KC

A4 - Quantum Atomic Structure

HERIOT WATT UNIVERSITY

  • A4 - Quantum Atomic Structure

  • Dr Robert Quinn (R.Quinn@hw.ac.uk)

  • Dr Nazia Farooqui (Nazia.Farooqui@hw.ac.uk)

Topic Overview

Session 1 – Electron Wavefunctions and Orbitals

  • History – Origins of the Quantum Atomic Model

  • Quantising – Wavefunctions

  • Electronic Transitions – Emission and Absorption in Hydrogen

Session 2 – Multi-Electron Systems

  • Electron Repulsion – Loss of Energy Degeneracy

  • Filling Rules – PEP, Hund’s Rules and Aufbau Principle

  • Exchange Energy – Origin of Half-Filled Shells

History of Atomic Structure

  • Discovery of Electrons

    • J.J. Thomson (1897) discovered the electron.

    • Concept challenged the notion of indivisible atoms.

  • Atomic Models:

    • Thompson's Plum Pudding Model (1904): Positively charged matter with embedded electrons.

    • Nagaoka’s Saturnian Model (1904): Electrons orbit a central positive charge.

  • Rutherford’s Experiments (1911): Helped determine the nuclear structure of the atom.

  • Bohr Model (1911-1918): Introduced quantised orbits for electrons.

Ancient Philosophy (~ 400 BCE)

  • Democritus and Leucippus proposed matter is made of indivisible particles called "atomos."

  • Aristotle rejected atoms, believed in four elements (earth, water, air, fire).

Modern Beginnings (Early 1800s)

  • John Dalton (1803): Proposed the first scientific atomic theory stating:

    • Atoms are indivisible.

    • Each element has unique atoms.

    • Atoms combine in fixed ratios to form compounds.

Discovery of Subatomic Particles (Late 1800s – Early 1900s)

J.J. Thomson (1897)

  • Discovered the electron using a cathode ray tube.

  • Proposed the Plum Pudding Model for atomic structure.

  • Limitations: Model couldn’t explain alpha particle scattering from later experiments.

Electrons in Atoms – 1904

  • Electrons thought to be suspended in a diffuse region of positive charge.

  • H. Nagaoka: Proposed a model with electrons orbiting central positive charge.

Rutherford's Experiments (1911)

  • Alpha Particle Scattering: Bombarded gold foil with alpha particles, leading to discoveries on atomic structure.

  • Conclusion: The existence of a small, dense nucleus in atoms.

  • Resulted in the Rutherford Planetary Model of the atom.

Modern Atomic Theory

Wave-Particle Duality

  • Quantum mechanics describes electrons as having both wave-like and particle-like properties.

Wavefunctions

  • Electrons described mathematically by complex wavefunctions defining probability distributions.

Quantum Mechanics

  • Provides a complete and accurate model of atomic structure.

Electronic Transitions and Quantum Theory

  • Neon light emission explained via Quantum Theory: excited electrons emit light when they drop to a lower energy level.

Electromagnetic Radiation

  • All types travel through vacuum at speed (c = 2.998 × 10^8 m/s).

  • Properties of waves: wavelength and frequency.

Quantisation of Energy – Planck’s Theory

  • Max Planck proposed that energy is absorbed or released in discrete packets (quanta).

  • Energy of a photon is linked to its frequency (E = hν).

Quantum Mechanics – Wave-Particle Duality – Einstein Theory

  • Einstein expanded on Planck’s theory proposing light exists as discrete packets or "photon."

  • Introduced wave-particle duality for light, stating radiant energy strikes surfaces like a stream of photons.

Bohr Model (1913)

  • Niels Bohr: Electrons in specific orbits around the nucleus with fixed energy levels.

  • Electron transitions involve absorption or emission of a photon corresponding to the energy difference between these levels.

  • Limitations of Bohr’s model noted for atoms with multiple electrons and wave-like properties.

Rydberg Equation and Energy Levels

  • Rydberg Equation calculates emitted or absorbed wavelengths for electron transitions in hydrogen.

  • Energy levels plotted, showing ionisation energy variations.

Energy and Light Relationships

  • Photons described by (E = hν), with Planck’s constant (h = 6.626 × 10^{−34} J.s).

  • Relationships established between energy, frequency, and wavelength.

Example Calculations

Energy Conversion Exercises

  1. Photons Energy Calculation: Energy (Joules) of a 121 nm photon.

  2. Frequency to Wavelength Conversion: Converting 820 THz to a wavelength.

  3. Joules to Electron Volt: Conversion of a photon with energy 1.3 x 10^(-20) J to eV.

The Balmer Series (n = 2) of H

  • Represents spectral lines emitted by hydrogen transitioning from higher to lower energy levels.

Overview of Exercises

  • In-depth calculations related to electronic configurations and transitions.

Multiple Electron Systems

  • Discusses interaction complexities in multiple electron systems (three-body problem).

Loss of Degeneracy

  • Electrons in different shells have varying energy levels due to electron-electron interactions.

Screening and Penetration in Electron Configurations

  • Electrons fill from core (1s) outward, affecting stability and energy considerations.

Aufbau Principle

  • Electrons fill orbitals starting from the lowest energy to higher energy shells.

Hund's Rules

  • Describe how electrons occupy subshells: singly before pairing, with aligned spins.

Exchange Interaction and Complications

  • Exception cases in electron configurations for specific atoms like Chromium and Copper due to spin alignment leading to lower energy states.

Exercise Overview

  • Exercises focusing on oxidation states, redox processes, and electronic configurations concluded the learning sessions.