The Absorption of Light by Flames Containing Sodium

The intensity of the light from flames containing sodium vapor was found to equal approximately $\frac{e}{a_0}\{{(1+2\mathrm{}{a}_{0}x)}^{\frac{1}{2}}-1\}$, where $x$ is the number of flames, $e$ the amount of light that would be emitted per unit thickness, if no light were being absorbed, and $a_0$ is the coefficient of absorption for the sodium light at the beginning of its passage through the vapor. This expression is based on the assumption that the coefficient of absorption becomes less the further the light passes through the vapor. This may be expressed by the formula $a=\frac{a_0}{(1+2\mathrm{}{a}_{0}x)}$, where $a$ is the coefficient for light that has passed through $x$ flames and $a_0$ is the value given above. The values found for $e$ and $a_0$ were 2.06 and 4.33 respectively, where one flame into which a 0.1 percent solution of NaCl was being sprayed was taken as the unit of intensity of light. The light from flames into which different concentrations of NaCl were sprayed varied less rapidly than the square root of the number of flames. This is explained by assuming that with greater concentrations the molecules of salt in the flame are less completely dissociated, and that this is due to a constant dissociation and recombination of the sodium and chlorine atoms in the flame.