Discussion  Fr 15.05.2009 at 12:15,  PK 11.2

Home work 5            Rotational and vibrational motion in molecules

 

Exercise 1: Rotational structure and spectra  

a)  The rotational constant B in the ground state of OH radical is 18.8 cm^-1. Using the Boltzmann formula show which rotational energy level J has the greatest population at room temperature?  

b) Calculate the total degeneracy of the rotational energy level J  for the following molecules:  CH₄,  CH₃Cl,  OH. Consider the cases K=0 and K=1.
 

Exercise 2:     Vibrational structure and spectra

a)   Calculate the wavelength and the frequency of the radiation which can excite a transition between vibrational energy levels in HCl molecule. To which part of the electromagnetic spectrum  belongs this radiation?

The elastic constant k for HCl is:  k = 516 N m^-1.

b)  Using the expressions for the vibrational wave function of a diatomic molecule and the value of the elastic constant from above, calculate the internuclear distances in pico meter which relate to the maximum probabilities |y|² of  finding the HCl molecule in the 2-nd (v=1)  vibrational energy state.

c)   Solve the previous problem for the 3-rd (v=2) vibrational energy state of HCl.

 

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