## 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:

1. 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.
2. All orbitals can hold a maximum of 2 electrons and they are paired up with opposite spins.
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 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

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

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:

## 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.