In this chapter, we will learn about the Aufbau principle. Filling of electrons into the orbitals of different atom take place according to Aufbau principle, which is based on the Pauli’s exclusion principle, Hund’s rule, and the relative energies of orbitals.
The Aufbau principle is a fundamental concept in quantum chemistry and atomic physics that explains how electrons are distributed in an atom’s orbitals. The term “Aufbau” is a German word which means “building up” or “construction”. That’s why it’s also called the building-up or construction principle. It is pronounced as of bow.
This principle gives us a sequence in which various subshells or orbitals are filled up with electrons based on the relative order of the energy of the subshells. The Aufbau principle states that the electrons are filled in orbitals in increasing order of their energy. We can also restate this principle in any of the following forms:
- The orbitals with the lowest energy are filled up with electrons first, followed by the orbitals with higher energy. In simple words, electrons are filled in orbital first, which have less energy.
- Electrons first occupy the subshells with the lowest energy and then occupy the subshells with higher energy.
The Aufbau Principle was explained by Niels Bohr and Wolfgang Pauli in the early 20th century, around 1920.
Order of Filling of Various Orbitals
The sequence in which the various orbitals are filled with electrons is the same as the relative order of the energy of orbitals. Thus, the order of filling of various orbitals with electrons is as follows:
1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s < 5f < 6d < 7p
For example, if there is only one electron, it first occupies the 1s orbital because it is more stable than the 2s orbital due to its lower energy level. Energy ↑ => Stability ↓
The sequence given above is represented diagrammatically in the below figure that will help you to remember the increasing order of energies of various orbitals.
In the above figure, there is no 2d orbital because for n = 2, the azimuthal quantum number (l) would be 2. However, this orbital is not possible since the principal quantum number (n) must always be greater than the azimuthal quantum number (l).
Similarly, the 3f orbital is not possible because for n = 3, the azimuthal quantum number l would be 3. The principal quantum number (n) must always be greater than the azimuthal quantum number (l). Since l cannot be equal to or greater than n, the 3f orbital does not exist.
Exceptions to Aufbau Principle:
The sequence shown in the above figure in which various orbitals are filled up with electrons has some exceptions.
(a) According to the expected sequence, after 6s-orbital the electron must enter 4f orbital but what actually happens is that after the 6s-orbital is filled, one electron first goes to 5d-orbital instead of 4f-orbital. After this single electron has been added to 5d-orbital, the filling of 4f-orbital begins and this filling continues until 4f-orbital is completely filled (4f14).
Once the 4f orbital is fully occupied, 5d-orbital, which already contains one electron (5d1) again starts to fill up and is completely filled. This exception occurs because 4f and 5d orbitals are almost of the same energy levels.
(b) Similarly, after the 7s orbital is completely filled, one or more electrons enter the 6d orbital before any electron goes into the 5f orbital. This exception is also explained by the fact that the 5f and 6d orbitals have nearly the same energy levels.
Examples of Aufbau Principle
Example 1: Hydrogen (H)
- Atomic number: 1
- Electron configuration: 1s¹
- The single electron occupies the lowest energy orbital (1s).
Example 2: Helium (He)
- Atomic number: 2
- Electron configuration: 1s²
- The two electrons fill the 1s orbital completely.
Example 3: Lithium (Li)
- Atomic number: 3
- Electron configuration: 1s² 2s¹
- The first two electrons fill the 1s orbital, and the third electron moves to the next available lowest energy orbital, that is 2s.
Example 4: Carbon (C)
- Atomic number: 6
- Electron configuration: 1s² 2s² 2p⁴
- The first two electrons go to 1s orbital, the next two fill 2s orbital, and the last two enter 2p orbitals, following Hund’s Rule.
Example 5: Neon (Ne)
- Atomic number: 10
- Electron configuration: 1s² 2s² 2p⁶
- The 2p orbital is completely filled, making neon a noble gas with a stable configuration.
Example 6: Sodium (Na)
- Atomic number: 11
- Electron configuration: 1s² 2s² 2p⁶ 3s¹
- The 11th electron enters the 3s orbital after the 2p orbital is filled.
Example 7: Calcium (Ca)
- Atomic number: 20
- Electron configuration: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s²
- The 4s orbital is filled before the 3d orbital due to its lower energy.
Example 8: Chromium (Cr)
- Atomic number: 24
- Expected configuration: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁴
- Actual configuration: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d⁵
- This exception occurs because a half-filled d-orbital (3d⁵) provides additional stability due to exchange energy and reduced electron repulsion.
Example 9: Copper (Cu)
- Atomic number: 29
- Expected configuration: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁹
- Actual configuration: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d¹⁰
- This exception occurs because a fully filled d-orbital (3d¹⁰) provides extra stability due to exchange energy and symmetrical electron distribution. Therefore, a fully filled 3d¹⁰ configuration is more stable than the expected configuration.
Example 10: Molybdenum (Mo)
- Atomic number: 42
- Expected Configuration: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d⁴
- Actual Configuration: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s¹ 4d⁵
- Similar to chromium, a half-filled d-orbital (4d⁵) provides extra stability.
