Chapter 8

Chapter 8: The Quantum Model of the Atom

8.1 A Brief Exploration of Light

• Dual Nature of Light:
  • Light exhibits both wave-like and particle-like properties.
  • Can be described as a moving wave of magnetic and electrical potential.
• Types of Waves:
  1. Mechanical Waves: Require a medium (e.g., sound waves, water waves).
  2. Electromagnetic Waves: Do not require a medium (e.g., light, microwaves, X-rays, radio waves).
• Characteristics of Waves:
  • Wavelength (λ): Distance between consecutive peaks or troughs. Units: meters (m).
  • Frequency (ν): Number of cycles that pass a point per unit time. Units: Hertz (Hz) or $s^{-1}$.
• Wavelength-Frequency Relationship:
  • Formula: c =
    u imes au where c = 2.998 imes 10^8 ext{ m/s}

8.2 The Bohr Model of the Atom

• Einstein’s Explanation of the Photoelectric Effect:
  • Light consists of particles called photons; energy of a photon is given by:
    E = h
    u where h = 6.626 imes 10^{-34} ext{ J·s}.
  • Photoelectrons are emitted when light hits a metal surface under vacuum conditions.
• Bohr Model:
  • Proposed by Niels Bohr, stating that:
  • Electrons exist in specific orbits at certain distances from the nucleus.
  • Electrons emit or absorb light when they change energy levels.
  • Energy Difference Formula:
    riangle E = -2.18 imes 10^{-18} ext{ J} igg( rac{1}{n{final}^2} - rac{1}{n{initial}^2} igg)

8.4 Orbitals and Quantum Numbers

• Orbitals:
  • Defined as areas around the nucleus where there is a high probability of finding an electron. Each orbital holds a maximum of two electrons.
• Quantum Numbers:
  • Describe properties of atomic orbitals:
  1. Principal Quantum Number (n):
     • Positive integers (1, 2, 3, …).
     • Indicates size and energy of the orbital.
  2. Angular Momentum Quantum Number (l):
     • Values from 0 to (n-1) indicate the shape of the orbital.
  3. Magnetic Quantum Number (ml):
     • Values from -l to +l indicating orbital orientation.
  4. Spin Quantum Number (ms):
     • Two possible values: + rac{1}{2} or - rac{1}{2}.

8.6 Orbital Diagrams and Electron Configurations

• Orbital Diagrams:
  • Graphical representations to show the arrangement of electrons in orbitals.
• Electron Configurations:
  • Describe how electrons are distributed among sublevels. Based on:
  • Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers.
  • Aufbau Principle: Electrons fill the lowest energy orbitals first.
  • Hund’s Rule: Electrons with the same spin are maximized in degenerate orbitals.
• Examples:
  • Ground state configurations for:
  • Hydrogen (H): 1s$^1$.
  • Oxygen (O): 1s$^2$ 2s$^2$ 2p$^4$.
  • Neon (Ne): 1s$^2$ 2s$^2$ 2p$^6$ (all paired, hence diamagnetic).

8.7 Predicting Electron Configurations

• Anomalous Configurations: Example configurations for transition metals like Chromium (Cr) and Copper (Cu), which differ from predicted configurations due to stability needs.
• Abbreviated Configurations: Use noble gas notation to represent core electrons.
• Configurations of Ions:
  • For anions, additional electrons fill according to Aufbau principle.
  • For cations, the electrons removed are typically the outermost or most recently added ones.