Information about the size distribution of radioactive aerosols in nanometre range is essential for the purposes of air contamination monitoring, dose assessment to respiratory tract and planning of protective measures. The diffusion battery, which allows capturing particles in the size range of 0.1-10 nm, has developed. Interpreting data obtained from diffusion battery is very complex. The method of expectation maximisation by Maher and Laird was chosen for indirect inversion data. The experiments were performed in the box with equivalent equilibrium concentration of radon in the range of 7000-10,000 Bq m(-3). The three modes of size distribution of radon decay products aerosols were obtained: activity median thermodynamic diameter (AMTD) 0.3, 1.5 and 5 nm. These modes can be identified as: AMTD 0.3 nm--atoms of radon progeny (218Po in general); AMTD 1.5 nm--clusters of radon progeny atoms and non-radioactive atoms in the atmosphere; AMTD 5 nm--particles formed by coagulation of previous mode clusters with existing aerosol particles or nucleation of condensation nuclei containing atoms of radon progeny.