Mobilities of Electrons in Gases

Motion of electrons through gases.—The theoretical equation for mobility constant obtained in a recent paper, is put in the form $K=2.54\left({10}^5\right)l_0{\left\{1+{[1+1.355({10}^6\left)M{l_0}^2{\left(\frac{E}{p}\right)}^2\right]}^{\frac{1}{2}}\right\}}^{-\frac{1}{2}}$ where $l_0$ is electronic mean free path at 1 mm pressure, $M$ is molecular weight relative to H, $E$ is the electrical field in volts/cm, and $p$ is pressure in mm Hg; and it is tested by comparison with recent experimental data obtained by Loeb and by Townsend and co-workers. Although the equation contains no arbitrary constant if $l_0$ is taken from kinetic theory, the agreement with experiments is good in the case of ${\mathrm{H}}_2$ and within a small factor in the case of He, ${\mathrm{N}}_2$ and A, for values of $\frac{E}{p}$ less than the critical value which is characteristic of each gas and equal to about 20 for ${\mathrm{H}}_2$, 1.3 for ${\mathrm{N}}_2$, 0.5 for A, and >.4 for He. Elasticity of collisions. In explanation it is suggested that when electrons collide at speeds greater than the critical for the gas, the collisions are no longer perfectly elastic, as assumed by the theory. In the region of elastic collisions, the equation may be used to compute the actual equivalent mean free paths for elastic spheres from the measured values of $K$, for comparison with the kinetic theory values of $l_0$. This free path in ${\mathrm{H}}_2$ is close to the kinetic theory value, in He it is a little less, while in ${\mathrm{N}}_2$ and A it is greater and varies with the speed, being greater at small speeds. These free paths are compared with values determined in other ways and the differences are attributed to differences in the meaning attached to the term collision. The data for ${\mathrm{O}}_2$ and C${\mathrm{O}}_2$ are insufficient to give the values of the critical $\frac{E}{p}$ but indicate that these are lower than for the other gases.