The Distribution of Mobilities of Ions in Moist Air

Abstract

A search was made in undried air for groups of ions having different mobilities and no such distinct groups were found among ions two or more seconds after their formation. A critical study was made of the effects of diffusion upon the distribution of ions moving in an electric field. Experimental results obtained for $N$, the volume density of ions which after a time $t$ are located at a distance $r$ from the origin agree fairly well with the theoretical formula $N=\frac{N_0}{{\left(4\mathrm{}\pi Dt\right)}^{\frac{3}{2}}}{e}^{-\frac{r^2}{4Dt}},$ where $D$ is the coefficient of diffusion. The mobilities and the spreading of the ions were measured by a modification of the author's method in which ions passing between two concentric cylinders under an electric field are simultaneously carried axially by a slow, non-turbulent current of air of known velocity. The ions entered the air stream through small openings in the walls of the outer cylinder and their distribution at the central cylinder was measured by catching them on a narrow insulated section of that cylinder which was connected to an electrometer. The ions were found to be confined to one group covering a range of mobilities in which the fastest ions have mobilities about 45 percent larger than the slowest for positive ions and about 30 percent larger for negative ions. The distribution would be explained if a number of unresolved permanent distinct groups exist, but a more probable explanation rests on the assumption that the ions are clusters which change in size under the influence of molecular bombardment, the life of each stage being sufficiently long so that the number of changes occurring during the time of passage of the ions is not very great. No certain change in the distribution was noted for changes of the time of passage of the ions between 0.05 sec. and 0.67 sec. The mobilities of the ions were determined under widely different conditions in air ranging in water content between 1.5 mg/liter and 7.6 mg/liter. Without weighting the observations, the average mobility found for the negative ions is 2.00 cm/sec·volt/cm for an average water content of 3.2 mg per liter of air, and the average for the positive ions is 1.22 cm/sec·volt/cm for an average water content of 2.7 mg per liter of air, the most probable error in each case being about one percent.