The unipolar charging phenomena of ultrafine aerosol particles less than 0.1 μm in diameter by positive gas molecule ions produced by α-ray irradiation are experimentally evaluated in helium, argon, nitrogen, and helium-argon mixture gases. The dependencies of the diffusion charging process of particles on ion species of positive helium, argon, and nitrogen ions are quantitatively well explained by a numerical solution of the population balance equations with the use of Fuchs' combination probability between particles and ions [N. A. Fuchs, Geofis. Pura Appl. 56, 185 (1963)]. The quantity of charge on particles decreases with an increase of ion mass in the order of the helium, nitrogen, and argon ions. The particle charging in a helium-argon mixture is determined by the ion concentration of both species.