or shells will fill up according to the rules set out above in the aufbau principle. The diagram opposite right shows the energy levels for each of the sub-levels and orbitals in a multi-electron atom. If we start at the bottom, that is the sub-level which is lowest in energy we can clearly work out the order in which to place the electrons in the sub-levels and orbitals, they will fill in the following order:

1s → 2s → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → 4f → 5d → 6p → 7s → 5f → 6d


orbital filling order You may also have seen a diagram similar to the one shown opposite left; it simply shows an easier way to remember the order in which the sub-shells or sub-levels fill. Simply start at the top and follow the arrows downwards to get the same order as shown above. The diagram below shows an outline of how to work out the electron configuration for the elements sodium (11Na), sulfur (16S) and the transition metal titanium (22Ti).

Now when you write out electron configurations for atoms the sub-level is written first and the number of electrons present in the sub-level is written as a superscript; for example if a 3p sub-level contains 5 electrons its electron configuration would be written as 3p5 and if a 2p sub-level contains 3 electrons it would be written as 2p3.


The easiest way to get the hang of working out electron configurations is simply practice writing them out. If you do this you will quickly notice some rather obvious patterns across the periodic table which should make sure you get the electron configuration correct every time.


Examples- electron configurations

The image below shows the electron configurations for the elements sodium, sulfur and titanium.

Example using the elements sodium, sulfur and titanium on how to work out the electronic configuration of an atom interms of levels and sub-levels.

The table below gives the electron arrangements for the first 10 elements found in the periodic table. Why not work them out yourself first and then check your answers with the ones below?

Electron arrangements for the first 10 elements

element atomic number 1s orbital 2s orbital 2p orbital electron arrangement
H 1 ↑ 1s1
He 2 ↑ ↓ 1s2
Li 3 ↑ ↓ ↑ 1s22s1
Be 4 ↑ ↓ ↑ ↓ 1s22s2
B 5 ↑ ↓ ↑ ↓ ↑ 1s22s22p1
C 6 ↑ ↓ ↑ ↓ ↑ ↑ 1s22s22p2
N 7 ↑ ↓ ↑ ↓ ↑ ↑ ↑ 1s22s22p3
O 8 ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↑ 1s22s22p4
F 9 ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ 1s22s22p5
Ne 10 ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑↓ 1s22s22p6

A good way to tell if you are working out the electron configurations correctly is that the noble gases always have filled p-orbitals, that is they are always ns2np6 (except helium), here n is simply the principal quantum number or shell number. In fact the periodic table can help you a lot in checking that you worked out the correct electron configuration for any particular element.

Now the elements in the periodic table are organised into blocks (s-block, p-block, d-block, and f-block) based on the sub-level (s, p, d, or f) occupied by their valence electrons (outermost electrons). These blocks are shown in the image of the periodic table below and again in a more concise form at the foot of the page:


electron blocks in the periodic table

Writing Shorthand electronic notation for atoms

Cartoon showing how to make things easy Element number 11 is the alkali metal sodium, it is found in period 3 of the periodic table, this means its outer valence electrons are in the third electron shell and since it is in the s-block these electrons will be in the 3s sub-shell. Now writing out electron configurations can become a bit tedious after a while, so we can use a shortened version of the electron configuration to make it easier and quicker to write out.

We can shorten the electronic configuration by simply writing out the inner electron configuration from the preceding noble gas e.g. the noble gas before the alkali metal sodium in the periodic table is neon, now neon's electronic configuration is 1s22s22p6, sodium the next element will have an electron configuration of 1s22s22p63s1 or [Ne]3s1. The noble gas Argon has an atomic number of 18, so its electron configuration will be 1s22s2263s23p6, so the next element after argon is the alkali metal potassium and it will have the electron configuration: 1s22s2263s23p64s1 or [Ar]4s1. Remember the 4s sub-shell is lower in energy than the 3d sub-shell so it fills first.

The table below gives the electronic configuration of the elements sodium to calcium. You may want to practice working them out and then checking your answers with that in the table below.

element atomic number 1s orbital 2s orbital 2p orbital 3s orbital 3p orbital 4s orbital electron arrangement
Na 11 ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ [Ne]3s1
Mg 12 ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ [Ne]3s2
Al 13 ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ [Ne]3s23p1
Si 14 ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↑ [Ne]3s23p2
P 15 ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↑ ↑ [Ne]3s23p3
S 16 ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↑ [Ne]3s23p4
Cl 17 ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ [Ne]3s23p5
Ar 18 ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ [Ne]3s23p6
K 19 ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ [Ar]4s1
Ca 20 ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ [Ar]4s2

The transition metals

After element 20; calcium the 4s sub-shell is full and we enter the d-block of the periodic table. This block houses the transition metals, elements whose unique properties largely stem from their partially filled d-orbitals. With five d-orbitals, each capable of holding two electrons, the d-block accommodates a total of 10 transition metals. The electronic configurations for the first ten transition metals is shown below:

element atomic number 1s orbital 2s orbital 2p orbital 3s orbital 3p orbital 4s orbital 3d electron arrangement
Sc 21 ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ [Ar]4s23d1
Ti 22 ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↑ [Ar]4s23d2
V 23 ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↑ ↑ [Ar]4s23d3
Cr 24 ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↑ ↑ ↑ ↑ ↑ [Ar]4s13d5
Mn 25 ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↑ ↑ ↑ ↑ [Ar]4s23d5
Fe 26 ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↑ ↑ ↑ [Ar]4s23d6
Co 27 ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑↓ ↑ ↓ ↑ ↑ ↑ [Ar]4s23d7
Ni 28 ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↑ [Ar]4s23d8
Cu 29 ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ [Ar]4s13d10
Zn 30 ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ ↑ ↓ [Ar]4s23d10

Anomalous electron configurations

You may have noticed something odd with the electron configurations of two of the d-block metals. Chromium for example has an electron configuration of [Ar]4s13d5 whereas you might have expected it to be [Ar]4s23d4, similarly copper has an electron configuration of [Ar] 4s13d10 whereas you might have expected it to be [Ar] 4s23d9. In both cases an electron from the 4s sub-shell has been promoted into the 3d sub-shell, the reason for this is due to the unusual stability associated with half-filled and full d sub-shells.

By promoting an electron from the 4s sub-shell in each case we end up with either a half-filled 3d sub-shell in the case of chromium and a full 3d sub-shell in the case of copper. This transfer of an electron from the 4s sub-shell lowers the overall energy of the atom.

While working out the electron configurations for the elements you will have no doubt noticed that the periodic table is divided into blocks based on the location of the outer shell electrons of a particular element, an outline of this is shown below:

s,p,d and f blocks in the periodic table

Key Points

Practice questions

Check your understanding - Questions on AUFBAU principle

Check your understanding - Additional questions on AUFBAU principle

Check your understanding - Multiple choice questions on AUFBAU principle

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