Quantum Chemistry/Example 27

Question Find the wavenumber (in cm-1) of the photon required to excite a CO molecule from its ground vibrational state to its first excited vibrational state, given that the force constant for the CO bond is k=1860 N.m-1. Solution The frequency of the photon required for this transition corresponds to the fundamental vibrational frequency of the molecule, . To determine the wavenumber of this transition, the first step is to calculate the reduced mass of the molecule. The reduced mass (\mu) for a diatomic molecule is given by the following equation: The obtained atomic masses of Carbon and Oxygen are as below: C= 12.011u, O =15.999u Plugging these values into the reduced mass equation gives: The unit conversion from atomic mass units (u) to kilograms (kg) is as follows: Now, we can calculate the frequency of the photon using the following equation: Plugging in the values for the reduced mass and force constant gives: Finally, we need to covert the frequency of the photon () in s-1 to the wavenumber (ṽ) in cm-1: By substituting the known values, the wavenumber of the photon can be determined as follows::