R/convert_Activity2Concentration.R
convert_Activity2Concentration.RdThe function performs the conversion of the specific activities into concentrations 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.
convert_Activity2Concentration(data, input_unit = "Bq/kg", verbose = TRUE)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.
character (with default): specify unit of input data given in the dose rate data frame, choose between 'Bq/kg' and 'ppm/%' the default is 'Bq/kg'
logical (with default): enable or disable verbose mode
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 ppm 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)
$$f.U = A_{U} / 10^6$$
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 concentration) of U-238, U-235 and U-234. In other words, 1 ppm 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.
0.1.1
Fuchs, M.C., 2023. convert_Activity2Concentration(): Convert Nuclide Activities to Concentrations and Vice Versa. Function version 0.1.1. 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., 2023. Luminescence: Comprehensive Luminescence Dating Data Analysis. R package version 0.9.23. https://CRAN.R-project.org/package=Luminescence
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
##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) CONC. (ppm/%)
#> 1 U-238 40 4 3.2398475
#> 2 Th-232 80 8 19.6469710
#> 3 K-40 100 10 0.3222668
#> CONC. ERROR (ppm/%)
#> 1 0.32398475
#> 2 1.96469710
#> 3 0.03222668