1. Incident photon
E = hn = hl/c
Let’s get excited!

2. Plan for the next ~3 hours of lecture
Explore the energy budget of the cell:
How much energy is available?
How do we capture it?
How do we store it?
How much do we need to make the components of a cell?
How efficient is the process?

3. The cell’s supply chain

4. Incident solar energy ½ * 1000 nm * 2 W per m^2 per nm = 1000 W/m^2
later we will use this to appreciate the efficiency of photosynthesis and compare it to, say, solar panels.
100 square microns = 1E-10 square meters surface area per cell
1E-7 W = 1E-7 J/s

5. Biological pigment absorptions are well-tuned to incident light wavelengths

6. Photon absorption by photosynthetic pigments ultimately excites and transfers an electron

7. Photosynthetic pigments have distinctive structures
Incident photon
E = hn = hl/c
Energy level spacing needs to match the energy of the incident photon. How to get the spacing between highest unoccupied molecular orbital and lowest occupied molecular orbital that will make this work.
Polyacetylene mentioned by Cassandra back in lecture 8
Beta-carotene

8. Why is it hard to harvest light energy through electron excitation?
Electrons in many atoms/molecules can be electronically excited by visible light, but that energy is typically lost as heat or light. The electron is not freed for transfer.
Balmer lines from one of Cassandra’s slides

9. Delocalized electrons in large pi bonding networks and conductivity
Graphite is conductive
Maybe also delocalized electrons and pKa? (phenol 10 vs. cyclohexane 16)

10. Net charges are stabilized in large pi bonding networks
Maybe also delocalized electrons and pKa? (phenol 10 vs. cyclohexane 16)

11. The length of the pi bonding network determines the wavelength absorbed
N=9: absorbing purple, blue; reflecting red through green.
N = 15: absorbing everything but red

12. Why does a long pi bonding network absorb light in the visible range?
Why do we need these long pi bonding networks to absorb light in the visible range?

13. Electrons in extended pi bonding networks as particles in 1D “box”
Electron can wander through this pi bonding network from the first carbon to the last and back again, but can never wander any further.

14. Two-step plan to find possible energies of the electron
Introduce the concept of operators. “Like a function that take as input the wavefunction, and returns some quantity of interest about the wavefunction, like its average position, velocity, energy, etc.”
Learn how to find the average kinetic energy from a wavefunction
Find the possible wavefunctions of the electron

15. Finding expectation values for wavefunctions
Finding the mean, variance, etc. for wavefunctions works exactly the way you’ve been practicing on problem set 5. Two things are important to know:
* The spatial probability distribution is the square of the absolute value of the wavefunction. Notice that this means the value will always be positive. This is a postulate.
* The wavefunction has a complex value. Here is a brief review of how we work with complex numbers.

16. Finding expectation values for wavefunctions
We’re now on track to find the average kinetic energy, ½m<v>2.
Let’s find an expression for the quantity in red.

17. Inspiration: Schroedinger’s equation
Schroedinger’s equation is presented as a postulate. Looks a little simpler in our case since we have one dimension and our potential function is simple.