Lecture Notes: Quantum Numbers and Electronic Configurations

Overview

• Sections Covered: 12.10, 12.11, 12.12, 12.13, 12.14
• Topics: Quantum numbers, electronic configurations, filling of orbitals, and periodic table relationships.

Quantum Numbers

1. Principal Quantum Number (n)

   • Describes the energy level of the electron (shells)
   • Example: n = 1, 2, 3

2. Azimuthal Quantum Number (l)

   • Describes the shape of the orbital (subshells)
   • Letter designations:
     • s-type (spherical)
     • p-type (dumbbell)
     • d-type (clover)
   • l values depend on n.

3. Magnetic Quantum Number (m_l)

   • Describes the orientation of the orbital in space
   • Examples:
     • s orbitals: 1 orientation
     • p orbitals: 3 orientations
     • d orbitals: 5 orientations

4. Spin Quantum Number (m_s)

   • Describes the electron's spin
   • Possible values: +1/2 or -1/2

Key Principles

• Pauli Exclusion Principle: No two electrons can have the same set of quantum numbers in an atom.
• Degeneracy: Orbitals with the same energy level.
• Magnetic Spin Experiment: Demonstrates m_s by deflecting hydrogen atoms in a magnetic field.
• Quantum Number Summary:
  • n: Energy
  • l: Shape
  • m_l: Orientation
  • m_s: Spin

Electronic Configuration

• Filling Order: Electrons fill orbitals starting from lowest to highest energy.
• Aufbau Principle: Fill lowest energy orbitals first.
• Hund's Rule: Spread out electrons in degenerate orbitals before pairing.

Example Configurations

• Hydrogen: 1s¹
• Helium: 1s²
• Lithium: 1s² 2s¹

Shielding and Effective Nuclear Charge

• Z Effective (Z_eff): Effective nuclear charge felt by an electron.
• Shielding effect: Inner electrons shield outer electrons from the nuclear charge.
• Penetration: s orbitals penetrate closer to the nucleus, are less shielded, and thus lower in energy than p orbitals.

Orbital Filling Order

• Use diagrams or n+l rule to determine order.
• n+l Rule: Lower sum of n+l indicates lower energy.

Electron Configuration Notation

• Noble Gas Shortcut: Use noble gases to simplify core electron representation.
  • Sodium: [Ne] 3s¹
  • Calcium: [Ar] 4s²

Periodic Table and Electronic Configuration

• Blocks:
  • s-block, p-block, d-block, f-block
• Exceptions:
  • Chromium: [Ar] 3d⁵ 4s¹
  • Copper: [Ar] 3d¹⁰ 4s¹

Conclusion

• Understand and practice electronic configurations using the periodic table.
• Remember exceptions like chromium and copper for exams.

Study Tips:

• Practice drawing orbital diagrams.
• Use periodic table relationships to predict configurations.
• Memorize key exceptions as they often appear on tests.