The arrangement of electrons within an atom’s orbitals is governed by a set of fundamental principles that dictate the most stable, lowest-energy configuration, known as the ground state. The Aufbau Principle establishes the order in which orbitals are filled, starting with the lowest energy levels closest to the nucleus. The Pauli Exclusion Principle then limits the occupation of any single orbital to a maximum of two electrons, which must possess opposite spins. While these two rules provide a framework for electron placement, they do not fully explain how electrons fill subshells that contain multiple orbitals of equal energy. For this specific scenario, a third rule, known as Hund’s Rule, is necessary to complete the picture of electron organization.
Defining Hund’s Rule
Hund’s Rule, often called the Rule of Maximum Multiplicity, specifies the manner in which electrons distribute themselves when multiple orbitals of the same energy are available to achieve the lowest energy state. First, electrons will occupy separate orbitals within a subshell singly before any orbital becomes doubly occupied. This means electrons will spread out as much as possible across the available spaces.
The second condition requires that all electrons occupying these separate orbitals must have parallel spins. Parallel spin means the electrons are all spinning in the same direction. This arrangement maximizes the total spin of the atom, leading to the highest multiplicity and consequently the greatest stability for that configuration.
The Environment of Degenerate Orbitals
Hund’s Rule is applied exclusively to orbitals that are considered degenerate, meaning they possess precisely the same energy level. These equal-energy orbitals exist within every subshell beyond the spherical \(s\) subshell. For example, the \(p\) subshell contains three distinct orbitals, all of which are degenerate.
Similarly, the \(d\) subshell is composed of five degenerate orbitals, and the \(f\) subshell contains seven. If the orbitals were not degenerate, the electrons would simply follow the Aufbau Principle and fill the single lowest-energy orbital first, regardless of other options. The existence of these multiple, equivalent energy spaces is what necessitates the specific distribution pattern described by Hund’s Rule.
Applying the Rule to Electron Configuration
To understand the practical application of Hund’s Rule, consider an atom like Nitrogen, which has an electron configuration ending in \(2p^3\). The \(2p\) subshell contains three degenerate orbitals, and Nitrogen has three electrons to place within them. The correct application of the rule dictates that each of the three \(p\) orbitals receives one electron before any of them receives a second electron.
Furthermore, these three singly-occupied electrons must all be assigned the same spin orientation, such as all “spin-up”. An incorrect configuration would be to place two electrons with opposite spins into one \(p\) orbital and the remaining electron into a second \(p\) orbital, leaving the third \(p\) orbital empty. This pairing in one orbital before all three are singly filled results in a higher energy state than the one with maximum unpaired electrons.
If the atom were Oxygen, with an electron configuration ending in \(2p^4\), the first three electrons would follow Hund’s Rule by occupying the three \(p\) orbitals singly with parallel spins. The fourth electron would then be forced to pair up in one of the three orbitals, since all separate orbitals are now occupied. The final configuration for the \(2p\) subshell would therefore show one paired orbital and two singly-occupied orbitals, with the two unpaired electrons maintaining parallel spins.
The Stability Achieved by Unpaired Electrons
The reason electrons follow Hund’s Rule is rooted in the atom’s drive to achieve the lowest possible energy state, which correlates with maximum stability. Electrons are negatively charged, and placing them into separate orbitals minimizes the electrostatic repulsion between them. By occupying different regions of space, the electrons are kept further apart on average, which lowers the overall potential energy of the atom.
An additional quantum mechanical effect known as exchange energy contributes to this stability. When electrons possess parallel spins, the mathematical description of their wave functions allows them to avoid each other more effectively, even beyond spatial separation. This effect is energetically favorable, which is why the lowest energy state maximizes the number of parallel-spin, unpaired electrons. This maximization of parallel spins, or maximum multiplicity, results in a more stable ground state compared to configurations where electrons are prematurely paired.