Two particles (masses m₁ and m₂) are attached to the ends of a massless rigid rod of length a. The system is free to rotate in three dimensions about the (fixed) center of mass.
(a) Show that the allowed energies of this rigid rotor are

is the moment of inertia of the system.
(b) What are the normalized eigenfunctions for this system? (Let θ and ϕ define the orientation of the rotor axis.) What is the degeneracy of the nth energy level?
(c) What spectrum would you expect for this system? (Give a formula for the frequencies of the spectral lines.)
(d) Figure 4.13 shows a portion of the rotational spectrum of carbon monoxide (CO). What is the frequency separation (Δv) between adjacent lines? Look up the masses of ¹²C and ¹⁶O, and from m₁, m₂, and Δv determine the distance between the atoms.

Figure 4.13

Transcribed Image Text:

En ħ2² = 27" = n(n+1). (n = 0, 1, 2,...), where I = m1m2 (m1 + m₂)