The various orbitals within a sublevel of a principle energy level are always of energy

 The Aufbau principle states that electrons will first fill the lowest energy electron shells in a neutral atom. Electrons fill orbitals from lowest energy orbitals to highest energy orbitals. The Aufbau principle helps to determine the electronic structure of an atom.

The general order shells are filled in is 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s. This order is also represented visually below.

The various orbitals within a sublevel of a principle energy level are always of energy

It may be helpful to notice a couple of patterns when trying to remember the ordering for the d- and f- orbitals. The p- and s- orbital always have the same principle energy level number as the row they are in.  When the d-block comes into play, its principle energy level number will always be one less than the row number or the value of the s- block it comes after. For the f-block, the principle energy level number will always be two less than the current row. A useful diagram of this concept is on this page on electronic structure. A different way to visualize the relative energies can be found here.

The s shell can hold two electrons. The p level can hold 6 electrons. The d level can hold 10 electrons. And finally, the f orbital holds up to 14 electrons.

When filling orbitals, the Pauli Exclusion Principle and Hund’s Rule must also be followed.

The word Aufbau comes from the German word building up or construction. The electrons in an atom must be built up from the lowest energy level to the highest energy level.

The Madelung Rule

Another way of determining which orbital will be filled next is using the value of n + l. n is the principle energy level or principle quantum number. l is the orbital type or azimuthal quantum number– s=0, p=1, d=2, and f=3. Whichever orbital has the lowest n+l value will be filled first. If two orbitals have the same value, the one with the lower n value will fill first.

Exceptions to the Aufbau Rule

There are a few exceptions to the Aufbau principle. These mainly come from atoms in the d- (transition metals) and f- (lanthanides and actinides) blocks of the periodic table. The exceptions also usually come from elements with an atomic number greater than 40.  These exceptions happen because there is increased stability from half and fully filled orbitals, which lowers the overall energy of the atom. In these instances, stability is increased because electrons can be further away from each other.  Additionally, the energy difference between orbitals is smaller at higher atomic numbers.

A few of the elements with exceptions:

  • Chromium (Cr) will be [Ar]3d54s1 instead of the expected [Ar]3d44s2.  This is because there is increased stability from having half-filled orbitals over partially filled orbitals.
  • Copper, silver, and gold (all in column 11) all have an electron that would be expected to be in the s orbital that goes into the d orbital instead
  • These are a few of the exceptions, some of the other elements that have exceptions are palladium, molybdenum, rhodium, and platinum.

Additionally, electrons do not always leave atoms from the highest energy shell based on the Aufbau rule. When an electron leaves, the atom becomes an ion and the Aufbau rule is no longer applicable.

Example Electron Configurations Using the Aufbau Principle

Carbon Electron Configuration

The atomic number of carbon is 6. Therefore carbon has six electrons. According to the Aufbau principle, we start filling from the lowest energy shell, 1s, which holds 2 electrons. Now there are 4 electrons left. Two electrons go into the 2s orbital next. And the remaining two electrons go into the 2p orbital. Written out, the electron configuration is 1s22s22p2.

Calcium Electron Configuration

The atomic number of calcium is 20. Therefore, calcium has twenty electrons. Instead of counting out shell by shell to twenty, we can simplify. We know that the first shell holds 2 electrons. And the next shell holds 8 electrons. That leaves us we 10 electrons left.  This is similar to using the shorthand method of electron configuration. So far we’ve written the noble gas configuration of neon(LINK). Calcium is in the fourth row though, so we can also jump to the noble gas configuration of argon.  After which we have 2 electrons left. The next lowest energy shell is the 4s.

The electron configuration of calcium then is 1s22s22p63s23p64s2 or [Ar]4s2.

Bromine Electron Configuration

Bromine is in the fourth row of the periodic table and has an atomic number of 35. Using the diagram from above we can count up to 35 electrons. Row 1 gives us two electrons. Row 2 provides eight electrons, as does row three. That’s 18 electrons total and the electron configuration of argon (Ar). We then work our way across row 4. First the 4s, then we get the d-block which will have the principle energy number of 3. Counting over to bromine shows us there are 5 electrons in the p-block.

Therefore, the electron configuration is 1s22s22p63s23p64s2 3d104p5 or [Ar]4s2 3d104p5.

Construction of a building begins at the bottom. The foundation is laid and the building goes up step by step. Construction obviously cannot start with the roof, since there is no place to hang it. The building goes from the lowest level to the highest level in a systematic way.

In order to create ground state electron configurations for any element, it is necessary to know the way in which the atomic sublevels are organized in order of increasing energy. In principle, the electron will fill available orbitals from the lowest energy towards the higher energy. However, as the energy shell increases (quantum number n), the number of energy subshells also increases (quantum number ml). At some point, some of the subshells overlap, and the actual energy order of orbitals is not as expected. for example, the orbital in the subshell 4s have lower energy than the orbitals in the 3d subshell. Figure \(\PageIndex{1}\) represents this phenomenon:

The various orbitals within a sublevel of a principle energy level are always of energy

Figure \(\PageIndex{2}\):Overlap in the energy sublevels. Principle energy levels are color coded, while sublevels are grouped together, and each color presents an energy level, while each line represents an energy sublevel.

Figure \(\PageIndex{2}\) shows the order of increasing energy of the sublevels.

The various orbitals within a sublevel of a principle energy level are always of energy
Figure \(\PageIndex{2}\): Electrons are added to atomic orbitals in order from low energy (bottom of the graph) to high (top of the graph), according to the Aufbau principle. Principle energy levels are color coded, while sublevels are grouped together, and each circle represents an orbital capable of holding two electrons.

The lowest energy sublevel is always the \(1s\) sublevel, which consists of one orbital. The single electron of the hydrogen atom will occupy the \(1s\) orbital when the atom is in its ground state. As we proceed to atoms with multiple electrons, those electrons are added to the next lowest sublevel: \(2s\), \(2p\), \(3s\), and so on. The Aufbau principle states that an electron occupies orbitals in order from lowest energy to highest. The Aufbau (German for building up, construction) principle is sometimes referred to as the "building up" principle. It is worth noting that in reality, atoms are not built by adding protons and electrons one at a time, and that this method is merely an aid to understand the end result.

As seen in the figure above, the energies of the sublevels in different principal energy levels eventually begin to overlap. After the \(3p\) sublevel, it would seem logical that the \(3d\) sublevel should be the next lowest in energy. However, the \(4s\) sublevel is slightly lower in energy than the \(3d\) sublevel and thus fills first. Following the filling of the \(3d\) sublevel is the \(4p\), then the \(5s\) and the \(4d\). Note that the \(4f\) sublevel does not fill until just after the \(6s\) sublevel. Figure \(\PageIndex{2}\) is a useful and simple aid for keeping track of the order of fill of the atomic sublevels.

The various orbitals within a sublevel of a principle energy level are always of energy
Figure \(\PageIndex{2}\): The Aufbau principle is illustrated in the diagram by following each red arrow in order from top to bottom: \(1s\), \(2s\), \(2p\), \(3s\), etc.