1. Consider treating polyenes, ethylene, butadiene, hexatriene etc., with the one-dimensional particle-in-the-box model. What length polyene that is number of C atoms is required to absorb light in the red region of the spectrum? Explain how does that compare with the conjugated portion of carotene?
2. Again utilizing the particle-in-the-box problem, predict in eV the first IP and electron affinity of hexatriene. Explain what temperature would be needed to achieve 10% population of the normally lowest unoccupied molecular orbital (LUMO)?
3. Consider an electron in one, two and three dimensional boxes with a side of 4 A. Explain how does the zero-point energy vary with increasing dimension?