The HOMO–LUMO+1 transition density is shown
below. Light regions represent increased density, dark regions represent decreased density.
a. Sketch the LUMO+1 of butadiene; the discussion of applications of the particle-in-a1D-box model in Chapter 5 may be beneficial.
b. Would you expect the HOMO–LUMO+1 transition to be dipole-allowed? Why or why not?
3. Acetylene, also known as ethylyne (C 2 H 2 ), is the
simplest stable linear hydrocarbon. Two of its
vibrational modes (symmetric C–C stretch and
asymmetric C–H stretch) are shown below.
H
H
C C
H
H
C C
a. How many total vibrational modes does
ethylene have?
b. Of the two vibrational modes shown, which
do you expect to be IR active? Which do you
expect to be Raman active?
4. Describe how you would use information given
about molecular fluorescence spectroscopy
to calculate Φ f for a set of data.
Hint: Use an appropriate equation and integrate
it to find g x and thus calculate Φ f .
5. What is the concentration fluctuation factor of
a surfactant that forms micelles with very large
molecular weight? Express your answer in
terms of the second virial coefficient.
6. (a) Explain in words why the distribution of
Rayleigh scattered light is a broad peak instead
of a sharp signal.
(b) If a laser emitting light at 700 nm is sent
through a dispersion and the Rayleigh scattered light is centered around 640 nm, what
can be deduced about the direction of motion
of the particles in solution?
(c) Does the shift mentioned in part (b) correspond to a red shift or blue shift?
7. (a) If the hydrodynamic radius of a particle
doubles, what happens to its diffusion speed?
(b) If the radius is halved, the temperature is
quadrupled, and the viscosity of solution
increases by half, by what factor does the diffusion speed change?
(c) In a solution of hexane, would one expect
to observe multiple signals? Explain why or
why not.
References and recommended reading
Berne, B. J. Dynamic Light Scattering: With Applications to
Chemistry, Biology, and Physics. 2000, Dover Publications, Mineola, NY. This book explains DLS and how
Maxwell’s equations lead to the intensity of the scattered
radiation. This is an advanced graduate-level textbook.
Fowles, G. R. Introduction to Modern Optics, 2nd ed. 1975,
Dover Publications, New York. This undergraduate textbook provides a good introduction to optics, including the
concept of the complex refractive index/dielectric function.
Skoog, D. A., Holler, F. J. and Crouch, S. R. Principles of
Instrumental Analysis, 7th ed. 2017, Brooks/Cole Boston.
This undergraduate textbook includes descriptions of
both the physical principles and instrumentation used in
many types of chemical and materials analysis.
Thulstrup, E. W. and Michel, J. Elementary Polarization
Spectroscopy. 1989, VCH Publishers, New York. While
principally focused on techniques involving polarized
light, which will be introduced in Chapter 8, this undergraduate textbook provides an excellent introduction to
optical transitions and their relationship to structural and
electronic properties of materials, including ordered
materials such as liquid crystals.
REFERENCES AND RECOMMENDED READING 215
below. Light regions represent increased density, dark regions represent decreased density.
a. Sketch the LUMO+1 of butadiene; the discussion of applications of the particle-in-a1D-box model in Chapter 5 may be beneficial.
b. Would you expect the HOMO–LUMO+1 transition to be dipole-allowed? Why or why not?
3. Acetylene, also known as ethylyne (C 2 H 2 ), is the
simplest stable linear hydrocarbon. Two of its
vibrational modes (symmetric C–C stretch and
asymmetric C–H stretch) are shown below.
H
H
C C
H
H
C C
a. How many total vibrational modes does
ethylene have?
b. Of the two vibrational modes shown, which
do you expect to be IR active? Which do you
expect to be Raman active?
4. Describe how you would use information given
about molecular fluorescence spectroscopy
to calculate Φ f for a set of data.
Hint: Use an appropriate equation and integrate
it to find g x and thus calculate Φ f .
5. What is the concentration fluctuation factor of
a surfactant that forms micelles with very large
molecular weight? Express your answer in
terms of the second virial coefficient.
6. (a) Explain in words why the distribution of
Rayleigh scattered light is a broad peak instead
of a sharp signal.
(b) If a laser emitting light at 700 nm is sent
through a dispersion and the Rayleigh scattered light is centered around 640 nm, what
can be deduced about the direction of motion
of the particles in solution?
(c) Does the shift mentioned in part (b) correspond to a red shift or blue shift?
7. (a) If the hydrodynamic radius of a particle
doubles, what happens to its diffusion speed?
(b) If the radius is halved, the temperature is
quadrupled, and the viscosity of solution
increases by half, by what factor does the diffusion speed change?
(c) In a solution of hexane, would one expect
to observe multiple signals? Explain why or
why not.
References and recommended reading
Berne, B. J. Dynamic Light Scattering: With Applications to
Chemistry, Biology, and Physics. 2000, Dover Publications, Mineola, NY. This book explains DLS and how
Maxwell’s equations lead to the intensity of the scattered
radiation. This is an advanced graduate-level textbook.
Fowles, G. R. Introduction to Modern Optics, 2nd ed. 1975,
Dover Publications, New York. This undergraduate textbook provides a good introduction to optics, including the
concept of the complex refractive index/dielectric function.
Skoog, D. A., Holler, F. J. and Crouch, S. R. Principles of
Instrumental Analysis, 7th ed. 2017, Brooks/Cole Boston.
This undergraduate textbook includes descriptions of
both the physical principles and instrumentation used in
many types of chemical and materials analysis.
Thulstrup, E. W. and Michel, J. Elementary Polarization
Spectroscopy. 1989, VCH Publishers, New York. While
principally focused on techniques involving polarized
light, which will be introduced in Chapter 8, this undergraduate textbook provides an excellent introduction to
optical transitions and their relationship to structural and
electronic properties of materials, including ordered
materials such as liquid crystals.
REFERENCES AND RECOMMENDED READING 215