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The Aufbau principle explains the arrangement of electrons in atoms. Electrons occupy shells, subshells, and orbitals, with each subshell having a maximum number of electrons. The principle states that electrons fill the lowest energy orbitals first, with exceptions for some elements. It is a useful tool for learning about atomic structure.
The Aufbau principle is a method of explaining the arrangements of electrons within the atoms of different chemical elements. Atomic theory can be complex and difficult, but this principle provides a simple set of rules that can explain the electronic configurations of the vast majority of elements. The term comes from a German word meaning “construction” and refers to the way electrons are added to atoms from lighter to heavier elements. The principle isn’t perfect and there are some exceptions, but it’s a very useful tool for learning about atomic structure.
Shells, subshells and orbitals
To understand the Aufbau principle, it is necessary to first examine the structure of the atom. The electrons can be said to orbit the positively charged nucleus; however, there are some rules that dictate how they can be arranged. In the generally accepted model, they occupy shells, which can be thought of as concentric, around the nucleus. Within these are the subshells, within which are the orbitals. An orbital describes the space inhabited by an electron.
The shells are numbered 1, 2, 3, etc., in order of increasing distance from the nucleus – and increasing energy levels – with the numbers also indicating how many subshells they may have. Subshells are labeled s, p, def, in general order of the energy possessed by the electrons in the orbitals they contain. Each has a maximum number of orbitals it can hold: s has only one, p has three, d has five, and f has seven, and each orbital can hold a maximum of two electrons. All orbitals within a subshell have the same energy level.
This is summarized in the table below:
Shells, subshells and orbitals
Shell Subshell Orbitals Maximum electrons
1s 12
2 s1 2
— p3 6
3 s1 2
— p3 6
— d5 10
4 s1 2
— p3 6
— d5 10
— f7 14
This shows, for example, that shell 3 has a subshell s, ap and ad. When filled completely, it would have a total of 2 + 6 + 10 = 18 electrons. The electron configuration of an element can be written, for example, as:
1s22s22p1
which is element number five, boron. This shows the shell number followed by the subshell letter, with the number of electrons it contains superscripted.
Building the elements
It is possible to imagine building progressively heavier elements by adding electrons, starting with the lightest element, hydrogen (1s1). As electrons are added, they fill the orbitals within the subshells within the shells. It is a general rule that any system will adopt the configuration with the lowest energy. Although this is a very simple rule, determining the lowest energy arrangement and explaining the configurations can lead to many complications, due to the interactions between the particles. Electrons will, of course, tend to fill lower energy orbitals before higher energy ones, and the Aufbau principle tries to explain how this happens.
The rules
The Aufbau principle has only three rules:
The electrons will fill the orbitals in increasing order of energy, i.e. they will fill the lowest energy orbitals first. Since all orbitals in a given subshell have the same energy level, they must be filled before the next subshell starts filling up.
Each orbital can hold a maximum of two electrons and these must have opposite spins.
Where two or more orbitals with the same energy level are available, none of them will be filled until they all have an electron. In other words, the electrons will try to spread evenly among available orbitals of the same energy wherever possible.
In the case of the simplest element, hydrogen, its single electron is in an orbital in the s subshell. The next element, helium, has a second electron entering the same orbital: 1s2. The orbital, subshell and shell 1 are now all filled. Lithium, with three electrons, has the same configuration as helium, but with an extra electron in the s subshell of shell 2, as this is the lowest energy orbital available: 1s22s1.
Leaving out a couple of elements, carbon, with six electrons, has a configuration 1s22s22p2: both s subshells are full, so the remaining two electrons go to the p subshell. They will go in different orbitals, according to the third rule of the Aufbau principle.
exceptions
As elements get heavier, their orbital arrangements become more complex, and sometimes the interactions between electrons can produce exceptions to the Aufbau principle. The rules apply up to element number 24, chromium. This is one of the few items that are not quite compliant. It leaves its 4s subshell empty, while there are five electrons in the next subshell, because, in this unusual case, it is a slightly lower energy configuration than expected by the rules. Other exceptions are copper and silver.
it is used
Despite the exceptions, the Aufbau principle is useful in chemistry courses where students discover the fundamental rules about atomic structure and the properties of elements. A graph or diagram can be used to show how the principle works for various example elements. This will usually show the shells, subshells and orbitals in a way that clearly illustrates how they are filled.
