###### Learning Outcomes:

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

• Understand the structure of many-electron atoms in terms of quantum mechanics

• Describe the orbital approximation and the Pauli principle

• Understand the effects of penetration, shielding, and the Aufbau principle on the atomic subshell energies and electron configurations of many-electron atoms

• Rationalise Periodic trends in some atomic properties

• Describe the importance of orbitals in theories of chemical bonding

• Understand the valence bond theory of diatomic and polyatomic molecules

• Identify the hybridisation of an atom in a molecule or ion

• Understand molecular orbital 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.

###### Indicative Module Content:

The classroom component is comprised of seven 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: The Electronic Structure of Many-Electron Atoms

Orbital Approximation, Pauli Exclusion Principle, Order of Orbitals, Shielding, Penetration, Aufbau Principle, Hund’s Rule, Chemical Periodicity of Elements, Electron Configurations of Ions, Paramagnetism, Diamagnetism, Ionisation Energies of Elements, Quantum Defects, Rydberg States

Part 7: Orbitals & 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, Reconsidering Resonance