Overview
This lecture covers quantum numbers, their significance, application in electronic configurations, isoelectronic species, orbital energies, and magnetic moments in multi-electron atoms and ions.
Quantum Numbers and Orbitals
- Quantum numbers (n, l, m, s) describe the state of electrons in atoms.
- Principal quantum number n = energy level; n = 1, 2, 3, ...
- Azimuthal quantum number l = shape of orbital; l = 0 to (n-1).
- Magnetic quantum number m = orientation; m = -l to +l.
- Spin quantum number s = spin direction; s = +1/2 or -1/2.
- 4f orbital: n=4, l=3, allowed m values are -3 to +3.
- Number of orbitals for given n: n²; for n=5, orbitals = 25.
- Number of subshells for n: n.
- Radial nodes = n - l - 1; angular nodes = l.
- Degenerate orbitals have the same energy in hydrogen but not in multi-electron atoms.
Isoelectronic Species and Ionic Radii
- Isoelectronic species = ions/atoms with the same number of electrons.
- Examples: K⁺, Ca²⁺, Sc³⁺, Cl⁻ are isoelectronic.
- For isoelectronic ions, ionic radius decreases with increasing nuclear charge.
- Order (smallest to largest for K⁺, Ca²⁺, Cl⁻, S²⁻): Ca²⁺ < K⁺ < Cl⁻ < S²⁻.
Electronic Configuration
- Electrons fill orbitals in order of increasing energy (Aufbau principle).
- Half-filled and fully-filled subshells are exceptionally stable.
- Cr and Cu show exceptions in electron configuration ([Ar] 3d⁵ 4s¹ for Cr).
- Outer electron configuration determines chemical properties and magnetic moment.
Orbital Energy and Magnetic Moment
- For hydrogen, all orbitals with same n have same energy.
- In multi-electron atoms, energy: ns < np < nd < nf for a given n.
- Magnetic moment depends on unpaired electrons: μ = √(n(n+2)) BM.
- More unpaired electrons = higher magnetic moment.
Key Terms & Definitions
- Isoelectronic species — Species with the same number of electrons.
- Degenerate orbitals — Orbitals with equal energy.
- Radial node — Region where electron probability is zero, depends on n and l.
- Angular node — Plane or cone where probability is zero, equals l.
- Aufbau principle — Rule for electron filling order by increasing energy.
- Spin quantum number (s) — Quantum number describing electron spin (+1/2 or -1/2).
- Magnetic moment — Measure of unpaired electrons, in Bohr Magneton (BM).
Action Items / Next Steps
- Review key quantum number definitions and rules for allowed values.
- Practice identifying isoelectronic species and ordering ionic radii.
- Complete homework exercises on electron configurations and quantum numbers.