Molecular Structure & Energy Levels Revision Session
Quantum Mechanics The de Broglie Hypothesis where p is particle momentum (mass x velocity) Heisenberg Uncertainty Relation • N: Normalisation Factor • : Probability • : Integrating across all space
Quantum Mechanics What does ψ look like? The wavefunction is finiteeverywhere Does not tend to infinity The wavefunction must be single valued Does not bend back on itself The wavefunction must be continuous Does not ‘kink’ or have sharp angles
Quantum Mechanics Eigenvalues : Operator f: Eigenfunction g: Eigenvalue (constant) of the Operator
Quantum Mechanics Particle in a 1-D Box
Example Example What is the probability of finding the particle in the middle third of the box in the n = 1 state?
Quantum Mechanics Electronic Spectra of Polyenes Consider butadiene Take average carbon-carbon bond length as 0.14 nm There are 4 pi electrons, filling n=1 and 2 levels What is the energy of the first transition (n=2 n=3)?
Quantum Mechanics Electronic Spectra of Polyenes