Experimental Proof of Light Scattering in Pure, Transparent Gases

J. Cabannes. Sur la diffusion de la lumière par les molécules des gaz transparents. Annales de Physique XV, 5—150, 1921.

The necessity of light scattering when it passes through a gas follows from the wave theory of molecular resonators. Under the assumption of isotropy (“sphericity”) of molecules, Lord Rayleigh found that the energy scattered by a unit volume of gas per second is expressed as follows:

\[ J = aE \frac{(\mu^2 - 1)^2}{n\lambda^4} \tag{1} \]

where \(\mu\) is the refractive index of the gas for the given wavelength \(\lambda\), \(n\) is the number of molecules in a cubic centimeter of gas, and \(E\) is the energy incident on 1 square centimeter:

\[ a = \frac{\pi^2}{2}. \tag{2} \]

Rayleigh’s theory gives an exhaustive explanation of the blue color of the sky, as was shown by the careful measurements of Abbot and Fowle, carried out in 1913. On the basis of measurements of the absorption of light in the atmosphere, these authors found from formula (1) the following value for Avogadro’s number (with Vessot-King’s corrections):

\[ N = 6.23 \cdot 10^{23}. \]

An attempt to detect the scattering of light by a gas under laboratory conditions was made as early as 1876 by Tyndall, but without result. The experiment was first successful for Cabannes in 1913–1915. A report on careful quantitative measurements in this field is contained in the extensive work under review.

The success of Cabannes’s experiments is explained above all by the adoption of every possible precaution against diffuse light scattered by the solid walls of the vessel containing the gas. The background against which the scattered light was observed was the aperture of an absolutely black body. The remaining walls were covered with black velvet. Cabannes’s preliminary experiments showed that black velvet scatters extremely little of the light of the quartz mercury lamp that served as the source in the subsequent investigations. The gases investigated were dried over calcium chloride and, for removal of dust, were passed through a cotton filter (25 cm long). In this way the gas was physically purified completely. A vessel with air filled in 1915 gave the same scattering effect in 1919.

The scattering of light by various gases can be observed without special effort by an eye adapted to darkness.

For quantitative measurements photographic registration was used.

In the interval from 1913 to 1921 the scattering of light by gases was also detected by Strutt and Wood.

In the first series of experiments Cabannes showed that the light scattered by a gas is of the same character as the incident light (the experiments were performed with complex and monochromatic exciting light). The intensity of the scattered light is proportional to the intensity of the incident light and to the pressure of the illuminated gas. The brightness of the scattered light depends on the nature of the gas; moreover, the dependence on the refractive index, following from Rayleigh’s law (1), is justified, though not quite exactly.

According to Rayleigh’s theory of “spherical” molecules, it necessarily follows that light scattered by a gas sideways must be completely linearly polarized. As early as Strutt (1918) found that this is not quite exactly borne out in experiment. Cabannes determined the following values for the ratio \(\rho\) of the energy of the component of the light vibrations parallel to the exciting beam to that perpendicular to it for the different gases investigated (Table 1):

Table 1.

Only the molecules of argon proved to be “spherical”; to the molecules of the remaining gases one must, purely formally, ascribe a certain “ellipsoidal character”—anisotropy. Lord Rayleigh (1918) also gave a formal theory of the scattering of light by anisotropic molecules. Cabannes develops an analogous theory in electronic terms, obtaining the following value for \(\alpha\) in formula (1):

\[ \alpha=\frac{3\pi^2(1+\rho)}{6-7\rho}. \tag{3} \]

where \(\rho\) corresponds to the above-mentioned ratio of the intensities of the two polarized components of the scattered light. The Rayleigh–Cabannes theory is well justified by experiment. The measurements of \(J\) in formula (1) and of \((\rho)\) in formula (3) are made independently; therefore, as before, there remains the possibility of verifying the theory by measuring the number. Avogadro Cabannes also carried out such a measurement for argon, illuminating it with the \(435.8\,\mu\mu\) light of a mercury lamp. The value found for \(N\) is as follows:

\[ N = (6.9 \pm 0.25)\cdot 10^{23}. \]

Introducing a correction for the anisotropy of the molecules of the gases of air, Cabannes obtains from the data of Abbot and Fowle the following value for \(N\):

\[ N = (6.54 \pm 0.12)\cdot 10^{23}. \]

Thus Rayleigh’s theory of the blue of the sky has received definitive laboratory confirmation. On the other hand, the study of the polarization of scattered light, as the experiments of Strutt and Cabannes show, provides a new method for investigating the structure of gas molecules.

Cabannes’s work contains detailed descriptions of the technical particulars of the experiments and an account of previous work in this field.

S. Vavilov.