This paper tackles the issue of interpreting the number of airborne particles adsorbed on a filter through which a certain volume of sampled air has been pumped. This number is equal to the product of the pumped volume and particle concentration in air, but only if the concentration is constant over time and if there is no substance decomposition on the filter during sampling. If this is not the case, one must take into account the inconstancy of the concentration and the decay law for a given substance, which is complicated even further if the flow rate through the filter is not constant. In this paper, we develop a formalism which considers all of these factors, resulting in a single, compact expression of general applicability. The use of this expression is exemplified by addressing a case of sampling airborne radioactive matter, where the decay law is already well known. This law is combined with three experimentally observed time dependences of the flow rate and two models for the time dependence of the particle concentration. We also discuss the implications of these calculations for certain other situations of interest to environmental studies.
KEY WORDS: air sampling filters; particle concentration; radioactivity; substance decompositionAir sampling for the purpose of determining the concentration (n) of an airborne substance is frequently carried out by pumping air through a sampling filter. The filter is subsequently subjected to an appropriate analysis and n should then be calculated from observables such as the volume (V) of the pumped air and the number (N F ) of the substance atoms or molecules adsorbed on the filter. The formula n=N F /V is valid only if n is constant during the sampling and the substance remains stable after it has been deposited onto the filter, which is not always the case (e.g., because of a radioactive decay or a spontaneous chemical decomposition). Generally speaking, one often has to develop a specific model for interpreting the relation between n, N F , and V rather than rely on the abovementioned simple ratio. For instance, a common outcome of such modelling is the correction to the calculated n (which is assumed to be constant) of a radioactive substance that has the half-life T 1/2 of the order of the sampling time T S (1). The situation may become even more complicated if the flow rate φ through the sampling filter also changes over time t, as demonstrated in the case of an exponentially decreasing φ(t) (2). Hence, inconstant n(t) and/or φ(t), as well as the decay of substances on the filter, cause deviations from N F =nV, which should not be neglected.In this paper, we develop a formalism that accounts for the interpretation of N F (T S ), which is N F at the end of a sampling at t=T S , in situations when a substance of interest decays over time, while either (or both) n(t) and φ(t) may be inconstant during the sampling. The profile of φ(t) is determined by the characteristics of a particular sampling system (e.g., reduction of filter porosity as the adsorption progr...