The AUFBAU principle

The aufbau principle

Rules for working out electron arrangements

The AUFBAU principle (from the German for building up) is a set of basic rules for working out the electron arrangments in atoms. The rules are easy to apply:

Lower energy levels fill before higher energy levels. So the first principal energy level, 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.
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 3 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 singularily with parallel spins before pairing up any electrons. When the electrons do start to pair up they pair up with opposite spins:

The three p-orbits below each contain 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.

↓

↑

Also the arrangement below is 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 shows the energy levels for each of the sub-shells 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 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 easiest way to get the hang of working out electron arrangements 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 arrangements correct every time. The table below gives the electron arrangements for the first 10 elements. 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 getting the electron arrangements correct is that the Noble gases always have filled p-orbitals, that is they are always np⁶ (except helium). In fact the periodic table can help a lot in checking you have the correct electron arrangements. The periodic table can be divided up into blocks. These blocks are called the s-block, the d-block and the p-block simply because the outer valence electrons in each block are in s, p or d sub-shells. These blocks are shown in the image of the periodic table below and again at the foot of the page:

Writing Shorthand electronic notation for atoms

Element number 11 is sodium, it is in period 3 in 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. Writing out electron arrangements can become a bit tedious after a while, so we can use a shortened version of the electron arrangement. We can shorten the electronic configuration by simply writing out the inner electron arrangement from the preceding noble gas e.g. The noble gas before sodium is neon, its electronic configuration is 1s²2s²2p⁶, sodium the next element will be 1s²2s²2p⁶3s¹ or [Ne]3s¹. The noble gas Argon has an atomic number of 18, its electronic configuration will be 1s²2s²2⁶3s²3p⁶, so the next element potassium will be 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.

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

After element 20, calcium the 4s sub-shell is full and we enter the d-block of the periodic table. This block contains the transition metals. Many of the characteristic properties of the transition metals are due to the d-electrons. There are 5 d-orbitals, each holding 2 electrons, so there are 10 transition metals. The electronic configuration of the first row of the 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 arrangements 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 of half-filled and full d-sub-shells. By promoting an electron from the 4s sub-shell in each case we end up with either 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 outer shell electrons. 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 will contain a number of orbitals. These orbitals of similar energy will be grouped into sub-shells or sub-levels. These orbitals are named s, p, d and f.
Each orbital can hold 2 electron, which according to Hund's rule are filled singularly before the electrons pair up. When they do pair up they have opposite spins.
The lowest available energy level is filled first before moving onto the next energy level.