Molecular Structure & Energy Levels Revision Session

The de Broglie Hypothesis Quantum Mechanics The de Broglie Hypothesis λ = h p where p is particle momentum (mass x velocity) ∆𝒑 𝒙 ∆𝒙 ≥ 𝒉 𝟒𝝅 Heisenberg Uncertainty Relation 𝑵 𝟐 𝝍 𝟐 𝒅𝝉=𝟏 N: Normalisation Factor 𝜓 2 : Probability 𝑑𝜏: Integrating across all space

What does ψ look like? Quantum Mechanics The wavefunction is finite everywhere 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

Eigenvalues Quantum Mechanics 𝐺 𝑓=𝑔𝑓 𝐺 : 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?

Example

Quantum Mechanics

Quantum Mechanics

Past Questions

Past Questions

Electronic Spectra of Polyenes 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)?

Electronic Spectra of Polyenes Quantum Mechanics Electronic Spectra of Polyenes