Two atoms of cesium (Cs) can form a $C{s}_2$ molecule. The equilibrium distance between the nuclei in a $C{s}_2$ molecule is $0.447$ nm. Calculate the moment of inertia about an axis through the center of mass of the two nuclei and perpendicular to the line joining them. The mass of a cesium atom is $2.21\times {10}^{-25}$ kg.

The rotational energy levels of CO are calculated in Example $42.2$. If the energy of the rotating molecule is described by the classical expression $K=(\(\frac\)12)I\(\omega\)^2$, for the $l = 1$ level, what is the rotational period (the time for one rotation)?

The rotational energy levels of CO are calculated in Example $42.2$. If the energy of the rotating molecule is described by the classical expression $K=(\(\frac\)12)I\(\omega\)^2$, for the $l = 1$ level, what is the angular speed of the rotating molecule?

The rotational energy levels of CO are calculated in Example $42.2$. If the energy of the rotating molecule is described by the classical expression $K=\left(\frac{1}{2}\right)I{\omega }^2$, for the $l=1$ level, what is the linear speed of each atom?

During each of these processes, a photon of light is given up. In each process, what wavelength of light is given up, and in what part of the electromagnetic spectrum is that wavelength? A molecule decreases its vibrational energy by $0.198$ eV.

The H₂ molecule has a moment of inertia of $4.6\times {10}^{-48}$ kg-m². What is the wavelength $l$ of the photon absorbed when H₂ makes a transition from the $l=3$ to the $l=4$ rotational level?

For the H₂ molecule the equilibrium spacing of the two protons is $0.074$ nm. The mass of a hydrogen atom is $1.67\times {10}^{-27}$ kg. Calculate the wavelength of the photon emitted in the rotational transition $l=2$ to $l=1$.