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- Determine the number of total degrees of freedom and the number of vibrational degrees of freedom for the following species. a Hydrogen sulfide, H2S b Carbonyl sulfide, OCS c The sulfate ion, SO42 d Phosgene, COCl2 e Elemental chlorine, Cl2 f A linear molecule having 20 atoms g A nonlinear molecule having 20 atomsTreat a vibrating HI molecule as a hydrogen atom oscillating towards and away from a stationary iodine atom. Given the force constant of the HI bond is 314 N m-1, calculate the vibrational frequency of the molecule.Rotational spectra are affected slightly by the fact that different isotopes have different masses. Suppose a sample of the common isotope 1H35Cl is changed to 1H37Cl. (a) By what fraction is the molecule’s rotational inertia different? (The bond length is 0.127 nm in each case.) (b) What is the change in energy of theℓ = 1 to theℓ = 0 transition if the isotope is changed?
- (hydrogen iodide, the superscripts represent the atomic mass number) (a) How fast will HI molecules rotate at the quantized rotational state with the rotational quantun number J of 2, given the bond length of 0.161 nim? (b) Calculate the effective force constant of the vibrational mode of HI at a wavenumber of 2300 cm' measured by infrared absorption spectrum. (c) HI has the bond energy of 3.06 eV. Applying the parabolic approximation to estimate the longest distance in which H and I atoms can be stretched before the dissociation of the molecular bond(A) Explain why the spacings between the bands in the vibrational spectrum of a diatomic molecule would be expected to decrease with increasing vibrational quantum number. (B) Explain why a molecule with no dipole moment is microwave inactive but may show an infrared spectrum. (C) Explain the occurrence of P and R branches in the rotational fine structure of a vibrational transition of a diatomic molecule such as HCl or CO.Explain the importance of the quantization of vibrational, rotational, and translational energy as it relates to the behavior of atoms and molecules.
- 7) Explain the basis of the Franck-Condon principle and how it leads to the formation of a vibrational progression.3. ^14N^16O (the superscripts represent the atomic mass number) (a) NO molecules rotate at an angular velocity of 2.01x10^12 rev/s, at the quantized rotational state with the rotational quantum number J of 3. Calculate the bond length of NO molecules. (b) Can NO molecules rotate under light irradiation? Explain your answer. (c) Calculate the effective force constant of the vibrational mode of NO at a frequency of 5.63x10^13 Hz measured by the infrared absorption spectrum. (d) NO has a bond energy of 6.29 eV. Applying the parabolic approximation to estimate the longest distance in which N and O atoms can be stretched before the dissociation of the molecular bond4. The infrared absorption spectrum of a diatomic molecule is shown in the figure. (a) Give the initial (J") and final (J') rotational quantum numbers corresponding to the peaks labeled A and B. (b) Estimate the vibrational frequency in wavenumbers (i) and the rotational constant in wavenumbers (B). (c) From the spacings of the peaks near 2700 cm and near 3050 cm, determine whether the average bond length increases or decreases with increasing vibrational quantum number. 20 18 A 14 12 2500 2600 2700 2800 2900 3000 3100 3200 wavenumber absorption intensity
- The Li2 molecule (7Li isotope) shows a very weak infrared line in its vibrational spectrum at a wavelength of 2.85 ×10-5m. Calculate the force constant for the Li2 molecule.Arrange the following energies in order of increasing magnitude: a) the typical energy of a covalent single bond; b) the mean molecular translational energy for a gas at room temperature; c) the mean rotational energy of a diatomic molecule at room temperature; d) the vibrational energy for a diatomic molecule at room temperature; e) the ionization energy of H. Justify your order.The force constant of 79Br79Br is 240 N.m−1 . Calculate the fundamental vibrational frequency and the zero-point energy of 79Br79Br.
