- Molecular Spectroscopy -
Discussion Fr 17.12.2004 at 10:30, PK11-2
Home work 7
Molecular rotation
Exercise 1: Moment of inertia
a) Show that sulfur hexafluoride SF6 is a spherical top. Calculate the moment of inertia. The S-F bond length is 168 pmb) 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.
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 107o.
Exercise 2: Rotational constants and rotational energy terms
a) Calculate the rotational constants for CO and CO2. Obtain the expression for rotational energy terms. The double C=O bond length is 124 pmb) 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, a C-H bond is 111 pm, and an HCH angle is 110.5o.
c) Consider CD3Br and CH3Cl molecules. Without calculations show which of them has more closely spaced rotational energy levels. Why?