fall somewhere in between the levels for a prolate and oblate symmetric 

 top molecule. To each value of the total angular momentum J of the 

 molecule, there are 2J+1 levels which arise because there are components 

 of the total angular moraentMn about the figure axis of the molecule. The 

 rotational spectrum resulting from transitions between the levels is compli- 

 cated and extends throughout the infrared. It is shown in Herzberg's book 

 for water vapor. Although extensive, there are numerous windows in the 

 vapor. However, the situation in the condensed or liquid state is far 

 from clear. It would seem that in the liquid, the molecules are not 

 freely rotating, but are in hindered rotational or torsional oscillating 

 states. Debyeo bases his theory of non-resonant dispersion in water on 

 the assumption that the rotations of the molecules are opposed by a viscous 



force. Bernal and Fowler believe that about l/6 of the molecules are 

 able to rotate freely, while PoplelO considers the molecules as under- 

 going at most torsional oscillations. In any event the rotational ab- 

 sorption lines will certainly be smeared out in the liquid, although the 

 smearing should be less the higher the frequency. The question of a window 

 would have to be decided on experimental grounds because of the uncertain 

 nature of the liquid. This question will be ^i <=cussed further below. 



The vibration modes also contribute to infrared absorption, and, to 

 some extent, absorption in the visible region of the spectrum. Thfere are 

 three normal modes of vibration possible for a water molecule; and for 

 each mode there exists a set of vibrational states. Since the spacing 

 between states decreases with increasing vibrational quantum number, tran- 

 sitions between states give rise to the well-known absorption bands. For 

 the water molecule, the three main bands corresponding to the three normal 

 modes occur at 6.3. 2,66. and 2,74 microns. In addition, other bands arise 

 because of the anharmonicity of the vibrations — overtone and combination 

 vibrations occur, which, however, will be much weaker than the fundamentals 

 since the anharmonicities are usually small. These bands extend well into 

 the visible spectrum and are tabulated in Herzberg's book. In the liquid 

 the fundamental bands occur at about the same frequency as in the vapor. 

 This is to be expected because of the very short period of the vibrations 

 compared to any reasonable estimate of collision times in the liquid. There 

 also appear new bands in the same region of the spectrum which are attri- 

 buted to molecular association. Absorption graphs will be shown below. 



At the high frequency side of the window, absorption results from 

 the electronic structure of the molecule. Like many molecules water pos- 

 sesses a continuous absorption band in the blue ultra-violet. These 

 electronic transitions are not affected very much in the liquid state except 

 that there is a shift of the band maximum to higher frequencies. It will 

 be seen below that absorption reaches a minimum in the visible and starts 

 up sharply on either side. 



Absorption at Longer Wavelengths (D.C. to Microwave ) 



At frequencies lower than infrared, the conductivity of water, most 

 of which arises from ions of sodium and chlorine, contributes to absorption 

 of radiation. This can be seen as follows: For a conducting medium, the 



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