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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 atomsExplain the importance of the quantization of vibrational, rotational, and translational energy as it relates to the behavior of atoms and molecules.The wavelength of the vibrational transition in the 79Br81Br molecule is3.09 × 10-5m. Calculate the force constant for the bond in this molecule.
- 6. The NaH molecule undergoes a rotational transition from J=0 to J=1 when it absorbs a photon of frequency 2.94×10' Hz. What is the equilibrium bond length of the molecule?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.How many vibrational modes are there for the molecule NC–(C≡C–C≡C–)8CN detected in an interstellar cloud?
- The hydrogen halides have the following fundamental vibrational wavenumbers: 4141.3 cm−1 (1H19F); 2988.9 cm−1 (1H35Cl); 2649.7 cm−1 (1H81Br); 2309.5 cm−1 (H127I). Calculate the force constants of the hydrogen–halogen bonds.7) Explain the basis of the Franck-Condon principle and how it leads to the formation of a vibrational progression.The force constant for the bond in CO is 1857 N m−1. Calculate the vibrational frequencies (in Hz) of 12C16O, 13C16O, 12C18O, and 13C18O. Use integer relative atomic masses for this estimate.
- Treat 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?4. The vibrational frequency of 'H³°C1 is 8.963 x 1013 Hz. What is the force X constant of the bond in this molecule?