Answer to Question #7878 Submitted to "Ask the Experts"

Having measured ¹³⁷Cs in a soil sample in Bq kg^-1, how could I convert it to Bq m^-2?

Knowing ¹³⁷Cs in Bq m^-2 from literature, would the reverse procedure hold for conversion to Bq kg^-1?

The fact that you have a measured value in Bq kg^-1 implies that the activity is distributed to some unspecified depth in the soil. Commonly, a soil sample would have been taken using a coring device that penetrates the ground to a specific depth. In such a case, if the entire core of soil is removed from the tool and the soil is mixed to make it more or less homogeneous before measurement, then the activity concentration reported is the average value throughout the depth of the sample, d. Then the reported mass concentration, C_m, is related to the “area” concentration, C_a, as follows:

C_a = C_mρd,

where ρ is the mass density of the soil. Note that the units of activity per unit area may be a bit misleading since they do not represent activity distributed over the surface of the soil (as might be the case when assessing fresh deposition of activity on to the ground surface from airborne contamination); rather, the meaning is that if I took a sample of fixed depth, sufficient to include all activity that has penetrated the soil, and uniform cross-sectional area, the total activity in the sample divided by the cross-sectional area of the sample would be the value of C_a.

For example, supposing that it was determined that activity of a particular radionuclide was confined to the first six inches of soil, a six-inch (15.24 cm) deep core sample was obtained with a coring tool with a two-inch diameter, the sample was mixed and measured, and an activity of 52 Bq was determined for the entire sample. If the density of the soil was 1.6 g cm^-3 (1.6 x 10³ kg m^-3), then the mass, m, of the sample would be

m = π(2.54 cm)²(15.24 cm)(1.6 g cm^-3) = 494 g = 0.494 kg.

The activity concentration on a mass basis would be

C_m = 52 Bq/0.494 kg = 105 Bq kg^-1,

and the value of C_a would then be

C_a = (105 Bq kg^-1)(1.6 x 10³ kg m^-3)(0.1524 m) = 2.56 x 10⁴ Bq m^-2.

Regarding the conversion of literature values in Bq m^-2 to mass concentration in Bq kg^-1, the same rationale applies as long as the literature source is talking about volume-distributed activity and not a surface deposition of activity. Then, from above,

C_{m =} C_a/ρd.

Hope this answers your question.

George Chabot, PhD, CHP