- Molecular Spectroscopy -
Discussion Fr 21.6.2002 at 10:30,
HR30.1 (Hagenring 30)
http://www.pci.tu-bs.de/aggericke/PC4/Uebungen/
Home work 8 Spectra and molecular constants
Exercise 1:
The two lowest excited energy levels of the symmetric stretch n1
of
water were found to be 3657 cm-1 and 7201 cm-1.
a) Calculate the quantities we
and
wexe.
b) What is the energy of the third excited vibrational energy level?
Compare your result with the experimental one: 10600 cm-1.
Exercise 2:
Determine the Franck-Condon factors -∞ò¥yv'yv"dt
for
transitions between two electronic states which are characterized by the
same bond strength but a different bond length, i.e. the corresponding
wave functions are the same, but shifted by a certain distance. To simplify
the calculations the wave functions for v = 0,1,2 are approximated by rectangular
functions (s. figure), where both the total width and the high are set
to 1.
Calculate the Franck-Condon factors for the transitions from v = 0
to v' = 0,1,2,
a) if the bond length of the molecule is the same for the ground and
for the excited state;
b) if the excited state is shifted by 1/3 to a larger bond length (s.
figure).
c) What is the most likely transition for emission from
v' = 2 to v = 0, or to v = 1, or to v = 2? (guess, don't calculate)
Exercise 3:
Develop the equations to determine the transition frequencies for the
R branch and for the P branch of a Σ-S
electronic
transition from v = 0 to v'=1.
Which transition reaches the level J'=0?