EN ISO 13160:2015

SLOVENSKI STANDARD
01-februar-2016
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Water quality - Strontium 90 and strontium 89 - Test methods using liquid scintillation
counting or proportional counting (ISO 13160:2012)
Wasserbeschaffenheit - Strontium 90 und Strontium 89 - Verfahren mittels
Flüssigszintillationszählung oder Proportionalzählung (ISO 13160:2012)
Qualité de l'eau - Strontium 90 et strontium 89 - Méthodes d'essai par comptage des
scintillations en milieu liquide ou par comptage proportionnel (ISO 13160:2012)
Ta slovenski standard je istoveten z: EN ISO 13160:2015
ICS:
13.060.60 Preiskava fizikalnih lastnosti Examination of physical
vode properties of water
17.240 Merjenje sevanja Radiation measurements
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EN ISO 13160
EUROPEAN STANDARD
NORME EUROPÉENNE
October 2015
EUROPÄISCHE NORM
ICS 13.060.60; 17.240
English Version
Water quality - Strontium 90 and strontium 89 - Test
methods using liquid scintillation counting or proportional
counting (ISO 13160:2012)
Qualité de l'eau - Strontium 90 et strontium 89 - Wasserbeschaffenheit - Strontium 90 und Strontium
Méthodes d'essai par comptage des scintillations en 89 - Verfahren mittels Flüssigszintillationszählung
milieu liquide ou par comptage proportionnel (ISO oder Proportionalzählung (ISO 13160:2012)
13160:2012)
This European Standard was approved by CEN on 27 September 2015.

CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this
European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references
concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN
member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by
translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management
Centre has the same status as the official versions.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and
United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2015 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 13160:2015 E
worldwide for CEN national Members.

Contents Page
European foreword . 3

European foreword
The text of ISO 13160:2012 has been prepared by Technical Committee ISO/TC 147 “Water quality” of
the International Organization for Standardization (ISO) and has been taken over as EN ISO 13160:2015
by Technical Committee CEN/TC 230 “Water analysis” the secretariat of which is held by DIN.
This European Standard shall be given the status of a national standard, either by publication of an
identical text or by endorsement, at the latest by April 2016, and conflicting national standards shall be
withdrawn at the latest by April 2016.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent
rights.
According to the CEN-CENELEC Internal Regulations, the national standards organizations of the
following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria,
Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia,
France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta,
Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Turkey and the United Kingdom.
Endorsement notice
The text of ISO 13160:2012 has been approved by CEN as EN ISO 13160:2015 without any modification.
INTERNATIONAL ISO
STANDARD 13160
First edition
2012-07-15
Water quality — Strontium 90 and strontium
89 — Test methods using liquid scintillation
counting or proportional counting
Qualité de l’eau — Strontium 90 et strontium 89 — Méthodes d’essai
par comptage des scintillations en milieu liquide ou par comptage
proportionnel
Reference number
ISO 13160:2012(E)
©
ISO 2012
ISO 13160:2012(E)
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or ISO’s
member body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2012 – All rights reserved

ISO 13160:2012(E)
Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Symbols, definitions, and units . 1
4 Principle . 2
4.1 General . 2
4.2 Chemical separation . 2
4.3 Detection . 3
5 Chemical reagents and equipment . 3
6 Procedure . 3
6.1 Test sample preparation . 3
6.2 Chemical separation . 3
6.3 Preparation of the source for test . 5
6.4 Measurement . 6
7 Expression of results . 8
90 90
7.1 Determination of Sr in equilibrium with Y . 8
90 90
7.2 Determination of Sr by ingrowth of Y . 9
90 89 90 90
7.3 Determination of Sr in presence of Sr when Sr is in equilibrium with Y . 11
7.4 Confidence limits .14
8 Quality control .14
9 Test report .15
89 90
Annex A (informative) Determination of Sr and Sr by precipitation and proportional counting .16
89 90
Annex B (informative) Determination of Sr and Sr by precipitation and liquid scintillation counting 20
90 90
Annex C (informative) Determination of Sr from its daughter product Y at equilibrium by organic
extraction and liquid scintillation counting.24
Annex D (informative) Determination of Sr after ionic exchange separation by proportional counting 26
Annex E (informative) Determination of Sr after separation on a crown ether specific resin and liquid
scintillation counting .29
90 90
Annex F (informative) Determination of Sr from its daughter product Y at equilibrium by organic
extraction by proportional counting .31
Annex G (informative) Correction factor for purity control using proportional counting .35
Bibliography .38
ISO 13160:2012(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the International
Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 13160 was prepared by Technical Committee ISO/TC 147, Water quality, Subcommittee SC 3,
Radiological methods.
iv © ISO 2012 – All rights reserved

INTERNATIONAL STANDARD ISO 13160:2012(E)
Water quality — Strontium 90 and strontium 89 — Test methods
using liquid scintillation counting or proportional counting
WARNING — Persons using this International Standard should be familiar with normal laboratory
practice. This document does not purport to address all of the safety problems, if any, associated with
its use. It is the responsibility of the user to establish appropriate safety and health practices and to
ensure compliance with any national regulatory conditions.
IMPORTANT — It is absolutely essential that tests conducted in accordance with this International
Standard be carried out by suitably qualified staff.
1 Scope
This International Standard specifies the test methods and their associated principles for the measurement
90 90 89
of the activity of Sr in equilibrium with Y, and Sr, pure beta-emitting radionuclides, in water samples.
Different chemical separation methods are presented to produce strontium and yttrium sources, the activity of
which is determined using a proportional counter (PC) or liquid scintillation counter (LSC). The selection of the
test method depends on the origin of the contamination, the characteristics of the water to be analysed, the
required accuracy of test results and the available resources of the laboratories.
These test methods are used for water monitoring following, past or present, accidental or routine, liquid or
gaseous discharges. It also covers the monitoring of contamination caused by global fallout.
When fallout occurs immediately following a nuclear accident, the contribution of Sr to the total amount of
strontium activity is not negligible. This International Standard provides the test methods to determine the
90 89
activity concentration of Sr in presence of Sr.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced document
(including any amendments) applies.
ISO 11929, Determination of the characteristic limits (decision threshold, detection limit and limits of the
confidence interval) for measurements of ionizing radiation — Fundamentals and application
ISO 80000-10, Quantities and units — Part 10: Atomic and nuclear physics
3 Symbols, definitions, and units
For the purposes of this document, the definitions, symbols, and abbreviated terms defined in ISO 11929 and
ISO 80000-10 and the following apply.
A calibration source activity of radionuclide i, at the time of calibration Bq
i
-1
c activity concentration of radionuclide i Bq l
A,i
-1
*
decision threshold of radionuclide i Bq l
c
A,i
-1
#
detection limit of radionuclide i Bq l
c
A,i
-1
lower and upper limits of the confidence interval of radionuclide i Bq l
 
c c
A,i A,i
,
ISO 13160:2012(E)
R chemical yield of the extraction of radionuclide i 1
c,i
-1
r background count rate s
-1
r background count rate for measurement j s
0j
-1
r gross count rate s
g
-1
r gross count rate for measurement j s
gj
-1
r net count rate for measurement j s
j
-1
r calibration source count rate s
s
90 90
t time elapsed between separation of Sr/ Y (t = 0) and counting s
t background counting time s
t , t start and finish time respectively of the measurement, referred to t = 0 s
d f
t sample counting time s
g
t start time of the measurement j, referred to t = 0 s
j
t calibration source counting time s
s
-1
U expanded uncertainty, calculated by U = ku(c ) with k = 1, 2 . Bq l
A
-1
u(c ) standard uncertainty associated with the measurement result Bq l
A
V volume of the test sample l
ε counting efficiency for radionuclide i 1
i
λ decay constant of radionuclide i 1
i
4 Principle
4.1 General
90 90 89
Sr, Y and Sr are pure beta-emitter radionuclides. Their beta-emission energies and half-lives are
given in Table 1.
90 90 89
Table 1 — Half-lives, maximum energies, and average energies of Sr, Y, and Sr
90 90 89
Parameter Sr Y Sr
Maximum energy 546,0 keV 2 283,9 keV 1 491,0 keV
Average energy 196,4 keV 935,3 keV 586,3 keV
Half-life 28,79 a 2,67 d 50,5 d
90 90
Sr can be directly measured or estimated through the measurement of its daughter product Y. All the
test methods are based on a chemical separation step followed by beta-counting of the element using PC or
LSC. See Table 2.
4.2 Chemical separation
Strontium is isolated from the water using precipitation, ion chromatography or specific chromatographic
separation using crown ether resin. Yttrium can be isolated by precipitation or liquid–liquid extraction.
The separation step should maximize the extraction of the pure element. The method chosen shall be selective
with a high chemical yield. When thorium, lead or bismuth radioisotopes are present at high activity levels,
2 © ISO 2012 – All rights reserved

ISO 13160:2012(E)
90 90 89
they may interfere with Sr, Y or Sr emission during the detection step. Other matrix constituents such as
alkaline earth metals and in particular calcium for strontium, or transuranic and lanthanide elements for yttrium,
reduce the chemical yield of the extraction.
The radiochemical separation yield is calculated using a carrier such as stable strontium or yttrium, or a
radioactive tracer such as Sr. Techniques like atomic absorption spectroscopy (AAS), inductively coupled
plasma–atomic emission spectroscopy (ICP–AES) or inductively coupled plasma–mass spectrometry (ICP–
MS) to measure the carrier, and gamma-spectrometry to measure Sr, are recommended. A carrier can
also be measured by gravimetric methods, but the presence of inactive elements, essentially alkaline earth
elements, in the leaching solutions can lead to an overestimation of the radiochemical separation yields,
particularly for the measurement of strontium.
When stable strontium is added as a carrier, the original strontium concentration in the test sample must be
known to avoid the overestimation of the radiochemical separation yield.
4.3 Detection
The use of LSC, which provides spectra and permits the detection of interference from unwanted radionuclides,
is recommended in preference to PC, which does not distinguish between emissions from different beta-
emitters. When PC is used, it is recommended that the purity of the precipitate be checked by following the
90 89
change over an appropriate time of the Y or Sr activity, even though this method is time consuming.
Six test methods are presented in Annexes A, B, C, D, E, and F.
5 Chemical reagents and equipment
The necessary chemical reagents and equipment for each strontium measurement method are specified in
Annexes A, B, C, D, E, and F.
During the analyses, unless otherwise stated, use only reagents of recognized analytical grade and laboratory
[1]
water such as distilled or demineralized water or water of equivalent purity as specified in ISO 3696.
6 Procedure
6.1 Test sample preparation
Strontium is determined from the water test sample.
If filtration is required, add the tracer or carrier after this step of the procedure and allow sufficient time to attain
chemical equilibrium before starting the test sample preparation.
If stable strontium is added as carrier, the original concentration shall be determined in the test sample in this
step of the procedure before the addition of the carrier.
6.2 Chemical separation
6.2.1 General
89 90
There are several routine analyses of Sr and Sr involved in the separation and purification of strontium:
precipitation, liquid–liquid extraction or chromatographic techniques (ion exchange or chromatographic
extraction). Annexes A, B, C, D, E, and F describe a test method for each of these techniques.
ISO 13160:2012(E)
Table 2 — Determination procedures for strontium depending on its origin
Origin Old contamination Fresh contamination
90 90
Sr+ Y
90 90
Radionuclide Sr+ Y
Sr
a
Y
Element Sr Sr
b b
Method Chromatography Precipitation Extraction Precipitation Chromatography Precipitation
90 90 90 89
Product Sr Y Sr+ Sr
85 85
Carrier or
Sr or stable Sr Stable Y Sr or stable Sr
c
Tracer
Equilibrium
90 90
Yes
Sr+ Y
No No Yes No
20 d
(recommended)
Number One One Two or more
Sr
Sr
Y
Emissions Y
Y
Sr
PC or LSC PC or LSC PC or LSC
Equipment
(total) (total or Cherenkov) (total)
Sr
90 90 90
Sr Sr+ Y
Calibration
90 90 90
Sr+ Y Y
Y
sources
90 89
Y Sr
Sr
90 90
a Y separation is performed following the Sr – Y equilibrium in the test sample.
b Liquid chromatography or specific chromatography using crown ether resin.
c   Carrier or tracer element measurements can be taken using gamma-spectrometry for Sr (tracer), by gravimetry, atomic absorption
spectrometry (AAS), inductively coupled plasma (ICP) or mass spectrometry (MS) for Sr and Y (tracer and/or carrier).
6.2.2 Precipitation techniques
The precipitation technique is suitable for the separation of all mineral elements, including strontium, in water
samples with high mineral salt contents. This technique is very efficient, but not selective for strontium. The use
of large quantities of nitric acid and the need to wait for the yttrium to reach equilibrium limit its use.
The addition of nitric acid leads to a strontium precipitate with other interfering elements. Successive dissolution–
precipitation cycles concentrate strontium in the precipitate, while yttrium and other elements remain in the
supernatant fraction. The most usual procedures lead to a SrCO precipitate.
90 90
For the test method with Sr and Y at equilibrium, either the global contribution of yttrium and strontium is
directly measured in the precipitate or the yttrium activity is measured after a last separation from the strontium.
In this latter case, the chemical yield is estimated by the addition of an yttrium carrier to the source before the
yttrium separation. The final product is an yttrium precipitate, usually in the form of an oxalate.
89 90 90 90 90
In the absence of Sr, Sr is measured by counting the beta-emission of Y or of Y and Sr in equilibrium.
4 © ISO 2012 – All rights reserved
Measurement(s) Separation
ISO 13160:2012(E)
When Sr in the water test sample cannot be neglected, the direct measurement method of strontium at two
different times shall be chosen.
89 90
Two precipitation methods are described: Annex A employs PC for Sr and Sr; Annex B employs LSC for
89 90
Sr and Sr.
6.2.3 Liquid–liquid extraction technique
This technique is based on the extraction using an organic solvent of Y at equilibrium with its radioactive
parent Sr. The chemical separation is fast and requires few technical resources. A provisional result may be
achieved after 3 d (approximately one yttrium decay period). However, total selectivity of the extraction is not
always possible. In the presence of high levels of natural radioactivity, interference may occur, making it difficult
to determine very low levels of strontium activity.
This test method is suitable for all samples with low activity of beta-emitting radionuclide.
Y is extracted from the water test sample fraction using an organic solvent, and then after re-extraction,
recovered in the form of an yttrium precipitate. Test methods are presented in Annexes C and F.
After the source preparation, the Y is measured by PC (Annex F) or by measuring the Cherenkov radiation
from the Y with LSC (Annex C).
The absence of other interfering beta-emitters is verified during the decay of Y by measuring the decrease in
count rate of the Y and once the decay is complete, comparing it with the background level activity.
6.2.4 Chromatographic technique
6.2.4.1 Ion exchange resin
This technique is based on Sr(II) exchange on a cationic resin and is used for separation and purification of strontium
in large volume samples. A method is presented in Annex D in which the measurement is carried out with a PC.
6.2.4.2 Crown ether resin
This technique is based on the selective chromatographic separation of strontium using a specific crown ether
resin. The chemical separation is fast and suitable for inspection and monitoring of the environment. A method
is presented in Annex E in which the measurement is carried out by LSC.
6.3 Preparation of the source for test
6.3.1 Source preparation for liquid scintillation counter
LSC measures directly the photons produced by the scintillations in the liquid as a result of the excitation
caused by the beta-emissions from the source.
A strontium or yttrium precipitate is dissolved and mixed with the liquid scintillator. When the strontium or
yttrium is in solution, it is mixed directly with the liquid scintillator. The volume depends on the equipment (vial
size) and the specific scintillator used.
90 89 90 90 90
The calibration source shall be prepared from a known activity of tracer ( Sr, Sr, Sr + Y or Y) with the
same geometry and chemical composition as the source to be measured.
The blank source should be prepared following the method chosen starting with a clean test sample (or water).
6.3.2 Source preparation for proportional counter
The PC measures directly the beta-emission from the source prepared from a thin layer deposit to minimize
the self-absorption effects.
ISO 13160:2012(E)
The strontium or yttrium precipitate is deposited on a filter by filtration or on a stainless steel planchet by
direct evaporation.
The filter or planchet size diameter should be similar to the detector size (see Annex A or D).
90 89 90 90 90
The calibration source shall be prepared from a known amount of tracer ( Sr, Sr, Sr + Y or Y) with the
same geometry and chemical composition as the source to be measured.
6.4 Measurement
6.4.1 General
The same equipment conditions should be used for the sample, the background and the calibration source
measurements.
The blank source should be prepared following the method chosen starting with laboratory water. Measure the
background using a blank source prepared for the method chosen.
The counting time used depends on the sample and background count rates and also on the detection limit and
decision threshold required.
6.4.2 Liquid scintillation counter
The scintillation phenomenon results from interactions of ionizing radiations with solvents and compounds
having fluorescent properties (scintillators). Both solvents and scintillators constitute the scintillation cocktail.
The scintillation mixture is achieved by adding the scintillation cocktail to the test sample in order to obtain a
homogeneous mixture.
The scintillation cocktail is chosen according to the characteristics of the sample to be analysed and according
[6]
to the properties of the detection equipment (see ISO 18589-5 ). It is recommended that a hydrophilic
scintillation cocktail be used, especially for the measurement of natural water.
The characteristics of the scintillation cocktail shall allow the mixture to be homogeneous and stable.
It is recommended that the scintillation cocktail be stored in the dark and, particularly just before use, exposure
to direct sunlight or fluorescent light avoided in order to prevent interfering luminescence and to comply with
the storage conditions specified by the scintillation cocktail supplier.
The mixtures (scintillation cocktail and test sample) should be disposed of as chemical waste, and, depending
on the radioactivity, may require disposal as radioactive waste.
The measurement can be affected by chemiluminescence phenomena or quench due to chemical entities and
to the presence of other radionuclides than yttrium. It is then necessary to take into account the characteristics
of the water sample.
90 90
When assessing the Sr activity by its measurement with Y in equilibrium, two cases arise:
89 90 90
— the presence of Sr can be neglected, the relevant contribution of Y in equilibrium with Sr can be
assessed using LSC;
— the presence of Sr cannot be neglected, it is necessary to measure the strontium at two different times,
to estimate the Sr activity through its decay.
90 90 90
When assessing Sr activity by Y measurement, if the presence of small amounts of Sr cannot be
90 90
excluded, then it is preferable to measure the Cherenkov radiation from the Y, as it is negligible for Sr.
6.4.3 Proportional counter
A PC measures directly the beta-radiation, without energy discrimination, from the source usually prepared as
a thin layer deposit.
6 © ISO 2012 – All rights reserved

ISO 13160:2012(E)
The use of double window (alpha and beta) in this type of counter allows the presence of alpha-emitter
contaminants in the source to be checked. If other short radioactive half-life beta-emitters are present, they
can be detected by performing successive measurements of the source at given times.
6.4.4 Efficiency calculation
The procedure to calibrate the counters is as follows:
— select t to collect at least 10 counts;
s
90 90
— determine the beta-count rate of the calibration source ( Sr in equilibrium with Y);
— calculate the counting efficiency of the counter by dividing the count rate measured by the activity of the
calibration source:
rr−
s0
ε =
i
A
i
6.4.5 Determination of the chemical yield
The chemical yield of the strontium, R , is calculated from strontium carrier or tracer by one of the
c,Sr
following procedures:
a) chemical yield calculated as the ratio of the mass of the collected strontium to the mass of the strontium
added as a carrier at the start of the procedure:
m
c,p
R = (1)
c,Sr
m
c,Sr
where
m is the mass of the strontium collected, determined by an appropriate method (AA, ICP–AES or
c,p
ICP–MS);
m is the mass of the strontium carrier added;
c,Sr
b) chemical yield calculated as the ratio of the activity of the Sr collected, measured by gamma- spectrometry,
over the theoretical activity of the equivalent Sr added as a tracer at the start of the procedure.
A
Sr,M
R = (2)
c,Sr
A
Sr,T
where
85 85
is the activity of Sr measured by gamma-spectrometry taking into account the Sr decay
A
Sr,M
from the start of procedure;
A is the theoretical activity of Sr added at the start of the procedure.
Sr,T
The chemical yield of the yttrium, R , is calculated from the yttrium carrier by a procedure similar to that
c,Y
presented for the chemical yield of the strontium.
ISO 13160:2012(E)
7 Expression of results
90 90
7.1 Determination of Sr in equilibrium with Y
7.1.1 Calculation of the activity concentration
The activity per unit mass in source samples where the Y has been completely separated from the parent
90 90
radionuclide Sr cannot be reassessed until the daughter nuclide Y has grown back in and is in equilibrium
90 90
with the parent nuclide Sr. This occurs 20 d after t = 0, where t = 0 is the time at which all the Y had been
removed from the sample.
90 90
The result of the measurement gives the gross number of counts from the Sr plus Y. Dividing the gross
counts by the counting time gives the gross count rate, r .
g
To apply this method, neglect the Sr contained in the test sample.
The gross count rate should be corrected by background count rate, r , which is obtained from the measurement
of a blank source.
90 90
The activity concentration of Sr plus Y, c , is calculated using Formula (3):
A,Sr +Y
rr−
g 0
c = (3)
A,Sr+Y
VR ε
c,Sr Sr+Y
and, the activity concentration of Sr, is
rr−
c
A,Sr+Y g0
c == =−rr w (4)
90 () 90
g0
A, Sr Sr
22×VR ε
c,Sr Sr+Y
with
w =
Sr
2×VR ε
c,Sr Sr+Y
7.1.2 Standard uncertainty
[7]
According to ISO/IEC Guide 98-3, the standard uncertainty of c is calculated by:
A, Sr
 
r
r
g
22 2 2 2 2 0 2 2
 
uc = wu ru+ rc+ uw = w  +  +cu w (5)
()
90 () 90 90
( ) g0 rel () rel ()
90 90 90090
A, Sr   Sr Sr
Sr A, Sr Sr   A, Sr
t t
g 0
 
where the uncertainties of the sample and background counting times are neglected and the relative standard
uncertainty of w is calculated using Formula (6):
2 2 2 2
uw =uR +uV +u ε (6)
() () ()
()90
rel rel c,Sr rel relSrY+
Sr
where the relative standard uncertainty of ε is calculated using Formula (7):
Sr + Y
 
r r
2 2 2 2
s 0
uu()ε =−()rr +uA() =+ ()rr− +uA() (7)
 
rel Sr++Yrel s0 rel Sr Y s 00rel Sr+Y
t t
 s 0 
in which
u (A ) includes all the uncertainties related to the calibration source, i.e. in the standard solution and
rel Sr + Y
the preparation of the calibration source;
u (R ) is the uncertainty related to the chemical yield, and depends on its method of evaluation.
rel c,Sr
8 © ISO 2012 – All rights reserved

ISO 13160:2012(E)

For the calculation of the characteristic limits according to ISO 11929, uc , i.e the standard uncertainty
90 )
(
A, Sr
of c as a function of its true value, is required, calculated by Formula (8):
A, Sr
 c 
 
r
2 A, Sr 22
 
   
uc =+w rt + ++cu w (8)
90 ()90
( ) 90 0 g 90 rel
A, Sr Sr
Sr   A, Sr
 w t 
90 0
 Sr 
 
7.1.3 Decision threshold
*

In accordance with ISO 11929, for c = 0 , the decision threshold, c , is obtained from
90 90
A, Sr A, Sr
Formula (8). This yields:
r r
* 00
ck==uk()0 w + (9)
90 90
11−−αα
A, Sr Sr
t t
g 0
α = 0,05 with k = 1,65 is often chosen by default.
1 - α
7.1.4 Detection limit
#
In accordance with ISO 11929, the detection limit, c , is calculated by
A, Sr
 
# * #
cc=+ ku c
90  
1−β
90 90
A, Sr
A, Sr A, Sr
 
#
 
  (10)
cc
 r 
 A, Sr 
* 2 0 # 2
=+ck w + rt + +cu ww
90 90
1−β 0 g rel()
90    90
A, Sr Sr
Sr
w t A, Sr
 
 
Sr
 
 
β = 0,05 with k = 1,65 is often chosen by default.
1 - β
#
The detection limit can be calculated by solving Formula (10) for c or, more simply, by iteration with a
A, Sr
# *
starting approximations cc= 2 .
A, Sr
A, Sr
When taking α = β, then k = k = k and the solution of Formula (10) is given by Formula (11):
1 - α 1 - β
∗ 2
2ck+ wt/
90 90
() g
A, Sr Sr
#
c = (11)
A, Sr
1−ku w
()90
rel
Sr
90 90
7.2 Determination of Sr by ingrowth of Y
7.2.1 Calculation of the activity concentration
The Y is measured immediately after its separation in the test sample when strontium and yttrium are in
90 90
equilibrium. The time when the Y is separated from the Sr and starts to decay with a half-life of 2,7 d is
taken as t = 0.
The result of the measurement is the gross number of counts from the Y, divided by the counting time, to give
the gross count rate, r .
g
The gross count rate should be corrected by background count rate, r , obtained from the measurement of a
blank source.
ISO 13160:2012(E)
The activity concentration of Y, c , is calculated at time t = 0, using Formula (12):
A,Y
rt −rt
gg 0 g
c = =−rr w (12)
()
A,Y gY0
t
f
ελVR exp.− ttd
()
Yc Y
∫
t
d
where
λ t
Yg
w = ×
Y
ε VR
expe−λλtt−−xp 
() ()
Yc
Yd Yf
 
R = R R
c c,Sr c,Y
The integral allows the activity of the decay of Y during the counting time to be corrected, t = t - t , and the
g f d
activity per unit of mass of Sr, is
cc== rr− w (13)
90 ()
A,Yg 0Y
A, Sr
7.2.2 Standard uncertainty
[7]
According to ISO/IEC Guide 98-3, the standard uncertainty of c is calculated by:
AS, r
 
r
rr
g
22 2 2 2 2 0 2 2
 
uc = wu ru+ rc+ uw =+w   +cu w (14)
() () ()
90 ()
( ) Yg 0 rel YY rel Y
90 90
A, Sr    
A, Sr A, Sr
t t
g 0
 
where the uncertainties of the sample and background counting times are neglected and the relative standard
uncertainty of w is calculated using Formula (15):
Y
2 2 2 2
uw() =uR +uV()+u ()ε (15)
()
rel Yrel crel relY
the relative standard uncertainty of ε is calculated by
Y
 
r r 2
2 2 2 s 0 2
uuε =−rr +uA =+ rr− +u A (16)
() () () () ()
 
rel Yrel s0 rel Y s 0 rrel Y
t t
 s 0 
in which u (A ) includes all the uncertainties related to the calibration source, i.e. in the standard solution and
rel Y
the preparation of the calibration source; and u (R ) is the uncertainty related with the chemical yield. It can
rel c
be calculated from
22 2
uR =uR +uR (17)
()
() ()
relc relc,Srrel c,Y
2 2
where uR ,uR are the squared relative uncertainties of the chemical yields of strontium and
relc(),Srrel ()c,Y
yttrium, respectively, and depends on their method of evaluation.

For the calculation of the characteristic limits according to ISO 11929, uc , i.e the standard uncertainty
90 )
(
A, Sr
of c as a function of its true value, is required, calculated by:
A, Sr
 c 
 
r
2 A, Sr 22
 
   
uc =+w rt + +c uw (18)
()
( ) Y 0 g 900 relY
A, Sr
 w  A, Sr
 t 
Y 0
 
 
10 © ISO 2012 – All rights reserved

ISO 13160:2012(E)
7.2.3 Decision threshold
*

In accordance with ISO 11929, for c = 0 , the decision threshold, c , is obtained from
90 90
A, Sr A, Sr
Formula (18). This yields:
r r
* 00
ck==uk()0 w + (19)
11−−αα Y
A, Sr
t t
g 0
α = 0,05 with k = 1,65 is often chosen by default.
1 - α
7.2.4 Detection limit
#
In accordance with ISO 11929, the detection limit, c , is calculated by
A, Sr
#
 
 
c
 r 
   
# * #* 2 A, Sr 0 #2 2

cc=+ ku cc=+ kw + rt + +cu ()w (20)
90 90
11−−ββ  Y 0 g rel Y
90 90    90
A, Sr A, Sr
A, Sr A, Sr w t A, Sr
 
Y 0
 
 
 
 
β = 0,05 with k = 1,65 is often chosen by default.
1 - β
#
The detection limit can be calculated by solving Formula (20) for c or, more simply, by iteration with
A, Sr
# *
starting approximations cc= 2 .
A, Sr
A, Sr
When taking α = β then k = k = k and the solution of Formula (20) is given by Formula (21):
1 - α 1 - β
∗ 2
2ck+ wt
()Yg
A, Sr
#
c = (21)
A, Sr
1−ku w
()
relY
90 89 90 90
7.3 Determination of Sr in presence of Sr when Sr is in equilibrium with Y
7.3.1 Calculation of the activity concentration
This method is based in the realization of two measurements of the same source at two different times t and
t after the time t = 0 of the separation of the yttrium present in the test sample. It is suggested that the same
counting time, t , is used for both measurements. The net count rates, r , of these measurements can be
g j
calculated from the gross count rates, r ,and the background count rates, r , as r = r - r .
gj 0j j gj 0j
90 90
If the measurements are made when equilibrium between the Sr and Y has been reached, then the net
90 89
count rates can be calculated using the equations below, considering that the Sr and Sr activities are
constant during the counting time, and the appropriate decay constants,
rA=+2 εε Atexp −λ
1190 90 89 89 ()89
Sr Sr+YSrSrSr
(22)
rA=+2 εε Atexp −λ
90 90 889 89 ()89
2 2
Sr Sr+Y Sr Sr Sr
From these equations
 
rr−−exp(λ tt− )
21 21
 Sr 
A =
Sr
 
21ελ−−exp(tt− )
90 89
{}21
Sr+YS r 
(23)
rr− exp +λ t
()
12 ()89 1
Sr
A =
Sr
 
ελ1−−exp(tt− )
89 89
{}21
Sr  Sr 
ISO 13160:2012(E)
The activity concentration, c , of the radionuclide i is calculated using Formula (24):
A,i
A
i
c = (24)
A,i
VR
c,Sr
and
cw=−rcr (25)
()
90 21
AS, r
where
w =
VR ××21ε ()−c
c,Sr
Y
Sr+
 
ct=−exp(λ −t )
Sr
 
and
cw=−()rr (26)
89 89 21
AS, r
where
 
exp +λ t
 89 
Sr
 
w =
VR ε c −1
()
c,Sr
Sr
 
ct=−exp(λ −t )
89 21
Sr
 
7.3.2 Standard uncertainty
[7]
When the measurements are made in equilibrium conditions and according to ISO/IEC Guide 98-3, the
standard uncertainty of c is calculated by:
A,i
22 22 2 2
 
uc = wu rc+ ur +cu w
() () ()
( ) 90 2 1990 rel 0
AS, r
 
AS, r
(27)
22 2 2 2
 
uc = wu ru+ rc+ uw()
() ()
( ) 89 1 28rel 9
A, Sr  
AS, r
assuming that u (c) = 0.
The relative standard uncertainty of r is calculated by:
j
r r
gjj0
ur =+ (28)
()
j
t t
g 0
The relative standard uncertainties of w and w are calculated by
90 89
2 2 2 2
uw =uR +uV +u ε
() ()
() 90
rel 90 rel c,Sr rel rel()
Sr+Y
(29)
2 2 2 2
uw =uuR +uV +u ε
() () ()
()89
rel 89 rel c,Sr rel rel
Sr
12 © ISO 2012 – All rights reserved

ISO 13160:2012(E)
The relative standard uncertainty of ε is calculated by
i
 r r 
2 2 2 s 0 2
uuε =−rr +uA =+ rr− +u A (30)
() () () () ()
 
rel iirel s0 rel s 0 rrel i
t t
 s 0 
where
u (A ) includes all the uncertainties related to the calibration source, i.e. in the standard solution
rel i
and the preparation of the calibration source;
u (R ) is the uncertainty related to the chemical yield, and depends on its method of evaluation.
rel c, Sr
For the calculation of the characteristic limits according to ISO 11929, uc , i.e the standard uncertainty of
()
A,i
A as a function of its true value, is required, calculated by:
i
  
2 c c  c
 
90 89 89
11 1+c
A,,SrA,SrA,Sr
2 2 22 2
   
uc =+wr cr  +  + − + +c uw (31)
()
( ) 90 ()02 01 rel 90
A, Sr
 
 tt tc1−  w w  wt  A, Sr
()
0 gg 90 89 89 g
 
 
 
 c cc 
 
  90 89 89
11 2
2 A, Sr A, Sr A, Sr 2 2
 
   
uc =+wr r  +  + − + +cu w (32)
() ()
( ) 89 01 02 89 rell 89
A, Sr
 
  A, Sr
 tt tc1− w w wt 
()
0 gg 990 89 89 g
 
 
 
7.3.3 Decision threshold
*

In accordance with ISO 11929, the decision thresholds, c , are obtained from the Formula (32) for c = 0
A,i A,i
. This yields:
c
  89
cc +1
11 ( ))
* 2 A, Sr

ck==uk()0 wr +cr  + +
90 11−−αα 90 ()02 01
A, Sr
 
tt ()c −1 tw
0 g g 89
 
(33)
c
  90
1 112
* A, Sr

ck==uk()0 wr + r  + +
()
11−−αα 89 01 02
A, Sr
 
t tt ()1−c w
0 gg 90
 
α = 0,05 with k = 1,65 is often chosen by default.
1 - α
ISO 13160:2012(E)
7.3.4 Detection limit
#
In accordance with ISO 11929, the detection limits, c , are calculated by
A,i
# *  # 
cc=+ ku c
90  
1−β
90 90
A, Sr
A, Sr AS, r
 
#
 2 
 
c
1+ c c c
  90 89 89
()
* 2  2  A, Sr A, Sr  A, Sr  #2 2
=+ck wr ++cr   + − ++ cu ()w
90 19−β 0 ()022 01 rel 90
 
A, Sr    
A, Sr
tt tc()1− w ww wt
0 gg 90 89 89 g
 
   
 
 
(34)
#*  # 
c =+ck uc
89  
1−β
89 89
A, Sr
AA, Sr AS, r
 
# #
 
 
c c
c
  90 89 89
11 2
* 2   A, Sr A, Sr  A, Sr  #2 2
=+ck wr()++r   + − ++ cu ()w
89 18−β 9 01102 rel 89
 
A, Sr    
A, Sr
tt tc()1− w w tw
09gg 089 g 89
 
   
 
 
β = 0,05 with k = 1,65 is often chosen by default.
1 - β
#
The detection limit can be calculated by solving Formula (34) for c or, more simply, by iteration with starting
A,i
# *
approximations cc= 2 .
A,i A,i
When taking α = β, then k = k = k and the solution of Formula (34) is given by the following formulae:
1 - α 1 - β
∗ 2 2
21ck++wc tc1−
()
90() g
A, Sr
#
c =
A, Sr
1−ku w
()
rel 90
(35)
∗ 2
21ck++wc ct−1
() ()
89 g
A, Sr
##
c =
A, Sr
1−ku w
()
rel 89
7.4 Confidence limits

Confidence limits can be calculated in accordance with ISO 11929. The values of lower limit, c , and upper
A,i

limit, c , are calculated using Formulae (36) and (37):
A,i
 γ 

cc=−ku cp =−ω 1 (36)
()
A,iA,i p A,i  
 
ωγ

cc=+ku cq =−1 (37)
()
A,iA,i q A,i
where ω = Φ[y/u(y)], Φ being the distribution function of the standardized normal distribution.
The value of ω can be set to 1, if
...