Aufbau Principle, Paulis Exclusion Principle and Hands Rule

Aufbau is a German word that means 'building up and is not the name of a scientist unlike many of the other principles of chemistry. This principle is concerned with the filling of the electrons in an orbital during the writing of an electronic configuration.

'Building up’, as the name suggests, is regarding the filling of the orbitals with electrons to build the electronic configuration in a particular way so that an orbital with lower energy is filled earlier and the orbital with higher energy is filled later.

In other words, “In a ground state of the atoms, the orbitals are filled in order of their increasing energies." i.e. an electron will initially occupy an orbital of lower energy level and when the lower energy level orbitals are occupied, then only they shall start occupying the higher energy level orbitals.

Salient Features of the Aufbau Principle

The energy of an orbital is determined by the (n+l) rule where ‘n’ stands for the Principal quantum number and ‘l’ stands for the Azimuthal quantum number. The lower the value of (n+l) for an orbital, the lower will be its energy. And, if two orbitals have the same value for (n+l) then the one with a higher value of n will have higher energy.

During filling up of electrons in the orbitals for completion of electronic configuration, electrons will first occupy the orbitals of lower energy; only after the lower energy orbitals are occupied, the electrons shall occupy the higher energy orbitals.

The order in which the energies of the electronic orbitals increase and their respective order of filling as per the Aufbau rule is as follows:

Figure 1. Order of filing of orbitals by Aufbau principle

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 4f, 5d, 6p, 7s…

This diagram is also referred to as the Aufbau principle diagram and is used to remember the order of the filling of the orbitals.

In a tabular form, the arrangement of orbitals with increasing energies as per The electronic(n+l) rule can be shown as follows:

Note: Values of Azimuthal quantum numbers are as follows: s=0, p=1, d=2, f=3.

Electronic Configuration using the Aufbau Principle

According to the Aufbau rule:

First electrons are filled in 1s orbital. Since each orbital can accommodate a maximum of only 2 electrons so 1s orbital contains 2 electrons. Then 2s orbital is filled as it is the one that comes after 1s in terms of energy level. This also can accommodate 2 electrons. Then, electrons are filled in the 2p atomic orbitals: 2px which are can accommodate 2 electrons, 2py which can accommodate 2 electrons, and 2pz which can accommodate 2 electrons. Since px, py, and Pz are degenerate orbitals, so their energy levels are also the same. So, the electrons can occupy either of the 3 in any order. Thus, 2p can accommodate a total of 6 electrons. Then, electrons are filled in the 3s orbital which can accommodate a total of 2 electrons, followed by the filling of the 3p orbitals similar to 2p orbitals and so on.

The filling of the orbitals goes on according to the Aufbau rule/Aufbau principle. However, the location, the order of the filling of electrons according to their spin while filling in the degenerate orbitals, and the spin of the 2 electrons filled in the same orbital itself are further basically governed by Hund’s rule and Pauli’s exclusion principle. 

Writing the Electronic Configuration of Sulfur

Sulfur has an atomic number of 16 i.e., it has 16 electrons in an atom. As stated above, the first 2 electrons will be occupied by the 1s orbital. The next 2 will be occupied by the 2s orbital. The next 6 electrons will be occupied by the 2p orbitals. The next 2 electrons will be occupied by the 3s orbital and the rest of the final 4 electrons will be occupied by the 3p orbitals. So, out of the 16 electrons, a total of 10 electrons lie in the 1st and the 2nd shell i.e. n=1 and n=2 and the last 6 electrons lie in the 3rd shell i.e. n=3. So, the valence shell is the 3rd shell, and the total number of valence electrons is 6 (2 electrons in 3s and 4 electrons in 3p) in sulfur. We filled electrons according to the Aufbau principle and used figure 1. 

The electronic configuration is written in the following fashion:

S = 16; Electronic configuration as per Aufbau rule: 1s2,2s2,2p6,3s2,3p4.

Writing the Electronic Configuration of Nitrogen

The electronic configuration of nitrogen is written similarly just like that of sulfur. Nitrogen has an atomic number of 7 i.e., it has 7 electrons in total. The first two electrons are occupied by the 1s orbital. The next 2 electrons lie in the 2s orbital and the last 3 electrons lie in the 2p orbitals. 

Therefore, the 1st shell has 2 electrons, and the 2nd shell has 5 electrons. So, the valence shell is the 2nd shell i.e. n=2 and the number of valence electrons are 5 (2 electrons in 2s and 3 electrons in 2p).

The electronic configuration is written in the following fashion:

N = 7; Electronic configuration as per Aufbau rule: 1s2,2s2,2p3.

Even though most of the electronic configurations follow the above order as stated in the Aufbau principle, there are certain exceptions. A handful of elements with atomic number greater than 20, such as Cu (Copper, atomic number = 29), Cr (Chromium, atomic number = 24, Mo (Molybdenum, atomic number = 42), etc., are exceptions. These exceptions arise because filled or half-filled atomic orbitals are more stable than any of the partially filled atomic orbitals because of symmetry and the release of exchange energy.

Paulis Exclusion Principle

According to the Pauli exclusion principle, no two electrons in a single atom will have an identical set or the same quantum numbers. Every electron should have or be in a distinct state. Pauli's Exclusion Principle essentially helps us comprehend the electron configurations in atoms and molecules and also explains the periodic table's classification of elements. The Pauli Exclusion Principle adheres to two major principles:

• Only two electrons can occupy the same orbital.

• The two electrons that are present in the same orbital must have opposite spins or they should be antiparallel.

Pauli's Exclusion Principle, on the other hand, does not only apply to electrons. It also applies to fermions and other particles with half-integer spin. It is significant for particles with integer spins, such as bosons, which have symmetric wave functions. Moreover, unlike fermions, bosons can share or have the same quantum states. Fermions are called after the Fermi–Dirac statistical distribution that they follow in terms of nomenclature. The Bose-Einstein distribution function, on the other hand, is where bosons derive their name.

Hund’s Rule

According to Hund's rule, a larger total spin state of an atom can occasionally make the atom more stable. This rule is fairly reliable (with a few exceptions) for determining the state of a given excited electron configuration. Friedrich Hund found it in the year 1925. According to Hund’s rule:

• Every orbital in the sub-level is singly occupied before the double occupation of any orbital.

• All electrons in a single-occupancy orbital have the same spin to maximize overall spin.

Because an electron can fill all of its orbitals with identical energy, it will not couple with another electron in a half-filled orbital. Atoms in their ground state contain a large number of unpaired electrons. When two electrons come into contact, they react in the same way as two magnets do. Before they have to couple up, the electrons want to go as far apart from each other as possible. Hund's Rule can assist anticipate atomic characteristics since paired and unpaired electrons have different properties (specifically with interactions with magnetic fields).