In the following, two selected procedures are evaluated with respect to LLD, MDA and uncertainty budget.

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^{226}**Ra through **^{222}**Rn ingrowth **(method 2.2.1.4., 24 h storage)

__Lower Limit of Detection__

The Minimum Detectable Activity MDA is calculated through LLD and the background without considering the uncertainties for analysis by

where f_{v} represents the volume factor, f_{t1} the daughter ingrowth factor and f_{t2} the decay factor between Rn extraction and mean measuring time. The following experimental parameters have to be considered for the calculation of MDA for the procedure of ^{226}Ra determination through Radon ingrowth with 24 h ingrowth storage:

**R _{0} ** 0.5 count / hour

**t **1 hour (measurement of sample and background)

ε** ** 300 %

**f _{v} ** 8/7 x 1000/12

**f _{t1} ** 1 / (1- exp-(24/92.16)

_{*}ln 2)

**f _{t2} ** 1 / exp-(3/92.16)

_{*}ln 2

**V** ** ** 12 mL

LLD = 2 _{*} 1.645 _{*} (2 _{*} 0.5 / 60^{2} _{*} 60^{2})^{1/2 }

LLD = 0.00091 sec^{-1} per sample

Minimum Detectable Activity:

MDA [Bq/L] = 0.00091/3 _{*} 95.2 _{*} 6.06 _{*} 1.02

MDA = 0.178 Bq/L

__Analysis of uncertainty__

Several parameters influence the variability of the analysis. The list of parameters and its relative standard uncertainty are:

The uncertainty parameters are assumed to be independent from each other; therefore the calculation of the analysis uncertainty U or u(y) is done by the law of propagation of errors (sum of errors in square)

Total analysis uncertainty: U = 6.5 %

^{226}**Ra by RAD Disk filter **(method 2.2.1.5.)

** **

**(a) Gel measurement of the EDTA eluate:**

__Lower Limit of Detection__

LLD = 2 _{*} 1.645 _{*} (2 _{*} 120 / 60^{2} _{*} 60^{2})^{½} = 0.014 sec^{-1} per sample

Minimum Detectable Activity:

MDA [Bq/L] = (LLD / e _{*} V) _{*} f_{t} = (0.014 / (0.9 _{*} 3) _{*} 1.02

MDA = 5.3 mBq/L

__Analysis uncertainties__

The following uncertainty parameters influence the analysis:

Total analysis uncertainty: U = 6.3 %

__Remark__: No influence by other radionuclides in absence of ^{224}Ra

**(b) Extraction of ^{222}Rn from EDTA eluate after equilibration (storage >25 days):**

__Lower Limit of Detection (LLD)__

After equilibration with ^{222}Rn (> 25 days, <1 % error), the LLD is calculated according to:

LLD = 0.00091 sec^{-1} (see ^{226}Ra) per sample

Minimum Detectable Activity

MDA [Bq/L] = (LLD / e _{*} V) _{*} f_{t }= (0.00091 / (3 _{*} 3) _{*} 1 _{*} 1.02

MDA = 0.1 mBq/L

The additional uncertainties of this method through Rn losses by emanation (4 %) and durig equilibration are compensated by a lower uncertainty for calibration of organic phases (no quenching and better PSD).