Lecture on Quantum Numbers

Introduction

• Electrons are both particles and waves.
• Arrangement of electrons in an atom is determined by four quantum numbers.
• Quantum numbers describe atomic orbitals.

Types of Orbitals

• s, p, d, and f orbitals:
  • Different shapes.
  • Regions in space where electrons can be found.
  • Each orbital can hold up to two electrons.

Quantum Numbers

Principal Quantum Number (n)

• Represents the energy level of the electron.
• Positive integer values.
• Larger n values indicate orbitals further from the nucleus.

Angular Momentum Quantum Number (l)

• Values range from 0 to n-1.
• Describes the shape of the orbital:
  • l = 0: s orbitals (spherical, 1 per energy level).
  • l = 1: p orbitals (three lobes, 3 per energy level).
  • l = 2: d orbitals (5 per energy level).
  • l = 3: f orbitals (7 per energy level).

Magnetic Quantum Number (m_l)

• Range from -l to +l.
• Determines the specific orbital among a type.
  • l = 0: m_l = 0 (1 s orbital per energy level).
  • l = 1: m_l = -1, 0, 1 (3 p orbitals).
  • l = 2: m_l = -2, -1, 0, 1, 2 (5 d orbitals).
  • l = 3: m_l = -3, -2, -1, 0, 1, 2, 3 (7 f orbitals).

Spin Quantum Number (m_s)

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

Electron Configuration

• 1s, 2s, 2p, 3s, 3p, etc.: Order of filling orbitals (Aufbau principle).
• Hund's Rule: Fill each orbital in a set halfway before pairing electrons.

Example: Chlorine

• Neutral chlorine atom has 17 electrons.
• Electron configuration: 1s² 2s² 2p⁶ 3s² 3p⁵.
• Use noble gas abbreviation (e.g., [Ne] 3s² 3p⁵).

Orbital Diagrams

• Visual representation of electron configurations.
• Atoms with unpaired electrons: paramagnetic.
• Atoms with all paired electrons: diamagnetic.

Summary

• n: Energy level.
• l: Type of orbital.
• m_l: Specific orbital among a set.
• m_s: Spin.
• Electrons fill orbitals according to specific principles until all have a place.