Electric charging of particles is a characteristic process occurring in aerodispersed systems under both external radioactive irradiation self-irradiation. Intensive investigations of this process started only in the 1970s-1980s. We call attention first to the works [1][2][3][4][5][6][7], which were concerned primarily with the investigation of the charging of hot particles. These works established that radioactive aerosols are unipolarly (positively) charged due to secondary-electron emission accompanying tx and/3-decay on particles. Thus one or two electrons emerge from a 1-/.tm in diameter particle in a single /~ decay and up to 40 secondary electrons are emitted in a single ot decay. Charging of radioactive aerosols is now under intensive study in the USA, Germany, Great Britain, and Japan. The most important theoretical results were obtained in [6], where the system of kinetic equations governing the charging for low particle activities were solved by means of computer modeling and the results agreed with the experimental data.It is significant that charging of aerosols leads not only to interaction of the particles with the electric field and a change in the efficiency of precipitation or particle confinement but also to higher diffusion mobility [8]. Obviously, that a knowledge of the characteristics of aerosol charging is important not only for determining aerosol precipitation on different surfaces but also for more efficient operation of the equipment used for purification of radioactive fluxes, in application, in particular, to accidents at nuclear power plants.Our objective in the present paper is to derive analytic formulas for the distribution of electric charge over/3-active particles in a bipolar atmosphere. Before proceeding to the calculation, we give a brief exposition of the extension of the method of detailed balance to stationary aerosol-charging processes.Method for Calculating the Distribution of Charge over Particles. Consider a quite rarefied aerodispersed system, in which collisions of aerosol particles (and the corresponding charge exchange) can be neglected. The charge on the aerosol particles can change as a result of absorption of electrons or ions from the atmosphere as well as the emission of charged particles. One particle can affect another only indirectly, through the general ionic atmosphere, and for this reason the distributions of charge over particles in different size fractions are independent of one another. Let the system contain N particles with radius R. Let nk(t) be the number of particles which at time t have electric charge ek, k = 0, +_ 1, +~ _+2 ..... where e is the elementary electric charge. At any time t the relation ,=~nk(t) = N, which follows from particle number conservation, must be satisfied. If we now introduce the probability wkJ of a change in the charge state of a particle per unit time, where ke is the particle charge before the change and je is the change in the charge as a result of a single charge exchange act, then the general form of the kinetic ...