CO2 has four vibrational modes that can be excited by infrared light. Absorption and emission of infrared light by CO2 plays a fundamental role in the process of anthropogenic climate change. (a) Suppose you take a rotationally-resolved vibrational spectrum of CO2 and discover that the spacing between rotational peaks is approximately 0.4 cm1. What is the value of the rotational constant B? (b) How could you use this information to estimate the equilibrium CO bond length R in CO2? Express your answer as an equation for R in terms of fundamental constants and other quantities that could be computed from the given information. (c) CO2 has two degenerate bending modes at roughly = 500 cm1, a symmetric stretching mode at roughly = 1500 cm1, and an asymmetric stretching mode at roughly = 2500 cm1. What is the total zero-point vibrational energy of CO2? You may leave your answer in terms of h and c. Hint: Here you can think of the four vibrational modes in CO2 as independent dimensions of a 4D quantum harmonic oscillator. When a total wavefunction is separable, as it is here, how is the total energy related to the energies of the component eigenfunctions?