quantum
33 results carry this thread across the degree.
The Bohr model of hydrogen
Quantised electron orbits give energy levels E_n = -13.6/n^2 eV.
The Rydberg formula
Every hydrogen spectral line from a single expression in 1/n^2.
Quantum numbers and atomic orbitals
Four quantum numbers label every electron in an atom.
The building-up principle
Aufbau order, Hund's rule and the Pauli principle fix ground-state configurations.
Periodic trends
Effective nuclear charge explains atomic size and ionisation energy across the table.
Ionisation and the photoelectric effect
Electrons are ejected only above a threshold photon energy.
Ionic bonding and the Born-Haber cycle
Lattice energy extracted from a thermodynamic cycle.
Lewis structures and the octet rule
Shared and lone pairs from electron bookkeeping.
VSEPR and molecular shape
Electron-pair repulsion predicts molecular geometry.
Orbital hybridisation
sp, sp2 and sp3 mixing rationalises bond angles.
Molecular orbital theory
Bonding and antibonding combinations give bond order and magnetism.
Electronegativity and bond polarity
Unequal sharing produces dipole moments.
The particle in a box
Quantised energies as a consequence of confinement.
The hydrogen atom
Atomic orbitals as exact solutions of the Schrodinger equation.
The variational principle
An upper bound on the ground-state energy.
Huckel theory
pi-electron energies of conjugated molecules.
The Born-Oppenheimer approximation
Separating slow nuclei from fast electrons.
LCAO molecular orbitals
Building molecular orbitals from atomic ones.
The Beer-Lambert law
Absorbance proportional to concentration and path length.
Rotational spectroscopy
Bond lengths from the rigid-rotor microwave spectrum.
Vibrational (IR) spectroscopy
The harmonic oscillator and vibrational selection rules.
NMR and the chemical shift
Reporting the nuclear environment through resonance.
UV-visible spectroscopy
Electronic transitions and chromophores.
Mass spectrometry
Molecular mass and structure from fragmentation.
The molecular partition function
The bridge from energy levels to thermodynamics.
The Boltzmann distribution of populations
How molecules populate available energy levels.
The equipartition theorem
An average of (1/2)kT per quadratic degree of freedom.
The statistical definition of entropy
Boltzmann's S = k ln W.
Heat capacity from energy levels
The Einstein and Debye models of solids.
The Hartree-Fock method
A self-consistent mean-field for many electrons.
Density functional theory
Energy as a functional of the electron density.
Basis sets
Representing orbitals for practical computation.
Potential energy surfaces
Geometries, transition states and reaction paths.