Overview
This lesson covers atomic orbitals and the four quantum numbers that identify an electron's position and properties within an atom, including their meanings, allowed values, and significance.
Atomic Orbitals
- Atomic orbitals are regions in space where electrons are likely to be found.
- S, p, d, and f orbitals have distinct shapes (s: spherical, p: dumbbell, d: cloverleaf/toroidal, f: complex).
- Each orbital holds a maximum of two electrons.
- The number of each orbital type per shell: 1 s, 3 p, 5 d, 7 f (pattern continues with g, h, etc.).
- Higher shells contain larger orbitals and may have radial nodes (regions with zero electron probability).
- Shapes and energy levels of orbitals are solutions to the Schrödinger equation.
Quantum Numbers
- Every electron is described by four quantum numbers, forming its unique "address" in the atom.
Principal Quantum Number (n)
- Symbol: n
- Indicates the shell (energy level) of the electron.
- Allowed values: Positive integers (1, 2, 3, ...).
Azimuthal Quantum Number (l)
- Symbol: l
- Indicates the subshell and shape of orbital (s, p, d, f).
- Allowed values: 0 up to n–1.
- l = 0: s, l = 1: p, l = 2: d, l = 3: f.
Magnetic Quantum Number (ml)
- Symbol: ml
- Specifies the orientation (specific orbital) within a subshell.
- Allowed values: Integers from –l to +l.
Spin Quantum Number (ms)
- Symbol: ms
- Describes electron spin, a fundamental property not from the Schrödinger equation.
- Allowed values: +½ or –½.
Applying Quantum Numbers
- No two electrons in an atom can have the same set of four quantum numbers (Pauli Exclusion Principle).
- Example: A 3p electron has n = 3, l = 1, ml = –1/0/+1, ms = +½ or –½.
- To determine if a quantum number set is possible: check that each value falls in the allowed range.
Key Terms & Definitions
- Orbital — 3D region around the nucleus where an electron is likely to be found.
- Quantum Number — Number describing a property of an electron in an atom.
- Principal Quantum Number (n) — Indicates shell (energy level).
- Azimuthal Quantum Number (l) — Indicates subshell and orbital shape.
- Magnetic Quantum Number (ml) — Indicates orientation of orbital.
- Spin Quantum Number (ms) — Indicates direction of electron spin.
Action Items / Next Steps
- Review and memorize the meanings, symbols, and allowed values for all four quantum numbers.
- Prepare for the next lesson on the Pauli Exclusion Principle and electron configurations.