Question

CHEM20020 Structure and Properties Question 8. [time = 10 minutes) Benzene (C6H) has a cyclic structure with Dh symmetry. Using a particle-on-a-ring model calculate the energy and wavelength for the lowest electronic trans elength for the lowest electronic transition of the benzene molecule. Clearly explain (using a diagram) which energy levers are sing a diagram) which energy levels are involved in the transition. Make the following assumptions: 1. The r electrons can be approximated as moving on a 2-D ring. 2. The C-C bond length is 0.139 nm. 3. There are 6 n electrons with 2 electrons accommodated in each particle-on-a-ring "orbital". man2 4. The particle-on-a-ring energy levels are given by Em = 5 2 where m is the quantum number (m = 0, +1, +2, +3 ...), me is the electron mass, and r is the radius of the ring.

Answer 1

WEKOU, T electnons in a Benzene ran be Considensd an a panticle in 2D-5uare oux. NOw ttu expaussion of Lor 2D-5duans ouxis enagy w herce nny is te Emepn) duantam Cemoo deg enuacy NUw. an de bux is a sdors so tRere TLD. NOw te eng level swil e an Surming 2.2.) n2, m2 C2.1 2- 1.2) E2) )ning Now AE = 8-5)h mep 3 mer 4S 8merxc 3h gA3K19xIm)08m/s 3 x6.626x1034 3S (2.12KID-8 So te wave leng tR witt de2-12x10-8 Jm 3h2 8merr- and enengy AE = -(936x10-18Joule