Aufbau Principle

Introduction 

Aufbau is a German word which means 'building up’, and is not the name of a scientist unlike many of the other principles of chemistry. This principle is basically concerned regarding 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 in order 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

  •  Energy of an orbital is determined by (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, lower will be its energy. And, if two orbitals have the same value for (n+l) then the one with 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 filling 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 as 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 (n+l) rule can be shown as follows:

  • OrbitalValue of ‘n’Value of ‘l’Value of (n+l)
    1s101 + 0 = 1
    2s202 + 0 = 2
    2p212 + 1 = 32p (n=2) has lower energy than 3s (n=3)
    3s303 + 0 = 3
    3p313 + 1 = 43p (n=3) has lower energy than 4s (n=4)
    4s404 + 0 = 4
    3d323 + 2 = 53d (n=3) has lower energy than 4p (n=4)
    4p414 + 1 = 5


    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 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.

    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 the Hund’s rule and the 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. Next 6 electrons will be occupied by the 2p orbitals. 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 are 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

    Electronic configuration of nitrogen is written in a similar fashion 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 per 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 a completely filled or half-filled atomic orbitals which are more stable than any of the partially filled atomic orbitals because of symmetry and release of exchange energy.