What is the Aufbau principle?

The Aufbau principle, also known as the »saw rule», is a very useful system that allows us to predict the electronic configuration of an element. The word Aufbau comes from the German verb meaning “to build” and, in fact, the aim of this principle is to “help build the atom”.

This principle will teach us a series of instructions that have to do with the location of the electrons in the orbitals of an atom.

Characteristics of this principle

• Stable atoms have as many electrons as protons in the nucleus. Electrons gather around the nucleus in quantum orbitals following four basic rules called the Aufbau principle.
• No two electrons in the atom share the same four quantum numbers n, l, m, and s.
• The electrons will first occupy the orbitals of the lowest energy level.
• Electrons will fill an orbital with the same spin number until the orbital is filled. This happens before it starts to fill with the opposite spin number.
• We will also be able to reach the subshells, whose shapes depend on the azimuthal quantum number and the magnetic number m.
• No two electrons in the atom share the same four quantum numbers n, l, m, and s.

The 4 quantum numbers

• The principal quantum number (n) describes the size of an orbital and largely determines its energy (The average distance of an electron from the nucleus. This can only take positive values.

• The angular momentum or azimuthal quantum number (l) determines the shape of the orbitals. Each principal number (n) will have levels and sublevels, however, each of these orbitals will maintain the same quantum number. Numbers are assigned to each value (l) to avoid confusion.

• The magnetic quantum number (m) describes the direction of the orbital movement of the electron in space and designates the number of orbitals contained in each sublevel.

• The number of spin or spin of the electron (s). Its orbitals are presented in a spherical shape, this number will have the values ​​-1/2 and +1/2 that show the possible spins of the electron on its own axis.

How to apply the Aufbau principle?

1. Write a column of s orbitals from 1 to 8.
2. Write a second column for the p orbitals starting at n = 2. (1p is not an orbital combination allowed by quantum mechanics.)
3. Write a column for the d orbitals starting at n = 3.
4. Write a final column for 4f and 5f. There are no items that need a 6f or 7f shell to fill.
5. Read the table by running the diagonals from 1. The graph shows this table and the arrows show the way to go. Now that we know the order of the orbitals to fill, we just need to memorize the size of each orbital.

S orbitals have a possible value of m to hold two electrons.
P orbitals have three possible values ​​of m to hold six electrons.
D orbitals have five possible values ​​of m to hold 10 electrons.
F orbitals have seven possible values ​​of m to hold 14 electrons.
This is all you need to determine the electronic configuration of a stable atom of an element.

For example, let’s take the element nitrogen, which has seven protons and therefore seven electrons.

The first orbital to fill is the 1s orbital. An s orbital contains two electrons, so five electrons remain.

The next orbital is the 2s orbital and contains the next two. The last three electrons will go to the 2p orbital, which can hold up to six electrons.

Sources

The Aufbau Principle (video) . Khan Academy. Available at https://es.khanacademy.org/science/chemistry/electronic-structure-of-atoms/electron-configurations-jay-sal/v/the-aufbau-principle  González, A. Aufbau principle. lifer. Available at https://www.lifeder.com/principio-aufbau/ .