Physical Chemistry , 1st ed.

15.7 & 15.8 Franck-Condon Principle and
Polyatomic Molecules

15.24.Figure 15.36 shows two vibronic levels of a molecule.
Indicate which sets of energy levels should have the largest
Franck-Condon overlap integral. Explain your answer.

15.25.Indicate, on the basis of general principles, whether or
not the following polyatomic ions are colored. (a)Nitrate,
NO 3 (b)Permanganate, MnO 4 (c)Ammonium, NH 4
(d)Dichromate, Cr 2 O 72 (e)Peroxide, O 22 (f)Acetylide,
C 22

15.26.For an electronic spectrum that has both vibrational
androtational structure (a rovibronic spectrum), suggest a
form for the complete transition moment.

15.27.Determine the symmetry labels of the allowed excited
states of H 2 O if the ground electronic state has a symmetry la-
bel of^1 A 1. (H 2 O has C2vsymmetry.)

15.9 & 15.10 Hückel Approximations
and Aromaticity

15.28.Justify in words why S 11 S 22 S 33 S 44 in the
Hückel approximation of the orbitals of butadiene.

15.29.What would change in the Hückel approximation of
ethylene if deuterium atoms were substituted for the hydro-
gen atoms in the molecule? Explain your reasoning.

15.30.Construct the Hückel determinants for cyclobutadiene
and cyclopentadiene. In what ways are they alike? In what
ways are they different?

15.31.Explain why cyclopentadiene easily accepts an elec-

tron to become cyclopentadienide (C 5 H 5    , which is abbrevi-

ated Cp in organic or organometallic chemistry).

15.32.Consider the following molecule:

Why can its stability be attributed to an internal charge sepa-

ration with a charge in the seven-membered ring and

a charge in the five-membered ring?

15.33.Within each of the following groups, predict which cy-

clopolyenes will be aromatic: (a)neutral, (b)single negative

charge, and (c)double negative charge.

15.34.Do the same as in exercise 15.33, but for cyclopoly-

enes with (a)a single positive charge and (b)double positive

charge.

15.11 & 15.12 Fluorescence, Phosphorescence,

and Lasers

15.35.Why can a population inversion notbe achieved by

simply heating a potentially laser-active material?

15.36.Suggest why phosphorescence spectra are sometimes

better for identifying useful electronic transitions for possible

laser transitions than are fluorescence spectra.

15.37.Would the light from fireflies be considered an exam-

ple of a fluorescence or a phosphorescence process?

15.38.Why is it not possible to obtain blue fluorescence from

a transition that initially absorbs red light?

15.39.CO 2 lasers are among the most powerful cw lasers

available; their most commonly emitted wavelength is 10.6

m. How many 10.6-m photons are generated each second

from a CO 2 laser that emits 300,000 J per second? (That makes

it a 300-kilowatt laser.)

15.40.How many 632.8-nm photons must a He-Ne laser

emit per second to achieve a power of 1 J/s?

15.41.Many high-power lasers emit only a little bit of energy

but in an extremely short pulse. What is the power of a laser

that emits a 300-millijoule pulse in 2.50 nanoseconds?

15.42.Explain why X-ray lasers would be extremely difficult

to build.

Azulene

Exercises for Chapter 15 559

Internuclear separation

Potential energy

Figure 15.36 Two vibronic levels of a molecule.