Orbitals

Wave Function

Quantum Numbers

Principal quantum number

• 1, 2, 3…
• Electron shell, electron energy and size of orbital $l$ Orbital Angualar Momentum Number
• $0-(n-1)$
• Shape of the orbital
  • 0 = s
  • 1 = p
  • 2 = d $m$ Z-component / Magentic of $l$
• $-l$ to $+l$
• Orientation of orbital

Filling

1. Aufbau
   • Start lowest in energy
2. Pauli’s Exclusion
   • Max two electrons per orbital
   • No two electrons can have same n, l, m, s tuple
3. Hund’s Rule of Maximum Multiplicity
   • Orbitals with same energy filled one at a time
   • Degenerate

Radial

• Z = Atomic number
• Bohr radius
  • $a_0=\frac \hbar {\alpha mc}$
• Normalisation
  • $\int_0^\infty r^2R_{nl}^*R_{nl}dr=1$