Question

Huckel/PIB

a) Calculate the ground-state energy levels of the π-network in hexatriene, model, and for each of them indicate the associated degeneracy. To ca molecule is linear and use the values 135 and 154 pm for C-C and C-C bonds CoHs, using the particle in the box lculate the box length, assume that the to induce a transition from the ground state to the first excited e can be obtained using Huckel theory. Knowing b) What is the wavelength of light required state? c) A more accurate description of the T-network in hexatrien t the Coulomb integral a -9.9 eV and the resonance integral B -1.3 ev, determine the wavelength of light required to induce a transition from the ground state to the first excited state. d) Describe the assumptions made in the "particle-in-the-box" model and Huckel theory e) Using the energy difference between ground state and first excited states obtained from Huckel theory, determine the ratio ni/no at 300 K, where no and ni correspond to the populations of the g excited states, respectively. Do hexatriene molecules at 300 K be have classically or quantum mechanically?

Answer 1

a)

(a) The ground state energy for particle in D box is given E = n^2 h^2/8m L^2 implies E_1 = h^2/8 m L^2 h = plank's constant = 6.6 times 10^-34 J.s m = mass of electrons = 9.1 times 10^-31 kg L = 50 + 135 + 154 + 135 + 154 + 135 + 50 L = 813 pm = 813 times 10^-10m implies E_1 = h^2/8m L^2 = (6.6 times 10^-34)^2/8 times (9.1 times 10^-31)(813 times 10^-12)^2 = 43.56 times 10^(-34 -34 + 31 + 12 + 12)/8 times 9.1 times 8.13 times 813 = 43.56/59186.4 times 10^-13 E_1 = 9.05 times 10^-20 T energy of ground state = 9.05 times 10^-20g for n = 1(level) In ground state, 6 electrons occupy till n = 6 E_1 = 9.05 times 10^-20 E_2 = n^2 E_1 E_3 = n^2 E_1 (b) iterative has 6 pi electrons for excitation, electrons from n = 3

b.

d) the assumptions made for particle in box are

1.it is assumed that the collisions at the ends are perfectly elastic, so the particle's energy--entirely kinetic--never changes.

2.outside the box the potential is infinity

3.at the ends of the box the function goes to zero, or vanishes

4.the function has continuous first and second derivatives