The measurement of positron-nucleus collisions was used to estimate the possibility of suppressing background events that simulate ββ decay in the emulsion region adjacent to molybdenum conglomerates. The range of the escape of two relativistic particles from the interaction was found to be < d >= (0.60 ± 0.03) µm, which approximately corresponds to the grain size of developed nuclear emulsion. No correlation of the values of d with the angle between two relativistic particles was observed. It was shown that it was possible to exclude ββ decay background from electrons emerging in the decay of elements of naturally occurring radioactive chains. The background from β decays of 90 Sr and 40 K available in emulsion around Mo conglomerates was determined by the ratio of the volume (∼ d 3 ) to the total volume of emulsion and was found to be 1.5 • 10 −2 . It was shown that the backgrounds from 40 K, 90 Sr and natural radioactivity could be significantly suppressed and would not limit the sensitivity of the experiment with 1 kg 100 Mo.