Lecture on Quantum Numbers

Introduction

• Electrons are both particles and waves.
• Arrangement in atoms is determined by four quantum numbers.
• Orbitals are regions of probability for finding electrons.
  • Types: S, P, D, and F
  • Each holds up to two electrons.

Quantum Numbers

Principal Quantum Number (n)

• Positive integer values.
• Represents the energy level of an electron.
• Larger n value = further from the nucleus.

Angular Momentum Quantum Number (L)

• Values range from 0 to n-1.
• Defines the shape of the orbital.
  • L = 0: S orbitals (spherical)
  • L = 1: P orbitals (3 lobes)
  • L = 2: D orbitals (5 shapes)
  • L = 3: F orbitals (7 shapes)

Magnetic Quantum Number (M sub L)

• Values from -L to L.
• Specifies the specific orbital among a type.
  • L = 0: 1 value (S orbital)
  • L = 1: 3 values (P orbitals)
  • L = 2: 5 values (D orbitals)
  • L = 3: 7 values (F orbitals)

Spin Quantum Number (M sub S)

• Values of +1/2 or -1/2.
• No two electrons can have the same set of quantum numbers (Pauli exclusion principle).

Electron Configuration

Aufbau Principle

• Electrons fill orbitals starting from the lowest energy.
• Sequence: 1s, 2s, 2p, 3s, 3p, etc.

Example: Chlorine

• 17 electrons.
• Configuration: 1s² 2s² 2p⁶ 3s² 3p⁵.

Hund's Rule

• Electrons fill each orbital singly before doubling up.

Periodic Table Shortcut

• S block, P block, D block, F block areas.
• Determine electron configurations by reading the table left to right, top to bottom.

Noble Gas Abbreviation

• Use to simplify configurations.
• Example: Chlorine = [Ne] 3s² 3p⁵.

Orbital Diagrams

• Visual representation of electron arrangement.
• Follow Hund's Rule.

Magnetism

• Paramagnetic: Unpaired electrons, attracted to magnetic fields.
• Diamagnetic: All electrons paired, not affected by magnetic fields.

Summary

• N = Energy level, L = Type of orbital, M sub L = Specific orbital, M sub S = Spin.
• Electrons fill orbitals per the Aufbau principle.