ZK C9550: Quantum Chemistry and Molecular Spectroscopy

                                        January 8^th, 2015

                                   Used also February 6^th, 2017



1.      Use the energy level scheme for a two-state model to illustrate the origin of the

(a)   Rayleigh scattering

(b)   Raman scattering: Stokes and Anti-Stokes lines

                                                                                         (2 points)











2.      A natural linewidth is a result of
                       (1 point)

(a)   disordered movements of molecules in the sample

(b)   intermolecular colissions

(c)    Heisenberg uncertainty relationships


3.      Which quantum-mechanical model is represented by the wavefunctions shown below? Fill into
the picture the quantum numbers corresponding to the individual wavefunctions.

                                                                                         (3 points)




4.      Which quantum-mechanical model is represented by the wavefunctions isosurfaces shown below?
Fill into the picture the values of the quantum numbers l and m[l] corresponding to the individual
wavefunctions.                                       (3 points)



































5.      Sketch out a qualitative scheme of the electromagnetic spectrum  and indicate the arts of
molecular excitations typical for the individual regions of the spectrum.

                                                                                         (4 points)












6.      Which parameter of the system determines line intensity for a spectroscopic transition
between two levels? How is this parameter qualitatively changing, for a constant temperature, from
low-energy transitions (NMR) to high-energy transitions (electronic
excitations)?
      (2 points)









7.      Write down the general relationship between the energy of a rigid rotor,  the angular
momentum and the momentum of inertia at the classical and the quantum mechanical levels (constants
do not matter).

                                                                                         (2 points)





8.      With the help of energy level scheme sketch out the origin of the structure of a
vibration-rotational band. Sketch out also the qualitative appearance of the vibration-rotational
band in a spectrum (line positions and intensities).

                                                                                         (3 points)










9.      The Franck-Condon factor is equal to

(a)

(b)

(c)


                                                                                          (1 point)


10.  Sketch out a qualitative electron spectrum for a system of energy levels in the following
figure. What determines the intensity of a particular spectral line?

                                                                                         (3 points)






11.  With the help of energy level scheme, sketch out the transitions observed during an EPR
experiment.

(3 body)







12.  (Voluntary) Explain, why in an NMR spectrum of N,N dimethylacetamid the temperature influences
the number of signals of interacting protons.

                                                                                        ( 3 points)