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:

One of these rules is the Pauli Exclusion Principle; named after the Austrian physicist Wolfgang Pauli. This principle states that no orbital can hold more than 2 electrons and that these electrons must have opposite spins, that is no two electrons in an atom can have the same four quantum numbers.

Image of Wolfgang Pauli and Friedrich Hund

The other rule is Hund's rule, names after the German physicist Friedrich Hund. Hund's rule states that when filling degenerate orbitals the electrons fill the orbitals singularly and with parallel spins before pairing up to fill the orbitals.

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:

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.
All orbitals can hold a maximum of 2 electrons and they are paired up with opposite spins-the Pauli Exclusion Principle.
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.

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

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

The electron shells with the same principal quantum number contain a number of orbitals. The orbitals with similar energy are grouped into sub-shells or sub-levels. These orbitals are named s, p, d, and f.
Each orbital can hold a maximum of 2 electrons, which, according to Hund's rule, are filled singly before the electrons pair up. When they do pair up, they have opposite spins.
The lowest available energy level is filled first before moving on to the next energy level.