Diatomic Molecules—Degrees of Freedom

Translation is completely described by three degrees of freedom—motion of the entire system in the x-, y-, or z- direction (the three motions on the top of Fig- 

FIGURE 3.12 Two masses can be described by six distinct motions, or degrees of freedom. The motions can be grouped logically into translations of the two masses together (top), rotations (middle) and a single vibration (bottom). In the absence of collisions, the six motions drawn here are completely separate from each other energy does not flow between rotations, vibrations, and translation. 

Rotational energy contributes to the internal energy of a diatomic molecule, and classically any rotational speed is possible. We will return to rotational properties in Chapter 8, when we discuss quantum mechanics, which imposes restrictions on the rotational energy we will find that transitions between allowed rotational states let us measure bond lengths or cook food in microwave ovens. 

Consider, for example, carbon monoxide. The mass of one mole of carbon-12 atoms is exactly 12 g dividing by Avogadro s number (and converting to kg) gives the mass of a single carbon-12 atom as 1.9926 x 10 26 kg. The mass of one mole of oxygen-16 atoms is 15.9949 g, so the mass of one atom is 2.6560 x 10-26 kg (masses in amu for many different isotopes are listed in Appendix A). The reduced mass y = memo/ me + mo) is then 1.1385 x 10-26 kg. 

We will show in Chapter 8 that the vibrational motion of atoms in molecules is responsible for the greenhouse effect which tends to increase the Earth s temperature. We will also show that the modem (quantum mechanical) picture does not permit the molecule to merely sit with its atoms separated by the minimum potential energy. Even at absolute zero, the molecule still has total energy E = hm/2, where ) = 1.054xl0 34 J s (see Appendix A). So the actual dissociation energy is always less than the depth of the potential well, as shown in Table 3.2. 

---