Discussion  Fr 08.05.2009 at 12:15,  PK 11.2

Home work 4            Molecular rotation
 

Exercise 1:  Moment of inertia     

b) 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 at the center of a cube with a side length a and the four hydrogen atoms to the appropriate cube corners. Draw three principal axes through the cube center perpendicular to the profile planes.   

c) 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

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

Hint: to simplify the calculation of the rotational constant B neglect the group of three H-atoms because they give only a small contribution to the moment of inertia I_^ compared to the heavy I and C atoms.

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

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