## University Physics with Modern Physics (14th Edition)

Equation 42.4 gives the reduced mass of a diatomic molecule. In $D_2$, each deuterium atom has about twice the mass as ordinary hydrogen, so the reduced mass is twice as great. Equation 42.6 shows that the moment of inertia for $D_2$ is twice as great as that of $H_2$, so the rotational energy levels will be closer together by a factor of 2, because their spacing is inversely proportional to the moment of inertia (equation 42.3). The vibrational energy levels will be closer together by a factor of $\sqrt{2}$, because their spacing is inversely proportional to the square root of reduced mass (equation 42.7).