Overview
This lecture covers quantum numbers, electron configuration, isoelectronic species, orbital energies, and magnetic moments, focusing on exam-style questions and concise factual recall.
Quantum Numbers and Orbitals
- Principal quantum number (n) is always a positive integer (n = 1, 2, 3, ...).
- Azimuthal quantum number (l) for a given n: l = 0 to (n-1); defines subshell type (s, p, d, f).
- Magnetic quantum number (ml): values from -l to +l; gives orbital orientation.
- Spin quantum number (ms): +1/2 or -1/2; describes electron spin direction.
- A correct set for 4f: n=4, l=3, valid ml (−3 to +3), ms=±1/2.
- Number of orbitals in shell n = n².
- Maximum electrons in shell n = 2n².
Isoelectronic Species and Ionic Radii
- Isoelectronic species have the same number of electrons (e.g., Na+, Mg2+, Al3+, Cl−).
- Among isoelectronic ions, increasing negative charge increases ionic radius.
Nodes and Electron Density
- Radial nodes = n − l − 1; angular nodes = l.
- Total nodes = n − 1.
- s-orbitals have only radial nodes; p and d have both angular and radial nodes.
Electron Configuration and Energy Order
- Electrons fill subshells in order of increasing (n+l); for equal (n+l), smaller n fills first (Aufbau principle).
- For transition metals, exceptions exist (e.g., Cr: [Ar] 3d5 4s1).
- Half-filled and fully filled subshells offer extra stability (exchange energy).
Magnetic Moments and Unpaired Electrons
- Magnetic moment (μ) = √[n(n+2)] BM; n = number of unpaired electrons.
- More unpaired electrons → higher magnetic moment.
Key Terms & Definitions
- Principal quantum number (n) — Specifies main energy level of an electron.
- Azimuthal quantum number (l) — Determines subshell and shape of orbital.
- Magnetic quantum number (ml) — Describes orientation of orbital.
- Spin quantum number (ms) — Indicates electron spin (+1/2 or −1/2).
- Isoelectronic species — Ions/atoms with the same electron count.
- Degenerate orbitals — Orbitals with the same energy level (in H atom).
- Radial node — Region with zero electron probability, depending on n and l.
- Angular node — Plane or cone with zero electron probability; equals l.
- Aufbau principle — Electrons fill lower energy orbitals first.
Action Items / Next Steps
- Review principal, azimuthal, magnetic, and spin quantum numbers with examples.
- Memorize electron configuration order and key exceptions (e.g., Cr, Cu).
- Practice identifying isoelectronic series and magnetic moment calculations.
- Complete textbook problems on quantum numbers and electron configurations.