Construction principle: examples, limitations and exceptions (2023)

The assembly principle is a key chemical principle for determining the electronic configuration of an atom in its ground state. The Aufbau principle requires the atom to apply Pauli's exclusion principle and Hund's rule, which states that each orbital can initially contain only one electron before it becomes doubly occupied (no two electrons in an orbital have the same spin).

Construction principle: examples, limitations and exceptions (1)


What is the construction principle?

According to the structuring principle, electrons fill the lowest energy levels of an atom first and the highest energy levels last. There are four different types of subshell shapes and seven different energy levels that electrons can occupy. The Aufbau principle contains historical predictions about the order in which they will be fulfilled.

So, the structuring principle tells how electrons are positioned in the atomic orbitals of the ground state of an atom. Therefore, electrons are placed in atomic orbitals in order of increasing orbital energy. The principle of construction states that the available atomic orbitals with the lowest energy levels are filled before those with the highest energy levels.

History of the start of construction

In the early 1920s, Niels Bohr and Wolfgang Pauli developed the Aufbau principle, which is a key concept in the new quantum theory.

This was an early attempt to explain chemical properties physically by applying quantum mechanics to the properties of electrons.

Before quantum mechanics, it was thought that according to the old quantum theory, electrons are in classical elliptical orbits. The "orbits" outside the inner electrons have the highest angular momentum, but the orbits of the s and p subshells have high subshell eccentricity, bringing them closer to the nucleus and making them less nuclear shielded on average. Demand.

Main features of the construction principle

  • The construction principle states that electrons occupy orbitals with the lowest energies first. This suggests that electrons move to higher energy orbitals only when lower energy orbitals are fully occupied.
  • The (n+l) rule, which states that the energy level of the orbital is determined by the sum of its principal and azimuth quantum numbers, can be used to determine the order in which the orbitals increase in energy.
  • Lower orbital energies are correlated with lower (n+l) values. The orbital with the smallest value of n is assigned the lowest energy when two orbitals have equal values ​​(n+l).
  • Orbitals are filled with electrons in the following order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, and so on .

Madelung's rule

The filling of atomic orbitals and the electronic configuration are described by Madelung's rule.

Charles Janet first described Madelung's rule, or Klechkowski's rule, in 1929, and Erwin Madelung rediscovered it in 1936. V.M. Klechkowski described the theoretical basis of Madelung's rule. The modern construction principle is based on the Madelung rule.

According to the rule:

(1)The energy increases as n + l increases.

(2)The energy increases with increasing n for the same values ​​of n and l.

Filling orbitals in the following order produces the following results:

1s, 2s, 2p, 3s, 3d, 4p, 5s, 4f, 5d, 6p, 7s, 5f, 6d und 7p (8s, 5g, 6f, 7d, 8p and 9s)

The ground state of the heaviest known atom, Z=118, does not contain any of the orbitals listed in parentheses. Since the inner electrons protect the nuclear charge, the orbitals are filled in this way. Therefore, for the orbital penetration: s > p > d > f

Steps for structure diagram

  1. First find out how many electrons are in the atom.
  2. Add the first two electrons to the s orbital in the first energy level (1s orbital).
  3. Insert the second two electrons into the s orbital of the second energy level (2s orbital).
  4. Start by placing an electron in each of the three p orbitals in the second energy level (2p orbitals), and if there are still electrons available, go back and add a second electron to complete the electron pairs.
  5. Continue in this manner through each subsequent energy level until all the electrons are distributed.

Filling of electrons in subshells

  • The state of an electron is given by a quantum number. There are four quantum numbers, two of which are related to sublevels. They are the azimuth quantum number l and the principal quantum number n.
  • The order of increasing energies of the sublevels is determined by the sum of n and l. According to the increasing value of (n+l), electrons fill the subshell. The values ​​of n and l are discrete, such as n = 0, 1, 2, ... and l = 0, 1, 2, and 3. For example, the 3p subshell is referenced by n = 3 and l = 1.
  • The electron is in the lower n subshell if two subshells have the same value (n+l). For example, the value (n+l) of 3p and 4s is 4. The electron is occupied by 3p instead of 4s because 3p has a smaller n-value.

The order in which the sublevels will be filled

bottom shellprincipal quantum number(s)Azimuthal quantum number (l)Soma (n + l)
3 Sek303
5 Sek505
19 o'clock718

build diagram

The construction principle states that as the values ​​(n + l) increase, the filling order of the sub-levels increases. Therefore, a diagram called an assembly diagram can serve as a representation of this information. Thus, for the construction of the diagram, the points listed below are taken into account.

  • A column on the left lists the n values, while the top lists l values ​​in a row.
  • Subshells are thus represented by the sum of n and l values.
  • Diagonal lines are drawn to connect sublevels with the same value (n + l).
  • There are arrows on the diagonals pointing in the direction of increase n.
Construction principle: examples, limitations and exceptions (2)

Electronic configuration according to the building principle

Finally, the 1s orbital, which is the smallest and has the lowest energy, comes first in the filling order. As a result, the first electron enters the 1s orbital, giving the hydrogen atom its 1s1electronic configuration. The second electron follows, and since the s orbital can hold two electrons, it also enters the 1s orbital. The electron configuration is now 1s2i.e. the noble gas helium. The atomic number increases by one for each electron added since a proton is also added.

The third electron enters the second orbital after the first is filled, giving the lithium atom, which is directly below hydrogen on the periodic table, its electron configuration of 1s22s1. So the same is true for beryllium, 1s22s2.

Electronic Configuration according to the building principle

ElementSymbolatomic number (Z)electronic configuration
SodiumAlready111s22s22p63 Sek1
Magnesiummg121s22s22p63 Sek2
PhosphorP151s22s22p63 Sek23p3
Argonar181s22s22p63 Sek23p6
Potassiumk191s22s22p63 Sek23p64s1
Scandiumsc211s22s22p63 Sek23p64s23d1
FerroBelieve261s22s22p63 Sek23p64s23d6
BromBr351s22s22p63 Sek23p64s23d104p5
KryptonKr361s22s22p63 Sek23p64s23d104p6
Zirconiumzr401s22s22p63 Sek23p64s23d104p65 Sek24d2
LataSn501s22s22p63 Sek23p64s23d104p65 Sek24d1017h2
PlutoniumPu941s22s22p63 Sek23p64s23d104p65 Sek24d1017h6
6s24f145d106 p.m67s25f6

Structure of the most important exceptions

The structural principle does not apply to all atoms in general. Spectroscopic investigations have shown that some atoms contradict the structural principle.

Transition metals, lanthanides and actinides

In particular, transition metals, lanthanides, and actinides have electronic configurations that contradict the Aufbau principle. The results include the following observations.

  • In transition metals, the s subshell donates an electron to the d subshell. However, palladium is an exception where the 5s subshell loses two electrons to the 4d subshell. The following figure is an example of this exception.
  • In some lanthanides and actinides, an electron from the f subshell is consumed by the d subshell. With the exception of thorium, the 6d subshell in thorium absorbs two electrons from the 5f shell.

This is due to a variety of factors, including the increased stability of the semi-filled subshells and the relatively small energy difference between the 3d and 4s subshells.

Construction principle: examples, limitations and exceptions (3)

Exception to the construction principle for transition elements

ElementSymbolatomic numberStructure forecastobserved experimentally

Exception to the design principle in lanthanides and actinides

ElementSymbolatomic numberStructure forecastobserved experimentally
LawrenceLr103[Rn]7s25f146d1[Rn]7s25f1419 o'clock1

Heavy cores

The construction principle is also violated by heavy nuclei (Z > 120). High electrostatic forces attract electrons to the nucleus with increasing charge. Its speeds are almost equal to the speed of light when it occurs. Therefore, the determination of the energies of electrons using a quantum mechanical approach is not successful.


Ruthenium is mainly used as an alloying ingredient for hardening platinum and palladium. The electron distribution in Ru is as follows: 1s22s22p63 Sek23p63d104s24p64d75 Sek1.

The energy of the 5s orbital in this meta is lower than that of the 4d orbital (n+1 for 4d is 7 and for 5s is 5). However, the 4D orbit begins to fill before the 5S orbit. Therefore instead of [Kr] 4d65 Sek2, the electronic configuration of Ru is [Kr] 4d75 Sek1.


Rhodium (Rh) also violates the building principle, as does ruthenium. It has atomic number 45. Although it has less energy than 5s, the 4d orbital in Rh fills up before the 5s orbital. Rhodium has the following electronic configuration: 1s22s22p63 Sek23p63d104s24p64d85 Sek1. The setting is [Kr] 4d75 Sek2if the principle of construction is observed.

Limitations of the design principle

According to the principle of Aufbau, electrons first occupy atomic orbitals in the lowest possible energy state before rising to the highest level. But this has some limitations, just like other ideas.

  • Similar to d- and f-block elements, which provide stability to atoms, whether filled or partially filled, they do not always follow the constructive principle.
  • The Aufbau principle states that the order of orbital energies between different and given elements is always fixed, but this is not entirely accurate. It's accurate to a degree and reasonably useful. Only two electrons can be placed in atomic orbitals with fixed energy according to the Bougie principle. The energy of the electrons in an atomic orbital depends on the total energy of the electrons in the atom.
  • Second, as we know, a hydrogen-like atom has only one electron, and the energy in the s-orbital and p-orbital shells is the same. However, the nucleus of a true hydrogen atom has a different number of protons. Thus, the magnetic field of the nucleus easily splits the energy levels, changing the energy of each electron in the process.
  • The Aufbau principle is extremely effective for the ground state of atoms up to the first 18 elements, but less effective for the remaining 100 electrons thereafter.


  • Lithium's first two electrons occupy the 1s orbital, and the third electron moves into the 2s orbital, the next lower available level. The electron configuration of lithium is 1s22s1.
Construction principle: examples, limitations and exceptions (4)
  • The occupation of the 2p subplane ends with the tenth electron. The electronic arrangement of neon is 1s22s22p6. The second neon energy shell, whose primary quantum number is 2, is full. Because of its exceptionally stable configuration, neon is chemically unreactive.
Construction principle: examples, limitations and exceptions (5)

Also read:

  • Trace elements and biological significance
  • Supramolecular Chemistry - Basic Concepts and Applications
  • Chlorine element - definition, properties, reactions, uses, effects
  • Beryllium: History, Properties, Important Applications, Toxicity, Safety, Facts
  • crystal field theory


  • Feynman, Richard; Leighton, Robert B.; Sands, Matthew (1964). "19. The Hydrogen Atom and the Periodic Table”.Feynman lectures on physics. Vol.3. Addison-Wesley
  • Miessler, Gary L.; Tarr, Donald A. (1998).Inorganic chemistry(2º). apprentice hall.
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