Unit 59: π-electronic Energy Levels
Practice Problems
Note: problem difficulty is ranked using a star system.
(*) One-star problems are fundamental to the unit, and can be done relatively quickly. Use these problems to introduce yourself to the material.
(**) Two-star problems are more difficult, and require an understanding of one or two key concepts. Use these problems to test your understanding of the material.
(***) Three-star problems are the most difficult, and require some creative thinking in addition to a deep familiarity with multiple key concepts. Use these problems to challenge yourself; if you can complete one of these, you’re on your way to mastering the material.
**Q59.1) Consider a molecule of 1,3,5-hexatriene (shown below) with a carbon-carbon bond length of 0.15nm:
C = C - C = C - C = C
a) Sketch π-electronic molecular energy level diagrams for the ground state and first-excited state.
b) Find the energies of the n=1, n=2, and n=3 pi-electronic energy levels in Joules and eV.
c) Find the energy of the highest completely-filled energy level in the first-excited state in Joules and eV.
**Q59.2) Imagine wrapping hexatriene around to connect its head to its tail, so that it forms the 6-membered carbon ring known as benzene (shown below) with a carbon-carbon bond length of 0.12nm:
a) Sketch π-electronic molecular energy level diagrams for the ground state and first-excited state.
b) Find the energies of the n=1, n=2, and n=3 pi-electronic energy levels in Joules and eV.
c) Find the energy of the lowest unfilled energy level in the ground state in Joules and eV.
**Q59.3) Consider a molecule of acetylene (shown below) with a carbon-carbon bond length of 0.15nm:
H - C ≡ C - H
Note: triple bonds involve one sigma bond and two pi bonds.
a) Sketch pi-electronic molecular energy level diagrams for the ground state and first-excited state.
b) Find the energies of the n=1, n=2, and n=3 pi-electronic energy levels in Joules and eV.
c) Find the energy of the lowest unfilled energy level in the ground state in Joules and eV.
**Q59.4) Consider a linear π-conjugated section of a molecule. Sketch a scale π-electronic molecular energy level diagram including the first four electronic levels (pay careful attention to the relative distance between adjacent levels).
***Q59.5) Consider the highest-filled π-electronic molecular energy level in the ground state of retinal (shown below):
Find the ratio of the level’s energy if the π-conjugated system is considered to be perfectly linear, to the level’s energy if the bond angle of 120° is accounted for. You may consider the π-conjugated part of retinal to be 11 π-bonds in length.