2.5. Energy Level Diagrams and Orbital Filling Order

A handy way to remember the order in which orbitals are filled is to draw a diagonal (Madelung) diagram:

1s
2s 2p
3s 3p 3d
4s 4p 4d 4f
5s 5p 5d 5f 5g
6s 6p 6d 6f 6g 6h

Then draw diagonal arrows from top right to bottom left. Following each arrow shows the sequence: 1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → 4f → 5d → 6p → 7s → … and so on.

The Aufbau order diagram is a visual representation of how electrons are added to the orbitals of an atom. The diagram shows a diagonal pattern indicating the sequence in which orbitals fill. For instance, the 1s orbital is filled first, followed by the 2s, then the 2p, and so on. The diagonal arrows represent the strongly observed energy ordering of the orbitals. By following these arrows, one can easily determine the filling order of electrons in various orbitals.

Imagine a building with multiple floors. Each floor represents a different energy level or shell. Like how people fill rooms in a building from the ground up, electrons fill orbitals starting from the lowest energy levels to higher ones, ensuring each room (orbital) is filled before moving to the next. This analogy illustrates the hierarchical structure of energy levels in atoms.

● Within a given principal quantum number n, the energy of subshells generally goes s < p < d < f.

● However, because of the way electron penetration (how close the electron’s probability cloud comes to the nucleus) and shielding (how inner electrons block nuclear charge) work, an orbital with a higher n but lower ℓ (for example, 4s) can be lower in energy than an orbital with a lower n but higher ℓ (for example, 3d) for neutral atoms.

The energy levels of subshells are influenced by both their shape and their distance from the nucleus. Typically, subshells filled in the order of s < p < d < f means that s orbitals are energy lowest, followed by p, d, and lastly f orbitals. However, not all fillings follow this order strictly due to the effects of electron penetration and shielding. For example, the 4s orbital can have a lower energy than the 3d orbital because the 4s electrons can penetrate the inner electrons and experience a stronger attraction to the nucleus. This means they are generally more stable when they are filled before the 3d orbitals.

Think of layers of clothing on a person. The innermost layer (like the 1s orbital) hugs the body most closely and provides the most warmth. However, adding too many layers of heavier clothing can actually trap heat and cause discomfort, just like how the higher energy layers (higher n levels) can make some orbitals (like the 4s) less stable than they may seem. Understanding which layers provide warmth best helps you dress properly for different weather conditions, similar to understanding how to fill orbitals efficiently.

● On paper, you draw each subshell as a horizontal line, label it with its orbital notation (for example, 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, …).

● Then you write small upward (↑) and downward (↓) arrows on each line to represent the electrons, filling from lowest to highest energy, and obeying Pauli’s exclusion (max two arrows per line, one up and one down) and Hund’s rule (in degenerate lines, put one up arrow in each before pairing them).

An energy level diagram is a visual way to represent how electrons are arranged in an atom. Each line in the diagram represents an orbital, and the direction of the arrows indicates the spin of the electrons. According to the Pauli Exclusion Principle, no two electrons can occupy the same space and must have opposite spins. Therefore, when filling an orbital, you place one electron in each degenerate orbital (equal energy) first, before pairing them, which minimizes electron repulsion and thereby stabilizes the atom.

Imagine a game of musical chairs, where each player (electron) has to find their seat (orbital). Players must first check every available chair (orbital) before two players can share one seat. This orderly manner of seating ensures everyone gets a chance to play comfortably, just as orderly filling of orbitals ensures that electrons are arranged stably.