The spectral notation is the arrangement of electron energy levels around the nucleus of an atom. According to the old Bohr atomic model, electrons occupy various levels in orbits around the nucleus, from the first shell closest to the nucleus, K, to the seventh shell, Q, which is the furthest from the nucleus.
In terms of a more refined quantum mechanical model, the KQ shells are subdivided into a set of orbitals, each of which can be occupied by no more than one pair of electrons.
Commonly, the electron configuration is used to describe the orbitals of an atom in its ground state, but it can also be used to represent an atom that has ionized into a cation or anion, compensating for the loss or gain of electrons in their respective orbitals.
Many of the physical and chemical properties of elements can be correlated to their unique electronic configurations. Valence electrons, the electrons in the outermost shell, are the determining factor for the element's unique chemistry.
When electrons in the outermost shell of an atom receive energy of some kind, they move into layers of higher energy. Thus, an electron in the K shell will be transferred to the L shell while in a higher energy state.
When the electron returns to its ground state, it releases the energy it absorbed by emitting an electromagnetic spectrum (light). Since each atom has a specific electronic configuration, it will also have a specific spectrum that will be called the absorption (or emission) spectrum.
For this reason, the term spectral notation is used to refer to electron configuration.
How to determine spectral notation: quantum numbers
A total of four quantum numbers are used to fully describe the motion and trajectories of each electron within an atom.
The combination of all the quantum numbers of all the electrons in an atom is described by a wave function that fulfills the Schrödinger equation. Each electron in an atom has a unique set of quantum numbers.
According to the Pauli Exclusion Principle, two electrons cannot share the same combination of four quantum numbers.
Quantum numbers are important because they can be used to determine the electron configuration of an atom and the likely location of the electrons in the atom.
Quantum numbers are also used to determine other characteristics of atoms, such as ionization energy and atomic radius.
Quantum numbers designate specific shells, subshells, orbitals, and spins of electrons.
This means that they fully describe the characteristics of an electron in an atom, that is, they describe each unique solution to the Schrödinger equation, or the wave function, of electrons in an atom.
There are a total of four quantum numbers: the principal quantum number (n), the orbital angular momentum quantum number (l), the magnetic quantum number (ml), and the electron spin quantum number (ms).
The principal quantum number, nn, describes the energy of an electron and the most probable distance of the electron from the nucleus. In other words, it refers to the size of the orbital and the energy level at which an electron is placed.
The number of subshells, or ll, describes the shape of the orbital. It can also be used to determine the number of angular nodes.
The magnetic quantum number, ml, describes the energy levels in a subshell, and ms refers to the spin on the electron, which can be up or down.
Aufbau principle
Aufbau comes from the German word "Aufbauen" which means "to build." In essence, by writing electron configurations we are building electron orbitals as we move from one atom to another.
As we write the electron configuration of an atom, we will fill in the orbitals in increasing order of atomic number.
The Aufbau principle originates from the Pauli exclusion principle which says that there are no two fermions (eg electrons) in an atom.
They can have the same set of quantum numbers, so they have to "stack" at higher energy levels. How electrons accumulate is a matter of electron configurations.
Stable atoms have as many electrons as protons do in the nucleus. Electrons gather around the nucleus in quantum orbitals following four basic rules called the Aufbau principle.
- There are no two electrons in the atom that share the same four quantum numbers n, l, m, and s.
- Electrons will occupy the lowest energy level orbitals first.
- The electrons will always fill the orbitals with the same spin number. When the orbitals are full it will start.
- The electrons will fill orbitals by the sum of the quantum numbers n and l. Orbitals with equal values of (n + l) will be filled first with the lower n values.
The second and fourth rules are basically the same. An example of rule four would be the 2p and 3s orbitals.
A 2p orbital is n = 2 and l = 2 and a 3s orbital is n = 3 and l = 1. (N + l) = 4 in both cases, but the 2p orbital has the lowest energy or lowest value n and will fill before the layer 3s.
Figure 2: Moeller diagram of filling the electron configuration.
Fortunately, the Moeller diagram shown in Figure 2 can be used to do electron filling. The graph is read by running the diagonals from 1s.
Figure 2 shows the atomic orbitals and the arrows follow the way forward.
Now that the order of the orbitals is known to be filled in, the only thing left is to memorize the size of each orbital.
S orbitals have 1 possible value of m l to contain 2 electrons
P orbitals have 3 possible values of ml to contain 6 electrons
D orbitals have 5 possible values of µl to hold 10 electrons
F orbitals have 7 possible values of m l to hold 14 electrons
This is all that is needed to determine the electronic configuration of a stable atom of an element.
For example, take the element nitrogen. Nitrogen has seven protons and therefore seven electrons. The first orbital to fill is the 1s orbital. An s orbital has two electrons, so there are five electrons left.
The next orbital is the 2s orbital and contains the next two. The final three electrons will go to the 2p orbital which can hold up to six electrons.
Hund rules
Aufbau's section discussed how electrons fill the lowest energy orbitals first and then move up to the highest energy orbitals only after the lowest energy orbitals are full.
However, there is a problem with this rule. Certainly, the 1s orbitals must be filled before the 2s orbitals, because the 1s orbitals have a lower value of n, and therefore a lower energy.
And the three different 2p orbitals? In what order should they be filled? The answer to this question involves Hund's rule.
Hund's rule states that:
- Each orbital in a sublevel is occupied individually before any orbital is doubly occupied.
- All electrons in individually occupied orbitals have the same spin (to maximize total spin).
When electrons are assigned to orbitals, an electron first seeks to fill all orbitals with similar energy (also called degenerate orbitals) before pairing up with another electron in a half-full orbital.
Atoms in the ground states tend to have as many unpaired electrons as possible. In visualizing this process, consider how electrons exhibit the same behavior as the same poles in a magnet if they were to come into contact.
When negatively charged electrons fill up the orbitals, they first try to get as far away from each other as possible before having to pair up.
References
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- Electron Configurations and the Properties of Atoms. (SF). Recovered from oneonta.edu.
- Encyclopædia Britannica. (2011, September 7). Electronic configuration. Recovered from britannica.com.
- Helmenstine, T. (2017, March 7). The Aufbau Principle - Electronic Structure and the Aufbau Principle. Recovered from thoughtco.com.
- Hund's Rules. (2015, July 18). Recovered from chem.libretexts.org.
- Spectroscopic Notation. (SF). Recovered from bcs.whfreeman.com.