Home work Physical and Theoretical Chemistry IV

- 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?