Quantum Numbers
Start with the big picture
The four quantum numbers—principal (n), azimuthal (l), magnetic (mₗ), and spin (mₛ)—provide a framework for describing electron states. Their allowed values determine shells, subshells, orbital orientations, and spin states. The topic also explains how these values relate to orbital and electron capacities, and how the Pauli exclusion principle, Aufbau principle, and Hund’s rule guide electron arrangements. Further connections include the origin of quantum numbers in solutions to the Schrödinger equation for hydrogenic atoms, energy and radius trends, subshell energy splitting, and selection rules for electronic transitions. Together, these concepts help explain relationships between atomic structure, periodic properties, spectroscopy, and magnetic behavior.
What you'll learn
- Define the four quantum numbers and identify their allowed values.
- Relate quantum numbers to shells, subshells, orbital orientations, and spin states.
- Apply the Pauli exclusion, Aufbau, and Hund’s principles to electron arrangements.
- Describe subshell and shell orbital and electron capacities.
- Connect quantum numbers with energy trends, transitions, and periodic properties.
Continue your study
Work through the complete notes and reinforce the topic with the study tools available in the full lesson.
