Home work Physical and Theoretical Chemistry IV

- Molecular Spectroscopy -

Discussion  Fr 28.01.2005 at 10:30,  PK11-2



  Home work 10     Structure of Electronic Transitions. Time-resolved molecular spectroscopy.

Exercise 1:       

a)  Spin-orbit interaction in OH radical is much smaller that the interaction between the pure rotational states. In the absence of spin-orbit interaction in the ground state of OH radical, 2Π1/2  the rotational states can be classified as K = 0, 1, 2,... In presence of the spin-orbit interaction each K-state is splitted into several states corresponding to the total angular momentum J of the molecule. What are the quantum numbers J, corresponding to each K = 0, 1, 2, 3?    

b) Which rotational branches are allowed for 1Σ→1Π and for 1Σ→1Σ electronic transitions in diatomic molecules? Why? Calculate the wave number of the X1Σg(v''=0, J''=4)→ q1Σu (v'=1, J'=3, and v'=1, J'=4) transition in N2 molecule using the the following spectroscopic constants: difference between the minima of the potential curves ΔUe=110654 cm-1 , ωe''= 2359 cm-1 , ωe'= 715 cm-1 , ωexe''=14.45 cm-1,  ωexe'=9.0 cm-1 ,               Be'' = 2.01 cm-1 , Be' = 1.13 cm-1.  Which spectral interval these transitions belong to?

Exercise 2:   

a)   Spin-orbit splitting between 3Π1 and 3Π2 , v = 0, energy levels of the d excited state in CO molecule is 52 cm-1 .   What can the maximum duration of a laser pulse which can be used for measuring this splitting using the quantum beat technique?  What is expected signal modulation frequency?    

b)   The excited state of the dye molecule rose bengal solved in methanole has a mean lifetime of 597 ps. What can be the maximum accuracy of measuring this lifetime with pump-and-probe technique using the laser pulses with duration τpulse = 5 ps?