Electron Configurations Using 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 the sub-levels within each principal energy level and how the energy of these sub-levels varies inside the atom. The image below shows a simplified model of the Bohr atom which is the model we used in GCSE chemistry to describe the internal structure of the atom, you can see the familiar electron energy levels or shells which surround the nucleus; while the model on the right shows a simplified representation of how the principal energy levels which were the shells in the GCSE model of the atom within are split in various sub-levels; which are designated s, p, d and f. For more details on sub-levels, orbitals and principal energy levels the visit the page on electrons, orbitals and quantum numbers.

Splitting the degeneracy within sub-levels

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 the presence of more than one electron introduces electron-electron repulsion which 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, this os outlined in the image below.

Additionally, there can be energy crossovers between the electron shells; for example the 3d sub-level has a higher energy than the 4s sub-level in some atoms, this might at first seem surprising but you may recall that as we move from one principal energy level to the next the energy separation between different principal energy levels decreases, so while the difference in energy between the first and second principal energy levels is quite large; the energy separation between the second and third principal energy levels is much smaller and the difference in energy between the third and fourth principal energy levels is even smaller.

Effective nuclear charge and electron-electron repulsion

Furthermore, as the principal quantum number increases, the energy differences between electron shells and sub-levels decrease dramatically. This is why electrons from higher shells or energy levels can be lost more easily, and why the order we fill the sub-levels is not simply always just "one shell after another".

The diagram below shows how these energies compare, take note for example of the large difference in energy between the first and second principal energy levels and the overlap of the sub-levels in the third and fourth energy levels, the 4s and 3d sub-levels do not follow the pattern you may have expected.

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 sub-level 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:

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.

Quick check questions

Check your understanding of Hund's Rule and the Pauli Exclusion Principle by answering the two questions below:

1. An analogy which is often used to describe Hund's rule of maximum multiplicity is that of passengers sitting on a bus, explain how we can use the seating patterns of passengers on a bus as an analogy to explain Hund's rule?

Comic style image of passengers on a bus, used to illustrate Hund's rule of maximum multiplicity.

The analogy of passengers boarding a bus and choosing seats is used to explain Hund's rule of maximum multiplicity. In this analogy the bus seats represent orbitals of equal energy within a subshell while the passengers represent electrons. The analogy works as follows:

Individual Occupancy: Just as passengers tend to occupy an empty seat alone before having to share a seat with someone else, electrons will occupy each orbital individually before any orbital is filled with a second electron- people for some reason don't like to sit beside other passengers; they would rather sit by themselves!

Parallel Spin: The passengers desire to sit alone in an empty seat and all facing the same way, probably towards the front of the bus represents electrons with parallel spins. This corresponds to the lower-energy, more stable state where electrons in different orbitals of the same sub-level have the same spin. This is a lower-energy, more stable arrangement.

Maximum Multiplicity: The state where each passenger has their own seat is the one with the maximum number of people sitting alone. Similarly, the most stable electron configuration is the one with the maximum number of unpaired electrons with parallel spins. This is known as maximum multiplicity.

2. Explain in simple terms what the Pauli exclusion principle is.

Image showing two electrons with opposite spins in an orbital- as per the Pauli Exclusion Principle.

The Pauli Exclusion Principle states that no two electrons in an atom can have the exact same set of quantum numbers.

As a consequence, an atomic orbital can hold a maximum of only two electrons, and these two electrons must have opposite spins. One electron is designated with a 'spin-up' (↑) or spin value of ½ while the other electron is assigned with a 'spin-down' (↓) spin or a spin value of -½. This fundamental principle is crucial for understanding the arrangement of electrons in atoms, leading to the familiar electron shell structure and the periodicity of elements in the periodic table

Filling the electron shells

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

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.

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:

Writing Shorthand electronic notation for atoms

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

For example 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.

Electronic configurations for the elements Na to Ca

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 those shown 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 electronic configurations for 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 are 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: