Overview
This lecture covers the four quantum numbers used to describe electron arrangement in atoms, the types of atomic orbitals, and how to determine electron configurations.
Quantum Numbers and Atomic Orbitals
- Electrons are described by four quantum numbers, which define their location and energy in an atom.
- An orbital is a region where there is a high probability of finding an electron.
- Types of orbitals: s (spherical), p (dumbbell-shaped), d, and f (complex shapes).
- Each orbital can hold up to two electrons with opposite spins.
The Four Quantum Numbers
- The principal quantum number (n) is a positive integer indicating the energy level and distance from the nucleus.
- The angular momentum quantum number (l) ranges from 0 to n-1 and describes orbital shape.
- l=0: s orbital (1 per energy level)
- l=1: p orbitals (3 per energy level)
- l=2: d orbitals (5 per energy level)
- l=3: f orbitals (7 per energy level)
- The magnetic quantum number (mₗ) ranges from –l to +l and specifies a particular orbital’s orientation.
- The spin quantum number (mₛ) can be +½ or –½, indicating the electron's spin direction.
Electron Arrangement Principles
- No two electrons can have the same set of four quantum numbers (Pauli exclusion principle).
- Each orbital can hold two electrons with opposite spins.
- The Aufbau principle: electrons fill orbitals in order of increasing energy (1s, 2s, 2p, etc.).
- Hund's rule: Electrons fill orbitals singly before pairing up within a subshell.
Electron Configurations and the Periodic Table
- Electron configuration shows how electrons populate orbitals (e.g., Cl: 1s² 2s² 2p⁶ 3s² 3p⁵).
- Use the periodic table blocks (s, p, d, f) to quickly determine electron configuration.
- Noble gas abbreviation uses the previous noble gas in brackets to simplify notation (e.g., [Ne] 3s² 3p⁵).
Visualizing Orbital Filling
- Orbital diagrams use arrows to show electron spin within each orbital.
- Atoms with unpaired electrons are paramagnetic (attracted to magnetic fields).
- Atoms with all electrons paired are diamagnetic (not attracted to magnetic fields).
Key Terms & Definitions
- Orbital — A 3D region around a nucleus where electrons are likely found.
- Principal quantum number (n) — Indicates energy level.
- Angular momentum quantum number (l) — Describes orbital shape (s, p, d, f).
- Magnetic quantum number (mₗ) — Specifies orbital orientation.
- Spin quantum number (mₛ) — Indicates electron spin (+½ or –½).
- Aufbau principle — Electrons occupy lowest energy orbitals first.
- Hund's rule — Electrons fill orbitals singly before pairing.
- Pauli exclusion principle — No two electrons in an atom have the same four quantum numbers.
- Paramagnetic — Atom with unpaired electrons.
- Diamagnetic — Atom with all electrons paired.
Action Items / Next Steps
- Practice writing electron configurations for elements using the periodic table.
- Review orbital diagrams and apply Hund's rule.
- Complete any assigned textbook readings or practice problems on quantum numbers.