Overview
This lecture covers the four quantum numbers that describe the "address" of an electron in an atom, including their meanings, allowed values, and significance in organizing the periodic table and electron configuration.
Principal Quantum Number (n)
- The principal quantum number (n) indicates the main energy level (shell) and size of an orbital.
- n is a positive integer (1, 2, 3,...), with n = 1 being the lowest energy.
- As n increases, the orbital is farther from the nucleus and has higher energy.
- The energy gap between levels decreases as n increases.
- The row number on the periodic table corresponds to the highest n for that atom.
Angular Momentum Quantum Number (l)
- The angular momentum quantum number (l) defines the shape of the orbital.
- l ranges from 0 to n-1 for a given n.
- l values correspond to orbital types: 0 = s (sphere), 1 = p (dumbbell), 2 = d (clover), 3 = f.
- Each orbital shape (subshell) has characteristic numbers of orbitals: s = 1, p = 3, d = 5, f = 7.
- The periodic table is divided into s, p, d, and f blocks based on these subshells.
Magnetic Quantum Number (ml)
- The magnetic quantum number (ml) specifies the orientation of an orbital within a subshell.
- ml ranges from -l to +l (including zero), so s has 1, p has 3, d has 5, and f has 7 orbitals.
- The number of possible ml values equals the number of orbitals in that subshell.
Spin Quantum Number (ms)
- The spin quantum number (ms) identifies the specific electron in an orbital.
- ms can be +½ or -½; each orbital can hold two electrons with opposite spins.
- No two electrons in an atom can have the same set of four quantum numbers (Pauli exclusion principle).
Applying Quantum Numbers & Periodic Table
- The periodic table helps determine n (row), block (type of subshell), and number of electrons each block can hold (s=2, p=6, d=10, f=14).
- Subshell notation combines n and orbital letter (e.g., 3p, 2s, 4f).
- Problems involve identifying subshells, possible values for l and ml, and counting orbitals using these rules.
Key Terms & Definitions
- Quantum Number — a value that describes specific properties of an electron's "address" in an atom.
- Principal Quantum Number (n) — indicates energy level and size of orbital.
- Angular Momentum Quantum Number (l) — indicates shape of orbital (s, p, d, f).
- Magnetic Quantum Number (ml) — indicates orientation of orbital within a subshell.
- Spin Quantum Number (ms) — indicates direction of electron spin; only two possible values.
- Orbital — region in space where there's a high probability of finding an electron.
- Node — region in an orbital where the probability of finding an electron is zero.
- Degenerate — orbitals with the same energy.
- Pauli Exclusion Principle — no two electrons can have exactly the same set of quantum numbers.
Action Items / Next Steps
- Practice identifying subshells and possible quantum numbers for given electrons.
- Prepare for exercises on electron configuration using the periodic table.