1) Consider the diatomic molecule, carbon monoxide, 12C16O, which has a fundamental vibrational frequency of 2170 cm-1.
(a) Determine the CO vibrational force constant, in N/m.
(b) Determine the vibrational Zero-Point Energy, Eo, and energy level spaces, ∆E, both in kJ/mol.
2) The 35Cl2 force constant is 320 N/m. Calculate the fundamental vibrational frequency of 35Cl2, in cm-1 .
3) The 4 vibrational frequencies of CO2 are: 2349 cm-1, 1334 cm-1, 667 cm-1, 667 cm-1.
(a) Calculate the Zero-Point vibrational energy, i.e. E(0,0,0,0) in : (1) cm-1 (i.e. E/hc), (2) J, (3) kJ/mol.
(b) Calculate the energy required to raise the vibrational state to (0, 2,1,0) in : (1) cm-1 (i.e. E/hc), (2) J, (3) kJ/mol.
4) The fundamental vibrational frequency of 127I2 (observed by Raman spectroscopy) is 215 cm-1.
(a) Calculate the I2 force constant, k, in N/m.
(b) Calculate the ratio of intensities of the first “hot” band (n=1 → n=2) to the fundamental band (n=0 → n=1) at 300oC.
5)The Thermodynamic Dissociation Energy of H35Cl is D0 = 428 kJ/mol, and the
fundamental vibrational frequency is 2990 cm-1. Calculate the Spectroscopic
Dissociation Energy of H35Cl, De.
6) The frequency of the photon that causes the v=0 to v=1 transition in the CO molecule is 6.42x1015 Hz. We ignore any changes in the rotational energy for this example :
Calculate the force constant k for this molecule
What is the classical amplitude A of vibration for this molecule in the v=0 vibration state?
