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Convert Nuclide Activities to Abundance and Vice Versa

Source: R/convert_Activity2Concentration.R
convert_Activity2Concentration.Rd

The function performs the conversion of the specific activities into mass abundance and vice versa for the radioelements U, Th, and K to harmonise the measurement unit with the required data input unit of potential analytical tools for, e.g. dose rate calculation or related functions such as use_DRAC.

Usage

convert_Activity2Concentration(data, input_unit = "activity", verbose = TRUE)

Arguments

data

data.frame (required): provide dose rate data (activity or concentration) in three columns. The first column indicates the nuclide, the 2nd column measured value and in the 3rd column its error value. Allowed nuclide data are 'U-238', 'Th-232' and 'K-40'. See examples for an example.

input_unit

character (with default): specify unit of input data given in the dose rate data frame, choose between "activity" (considered as given Bq/kg) and "abundance" (considered as given in mug/g or mass. %). The default value is "activity"

verbose

logical (with default): enable or disable verbose mode

Value

Returns an RLum.Results object with a data.frame containing input and newly calculated values. Please not that in the column header µg/g is written as mug/g due to the R requirement to maintain packages portable using ASCII characters only.

Details

The conversion from nuclide activity of a sample to nuclide concentration is performed using conversion factors that are based on the mass-related specific activity of the respective nuclide.

Constants used in this function were obtained from https://physics.nist.gov/cuu/Constants/ all atomic weights and composition values from https://www.nist.gov/pml/atomic-weights-and-isotopic-compositions-relative-atomic-masses and the nuclide data from https://www.iaea.org/resources/databases/livechart-of-nuclides-advanced-version

The factors can be calculated using the equation:

$$ A = N_A \frac{N_{abund}}{N_{mol.mass}} ln(2) / N.half.life $$

to convert in µg/g we further use:

$$ f = A / 10^6 $$

where:

  • N_A - Avogadro constant in 1/mol

  • A - specific activity of the nuclide in Bq/kg

  • N.abund - relative natural abundance of the isotope

  • N.mol.mass molar mass in kg/mol

  • N.half.life half-life of the nuclide in s

example for calculating the activity of the radionuclide U-238:

  • N_A = 6.02214076e+23 (1/mol)

  • T_0.5 = 1.41e+17 (s)

  • m_U_238 = 0.23802891 (kg/mol)

  • U_abund = 0.992745 (unitless)

$$A_{U} = N_{A} * U_{abund} / m_{U_238} * ln(2) / T_{1/2} = 2347046$$ (Bq/kg)

$$f.U = A_{U} / 10^6$$

Note

Although written otherwise for historical reasons. Input values must be element values. For instance, if a value is provided for U-238 the function assumes that this value represents the sum (activity or abundance) of U-238, U-235 and U-234. In other words, 1 µg/g of U means that this is the composition of 0.992 parts of U-238, 0.000054 parts of U-234, and 0.00072 parts of U-235.

Function version

0.1.2

How to cite

Fuchs, M.C., 2024. convert_Activity2Concentration(): Convert Nuclide Activities to Abundance and Vice Versa. Function version 0.1.2. In: Kreutzer, S., Burow, C., Dietze, M., Fuchs, M.C., Schmidt, C., Fischer, M., Friedrich, J., Mercier, N., Philippe, A., Riedesel, S., Autzen, M., Mittelstrass, D., Gray, H.J., Galharret, J., Colombo, M., 2024. Luminescence: Comprehensive Luminescence Dating Data Analysis. R package version 0.9.26. https://r-lum.github.io/Luminescence/

References

Debertin, K., Helmer, R.G., 1988. Gamma- and X-ray Spectrometry with Semiconductor Detectors, Elsevier Science Publishers, p.283

Wiechen, A., Ruehle, H., Vogl, K., 2013. Bestimmung der massebezogenen Aktivitaet von Radionukliden. AEQUIVAL/MASSAKT, ISSN 1865-8725, https://www.bmuv.de/fileadmin/Daten_BMU/Download_PDF/Strahlenschutz/aequival-massakt_v2013-07_bf.pdf

Author

Margret C. Fuchs, Helmholtz-Institute Freiberg for Resource Technology (Germany) , RLum Developer Team

Examples


##construct data.frame
data <- data.frame(
 NUCLIDES = c("U-238", "Th-232", "K-40"),
 VALUE = c(40,80,100),
 VALUE_ERROR = c(4,8,10),
 stringsAsFactors = FALSE)

##perform analysis
convert_Activity2Concentration(data)
#>   NUCLIDE ACTIVIY (Bq/kg) ACTIVIY ERROR (Bq/kg) ABUND. (mug/g or mass. %)
#> 1   U-238              40                     4                 3.2398475
#> 2  Th-232              80                     8                19.6469710
#> 3    K-40             100                    10                 0.3222668
#>   ABUND. ERROR (mug/g or mass. %)
#> 1                      0.32398475
#> 2                      1.96469710
#> 3                      0.03222668