•• The first four lines in the rotational spectrum of CaCl are shown schematically in Fig....

•• The first four lines in the rotational spectrum of CaCl are shown schematically in Fig. 1. (The relative strengths of the four lines depend on the temperature and need not concern you here.) Use this information to find the bond length of CaCl. (Since the two masses are comparable, you will need to use the reduced mass introduced in Problem 1. Assume that the Cl is chlorine 35.)

FIGURE 1

Problem 1

• Consider two atoms of masses m and m′, bound a distance R0 apart and rotating about their center of mass (as in Fig. 12.26). (a) Calculate their moment of inertia, I, and prove that it can be written as I = μR02, where μ is the reduced mass

This shows that one can treat the rotational motion of any diatomic molecule as if only one of the atoms were moving, provided that one takes its mass to be μ. (b) Prove that if m ≪ m′ then μ ≈ m.