2. a. In terms of energies, derive the 12.45 equations in the Atkins text. Then convert these equations to be in terms of wavenumbers. b. In terms of energies (and using the equations you derived in part a), derive the 12.46 equations in the Atkins text. Then convert these equations to be in terms of wavenumbers. c. In terms of energies (and using the equations you derived in parts a and b), derive the 12.47 equations in the Atkins text. Then convert these equations to be in terms of wavenumbers. d. Now use the equations that you have derived in parts a, b, and c to determine, for each of the four atomic gases, the rotation constants, the moments of inertia, the equilibrium bond distances, the fundamental vibration frequencies, and the force constants of the fundamental vibrations.