Quantum Numbers and Electron Arrangement

Aug 1, 2025

Overview

This lecture explains the four quantum numbers that define electron arrangement in atoms, their relationship to atomic orbitals, and how to determine electron configurations.

Quantum Numbers and Atomic Orbitals

  • Atoms have electrons arranged in orbitals, which are regions of probability where electrons may be found.
  • Orbitals come in four types: s (spherical), p (dumbbell-shaped), d, and f, each holding up to two electrons.
  • More electrons mean more orbitals are needed in an atom.

The Four Quantum Numbers

  • Principal quantum number (n): Any positive integer; represents energy level and distance from the nucleus.
  • Angular momentum quantum number (l): From 0 to n-1; determines orbital shape (s: l=0, p: l=1, d: l=2, f: l=3).
  • Magnetic quantum number (mₗ): From -l to +l; specifies a particular orbital within a set.
  • Spin quantum number (mₛ): Either +½ or -½; indicates electron spin direction.

Rules for Electron Arrangement

  • No two electrons in the same atom have the same set of all four quantum numbers (Pauli exclusion principle).
  • Each orbital holds up to two electrons with opposite spins.
  • The Aufbau principle states: orbitals fill in order of increasing energy (1s, 2s, 2p, 3s, etc.).
  • Hund’s rule: fill each degenerate orbital singly before pairing electrons.

Electron Configuration and the Periodic Table

  • Electron configuration shows how electrons fill available orbitals in sequence.
  • Use the periodic table blocks (s, p, d, f) to determine electron filling order.
  • Abbreviate electron configurations using noble gas cores for simplicity.
  • Orbital diagrams visually show electron filling in boxes with arrows indicating spin.

Magnetic Properties

  • Atoms with unpaired electrons are paramagnetic and attracted to magnetic fields.
  • Atoms with all electrons paired are diamagnetic and not affected by magnetic fields.

Key Terms & Definitions

  • Quantum number — a value specifying the properties of an electron in an atom.
  • Orbital — region in space with a high probability of finding an electron.
  • Aufbau principle — electrons fill lowest energy orbitals first.
  • Pauli exclusion principle — no two electrons in the same atom have identical quantum numbers.
  • Hund’s rule — electrons fill orbitals singly before pairing.
  • Paramagnetic — atom with unpaired electrons, attracted to magnetic fields.
  • Diamagnetic — atom with all paired electrons, not affected by magnetic fields.

Action Items / Next Steps

  • Review how to write electron configurations and draw orbital diagrams for given elements.
  • Practice identifying quantum numbers for specific electrons.
  • Read textbook sections on quantum numbers and electron configuration for reinforcement.