Rotational energy states

The Seetion entitled The BasiC ToolS Of Quantum Mechanics treats the fundamental postulates of quantum meehanies and several applieations to exaetly soluble model problems. These problems inelude the eonventional partiele-in-a-box (in one and more dimensions), rigid-rotor, harmonie oseillator, and one-eleetron hydrogenie atomie orbitals. The eoneept of the Bom-Oppenheimer separation of eleetronie and vibration-rotation motions is introdueed here. Moreover, the vibrational and rotational energies, states, and wavefunetions of diatomie, linear polyatomie and non-linear polyatomie moleeules are diseussed here at an introduetory level. This seetion also introduees the variational method and perturbation theory as tools that are used to deal with problems that ean not be solved exaetly. 

And third, energy is possessed by virtue of the potential energy, and the translational, vibrational, rotational energy states of the atoms and bonds within the substance, be it atomic, molecular or ionic. The energy within each of these states is quantized, and will be discussed in greater detail in Chapter 9 within the subject of spectroscopy. These energies are normally much smaller than the energies of chemical bonds. 

Whether rotation-vibration transfer occurs, and how important it is, are questions of considerable dispute. The experimental observation by Millikan106,107, that vibrational deactivation of CO in collision with p-H2 is more than twice as efficient as in collision with o-H2, seems to provide some evidence that rotational energy participates in vibrational relaxation. The only significant difference between o- and p-H2 in the context of this experiment would appear to be the difference in rotational energy states, as illustrated by the fact that at 288 °K (the temperature of the experiment) the rotational specific heat of o-H2 is 2.22, while that of p-H2 is 1.80 cal.mole-1.deg-1. Cottrell et a/.108-110 have measured the vibrational relaxation times of a number of hydrides and the corresponding deuterides. On the basis of SSH theory for vibration-translation transfer the relaxation times of the deuterides should be systematically shorter than those of the hydrides. The... 

Radar employs microwave radiation. Microwave ovens use this radiation to excite rotational energy states of water and other molecules in food. 

As noted in Section 24C-2, absorption of ultraviolet and visible radiation by molecules generally occurs in one or more electronic absorption bands, each of which is made up of many closely packed but discrete lines. Each line arises from the transition of an electron from the ground state to one of the many vibrational and rotational energy states associated with each excited electronic energy state. Because there are so many of these vibrational and rotational states and because their energies differ only slightly, the number of lines contained in the typical band is quite large and their displacement from one very small. 

With gas-phase atoms or ions, there are no vibrational or rotational energy states. This means that only electronic transitions occur. Thus, atomic emission, absorption, and fluorescence spectra are made up of a limited number of narrow spectral lines. 

Rotational transition A change in quantized rotational energy states in a molecule. 

As can be seen in Figure 14-la. the visible absorption spectrum for 1.2,4.5-ictrazine vapor shows the line structure that is due lo the numerous rotational and vibrational levels associated wiih the excited electronic states of this aromatic molecule. In the gaseous state, the individual tetrazine molecules are suflicicntly separated from one another to vibrate and rotate freely, and the many individual absorption lines appear as a rcsuli of the large number ol vibrational and rotational energy states. In the condensed slate or in solution, however, the lelrazine molecules have little freedom to rotate, so lines due to dil ferencos in rotational cnergv... 

IK absorption, emission, and reflection spectra for molecular species can be rationalized by assuming that all arise from various changes in energy brought about by transitions of molecules from one vibrational or rotational energy state lo another. In ilits section we use molecular absorption to illustrate the nature of these transitions. 

The question next arises how rotational energy states are to be specified. The proportionality of energy and frequency is here meaningless, since a rotation possesses no natural frequency, but merely one depending upon the energy, and which vanishes as this energy falls to zero. 

In analytical atomic fluorescence the sample is reduced to an atomic vapor and excited by radiant energy of a suitable wavelength. The excited atoms emit energy when they return to a lower excited state or the atomic ground state. The intensity of emitted fluorescence energy is measured and is a function of the concentration of the atoms in the sample. Fluorescence spectra of atoms are simple and uncomplicated, in contrast to fluorescence spectra of molecules, since atomic spectra are not affected by vibrational and rotational energy states that exist in molecules. 

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