## The Building-Up (Aufbau) Principle

#### Learning Objective

• Write electron configurations for elements in standard notation.

#### Key Points

• The Madelung rule defines the order in which atomic orbitals are filled with electrons. Electrons fill orbitals starting at the lowest available energy state before filling higher states.
• Aufbau procedure: Determine number of electrons for the atom of interest. Fill available orbitals starting with the lowest-energy levels first and avoid pairing electrons in a single orbital until it is necessary.
• Electron configuration notation describes the energy levels, orbitals, and the number of electron. The number and letter describe the energy level and orbital respectively, and the superscript number shows how many electrons are in that orbital.
• The Aufbau principle works well for the first 18 elements but then becomes less useful.

#### Term

• Pauli Exclusion PrincipleThe quantum mechanical principle that no two identical fermions (particles with half-integer spin) may occupy the same quantum state simultaneously.

## Atoms Are Built Up by Adding Electrons

Although the nucleus of an atom is very dense, the electrons around it can take on a variety of positions which can be summarized as an electron configuration. An element’s electron configuration can be represented using energy level diagrams, or Aufbau diagrams. The Aufbau principle (from the German Aufbau meaning “building up, construction”) describes a model-building method in which an atom is “built up” by progressively adding electrons. As electrons are added, they assume the most stable shells with respect to the nucleus and the electrons already present.

## Filling in an Aufbau Diagram

The order in which orbitals are filled is given by the Madelung rule. The rule is based on the total number of nodes in the atomic orbital, n + ℓ, which is related to the energy. In this context, n represents the principal quantum number and ℓ represents the azimuthal quantum number. The values ℓ = 0, 1, 2, 3 correspond to the s, p, d, and f labels, respectively. According to the principle, electrons fill orbitals starting at the lowest available energy states before filling higher states (e.g., 1s before 2s).

An Aufbau diagram uses arrows to represent electrons. When there are two electrons in an orbital, the electrons are called an electron pair. Electron pairs are shown with arrows pointing in opposite directions. According to the Pauli Exclusion Principle, two electrons in an orbital will not spin the same way. That is, an Aufbau diagram uses arrows pointing in opposite directions. An arrow pointing up denotes an electron spinning one way and an arrow pointing downwards denotes an electron spinning the other way. If the orbital only has one electron, this electron is called an unpaired electron.

The following steps detail how to draw an Aufbau diagram:

1. Determine the number of electrons that the atom has.
2. Fill the s orbital in the first energy level (the 1s orbital) with the first two electrons.
3. Fill the s orbital in the second energy level (the 2s orbital) with the second two electrons.
4. Put one electron in each of the three p orbitals in the second energy level (the 2p orbitals) and then if there are still electrons remaining, go back and place a second electron in each of the 2p orbitals to complete the electron pairs.
5. Continue in this way through each of the successive energy levels until all the electrons have been drawn.