Scattering from a Dilute Gas

For a gas containing v molecules per cc. the turbidity due to scattering is found to be given by the formula (see for instance Debye, 1944) 

Since it is clear that the scattered intensity must be proportional to the first power of v, with dimensions cm-3, and to the second power of a, with dimensions cm3, it is immediately apparent that a factor inversely proportional to the fourth power of the wavelength must enter into the equation in order to obtain the turbidity with dimensions cm-1. 

The polarizability a is a molecular quantity, not directly given by experiment, and in order to correlate equation (7) with the results of experimental measurements, we make use of the relation between the refractive index (n) of the gaseous medium and the polarizability, a. 

All the quantities in equation (9) are susceptible of direct measurement except v, the number of molecules per cc. This can, therefore, be deduced from measurements of refractive index and of turbidity, if the wavelength of the light employed is known. 

In the case of a gas we have assumed that the intensity of scattering from v molecules in a given volume is v times as great as that from a single molecule enclosed in the same volume. This is justifiable for a 

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