The potential energy between the atoms of a hydrogen molecule is given by the (semiempirical) Morse potential

\[
V(r)=V_{0}\left\{e^{-2\left(r-r_{0}ight) / a}-2 e^{-\left(r-r_{0}ight) / a}ight\}
\]

where \(V_{0}=7 \times 10^{-12} \mathrm{erg}, r_{0}=8 \times 10^{-9} \mathrm{~cm}\), and \(a=5 \times 10^{-9} \mathrm{~cm}\). Evaluate the rotational and vibrational quanta of energy, and estimate the temperatures at which the rotational and vibrational modes of the molecules would begin to contribute toward the specific heat of the hydrogen gas.