Diatomic Molecule

A diatomic molecule -- two atoms bound together by an interatomic force, physically modelled as two point masses connected by a massless elastic spring lying along the molecular axis -- behaves differently depending on the temperature.

At normal temperature. The molecule's centre of mass can move freely in three independent directions, giving three translational degrees of freedom (Figure 9.5(a)). In addition, the molecule can rotate about two mutually perpendicular axes that are both perpendicular to the molecular (bond) axis (Figure 9.5(b)) -- but rotation about the bond axis itself is not counted, because the moment of inertia of a diatomic molecule about its own molecular axis is essentially negligible (all the mass sits essentially on that axis), so spinning about it stores no meaningful rotational energy. This gives exactly two rotational degrees of freedom, not three. Adding the translational and rotational contributions,

At high temperature. At a very high temperature (of order 5000 K), the two atoms also start to vibrate noticeably along the molecular axis (Figure 9.5(c)), stretching and compressing the bond like a spring. Vibrational motion contributes two degrees of freedom rather than one, because it stores energy in two separate forms simultaneously -- kinetic energy of the vibrational motion, and potential energy of the stretched/compressed bond. Adding this to the five degrees of freedom already counted, …