CHEM20120

Learning Outcomes:

On completion of the module, students will be able to:

• Understand the origins of quantum mechanics in terms of energy quantisation and wave-particle duality
• Describe the dynamics of microscopic systems in terms of the Schrödinger equation and the Born interpretation of the wavefunction
• Use key principles of quantum mechanics to determine the information in a wavefunction and to describe the nature and ramifications of the uncertainty principle
• Apply quantum mechanics to the description of translational motion, confinement (particle-in-a-box), tunneling, rotational motion (particle-on-a-ring and particle-on-a-sphere) and vibrational motion (harmonic oscillator)
• Describe the property of particle spin
• Understand the structure of hydrogenic atoms in terms of quantum mechanics
• Define the four quantum numbers (n, l, ml, and ms) and recognise their relationship to electronic structure
• Describe the permitted energies of hydrogenic atoms and the shapes of atomic orbitals
• Describe the spectroscopic transitions and selection rules of hydrogenic atoms
• Describe the importance of orbitals in theories of chemical bonding
• Understand the valence bond theory of diatomic and polyatomic molecules
• Identify the hybridisation of orbitals in a molecule or ion and use this information to predict molecular geometries
• Understand molecular orbital (MO) theory in terms of linear combinations of atomic orbitals
• Understand the differences between bonding and anti-bonding molecular orbitals and write the molecular orbital configurations for simple diatomic molecules
• Understand the principles and practice of atomic and molecular spectroscopy
• Understand what molecular features lead to electron delocalization
• Understand the concept of resonance
• Understand the concepts of aromaticity and delocalization of pi-electrons
• Understand the conceptual and mathematical bases of the Hückel theory and use this theory to predict relative stability of conjugated hydrocarbons and aromatic hydrocarbons, such as benzene
• Understand aspects of the principles and practice of atomic and molecular spectroscopy

Indicative Module Content:

The classroom component is comprised of six parts as follows:

Part 1: The Concept of Quantisation
Introduction, Classical Mechanics, Particle in 1-D, Hamiltonian, Waves, Light as a Wave Phenomenon, Electromagnetic Radiation, Blackbody Radiation, Planck's Equation, Atomic Emission Spectra, Bohr Model of H Atom

Part 2: From Quantisation to Wave-Particle Duality
Photoelectric Effect, de Broglie Relation

Part 3: Impact of Quantisation & Wave-Particle Duality – The Dynamics of Microscopic Systems
Time-independent Schrodinger Equation in 1-D, Born's Interpretation of the Wavefunction, Normalisation, Origins of Quantisation, Particle Moving in 1-D – Probability Density Examples, Operators, Eigenvalues, Eigenfunctions, Observables, Eigenvalue Equations, Setting up an Operator and Using it to Determine the Value of an Observable, Curvature of Wavefunction, Hermitian Operators, Superpositions/Linear Combinations of Wavefunctions, Measurements, Expectation Values, Heisenberg Uncertainty Principle, Complementary Observables

Part 4: Quantum Mechanics – Techniques & Applications
Particle in a Box in 1-D and in 2-D, Separation of Variables, Degeneracy, Particle in a Well of Finite Depth, Tunneling, Simple Harmonic Oscillator, A Particle on a Ring, A Particle on a Sphere, Quantisation of Space, Spin

Part 5: The Electronic Structure of the Hydrogen Atom
Hamiltonian and Schrodinger Equation for H Atom, Separation of Variables, Radial Wave Equation, Radial Wavefunctions and Energies, Link to H Atom Spectrum and Ionisation Energy, Angular Wave Equation, Combining Radial and Angular Wavefunctions, Quantum Numbers, Shells, Sub-shells, Orbitals, Radial Distribution Functions, Role of Selection Rules in H Atom Spectra

Part 6: Orbitals and Theories of Chemical Bonding
Lewis Model of Covalent Bonding, Bond Order, Length and Strength, Valence Bond Model of Covalent Bonding, Valence Shell Electron Pair Repulsion, Orbital Hybridisation, Cis-trans Isomerism, Resonance, Molecular Orbital Model of Covalent Bonding, Bonding and Anti-bonding Molecular Orbitals, Bond Order, Homonuclear Diatomic Molecules, Sigma and Pi Molecular Orbitals, Paramagnetism of Dioxygen, Heteronuclear Diatomic Molecules, Polyatomic Molecules, Nonbonding Molecular Orbitals, Resonance, Aromaticity, Pi-electron delocalization, Hückel theory, Delocalization Energy

Student Effort Hours:

Approaches to Teaching and Learning:

Requirements, Exclusions and Recommendations

Students registering for this module should have completed CHEM00010 Introductory Chemistry OR achieved a minimum grade of C in Leaving Certificate Honours Chemistry or equivalent AND have completed CHEM20080 Basis of Physical Chemistry.

Module Requisites and Incompatibles

Assessment Strategy

Feedback Strategy/Strategies

• Group/class feedback, post-assessment

How will my Feedback be Delivered?

There will be four assignments based on problem solving with a particular emphasis on numerical skills development Tutor will provide in-person tutorials to describe aim of each question, relevance to lecture material, approach to solution, and worked solution Assignment questions will bridge between the in-class lecture material, the learning outcomes, and the end-of-trimester exam