1. Molecular Structure & Energy Levels
Revision Session

2. 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

3. 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

4. Eigenvalues Quantum Mechanics
𝐺 𝑓=𝑔𝑓 𝐺 : Operator f: Eigenfunction g: Eigenvalue (constant) of the Operator

5. Quantum Mechanics
Particle in a 1-D Box

6. Example
Example
What is the probability of finding the particle in the middle third of the box in the n = 1 state?

7. Example

8. Quantum Mechanics

9. Quantum Mechanics

10. Past Questions

11. Past Questions

12. 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)?

13. Electronic Spectra of Polyenes
Quantum Mechanics
Electronic Spectra of Polyenes