At T =300K, 1bar of "00 in a 1m box (lengths a= ay = a, = 1m) can be considered as an ideal gas. In that case, the average translational energy in each dimension for a molecule is given by: E=E=E= KT where k=1.38 x 10 J/K is the Boltzmann constant. The average rotational energy about an axis perpendicular to the O-O bond is: Ert-kT, and the average vibrational energy is: Evib kT. Given that the fundamental vibrational frequency for OO is w=4.741 10 Hz, find the values of the quantum numbers n., J, and u for an average 0"O molecule in this system.