To calculate the molecular vibrational frequencies of a carbon monoxide CO molecule using the harmonic oscillator model, we can use the following formula:v = 1 / 2 * k / where v is the vibrational frequency, k is the force constant, and is the reduced mass of the CO molecule.First, we need to determine the reduced mass of the CO molecule. The reduced mass can be calculated using the formula: = m1 * m2 / m1 + m2 where m1 and m2 are the masses of the carbon and oxygen atoms, respectively. The atomic masses of carbon and oxygen are approximately 12 amu and 16 amu, respectively. To convert these atomic masses to kilograms, we can use the conversion factor:1 amu = 1.66054 10^-27 kgSo, the masses of carbon and oxygen in kilograms are:m1 = 12 amu * 1.66054 10^-27 kg/amu = 1.99265 10^-26 kgm2 = 16 amu * 1.66054 10^-27 kg/amu = 2.65672 10^-26 kgNow, we can calculate the reduced mass : = 1.99265 10^-26 kg * 2.65672 10^-26 kg / 1.99265 10^-26 kg + 2.65672 10^-26 kg = 1.13867 10^-26 kgNow that we have the reduced mass, we can calculate the vibrational frequency v using the given force constant k = 1880 N/m :v = 1 / 2 * 1880 N/m / 1.13867 10^-26 kg v = 1 / 2 * 1.65125 10^14 s^-2 v = 2.036 10^13 HzThe molecular vibrational frequency of the carbon monoxide CO molecule is approximately 2.036 10^13 Hz.To determine the corresponding infrared spectra, we can convert the frequency to wavenumber using the speed of light c : = v / cwhere c is the speed of light approximately 3 10^8 m/s . = 2.036 10^13 Hz / 3 10^8 m/s = 6.787 10^4 m^-1 The corresponding infrared spectra of the carbon monoxide CO molecule is approximately 6.787 10^4 m^-1 or 6787 cm^-1 .