The arrangement of electrons within an atom dictates its chemical behavior. An atomic orbital describes the region of space where the probability of finding an electron is highest. The specific distribution of electrons across these orbitals is known as the electron configuration. Determining this configuration is governed by three fundamental principles derived from quantum mechanics. These rules ensure that an atom exists in its most stable, lowest-energy state, known as the ground state.
The Rule Governing Energy Sequence
The first principle dictates the order in which electrons are added to an atom’s orbitals. Electrons will always occupy the lowest available energy level first before moving to higher ones. This rule is particularly relevant in multi-electron atoms where the energy levels of different orbitals can overlap.
The energy of an orbital is primarily determined by its principal quantum number (n), which defines the electron shell, and its angular momentum quantum number (l), which defines the orbital shape (s, p, d, f). A simpler approximation for determining the relative energy of an orbital is the n+l rule. For example, the 4s orbital has an n+l value of 4, while the 3d orbital has a value of 5.
Because the 4s orbital possesses the lower sum, it is filled with electrons before the 3d orbital, even though 4s belongs to a higher principal quantum shell. This systematic filling order, which proceeds as 1s, 2s, 2p, 3s, 3p, 4s, 3d, and so on, ensures the atom achieves the lowest possible energy state. Electrons only progress to orbitals with higher energy once all orbitals at a lower energy level are completely filled.
The Rule Governing Orbital Capacity
The second fundamental principle establishes the maximum number of electrons that can reside within any single atomic orbital. This rule states that no two electrons in an atom can share the exact same set of four quantum numbers. These numbers describe an electron’s state: energy level (n), orbital shape (l), orbital orientation (m_l), and intrinsic spin direction (m_s).
Since an orbital defines the first three quantum numbers for any electron it contains, the spin quantum number (m_s) must be unique for each electron within that orbital. The spin quantum number can only have two possible values, represented as +1/2 (“spin up”) and -1/2 (“spin down”). Consequently, an orbital can accommodate a maximum of two electrons, provided they possess opposite spins.
If a third electron were to enter the same orbital, it would be forced to have the identical set of all four quantum numbers as one of the first two electrons, which is forbidden. This restriction explains why electron capacity is limited to two per orbital. The requirement for opposite spins, known as spin pairing, serves to distinguish the two electrons.
The Rule Governing Degenerate Filling
The third rule addresses how electrons behave when multiple orbitals of exactly the same energy are available for filling. Orbitals that share the same energy level, such as the three p orbitals or the five d orbitals within a subshell, are referred to as degenerate orbitals. Electrons follow a pattern that minimizes electron-electron repulsion.
Electrons will first occupy each degenerate orbital singly before any orbital receives a second electron. Furthermore, all of these single electrons must possess parallel spins, meaning their spin quantum numbers are the same. This preference for spreading out is analogous to passengers on a bus selecting an empty row before sitting next to someone else.
By occupying separate orbitals, the electrons maximize the distance between their negative charges, thereby reducing the repulsive forces and achieving a lower, more stable energy configuration for the atom. Only after every orbital in the degenerate set contains one electron does the pairing process begin, with the new electrons having the opposite spin to the ones already present. This systematic filling maximizes the total spin of the electrons, which contributes to the overall stability of the electronic arrangement.