Quantum Numbers, Atomic Orbitals, and Electron Configurations

Vocabulary flashcards covering quantum numbers, orbital shapes and nodes, energy levels, electron configurations, and fundamental filling principles.

Spin quantum number ($m_s$)

The fourth quantum number that describes an electron spinning clockwise or counterclockwise around its axis, creating a tiny magnetic field; it always has a value of either $+\frac{1}{2}$ or $-\frac{1}{2}$.

Node

A place or region where there is zero probability of finding an electron, occurring where the wave function passes through zero.

Spherical node

A concentric spherical region of zero electron density separating the shells of higher-level s orbitals.

Planar node

A flat nodal region of zero electron density located between the two lobes of a dumbbell-shaped p orbital.

$d_{z^2}$ orbital

A d orbital uniquely shaped as a single dumbbell with a ring around it, containing a planar node in the xy-plane and a conical node.

Degenerate orbitals

Orbitals that reside at the exact same energy level and cannot be distinguished from each other based on energy.

Electron configuration

A notation indicating how electrons are distributed among the various atomic orbitals, written in order of increasing energy.

Ground state electron configuration

The lowest energy electron configuration of an atom, constructed by occupying orbitals starting from the lowest energy level.

Valence electrons

Electrons located in the outermost principal quantum level, corresponding to the highest principal quantum number ($n$).

Core electrons

Electrons located in completely filled inner shells at lower principal quantum numbers ($n$) beneath the valence level.

Pseudo-core electrons

Electrons in a d subshell that initially behave like inner core electrons during ionization, but can subsequently behave like valence electrons and be removed under certain conditions.

Pauli exclusion principle

The principle stating that no two electrons in an atom can have identical sets of all four quantum numbers, limiting every orbital to a maximum of two electrons with opposing spins.

Paramagnetic behavior

Magnetic behavior observed when an atom possesses unpaired electrons whose magnetic fields are not cancelled by opposing spins when placed in a magnetic field.

Aufbau principle

The building-up principle which dictates that lower-energy atomic orbitals must be completely filled before electrons occupy higher-energy orbitals.

Hund's rule

The rule stating that when electrons occupy degenerate orbitals, each orbital receives a single electron with parallel spin before any orbital receives a second, paired electron.