2.3. Aufbau Principle, Pauli Exclusion Principle, and Hund’s Rule

1. Aufbau Principle (“Building Up”)

• Electrons occupy the lowest-energy orbitals available before filling higher-energy ones.
• The typical order of orbital energies (for many-electron atoms) is as follows: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, …
• Notice that 4s is filled before 3d because 4s is slightly lower in energy than 3d for neutral atoms. However, once electrons occupy 3d, the energy ordering can shift.

The Aufbau Principle states that electrons fill atomic orbitals starting from the lowest energy levels to the highest. This is important because it determines an atom's electron configuration, which in turn influences its chemical properties. For example, electrons will fill the 1s orbital before moving on to the 2s and 2p orbitals, and they will continue filling according to a specified order of energy levels. It’s essential to know this order when predicting how an atom will react in chemical reactions.

Think of filling a series of stacked boxes with items. You wouldn't put things into a higher box if there's space in a lower box; you'd fill the lower boxes first. Similarly, electrons fill lower energy orbitals before moving to those with higher energy.

2. Pauli Exclusion Principle

• Each orbital can hold at most two electrons, and those two must have opposite spins. In other words, no two electrons in an atom can simultaneously have the same four quantum numbers (n, ℓ, m_ℓ, and m_s).

The Pauli Exclusion Principle ensures that each electron in an atom possesses a unique set of quantum numbers, meaning that two electrons cannot occupy the same state. This principle is crucial for understanding the structure of the periodic table and how orbitals are filled with electrons. For example, in an orbital that can hold two electrons, one must spin in the opposite direction to the other, helping to maintain stability in the atom.

Imagine a two-person lift. If both individuals have unique identifiers (like their names), they cannot occupy the same space at the same time. This is similar to electrons in an atom; each must be uniquely defined so they don't end up in the same state.

3. Hund’s Rule of Maximum Multiplicity

• When electrons occupy a set of degenerate orbitals (orbitals of exactly the same energy, such as the three 2p orbitals), they fill each orbital singly first, all with parallel spins (same m_s), before any orbital gets a second electron. This arrangement minimizes electron-electron repulsion and leads to a lower total energy for the atom.

Hund’s Rule states that when electrons are placed in orbitals of the same energy, they will first fill empty orbitals singly before pairing up. This method reduces repulsion between electrons, as they have more space when they are in separate orbitals. For instance, in the p subshell, which has three orbitals, electrons will occupy each of the three orbitals with parallel spins before any one orbital can hold two electrons. This principle helps to create a more stable electron configuration.

Think of a row of three chairs at a movie theater. If each chair can hold two people but the seats are first-come-first-served, everyone would prefer to sit in separate chairs before doubling up in one chair. In a similar way, electrons prefer to spread out to lower their overall energy state.