Interaction between Rotational and Vibrational States (rotational Clause Samples

Interaction between Rotational and Vibrational States (rotational vibrational spectra) Figure 1 illustrates the energy levels for the two lowest vibrational states of a diatomic molecule and shows some of the transitions that are allowed between the sublevels. Also shown is an IR spectrum of HCl. Notice that the spectrum is separated into two branches, with a gap between them. The gap is where the infrared transitions would be if no change in the J value occurred, i.e, ΔJ = 0. This region is known as the Q branch and only involves a change in the vibrational quantum number. The low frequency branch (P branch) consists of ΔJ = −1 transitions and the high frequency branch (R branch) consists of ΔJ = +1 transitions. Note that the quantum numbers for the lower state in the transition are traditionally labelled as υ” and J” while those for the upper state are labelled υ’ and J’. Figure 1: Spectral lines and allowed transitions of a ro-vib spectrum. The splitting arises from the H35Cl and H37Cl (isotope effect) with H35Cl peaks being the dominant. To begin the assignment work, we have to decide on consistent units for the parameters in this experiment. The following Table provides values that may be helpful. Table 1: Useful constants and conversion factors.
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Interaction between Rotational and Vibrational States (rotational vibrational spectra) Figure 1 illustrates the energy levels for the two lowest vibrational states of a diatomic molecule and shows some of the transitions that are allowed between the sublevels. Also shown is an IR spectrum of HCl. Notice that the spectrum is separated into two branches, with a gap between them. The gap is where the infrared transitions would be if no change in the J value occurred, i.e, ΔJ = 0. This region is known as the Q branch and only involves a change in the vibrational quantum number. The low frequency branch (P branch) consists of ΔJ = −1 transitions and the high frequency branch (R branch) consists of ΔJ = +1 transitions. Note that the quantum numbers for the lower state in the transition are traditionally labelled as υ” and J” while those for the upper state are labelled υ’ and J’. Figure 1: Spectral lines and allowed transitions of a ro-vib spectrum. The splitting arises from the H35Cl and H37Cl (isotope effect) with H35Cl peaks being the dominant. To begin the assignment work, we have to decide on consistent units for the parameters in this experiment. The following Table provides values that may be helpful. h 6.626 × 10- 27 erg s 6.6261 × 10-34 Js k 1.381 × 10- 16 erg/K 1.38066 × 10-23 J/K 1 cm-1 1.986 × 10- 16 erg 1.98630 × 10-34 J m1H 1.007825 amu 1.672623 × 10- 27 kg m2D 2.0140 amu 3.3425 × 10-27 kg m35Cl 34.968852 amu 5.803558 × 10- kg 26 m37Cl 36.965903 amu 6.135000 × 10- 26 kg
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