1.a) Derive an expression for the value of J corresponding to the most highly populated
rotational energy level of a spherical rotator (max). For spherical rotator each energy
level is (2J + 1)2 – fold degenerate and energy is given by E, = hcĒJ( + 1).
The population N, of molecules in energy level J is given by the Boltzmann expression
N, = Ng,e-Ey/KT
where N is the total number of molecules in the sample, g, is the degeneracy of level
J, k is the Boltzmann constant, and T is the absolute temperature.
b) Evaluate Imax for CH4if B = 5.24 cm-1 at 25 °C.
The total tt -electron energy of naphthalene is given by
En = 10a + 13.68B
Calculate the delocalization energy of naphthalene.
Predict the shape of nitronium ion, No7, from its Lewis structure and VSEPRT
model. It has one Raman active vibrational mode at 1400 cm-1, two strong IR active
modes at 2360 and 540 cm-1, and one weak IR mode at 3735 cm-1. Are these data
consistent with the predicted shape of the molecule? Assign the vibrational
wavenumbers to the modes from which they arise.
In the group theoretical language, a spherical rotator is a molecule that belongs to a
cubic or icosahedral point group, a symmetric rotator is a molecule with at least a
threefold axis of symmetry, and an asymmetric rotator is a molecule without a
threefold (or higher) axis. Linear molecules are linear rotators. Classify each of the
following molecules as a spherical, symmetric, linear, or asymmetric rotator and
justify your answers. (a) CH4, (b) CH3CN, (C) CO2, (d) CH3OH, (e) C6H6 (benzene),
(f) Identify molecules that are rotationally Raman inactive.
Confirm that a Morse Oscillator has a finite number of bound states, the states with