Discussion  Fr 20.01.2006 at 12:15,  HR30.1

Home work 10            Molecular rotation
 

Exercise 1:  Moment of inertia     

a) Show that methane CH₄  is a spherical top. Calculate the moment of inertia. The C-H bond length is 114 pm

Hint: knowing that methane has a tetrahedral structure put the carbon atom to the center of a cube with a side a and the four hydrogen atoms to the appropriate cube corners. Draw three principal axes through the cube center perpendicular to the profile planes.   

b) Show that CH³⁵Cl₃ is a symmetric top. Calculate the moment of inertia around the principal axis which contains the C-H bond. The C-Cl bond length is 177 pm and the HCCl angle is 107^o.

Exercise 2:     Rotational constants and rotational energy terms

a)  Which rotational group CH₃I  molecule belongs to?  Calculate the rotational constants and obtain the expression for rotational energy terms. The C-I bond length is 210 pm, the C-H bond length is 111 pm, and the HCH angle is 110.5^o.

b)  Consider CD₃Br and CH₃Cl molecules. Without calculations show which of them has more closely spaced rotational energy levels. Why?

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