Question

A free-electron model for a benzene molecule can be approximated via a particle rotating in a ring (2-D rigid rotor problem). Use this model assuming the radius of benzene of 1.39 ˚A to answer the following questions:

a) Find the energies of the occupied electronic levels; plot a schematic diagram of the electronic levels.

b) Calculate the wavelength (in nm) of the lowest-energy electronic transition in benzene.

c) In what region of the electromagnetic spectrum is this transition? How does it agree with the experimental absorption of 268 nm?

d) Compare your results with those obtained via modeling this molecule as a particle in 2-D box with the size of 2.78 ˚A. Which results are more accurate? Why?

Answer 1

The energy level diagram will be:

m 2 2 m=1 m=0

The longest wavelength of absorption in the benzene spectrum can be given as

hc / λ = E2 − E1 = 2 /2mR² (2² − 1 ² )

Where h = planck's constant

c= speed of light

R = Radius

The ring radius R can be approximated by the C–C distance in benzene, 1.39 ˚A.

On calculating λ ≈ 210 nm, These are in the ultraviolet.