CHM 3411
Third Hour Exam
April 9th, 2010
There are five problems on this exam. Do all of the problems. Show your work.
1. (15 points) Cyclic C5H5 has been considered as a possible intermediate in the formation of polycyclic aromatic hydrocarbons (PAHs). The sigma bonding structure for C5H5 is shown below, along with a numbering scheme for the carbon atoms.
a) Write the secular determinant for pi bonding in C5H5.
b) Diagonalization of the secular determinant in part a gives the following energy levels for the pi molecular orbitals in C5H5.
+ 2 (1 level) + 0.62 (2 levels) - 1.62 (2 levels)
Based on this information give the total pi-bonding energy for C5H5.
c) What is S, the total spin, for the ground electronic state of C5H5?
d) At what energy will the lowest energy electronic transition in C5H5 take place? Give your energy in terms of and/or .
2. (20 points) Astrophysicists are interested in the pure rotational spectrum of the HS radical as a means of detecting interstellar clouds from which new stars may form. In the mid-1990s Klisch and coworkers measured the microwave spectrum of 1H32S and found that the J = 0 1 transition occurs at an energy E = 18.919 cm-1.
a) What is the value for the rotational constant, B, for 1H32S? Give your answer in units of cm-1.
b) What is the value for r, the bond distance, in 1H32S? Give your answer in units of nm.
c) There is a small amount of 2H32S in interstellar space. At what energy would the J = 0 1 transition in 2H32S be expected to occur? Give your answer in units of cm-1.
Isotopic masses are as follows
m(1H) = 1.0078 amum(2H) = 2.0140 amum(32S) = 31.9721 amu
3. (18 points) Consider the following molecules
1,3,5 trifluorobenzene (C6H3F3)formaldehyde (H2CO)
trichloromethane (CHCl3)sulfur hexafluoride (SF6)
a) Which of the above molecules (if any) will exhibit a pure rotational absorption spectrum?
b) Which of the above molecules (if any) will exhibit a pure rotational Raman spectrum?
c) For 1,3,5 trifluorobenzene only, list all of the symmetry elements present in the molecule.
d) For formasldehyde only, give the total number of normal mode vibrations.
4. (32 points) To a good approximation the vibrational-rotational energy levels for a diatomic molecule are given by the expression
Ev,J = e (v + 1/2) - exe (v + 1/2)2 + Bv J (J+1)
The following data are for the diatomic molecule 127I19F, and may be used in this problem
e = 610.26 cm-1B0 = 0.2788 cm-1 m(19F) = 18.9984 amu
exe = 3.14 cm-1 B1 = 0.2769 cm-1 m(127I) = 126.904 amu
a) What is k, the force constant, for the bond in 127I19F? Give your answer in units of N/m.
b) Estimate the value for D, the dissociation energy for 127I19F. Give your answer in units of cm-1.
c) At what energy, in cm-1, will the R(5) transition be observed in 127I19F?
d) An argon ion laser operating at a wavelength = 514.22 nm is used to study the vibrational Raman spectrum of 127I19F. At what wavelength (in nm) will the Stokes transition (v" = 0 v' = 1) occur? Ignore rotational structure.
5. (15 points) The ground electronic state and first excited electronic state in SrS are both 1+ states. The following two transitions are observed in the electronic absorption spectrum of SrS (note that v" is the vibrational quantum number for molecules in the ground electronic state, and v' is the vibrational quantum number for molecules in the first excited electronic state).
v" = 0 v' = 013908. cm-1
v" = 0 v' = 114247. cm-1
In a separate experiment, the vibrational constant for molecules in the ground electronic state is found to be e" = 388. cm-1.
a) Are the above transitions allowed or forbidden transitions?
b) Based on the above data, estimate the values for e' and Te' for the excited electronic state in SrS.