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.