Understanding Pauli Exclusion, Hund's Rule, and Aufbau Principle

The Pauli Exclusion Principle

The Pauli Exclusion Principle states that, in an atom or molecule, no two electrons can have the same four electronic quantum numbers. As an orbital can contain a maximum of only two electrons, these two electrons must have opposing spins. This means if one is assigned an up-spin (+1/2), the other must be down-spin (-1/2).

Electrons in the same orbital have the same first three quantum numbers (e.g., n=1, l=0, m_l=0 for the 1s subshell). Only two electrons can have these numbers, so their spin moments must be either m_s = -1/2 or m_s = +1/2. If the 1s orbital contains only one electron, we have one m_s value and the electron configuration is written as 1s¹ (corresponding to hydrogen). If it is fully occupied, we have two m_s values, and the electron configuration is 1s² (corresponding to helium).

Hund's Rule

Hund's rule states that:

• Every orbital in a sublevel is singly occupied before any orbital is doubly occupied.
• All of the electrons in singly occupied orbitals have the same spin (to maximize total spin).

When assigning electrons to orbitals, an electron first seeks to fill all the orbitals with similar energy (also referred to as degenerate orbitals) before pairing with another electron in a half-filled orbital. Atoms at ground states tend to have as many unpaired electrons as possible. In visualizing this process, consider how electrons exhibit the same behavior as the same poles on a magnet; as the negatively charged electrons fill orbitals, they first try to get as far as possible from each other before having to pair up.

The Aufbau Principle

The Aufbau principle states that, hypothetically, electrons orbiting one or more atoms fill the lowest available energy levels before filling higher levels (e.g., 1s before 2s). In this way, the electrons of an atom, molecule, or ion harmonize into the most stable electron configuration possible.

Electron Gain Enthalpy

Electron Gain Enthalpy is defined as the enthalpy change taking place when an isolated gaseous atom accepts an electron to form a monovalent gaseous anion.

Variation Across a Period

It tends to become more negative as we go from left to right across a period. Because the tendency of the element to accept an electron increases, a large amount of energy is released, or electron gain enthalpy becomes more negative. For example, fluorine has a more negative electron gain enthalpy compared to boron in the same period.

Variation Down a Group

It becomes less negative on going down a group. As we move down the group, the element's tendency to accept an electron decreases. For example, iodine has a less negative electron gain enthalpy than fluorine in the same group.