Standard atomic weights of the elements 2021 (IUPAC Technical Report)

<!DOCTYPE html> <html lang="en" xmlns:mml="http://www.w3.org/1998/Math/MathML"> <head> <meta charset="utf-8"> <meta http-equiv="x-ua-compatible" content="ie=edge"> <title>Standard atomic weights of the elements 2021 (IUPAC Technical Report)</title>  <link rel="preload" href="/assets/fonts/montserrat-v15-latin-ext_cyrillic-ext-regular.woff2" as="font" type="font/woff2" crossorigin="anonymous"> <link rel="preload" href="/assets/fonts/montserrat-v25-latin-ext_cyrillic-ext-500.woff2" as="font" type="font/woff2" crossorigin="anonymous"> <link rel="preload" href="/assets/fonts/montserrat-v15-latin-ext_cyrillic-ext-700.woff2" as="font" type="font/woff2" crossorigin="anonymous">  <link rel="preload" href="/assets/fonts/merriweather-v30-latin-ext_cyrillic-ext-300.woff2" as="font" type="font/woff2" crossorigin="anonymous"> <link rel="preload" href="/assets/fonts/merriweather-v22-latin-ext_cyrillic-ext-regular.woff2" as="font" type="font/woff2" crossorigin="anonymous"> <link rel="preload" href="/assets/fonts/merriweather-v22-latin-ext_cyrillic-ext-700.woff2" as="font" type="font/woff2" crossorigin="anonymous">  <link rel="preload" href="/assets/stylesheets/fontawesome.woff2" as="font" type="font/woff2" crossorigin="anonymous"> <link rel="stylesheet" media="all" href='/assets/stylesheets/02f295d1f6a8e9c282e7831cd493e8ff-bootstrap.purged.min.css' /> <link rel="stylesheet" media="all" href='/assets/stylesheets/5337b0511e7530e28f005276f70cde44-main.min.css' /> <link rel="stylesheet" media="all" href='/assets/stylesheets/13761c60ba5201f465803f3005ccd7ef-fontawesome-codes.css' /> <link rel="shortcut icon" type="image/x-icon" href='/assets/images/ec7d7606b4e2f3f921b5e1700948efb6-favicon.ico' /> <link rel="alternate" hreflang="en" href="https://www.degruyter.com/document/doi/10.1515/pac-2019-0603/html?lang=en" /> <link rel="alternate" hreflang="de" href="https://www.degruyter.com/document/doi/10.1515/pac-2019-0603/html?lang=de" /> <link rel="alternate" hreflang="x-default" href="https://www.degruyter.com/document/doi/10.1515/pac-2019-0603/html" />  <link rel="schema.dcterms" href="http://purl.org/dc/terms/"> <meta name="dcterms.rightsHolder" content="Walter de Gruyter GmbH"> <meta name="dcterms.rights" content="De Gruyter expressly reserves the right to use all content for commercial text and data mining within the meaning of Section 44b of the German Copyright Act."> <link rel="dns-prefetch" href="https://www.google-analytics.com" /> <meta name="google" content="notranslate" /> <meta name="viewport" content="width=device-width, initial-scale=1" /> <meta name="description" content="Following the reviews of atomic-weight determinations and other cognate data in 2015, 2017, 2019 and 2021, the IUPAC (International Union of Pure and Applied Chemistry) Commission on Isotopic Abundances and Atomic Weights (CIAAW) reports changes of standard atomic weights. The symbol A r °(E) was selected for standard atomic weight of an element to distinguish it from the atomic weight of an element E in a specific substance P, designated A r (E, P). The CIAAW has changed the values of the standard atomic weights of five elements based on recent determinations of terrestrial isotopic abundances: Ar (argon): from 39.948 ± 0.001 to [39.792, 39.963] Hf (hafnium): from 178.49 ± 0.02 to 178.486 ± 0.006 Ir (iridium): from 192.217 ± 0.003 to 192.217 ± 0.002 Pb (lead): from 207.2 ± 0.1 to [206.14, 207.94] Yb (ytterbium): from 173.054 ± 0.005 to 173.045 ± 0.010 The standard atomic weight of argon and lead have changed to an interval to reflect that the natural variation in isotopic composition exceeds the measurement uncertainty of A r (Ar) and A r (Pb) in a specific substance. The standard atomic weights and/or the uncertainties of fourteen elements have been changed based on the Atomic Mass Evaluations 2016 and 2020 accomplished under the auspices of the International Union of Pure and Applied Physics (IUPAP). A r ° of Ho, Tb, Tm and Y were changed in 2017 and again updated in 2021: Al (aluminium), 2017: from 26.981 5385 ± 0.000 0007 to 26.981 5384 ± 0.000 0003 Au (gold), 2017: from 196.966 569 ± 0.000 005 to 196.966 570 ± 0.000 004 Co (cobalt), 2017: from 58.933 194 ± 0.000 004 to 58.933 194 ± 0.000 003 F (fluorine), 2021: from 18.998 403 163 ± 0.000 000 006 to 18.998 403 162 ± 0.000 000 005 (Ho (holmium), 2017: from 164.930 33 ± 0.000 02 to 164.930 328 ± 0.000 007) Ho (holmium), 2021: from 164.930 328 ± 0.000 007 to 164.930 329 ± 0.000 005 Mn (manganese), 2017: from 54.938 044 ± 0.000 003 to 54.938 043 ± 0.000 002 Nb (niobium), 2017: from 92.906 37 ± 0.000 02 to 92.906 37 ± 0.000 01 Pa (protactinium), 2017: from 231.035 88 ± 0.000 02 to 231.035 88 ± 0.000 01 Pr (praseodymium), 2017: from 140.907 66 ± 0.000 02 to 140.907 66 ± 0.000 01 Rh (rhodium), 2017: from 102.905 50 ± 0.000 02 to 102.905 49 ± 0.000 02 Sc (scandium), 2021: from 44.955 908 ± 0.000 005 to 44.955 907 ± 0.000 004 (Tb (terbium), 2017: from 158.925 35 ± 0.000 02 to 158.925 354 ± 0.000 008) Tb (terbium), 2021: from 158.925 354 ± 0.000 008 to 158.925 354 ± 0.000 007 (Tm (thulium), 2017: from 168.934 22 ± 0.000 02 to 168.934 218 ± 0.000 006) Tm (thulium), 2021: from 168.934 218 ± 0.000 006 to 168.934 219 ± 0.000 005 (Y (yttrium), 2017: from 88.905 84 ± 0.000 02 to 88.905 84 ± 0.000 01) Y (yttrium), 2021: from 88.905 84 ± 0.000 01 to 88.905 838 ± 0.000 002"/> <meta property="og:url" content="https://www.degruyter.com/document/doi/10.1515/pac-2019-0603/html"/><meta property="og:site_name" content="De Gruyter"/><meta property="og:title" content="Standard atomic weights of the elements 2021 (IUPAC Technical Report)"/><meta property="og:type" content="article"/><meta property="og:locale" content="en"/><meta property="og:image" content="https://www.degruyter.com/document/cover/journal_key/PAC/product"/><meta property="og:image:type" content="image/jpeg"/><meta property="og:description" content="Following the reviews of atomic-weight determinations and other cognate data in 2015, 2017, 2019 and 2021, the IUPAC (International Union of Pure and Applied Chemistry) Commission on Isotopic Abundances and Atomic Weights (CIAAW) reports changes of standard atomic weights. The symbol A r °(E) was selected for standard atomic weight of an element to distinguish it from the atomic weight of an element E in a specific substance P, designated A r (E, P). The CIAAW has changed the values of the standard atomic weights of five elements based on recent determinations of terrestrial isotopic abundances: Ar (argon): from 39.948 ± 0.001 to [39.792, 39.963] Hf (hafnium): from 178.49 ± 0.02 to 178.486 ± 0.006 Ir (iridium): from 192.217 ± 0.003 to 192.217 ± 0.002 Pb (lead): from 207.2 ± 0.1 to [206.14, 207.94] Yb (ytterbium): from 173.054 ± 0.005 to 173.045 ± 0.010 The standard atomic weight of argon and lead have changed to an interval to reflect that the natural variation in isotopic composition exceeds the measurement uncertainty of A r (Ar) and A r (Pb) in a specific substance. The standard atomic weights and/or the uncertainties of fourteen elements have been changed based on the Atomic Mass Evaluations 2016 and 2020 accomplished under the auspices of the International Union of Pure and Applied Physics (IUPAP). A r ° of Ho, Tb, Tm and Y were changed in 2017 and again updated in 2021: Al (aluminium), 2017: from 26.981 5385 ± 0.000 0007 to 26.981 5384 ± 0.000 0003 Au (gold), 2017: from 196.966 569 ± 0.000 005 to 196.966 570 ± 0.000 004 Co (cobalt), 2017: from 58.933 194 ± 0.000 004 to 58.933 194 ± 0.000 003 F (fluorine), 2021: from 18.998 403 163 ± 0.000 000 006 to 18.998 403 162 ± 0.000 000 005 (Ho (holmium), 2017: from 164.930 33 ± 0.000 02 to 164.930 328 ± 0.000 007) Ho (holmium), 2021: from 164.930 328 ± 0.000 007 to 164.930 329 ± 0.000 005 Mn (manganese), 2017: from 54.938 044 ± 0.000 003 to 54.938 043 ± 0.000 002 Nb (niobium), 2017: from 92.906 37 ± 0.000 02 to 92.906 37 ± 0.000 01 Pa (protactinium), 2017: from 231.035 88 ± 0.000 02 to 231.035 88 ± 0.000 01 Pr (praseodymium), 2017: from 140.907 66 ± 0.000 02 to 140.907 66 ± 0.000 01 Rh (rhodium), 2017: from 102.905 50 ± 0.000 02 to 102.905 49 ± 0.000 02 Sc (scandium), 2021: from 44.955 908 ± 0.000 005 to 44.955 907 ± 0.000 004 (Tb (terbium), 2017: from 158.925 35 ± 0.000 02 to 158.925 354 ± 0.000 008) Tb (terbium), 2021: from 158.925 354 ± 0.000 008 to 158.925 354 ± 0.000 007 (Tm (thulium), 2017: from 168.934 22 ± 0.000 02 to 168.934 218 ± 0.000 006) Tm (thulium), 2021: from 168.934 218 ± 0.000 006 to 168.934 219 ± 0.000 005 (Y (yttrium), 2017: from 88.905 84 ± 0.000 02 to 88.905 84 ± 0.000 01) Y (yttrium), 2021: from 88.905 84 ± 0.000 01 to 88.905 838 ± 0.000 002"/><meta property="og:locale:alternate" content="de"/><meta property="article:author" content="Thomas Prohaska"/><meta property="article:author" content="Johanna Irrgeher"/><meta property="article:author" content="Jacqueline Benefield"/><meta property="article:author" content="John K. Böhlke"/><meta property="article:author" content="Lesley A. Chesson"/><meta property="article:author" content="Tyler B. Coplen"/><meta property="article:author" content="Tiping Ding"/><meta property="article:author" content="Philip J. H. Dunn"/><meta property="article:author" content="Manfred Gröning"/><meta property="article:author" content="Norman E. Holden"/><meta property="article:author" content="Harro A. J. Meijer"/><meta property="article:author" content="Heiko Moossen"/><meta property="article:author" content="Antonio Possolo"/><meta property="article:author" content="Yoshio Takahashi"/><meta property="article:author" content="Jochen Vogl"/><meta property="article:author" content="Thomas Walczyk"/><meta property="article:author" content="Jun Wang"/><meta property="article:author" content="Michael E. Wieser"/><meta property="article:author" content="Shigekazu Yoneda"/><meta property="article:author" content="Xiang-Kun Zhu"/><meta property="article:author" content="Juris Meija"/><meta property="article:tag" content="Argon"/><meta property="article:tag" content="ciaaw.org"/><meta property="article:tag" content="hafnium"/><meta property="article:tag" content="iridium"/><meta property="article:tag" content="lead"/><meta property="article:tag" content="LSVEC"/><meta property="article:tag" content="ytterbium"/><meta property="article:published_time" content="2022-05-01"/><meta property="article:section" content="Pure and Applied Chemistry"/> <meta name="citation_firstpage" content="573" /> <meta name="citation_lastpage" content="600" /> <meta name="citation_issue" content="5" /> <meta name="citation_issn" content="1365-3075" /> <meta name="citation_language" content='en' /> <meta name="citation_volume" content="94" /> <meta name="citation_publisher" content='De Gruyter' /> <meta name="citation_pdf_url" content="https://www.degruyter.com/document/doi/10.1515/pac-2019-0603/pdf" /> <meta name="citation_keywords" content='Argon; ciaaw.org; hafnium; iridium; lead; LSVEC; ytterbium' /> <meta name="citation_author" content="Thomas Prohaska" /> <meta name="citation_author" content="Johanna Irrgeher" /> <meta name="citation_author" content="Jacqueline Benefield" /> <meta name="citation_author" content="John K. 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Your documents are now available to view.</p> <div id="orderCompleteItemList"> </div> </div> </div> </div> </div> <main id="main" class='language_en min-vh-100 '> <div class="row no-theme-gutter-x g-0 " id="docContent"> <div class='offset-lg-1 col-lg-8 pb-2'> <div class='row g-0 '> <div class="col p-3 pt-5"> <div class="d-flex flex-wrap flex-column flex-md-row justify-content-between"> <div> <div class="mb-2"> <span> <a class="creative-commons-license ga_creative_commons_license text-decoration-none" href="https://creativecommons.org/licenses/by-nc-nd/4.0/" title='Creative Commons - Some Rights Reserved'> <img src="/assets/images/cc-licenses/by-nc-nd.eu.svg" height="100%" width="100%" alt='BY-NC-ND 4.0 license'/> </a> </span> <span class="fa fas fa-icon-open-access"></span> <span class="accessOpenAccess me-2">Open Access</span> <span class="publisherAndPublicationDate metadataInfoMainContent"> <span class="publisher"> Published by <a class="ga_published_by ga_published_by_header" href='/search?query=*&publisherFacet=De+Gruyter'>De Gruyter</a> </span> <span class="publicationDate">May 4, 2022</span> </span> </div> <div id="mobilePurchaseDiv" class="d-none"> <a class="mobilePurchaseButton" href="#"> Purchase article <svg width="17" height="16" viewBox="0 0 17 16" fill="none" xmlns="http://www.w3.org/2000/svg"> <path fill-rule="evenodd" clip-rule="evenodd" d="M12.75 10.3238L11.4513 9L9.5 11.1469L9.5 1L7.5 1L7.5 11.1473L5.54829 9L4.24962 10.3238L8.49981 15L12.75 10.3238Z" fill="#007596"/> </svg> </a> </div> <h1>Standard atomic weights of the elements 2021 (IUPAC Technical Report)</h1> <ul class="contributors list-unstyled mb-2"> <li class="contributors-AUTHOR mb-2"> <span class="metadataAndContributorsFont"><span class="contributor"> <span class="displayName linkAnimation">Thomas Prohaska</span> <contributor-popdown name="Thomas Prohaska" position="1" email="thomas.prohaska@unileoben.ac.at" affiliations="Montanuniversität Leoben, Leoben, Austria; National Institute of Metrology, Beijing, China" > </contributor-popdown> <a href="mailto:thomas.prohaska@unileoben.ac.at"> <img alt="EMAIL logo" src='/assets/images/db2546a9d03b905bae083962a41791e1-mail.svg' width="16" height="12" /> </a> </span><span class="comma">, </span><span class="contributor"> <span class="displayName linkAnimation">Johanna Irrgeher</span> <contributor-popdown name="Johanna Irrgeher" position="2" email="" affiliations="Montanuniversität Leoben, Leoben, Austria; University of Natural Resources and Life Sciences Vienna, Tulln, Austria; Helmholtz-Zentrum Hereon, Geesthacht, Germany; University of Calgary, Calgary, Canada" > </contributor-popdown> </span><span class="comma">, </span><span class="contributor"> <span class="displayName linkAnimation">Jacqueline Benefield</span> <contributor-popdown name="Jacqueline Benefield" position="3" email="" affiliations="U.S. Geological Survey, Reston, VA, USA" > </contributor-popdown> </span><span class="comma">, </span><span class="contributor"> <span class="displayName linkAnimation">John K. Böhlke</span> <contributor-popdown name="John K. Böhlke" position="4" email="" affiliations="U.S. Geological Survey, Reston, VA, USA" > </contributor-popdown> </span><span class="comma">, </span><span class="contributor"> <span class="displayName linkAnimation">Lesley A. Chesson</span> <contributor-popdown name="Lesley A. Chesson" position="5" email="" affiliations="PAE, contractor at the Defense POW/MIA Accounting Agency (DPAA) Laboratory, Joint Base Pearl Harbor-Hickam, HI, USA" > </contributor-popdown> </span><span class="comma">, </span><span class="contributor"> <span class="displayName linkAnimation">Tyler B. Coplen</span> <contributor-popdown name="Tyler B. Coplen" position="6" email="" affiliations="U.S. Geological Survey, Reston, VA, USA" > </contributor-popdown> </span><span class="comma">, </span><span class="contributor"> <span class="displayName linkAnimation">Tiping Ding</span> <contributor-popdown name="Tiping Ding" position="7" email="" affiliations="Institute of Mineral Resources, Chinese Academy of Geological Sciences, Beijing, China" > </contributor-popdown> </span><span class="comma">, </span><span class="contributor"> <span class="displayName linkAnimation">Philip J. H. Dunn</span> <contributor-popdown name="Philip J. H. Dunn" position="8" email="" affiliations="National Measurement Laboratory, LGC, Teddington, UK" orcid="https://orcid.org/0000-0002-3848-6187" > </contributor-popdown> <a href="https://orcid.org/0000-0002-3848-6187" target="_blank"> <img alt="ORCID logo" src='/assets/images/661a4eb80b7527d6467b6e5742778cc1-orcid.svg' width="16" height="16" /> </a> </span><span class="comma">, </span><span class="contributor"> <span class="displayName linkAnimation">Manfred Gröning</span> <contributor-popdown name="Manfred Gröning" position="9" email="" affiliations="Terrestrial Environmental Radiochemistry Laboratory, Department of Nuclear Sciences and Applications, International Atomic Energy Agency, Vienna, Austria" > </contributor-popdown> </span><span class="comma">, </span><span class="contributor"> <span class="displayName linkAnimation">Norman E. Holden</span> <contributor-popdown name="Norman E. Holden" position="10" email="" affiliations="National Nuclear Data Center, Brookhaven National Laboratory, Upton, NY, USA" > </contributor-popdown> </span><span class="comma">, </span><span class="contributor"> <span class="displayName linkAnimation">Harro A. J. Meijer</span> <contributor-popdown name="Harro A. J. Meijer" position="11" email="" affiliations="Centre for Isotope Research (CIO), University of Groningen, Groningen, The Netherlands" > </contributor-popdown> </span><span class="comma">, </span><span class="contributor"> <span class="displayName linkAnimation">Heiko Moossen</span> <contributor-popdown name="Heiko Moossen" position="12" email="" affiliations="Max Planck Institute for Biogeochemistry, Jena, Germany" > </contributor-popdown> </span><span class="comma">, </span><span class="contributor"> <span class="displayName linkAnimation">Antonio Possolo</span> <contributor-popdown name="Antonio Possolo" position="13" email="" affiliations="National Institute of Standards and Technology, Gaithersburg, MD, USA" > </contributor-popdown> </span><span class="comma">, </span><span class="contributor"> <span class="displayName linkAnimation">Yoshio Takahashi</span> <contributor-popdown name="Yoshio Takahashi" position="14" email="" affiliations="The University of Tokyo, Tokyo, Japan" > </contributor-popdown> </span><span class="comma">, </span><span class="contributor"> <span class="displayName linkAnimation">Jochen Vogl</span> <contributor-popdown name="Jochen Vogl" position="15" email="" affiliations="Bundesanstalt für Materialforschung und -prüfung (BAM), Berlin, Germany" > </contributor-popdown> </span><span class="comma">, </span><span class="contributor"> <span class="displayName linkAnimation">Thomas Walczyk</span> <contributor-popdown name="Thomas Walczyk" position="16" email="" affiliations="Department of Chemistry, National University of Singapore, Singapore, Singapore" > </contributor-popdown> </span><span class="comma">, </span><span class="contributor"> <span class="displayName linkAnimation">Jun Wang</span> <contributor-popdown name="Jun Wang" position="17" email="" affiliations="National Institute of Metrology, Beijing, China" > </contributor-popdown> </span><span class="comma">, </span><span class="contributor"> <span class="displayName linkAnimation">Michael E. Wieser</span> <contributor-popdown name="Michael E. Wieser" position="18" email="" affiliations="University of Calgary, Calgary, Canada" > </contributor-popdown> </span><span class="comma">, </span><span class="contributor"> <span class="displayName linkAnimation">Shigekazu Yoneda</span> <contributor-popdown name="Shigekazu Yoneda" position="19" email="" affiliations="National Museum of Nature and Science, Tokyo, Japan" > </contributor-popdown> </span><span class="comma">, </span><span class="contributor"> <span class="displayName linkAnimation">Xiang-Kun Zhu</span> <contributor-popdown name="Xiang-Kun Zhu" position="20" email="" affiliations="Institute of Geology, Chinese Academy of Geological Sciences, Beijing, China" > </contributor-popdown> </span> and <span class="contributor"> <span class="displayName linkAnimation">Juris Meija</span> <contributor-popdown name="Juris Meija" position="21" email="" affiliations="National Research Council of Canada, Ottawa, Canada" orcid="https://orcid.org/0000-0002-3349-5535" > </contributor-popdown> <a href="https://orcid.org/0000-0002-3349-5535" target="_blank"> <img alt="ORCID logo" src='/assets/images/661a4eb80b7527d6467b6e5742778cc1-orcid.svg' width="16" height="16" /> </a> </span></span> </li> </ul> <div class="subTitleInfoProductPage">From the journal <a class="ga_parent ga_parent_journal" href="/journal/key/pac/html">Pure and Applied Chemistry</a></div> <div class="doi"><a href="https://doi.org/10.1515/pac-2019-0603" class="linkWithoutStyle subTitleInfoProductPage ga_doi" target="_blank">https://doi.org/10.1515/pac-2019-0603</a></div> </div> <div class="d-sm-none pt-3 pb-3 border-bottom"> <div class="alternateForms d-none"> <a href="/document/doi/10.1515/pac-2019-0603/pdf?licenseType=open-access" data-doi="10.1515/pac-2019-0603" class="ga_download_button_pdf_article downloadCompletePdfArticle downloadPdf btn btn-primary fw-bold py-2 w-100 vgwort-click"> <span>Download article (PDF)</span> <span class="fa fas fa-download-button"></span> </a> </div> </div> </div> </div> <div class="d-flex align-items-center flex-wrap px-4 px-lg-2 "> <button id='citationsModalButton' type="button" class="btn btn-main-content ga_cite_this me-2" href='#citationsModal' data-bs-toggle="modal" data-bs-target="#citationsModal" data-doi="10.1515/pac-2019-0603" aria-controls='citationsModal'> Cite this </button> <button id="socialModalButton" type="button" class="btn btn-main-content ga_share_this me-2" href="#socialModal" data-bs-toggle="modal" data-bs-target="#socialModal" aria-controls="socialModal"> Share this </button> <div class="dimensions __dimensions_badge_embed__ ga_dimensions_citation me-2" data-doi="10.1515/pac-2019-0603" data-hide-zero-citations="true" data-legend="never" data-style="large_rectangle"></div> </div> <div id="div-document-progress-bar" class="sticky-top d-none"> <div class="row"> <div class="col-12"> <div class="progress progress-bar-toolbar"> <div id="document-progress-bar" class="progress-bar bg-primary" role="progressbar" aria-label="Document progress bar" aria-valuenow="0" aria-valuemin="0" aria-valuemax="100"></div> </div> </div> </div> </div> <div id="document-main-content" class='row'> <div class="container-fluid px-3 px-lg-0 py-2"> <div class="col"> <div class="d-none analyticsHolder" data-subjects='CH|CH-06|CH-12|CH-22' data-publisherCode='DEG' data-license='open-access' data-publisher='De Gruyter' data-contentName='Standard atomic weights of the elements 2021 (IUPAC Technical Report)' data-doi='10.1515/pac-2019-0603' data-parentIdentifier='PAC' data-parentName='Pure and Applied Chemistry' data-languages='en' ></div> <div id="documentContent" class="content py-2" data-doi='10.1515/pac-2019-0603' data-accessrestricted="false" data-countertype="document"> <div class="px-2"> <div id="text-container"> <div xmlns:dgdoi="http://degruyter.com/resources/doi-from-crossref" xmlns:dgpm="http://degruyter.com/resources/fetched-pubmed-id" class="contentWrapper"><div class="article" lang="en"><div class="abstract"> <h2 class="subheading">Abstract</h2> <p>Following the reviews of atomic-weight determinations and other cognate data in 2015, 2017, 2019 and 2021, the IUPAC (International Union of Pure and Applied Chemistry) Commission on Isotopic Abundances and Atomic Weights (CIAAW) reports changes of standard atomic weights. The symbol <em>A</em><sub>r</sub>°(E) was selected for standard atomic weight of an element to distinguish it from the atomic weight of an element E in a specific substance P, designated <em>A</em><sub>r</sub>(E, P). The CIAAW has changed the values of the standard atomic weights of five elements based on recent determinations of terrestrial isotopic abundances:</p> <p> <div class="table-wrap mb-4" id="j_pac-2019-0603_tab_001" position="anchor" orientation="portrait"> <table xmlns:env="http://degruyter.com/resources/metadata" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:dgror="http://degruyter.com/resources/fetched-ror-id" xmlns:m="http://degruyter.com/resources/metadata" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:tei="http://www.tei-c.org/ns/1.0" rules="groups" frame="hsides" class="content-table"> <colgroup> <col align="left"></col> <col align="left"></col> <col align="left"></col> <col align="left"></col> </colgroup> <tbody> <tr> <td style="text-align: left">Ar (argon):</td> <td style="text-align: left">from 39.948 ± 0.001</td> <td style="text-align: left">to</td> <td style="text-align: left">[39.792, 39.963]</td> </tr> <tr> <td style="text-align: left">Hf (hafnium):</td> <td style="text-align: left">from 178.49 ± 0.02</td> <td style="text-align: left">to</td> <td style="text-align: left">178.486 ± 0.006</td> </tr> <tr> <td style="text-align: left">Ir (iridium):</td> <td style="text-align: left">from 192.217 ± 0.003</td> <td style="text-align: left">to</td> <td style="text-align: left">192.217 ± 0.002</td> </tr> <tr> <td style="text-align: left">Pb (lead):</td> <td style="text-align: left">from 207.2 ± 0.1</td> <td style="text-align: left">to</td> <td style="text-align: left">[206.14, 207.94]</td> </tr> <tr> <td style="text-align: left">Yb (ytterbium):</td> <td style="text-align: left">from 173.054 ± 0.005</td> <td style="text-align: left">to</td> <td style="text-align: left">173.045 ± 0.010</td> </tr> </tbody> </table> </div> </p> <p>The standard atomic weight of argon and lead have changed to an interval to reflect that the natural variation in isotopic composition exceeds the measurement uncertainty of <em>A</em><sub>r</sub>(Ar) and <em>A</em><sub>r</sub>(Pb) in a specific substance. The standard atomic weights and/or the uncertainties of fourteen elements have been changed based on the Atomic Mass Evaluations 2016 and 2020 accomplished under the auspices of the International Union of Pure and Applied Physics (IUPAP). <em>A</em><sub>r</sub>° of Ho, Tb, Tm and Y were changed in 2017 and again updated in 2021:</p> <p> <div class="table-wrap mb-4" id="j_pac-2019-0603_tab_002" position="anchor" orientation="portrait"> <table xmlns:env="http://degruyter.com/resources/metadata" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:dgror="http://degruyter.com/resources/fetched-ror-id" xmlns:m="http://degruyter.com/resources/metadata" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:tei="http://www.tei-c.org/ns/1.0" rules="groups" frame="hsides" class="content-table"> <colgroup> <col align="left"></col> <col align="left"></col> <col align="left"></col> <col align="left"></col> </colgroup> <tbody> <tr> <td style="text-align: left">Al (aluminium), 2017:</td> <td style="text-align: left">from 26.981 5385 ± 0.000 0007</td> <td style="text-align: left">to</td> <td style="text-align: left">26.981 5384 ± 0.000 0003</td> </tr> <tr> <td style="text-align: left">Au (gold), 2017:</td> <td style="text-align: left">from 196.966 569 ± 0.000 005</td> <td style="text-align: left">to</td> <td style="text-align: left">196.966 570 ± 0.000 004</td> </tr> <tr> <td style="text-align: left">Co (cobalt), 2017:</td> <td style="text-align: left">from 58.933 194 ± 0.000 004</td> <td style="text-align: left">to</td> <td style="text-align: left">58.933 194 ± 0.000 003</td> </tr> <tr> <td style="text-align: left">F (fluorine), 2021:</td> <td style="text-align: left">from 18.998 403 163 ± 0.000 000 006</td> <td style="text-align: left">to</td> <td style="text-align: left">18.998 403 162 ± 0.000 000 005</td> </tr> <tr> <td style="text-align: left">(Ho (holmium), 2017:</td> <td style="text-align: left">from 164.930 33 ± 0.000 02</td> <td style="text-align: left">to</td> <td style="text-align: left">164.930 328 ± 0.000 007)</td> </tr> <tr> <td style="text-align: left">Ho (holmium), 2021:</td> <td style="text-align: left">from 164.930 328 ± 0.000 007</td> <td style="text-align: left">to</td> <td style="text-align: left">164.930 329 ± 0.000 005</td> </tr> <tr> <td style="text-align: left">Mn (manganese), 2017:</td> <td style="text-align: left">from 54.938 044 ± 0.000 003</td> <td style="text-align: left">to</td> <td style="text-align: left">54.938 043 ± 0.000 002</td> </tr> <tr> <td style="text-align: left">Nb (niobium), 2017:</td> <td style="text-align: left">from 92.906 37 ± 0.000 02</td> <td style="text-align: left">to</td> <td style="text-align: left">92.906 37 ± 0.000 01</td> </tr> <tr> <td style="text-align: left">Pa (protactinium), 2017:</td> <td style="text-align: left">from 231.035 88 ± 0.000 02</td> <td style="text-align: left">to</td> <td style="text-align: left">231.035 88 ± 0.000 01</td> </tr> <tr> <td style="text-align: left">Pr (praseodymium), 2017:</td> <td style="text-align: left">from 140.907 66 ± 0.000 02</td> <td style="text-align: left">to</td> <td style="text-align: left">140.907 66 ± 0.000 01</td> </tr> <tr> <td style="text-align: left">Rh (rhodium), 2017:</td> <td style="text-align: left">from 102.905 50 ± 0.000 02</td> <td style="text-align: left">to</td> <td style="text-align: left">102.905 49 ± 0.000 02</td> </tr> <tr> <td style="text-align: left">Sc (scandium), 2021:</td> <td style="text-align: left">from 44.955 908 ± 0.000 005</td> <td style="text-align: left">to</td> <td style="text-align: left">44.955 907 ± 0.000 004</td> </tr> <tr> <td style="text-align: left">(Tb (terbium), 2017:</td> <td style="text-align: left">from 158.925 35 ± 0.000 02</td> <td style="text-align: left">to</td> <td style="text-align: left">158.925 354 ± 0.000 008)</td> </tr> <tr> <td style="text-align: left">Tb (terbium), 2021:</td> <td style="text-align: left">from 158.925 354 ± 0.000 008</td> <td style="text-align: left">to</td> <td style="text-align: left">158.925 354 ± 0.000 007</td> </tr> <tr> <td style="text-align: left">(Tm (thulium), 2017:</td> <td style="text-align: left">from 168.934 22 ± 0.000 02</td> <td style="text-align: left">to</td> <td style="text-align: left">168.934 218 ± 0.000 006)</td> </tr> <tr> <td style="text-align: left">Tm (thulium), 2021:</td> <td style="text-align: left">from 168.934 218 ± 0.000 006</td> <td style="text-align: left">to</td> <td style="text-align: left">168.934 219 ± 0.000 005</td> </tr> <tr> <td style="text-align: left">(Y (yttrium), 2017:</td> <td style="text-align: left">from 88.905 84 ± 0.000 02</td> <td style="text-align: left">to</td> <td style="text-align: left">88.905 84 ± 0.000 01)</td> </tr> <tr> <td style="text-align: left">Y (yttrium), 2021:</td> <td style="text-align: left">from 88.905 84 ± 0.000 01</td> <td style="text-align: left">to</td> <td style="text-align: left">88.905 838 ± 0.000 002</td> </tr> </tbody> </table> </div> </p> </div><div class="keywords mb-3">Keywords: <a href="/search?query=keywordValues%3A%28%22Argon%22%29%20AND%20journalKey%3A%28%22PAC%22%29&documentVisibility=all&documentTypeFacet=article" class="ga_keyword">Argon</a>; <a href="/search?query=keywordValues%3A%28%22ciaaw.org%22%29%20AND%20journalKey%3A%28%22PAC%22%29&documentVisibility=all&documentTypeFacet=article" class="ga_keyword">ciaaw.org</a>; <a href="/search?query=keywordValues%3A%28%22hafnium%22%29%20AND%20journalKey%3A%28%22PAC%22%29&documentVisibility=all&documentTypeFacet=article" class="ga_keyword">hafnium</a>; <a href="/search?query=keywordValues%3A%28%22iridium%22%29%20AND%20journalKey%3A%28%22PAC%22%29&documentVisibility=all&documentTypeFacet=article" class="ga_keyword">iridium</a>; <a href="/search?query=keywordValues%3A%28%22lead%22%29%20AND%20journalKey%3A%28%22PAC%22%29&documentVisibility=all&documentTypeFacet=article" class="ga_keyword">lead</a>; <a href="/search?query=keywordValues%3A%28%22LSVEC%22%29%20AND%20journalKey%3A%28%22PAC%22%29&documentVisibility=all&documentTypeFacet=article" class="ga_keyword">LSVEC</a>; <a href="/search?query=keywordValues%3A%28%22ytterbium%22%29%20AND%20journalKey%3A%28%22PAC%22%29&documentVisibility=all&documentTypeFacet=article" class="ga_keyword">ytterbium</a></div><div class="body"> <section id="j_pac-2019-0603_s_001"> <h2 class="subheading">1 Introduction</h2> <p>The Commission on Isotopic Abundances and Atomic Weights (CIAAW, hereafter called the Commission) convenes biennially to evaluate recent developments in isotope measurement science and deliberate on related matters. The Commission met in Tulln (Austria) from 3 to 4 August 2015, Groningen (The Netherlands) from 16 to 18 September 2017, in Berlin (Germany) from 3 to 4 July 2019 and in a virtual meeting 27 to 28 July 2021 under the chairmanship of Juris Meija. At these meetings, the Commission reviewed recommendations of its Subcommittees (Subcommittee on Natural Assessment of Fundamental Understanding of Isotopes, Subcommittee on Isotopic Abundance Measurements, and Subcommittee on Stable Isotope Reference Material Assessment). The recommendations included modifying the definition of normal materials and changing the expression of uncertainty of standard atomic weights and isotopic composition values. Additionally, the Commission reviewed the recommendations to change the standard atomic weights of Yb (2015), Ar (2017), Ir (2017), Hf (2019), and Pb (2021) based on the review of published data on the isotopic composition of these elements, as well as the standard atomic weights of 14 other elements (2017, 2021) based on the Atomic Mass Evaluation 2016 and 2020 under the auspices of the International Union of Pure and Applied Physics (Al, Au, Co, F, Ho, Mn, Nb, Pa, Pr, Rh, Sc, Tb, Tm, Y).</p> <p>The creation of an international commission assigned with the evaluation of the atomic weights dates back to 1897, when soon-to-be Nobel laureate Hermann Emil Fischer proposed the creation of a working committee to report on atomic weights. The working committee consisted of Wilhelm Ostwald (University of Leipzig), Karl Seubert (University of Hanover), and Hans H. Landolt (Berlin University), serving as chair. This committee published its first report in 1898, wherein it suggested the desirability of an International Committee on Atomic Weights. To this end, on 30 March 1899 the invitation was sent to national scientific organizations worldwide to appoint delegates to the International Committee on Atomic Weights, which was formed in 1899, and consisted of 56 delegates from 11 countries. Dated Tables of Atomic Weights published by the Commission refer to our best knowledge of the elements in natural terrestrial sources and have been published since 1902 [<a href="#j_pac-2019-0603_ref_001" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_001" data-bs-toggle="tooltip" title="1. F. W. Clarke, T. E. Thorpe, K. Seubert. Z. Anorg. Chem.33, 241 (1902).10.1002/zaac.19030330132Search in Google Scholar">1</a>]. The previous Commission report was published following its 2013 meeting [<a href="#j_pac-2019-0603_ref_002" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_002" data-bs-toggle="tooltip" title="2. J. Meija, T. B. Coplen, M. Berglund, W. A. Brand, P. De Bièvre, M. Gröning, N. E. Holden, J. Irrgeher, R. D. Loss, T. Walczyk, T. Prohaska. Pure Appl. Chem.88, 265 (2016).10.1515/pac-2015-0305Search in Google Scholar">2</a>] and the current report is a result of the deliberations during the 2015, 2017, 2019 and 2021 meetings of the Commission. Data are also provided in IUPAC news releases [<a href="#j_pac-2019-0603_ref_003" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_003" data-bs-toggle="tooltip" title="3. J. Meija. Chem. Int.37(5), 26 (2015), https://doi.org/10.1515/ci-2015-0512, https://iupac.org/standard-atomic-weight-of-ytterbium-revised/, (accessed Jan 21, 2021).Search in Google Scholar">3</a>], [<a href="#j_pac-2019-0603_ref_004" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_004" data-bs-toggle="tooltip" title="4. J. Meija. Chem. Int.40(4), 23 (2018), https://doi.org/10.1515/ci-2018-0409, https://iupac.org/standard-atomic-weights-of-14-chemical-elements-revised/, (accessed Jan 23, 2021).Search in Google Scholar">4</a>], [<a href="#j_pac-2019-0603_ref_005" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_005" data-bs-toggle="tooltip" title="5. J. Meija. Chem. Int.42(2), 31 (2020), https://doi.org/10.1515/ci-2020-0222, https://iupac.org/standard-atomic-weight-of-hafnium-revised/, (accessed Jan 23, 2021).Search in Google Scholar">5</a>] and the IUPAC Periodic Table of the Elements and Isotopes (IPTEI) for the Education Community [<a href="#j_pac-2019-0603_ref_006" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_006" data-bs-toggle="tooltip" title="6. N. E. Holden, T. B. Coplen, J. K. Böhlke, L. V. Tarbox, J. Benefield, J. R. de Laeter, P. G. Mahaffy, G. O’Connor, E. Roth, D. H. Tepper, T. Walczyk, M. E. Wieser, S. Yoneda. Pure Appl. Chem.90, 1833 (2018).10.1515/pac-2015-0703Search in Google Scholar">6</a>]. Additionally, data are reported on the CIAAW website (<a href="http://ciaaw.org" class="link link-external" rel="noopener noreferrer nofollow" target="_blank">ciaaw.org</a>), and the online periodic table of the elements and isotopes is provided by the IUPAC [<a href="#j_pac-2019-0603_ref_007" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_007" data-bs-toggle="tooltip" title="7. 
 CIAAW. Commission on Isotopic Abundances and Atomic Weights, https://ciaaw.org (accessed Jan 25, 2021).Search in Google Scholar">7</a>, <a href="#j_pac-2019-0603_ref_008" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_008" data-bs-toggle="tooltip" title="8. 
 Isotopes Matter, https://www.isotopesmatter.com (accessed Jan 25, 2021).Search in Google Scholar">8</a>].</p> <p>Because standard atomic weights of elements in normal terrestrial materials and chemicals are widely used in science and the uncertainties associated with these values are not well understood, a technical report provides guidelines for the use of standard atomic weights [<a href="#j_pac-2019-0603_ref_009" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_009" data-bs-toggle="tooltip" title="9. A. M. H. van der Veen, J. Meija, A. Possolo, D. B. Hibbert. Pure Appl. Chem.93, 629 (2021).10.1515/pac-2017-1002Search in Google Scholar">9</a>].</p> </section> <section id="j_pac-2019-0603_s_002"> <h2 class="subheading">2 General terms</h2> <p>The <strong>atomic mass</strong>, <strong><em>m</em></strong><sub><strong>a</strong></sub><strong>(</strong><sup><strong><em>i</em></strong></sup><strong>E)</strong>, of an unbound neutral atom of a nuclide <sup><em>i</em></sup>E of an element E with the mass number <em>i</em> is defined as “rest mass of an atom in its ground state” [<a href="#j_pac-2019-0603_ref_010" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_010" data-bs-toggle="tooltip" title="10. 
 IUPAC. Compendium of Chemical Terminology, Blackwell Scientific Publications, Oxford, 2nd ed. (1997), (the “Gold Book”). Compiled by A. D. McNaught and A. Wilkinson, 0-9678550-9-8, Online version (2019-) created by S. J. ChalkURL, https://doi.org/10.1351/goldbook (accessed Jan 24, 2021).Search in Google Scholar">10</a>]. The commonly used unit is the unified atomic mass unit or dalton [<a href="#j_pac-2019-0603_ref_010" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_010" data-bs-toggle="tooltip" title="10. 
 IUPAC. Compendium of Chemical Terminology, Blackwell Scientific Publications, Oxford, 2nd ed. (1997), (the “Gold Book”). Compiled by A. D. McNaught and A. Wilkinson, 0-9678550-9-8, Online version (2019-) created by S. J. ChalkURL, https://doi.org/10.1351/goldbook (accessed Jan 24, 2021).Search in Google Scholar">10</a>]. The 2020 Atomic Mass Evaluation report (AME2020) is a recent authoritative document containing the nuclide masses and their uncertainties using least-squares adjustments of all evaluated and accepted experimental data [<a href="#j_pac-2019-0603_ref_011" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_011" data-bs-toggle="tooltip" title="11. M. Wang, W. J. Huang, F. G. Kondev, G. Audi, S. Naimi. Chin. Phys. C45, 030003 (2021).10.1088/1674-1137/abddafSearch in Google Scholar">11</a>]. These masses are used for calculating the atomic weights and standard atomic weights of the elements.</p> <p>The <strong>atomic weight</strong> (this term is further used in the manuscript) or <strong>relative atomic mass</strong>, <em>A</em><sub>r</sub>(<sup><em>i</em></sup>E), <strong>of an atom</strong> (the unbound neutral nuclide) <sup><em>i</em></sup>E of element E is defined as the “ratio of the mass of the atom to the unified atomic mass unit” [<a href="#j_pac-2019-0603_ref_010" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_010" data-bs-toggle="tooltip" title="10. 
 IUPAC. Compendium of Chemical Terminology, Blackwell Scientific Publications, Oxford, 2nd ed. (1997), (the “Gold Book”). Compiled by A. D. McNaught and A. Wilkinson, 0-9678550-9-8, Online version (2019-) created by S. J. ChalkURL, https://doi.org/10.1351/goldbook (accessed Jan 24, 2021).Search in Google Scholar">10</a>]. The atomic mass constant <em>m</em><sub>u</sub> is equal to the dalton, Da, or the unified atomic mass unit, u, and is defined in terms of the mass of the carbon-12 atom: <em>m</em><sub>u</sub> = 1 u = 1 Da = <em>m</em><sub>a</sub>(<sup>12</sup>C)/12 [<a href="#j_pac-2019-0603_ref_012" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_012" data-bs-toggle="tooltip" title="12. 
 Quantities, Units, and Symbols in Physical Chemistry, IUPAC Green Book, prepared for publication by E.R. Cohen, T. Cvitas, J.G Frey, B. Holmstrom, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, H. Strauss, M. Takami, and A.J. Thor, RSC Publishing, 3rd ed. (2007).Search in Google Scholar">12</a>]. Thus, the atomic weight is a quantity of dimension 1 (dimensionless quantity):</p><div class="formula" id="j_pac-2019-0603_eq_001"><span class="label">(1)</span><span class="alternatives"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">r</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mmultiscripts><mml:mtext>E</mml:mtext><mml:mprescripts></mml:mprescripts><mml:none></mml:none><mml:mi>i</mml:mi></mml:mmultiscripts><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mmultiscripts><mml:mtext>E</mml:mtext><mml:mprescripts></mml:mprescripts><mml:none></mml:none><mml:mi>i</mml:mi></mml:mmultiscripts><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mmultiscripts><mml:mtext>C</mml:mtext><mml:mprescripts></mml:mprescripts><mml:none></mml:none><mml:mn>12</mml:mn></mml:mmultiscripts><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>/</mml:mo><mml:mn>12</mml:mn></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></span></div> <p>The <strong>atomic weight of an element</strong> E, in a substance P, <em>A</em><sub>r</sub>(E, P), is the weighted average of the atomic weights <em>A</em><sub>r</sub>(<sup><em>i</em></sup>E) of the isotopes (nuclides) <sup><em>i</em></sup>E of this element in substance P:</p><div class="formula" id="j_pac-2019-0603_eq_002"><span class="label">(2)</span><span class="alternatives"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">r</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mtext>E</mml:mtext><mml:mo>,</mml:mo><mml:mtext> P</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mo>∑</mml:mo><mml:mrow><mml:mi>x</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mmultiscripts><mml:mtext>E</mml:mtext><mml:mprescripts></mml:mprescripts><mml:none></mml:none><mml:mi>i</mml:mi></mml:mmultiscripts><mml:mo>,</mml:mo><mml:mtext> P</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">r</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mmultiscripts><mml:mtext>E</mml:mtext><mml:mprescripts></mml:mprescripts><mml:none></mml:none><mml:mi>i</mml:mi></mml:mmultiscripts><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mstyle></mml:mrow></mml:math></span></div> <p>Here, <em>x</em>(<sup><em>i</em></sup>E, P) is the amount fraction of isotope <sup><em>i</em></sup>E in substance P (also called the isotopic abundance) and the summation is over all stable isotopes and radioactive isotopes having characteristic terrestrial isotopic signatures [<a href="#j_pac-2019-0603_ref_006" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_006" data-bs-toggle="tooltip" title="6. N. E. Holden, T. B. Coplen, J. K. Böhlke, L. V. Tarbox, J. Benefield, J. R. de Laeter, P. G. Mahaffy, G. O’Connor, E. Roth, D. H. Tepper, T. Walczyk, M. E. Wieser, S. Yoneda. Pure Appl. Chem.90, 1833 (2018).10.1515/pac-2015-0703Search in Google Scholar">6</a>], and they are listed in the Commissions Table of Isotopic Compositions of the Elements. The atomic weight of an element in a given substance can be determined from the knowledge of the atomic masses of the isotopes and the corresponding amount fractions of the isotopes of that element in this specific substance.</p> <p>The <strong>standard atomic weight of an element</strong>, <em>A</em><sub>r</sub>°(E), is the “recommended value of atomic weight (relative atomic mass) of an element revised biennially by the CIAAW and applicable to elements in any normal material with a high level of confidence” [<a href="#j_pac-2019-0603_ref_010" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_010" data-bs-toggle="tooltip" title="10. 
 IUPAC. Compendium of Chemical Terminology, Blackwell Scientific Publications, Oxford, 2nd ed. (1997), (the “Gold Book”). Compiled by A. D. McNaught and A. Wilkinson, 0-9678550-9-8, Online version (2019-) created by S. J. ChalkURL, https://doi.org/10.1351/goldbook (accessed Jan 24, 2021).Search in Google Scholar">10</a>]. It is comprised of either an interval (currently used for 14 elements) or a value and an uncertainty (a standard atomic-weight uncertainty), which are currently used for 71 elements (see also <a href="#j_pac-2019-0603_s_004" class="link link-sec" data-bs-target="j_pac-2019-0603_s_004">Sections 4</a> and <a href="#j_pac-2019-0603_s_006" class="link link-sec" data-bs-target="j_pac-2019-0603_s_006">6</a>). A standard atomic weight is determined from an evaluation of peer-reviewed scientific publications. The standard atomic weights are consistent with the atomic weight values calculated from the isotopic abundances listed in Column 9 of the Table of Isotopic Composition of the Elements [<a href="#j_pac-2019-0603_ref_013" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_013" data-bs-toggle="tooltip" title="13. J. Meija, T. B. Coplen, M. Berglund, W. A. Brand, P. De Bièvre, M. Gröning, N. E. Holden, J. Irrgeher, R. D. Loss, T. Walczyk, T. Prohaska. Pure Appl. Chem.88, 293 (2016).10.1515/pac-2015-0503Search in Google Scholar">13</a>].</p> <p>Based on the report of the Subcommittee on Natural Assessment of Fundamental Understanding of Isotopes of the Commission, a <strong>normal material</strong> is a material which originates from a terrestrial source that satisfies the following definition [<a href="#j_pac-2019-0603_ref_014" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_014" data-bs-toggle="tooltip" title="14. T. B. Coplen, N. E. Holden, M. E. Wieser, J. K. Böhlke. Pure Appl. Chem.90, 1221 (2018).10.1515/pac-2017-0301Search in Google Scholar">14</a>]:</p><blockquote class="blockquote mx-4 disp-quote"><p>Normal materials include all substances, except (1) those subjected to substantial deliberate, undisclosed, or inadvertent artificial isotopic modification, (2) extraterrestrial materials, and (3) isotopically anomalous specimens, such as natural nuclear reactor products from Oklo (Gabon) or other unique occurrences.</p></blockquote> <p>In contrast to the previous definition (see [<a href="#j_pac-2019-0603_ref_014" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_014" data-bs-toggle="tooltip" title="14. T. B. Coplen, N. E. Holden, M. E. Wieser, J. K. Böhlke. Pure Appl. Chem.90, 1221 (2018).10.1515/pac-2017-0301Search in Google Scholar">14</a>]), this revised definition recognizes the fact that the variation of the atomic weight of some elements is caused by isotopic fractionation processes that operate on many different time scales. It also reintroduces the exclusion of extraterrestrial materials from the determination of standard atomic weights. The new definition is more inclusive than some earlier versions with respect to naturally occurring materials having nucleogenic and radiogenic isotopic variation, as exemplified by argon [<a href="#j_pac-2019-0603_ref_015" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_015" data-bs-toggle="tooltip" title="15. J. K. Böhlke. Pure Appl. Chem.86, 1421 (2014).10.1515/pac-2013-0918Search in Google Scholar">15</a>] and lead [<a href="#j_pac-2019-0603_ref_016" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_016" data-bs-toggle="tooltip" title="16. X. K. Zhu, J. Benefield, T. B. Coplen, Z. Gao, N. Holden. Pure Appl. Chem.93, 155 (2021).10.1515/pac-2018-0916Search in Google Scholar">16</a>].</p> </section> <section id="j_pac-2019-0603_s_003"> <h2 class="subheading">3 Categorization of elements by their atomic weight and isotopic composition variations</h2> <p>Because variation in isotopic composition of an element impacts its atomic weight, the Commission has undertaken a periodic assessment of variations of isotopic compositions in the published literature, both through its Subcommittees and through IUPAC projects [<a href="#j_pac-2019-0603_ref_017" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_017" data-bs-toggle="tooltip" title="17. T. B. Coplen, N. E. Holden, T. Ding, H. A. J. Meijer, J. Vogl, X. Zhu. Rapid Commun. Mass Spectrom., e8864 (2020).Search in Google Scholar">17</a>]. All known elements can be categorized according to the following constraints on their standard atomic weights:<ol type="1" class="list " id="j_pac-2019-0603_list_001" list-type="order"><li class="listItem" id="j_pac-2019-0603_li_001"><div class="listItem-contents"><p>Elements with no stable isotope and with no characteristic terrestrial isotopic composition in normal materials (<em>e.g.</em> radon). No standard atomic weight can be determined and no value is provided in the Table of Standard Atomic Weights for these elements. These elements have a white background of the entries in the IUPAC Periodic Table of the Elements and Isotopes [<a href="#j_pac-2019-0603_ref_006" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_006" data-bs-toggle="tooltip" title="6. N. E. Holden, T. B. Coplen, J. K. Böhlke, L. V. Tarbox, J. Benefield, J. R. de Laeter, P. G. Mahaffy, G. O’Connor, E. Roth, D. H. Tepper, T. Walczyk, M. E. Wieser, S. Yoneda. Pure Appl. Chem.90, 1833 (2018).10.1515/pac-2015-0703Search in Google Scholar">6</a>].</p></div></li><li class="listItem" id="j_pac-2019-0603_li_002"><div class="listItem-contents"><p>Elements whose standard atomic weights are determined by only one isotope (<em>e.g.</em> sodium). The standard atomic weight is derived from the atomic weight of its stable or long-lived isotope (<em>e.g.</em> bismuth or protactinium). These elements have a blue background of the entries in the IUPAC Periodic Table of the Elements and Isotopes [<a href="#j_pac-2019-0603_ref_006" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_006" data-bs-toggle="tooltip" title="6. N. E. Holden, T. B. Coplen, J. K. Böhlke, L. V. Tarbox, J. Benefield, J. R. de Laeter, P. G. Mahaffy, G. O’Connor, E. Roth, D. H. Tepper, T. Walczyk, M. E. Wieser, S. Yoneda. Pure Appl. Chem.90, 1833 (2018).10.1515/pac-2015-0703Search in Google Scholar">6</a>].</p></div></li><li class="listItem" id="j_pac-2019-0603_li_003"><div class="listItem-contents"><p>Elements whose standard atomic weights are determined by more than one isotope are shown on the IUPAC Periodic Table of the Elements and Isotopes with a yellow background of the entries [<a href="#j_pac-2019-0603_ref_006" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_006" data-bs-toggle="tooltip" title="6. N. E. Holden, T. B. Coplen, J. K. Böhlke, L. V. Tarbox, J. Benefield, J. R. de Laeter, P. G. Mahaffy, G. O’Connor, E. Roth, D. H. Tepper, T. Walczyk, M. E. Wieser, S. Yoneda. Pure Appl. Chem.90, 1833 (2018).10.1515/pac-2015-0703Search in Google Scholar">6</a>]. They are subdivided into three subcategories:<ol type="1" class="list " id="j_pac-2019-0603_list_002" list-type="simple"><li class="listItem ps-2" id="j_pac-2019-0603_li_004" style="list-style-type:'a.';"><div class="listItem-contents"><p>Elements that have no documented evidence of variation in the atomic weight for normal materials, or elements that have not been evaluated for variation in isotopic composition by an IUPAC project (<em>e.g.</em> indium). Elements in this subcategory may enter category 3b as more accurate isotopic abundance measurements are published.</p></div></li><li class="listItem ps-2" id="j_pac-2019-0603_li_005" style="list-style-type:'b.';"><div class="listItem-contents"><p>Elements that have known variations in the atomic weight in normal materials, but these variations do not exceed the evaluated measurement uncertainty of the atomic weight derived from the “best measurement” of the isotopic abundances of an element (<em>e.g.</em> molybdenum). Elements in this subcategory can advance to category 3c or 4 as measurement results improve.</p></div></li><li class="listItem ps-2" id="j_pac-2019-0603_li_006" style="list-style-type:'c.';"><div class="listItem-contents"><p>Elements that have known variations in the atomic weight in normal materials that exceed the uncertainty of the atomic weight derived from a “best measurement” of isotopic abundances, but are not yet assigned a standard atomic weight interval by the Commission (<em>e.g.</em> copper). Elements in this subcategory can advance to category 4 as the Commission completes evaluations and assigns standard atomic weight intervals. The Commission uses the footnote “r” to identify elements in this subcategory for which the standard atomic weight uncertainty has been expanded to account for known atomic weight variability.</p></div></li></ol></p></div></li><li class="listItem" id="j_pac-2019-0603_li_007"><div class="listItem-contents"><p>Elements with two or more isotopes having known variations in the atomic weight in normal materials that exceed the uncertainty of the atomic weight derived from a “best measurement” of isotopic abundances and having upper and lower atomic weight bounds determined by the Commission from evaluated, peer reviewed, published data (<em>e.g.</em> hydrogen). These elements have a pink background for each element cell on the IUPAC Periodic Table of the Elements and Isotopes [<a href="#j_pac-2019-0603_ref_006" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_006" data-bs-toggle="tooltip" title="6. N. E. Holden, T. B. Coplen, J. K. Böhlke, L. V. Tarbox, J. Benefield, J. R. de Laeter, P. G. Mahaffy, G. O’Connor, E. Roth, D. H. Tepper, T. Walczyk, M. E. Wieser, S. Yoneda. Pure Appl. Chem.90, 1833 (2018).10.1515/pac-2015-0703Search in Google Scholar">6</a>].</p></div></li></ol></p> <p>The Commission uses the footnote “g” to identify chemical elements for which the reported standard atomic weight and its associated uncertainty do not include all known variations (see definition of the term “normal” material above). For example, some elements are anomalously enriched in fissionogenic or nucleogenic isotopes at the Oklo natural nuclear reactor site in Gabon, Africa, and the atomic weights in those materials are not included in the determination of the standard atomic weight (exception (3) in the definition of the term “normal” material). For elements in categories 3 and 4, the Commission uses the footnote “m” to identify those elements for which the standard atomic weight and its associated uncertainty in commercially available material do not include variations due to undisclosed or inadvertent isotopic fractionation (exception (1) in the definition of the term “normal” material). Minor periodic changes to the standard atomic weight values and uncertainties result from improved measurements of the atomic masses, and these changes primarily affect category-2 elements.</p> </section> <section id="j_pac-2019-0603_s_004"> <h2 class="subheading">4 Standard atomic weight intervals</h2> <p>Many elements can be found on Earth in a variety of substances with substantially different genesis. As a consequence, the atomic weights of some elements vary significantly depending on the origin and age of these substances. In 2009 the Commission introduced the interval notation for those elements whose atomic weights vary significantly in nature, exceeding the measurement uncertainty of <em>A</em><sub>r</sub> for an element in a specific substance, and where such variations have been well documented. “Well-documented” is to be understood as reported in a peer-reviewed publication on the matter of natural variations of an element. The interval notation does not alter the meaning of the standard atomic weight, nor does it constitute “a new definition” of standard atomic weights. Rather, it is an alternative means for expressing the uncertainty of this quantity. Writing the standard atomic weight of carbon as <em>A</em><sub>r</sub>°(C) = [12.0096, 12.0116] indicates that at the current status of knowledge its atomic weight in any normal material will be greater than or equal to 12.0096 and will be less than or equal to 12.0116 [<a href="#j_pac-2019-0603_ref_018" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_018" data-bs-toggle="tooltip" title="18. M. E. Wieser, T. B. Coplen. Pure Appl. Chem.83, 359 (2011). http://dx.doi.org/10.1351/PAC-REP-10-09-1410.1351/PAC-REP-10-09-14Search in Google Scholar">18</a>]. Thus, the standard atomic weight is represented by an interval, which encompasses atomic weights of normal materials. It is important to note that no particular value in the interval should be regarded as more representative than any other and that the natural variability of the isotopic composition is the dominant source of the uncertainty expressed by the interval. To date, the Commission provides the standard atomic weight as an interval for 14 elements: argon, boron, bromine, carbon, chlorine, hydrogen, lead, lithium, magnesium, nitrogen, oxygen, silicon, sulfur, and thallium [<a href="#j_pac-2019-0603_ref_004" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_004" data-bs-toggle="tooltip" title="4. J. Meija. Chem. Int.40(4), 23 (2018), https://doi.org/10.1515/ci-2018-0409, https://iupac.org/standard-atomic-weights-of-14-chemical-elements-revised/, (accessed Jan 23, 2021).Search in Google Scholar">4</a>, <a href="#j_pac-2019-0603_ref_018" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_018" data-bs-toggle="tooltip" title="18. M. E. Wieser, T. B. Coplen. Pure Appl. Chem.83, 359 (2011). http://dx.doi.org/10.1351/PAC-REP-10-09-1410.1351/PAC-REP-10-09-14Search in Google Scholar">18</a>, <a href="#j_pac-2019-0603_ref_019" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_019" data-bs-toggle="tooltip" title="19. M. E. Wieser, N. E. Holden, T. B. Coplen, J. K. Böhlke, M. Berglund, W. A. Brand, P. De Bièvre, M. Gröning, R. D. Loss, J. Meija, T. Hirata, T. Prohaska, R. Schoenberg, G. O’Connor, T. Walczyk, S. Yoneda, X. Zhu. Pure Appl. Chem.85, 1047 (2013).10.1351/PAC-REP-13-03-02Search in Google Scholar">19</a>].</p> <p>For some elements, atomic weights calculated from published variations in isotopic compositions of different substances can span intervals which are large compared to measurement uncertainties of atomic weights, which are determined in a specific substance P, <em>A</em><sub>r</sub>(E, P). For example, the atomic weight of carbon in normal materials spans the interval from 12.0096 to 12.0116 and leads to a standard atomic weight of <em>A</em><sub>r</sub>°(C) = [12.0096, 12.0116]. In contrast, the uncertainty of the atomic weight calculated from the isotopic abundance of carbon in a specific material (NBS 19 calcium carbonate) is approximately 50 times smaller [<a href="#j_pac-2019-0603_ref_018" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_018" data-bs-toggle="tooltip" title="18. M. E. Wieser, T. B. Coplen. Pure Appl. Chem.83, 359 (2011). http://dx.doi.org/10.1351/PAC-REP-10-09-1410.1351/PAC-REP-10-09-14Search in Google Scholar">18</a>]: <em>A</em><sub>r</sub>(C, NBS 19) = 12.011 12 ± 0.000 02 (<em>k</em> = 2). The atomic weight of boron in normal materials spans an interval from 10.806 to 10.821 (standard atomic weight <em>A</em><sub>r</sub>°(B) = [10.806, 10.821]). In contrast, the atomic weight of boron in a specific substance can be measured down to the fourth decimal place. For example, the atomic weight of boron in the NIST reference material of boric acid SRM 951a [<a href="#j_pac-2019-0603_ref_020" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_020" data-bs-toggle="tooltip" title="20. 
 NIST. NBS 951a certificate (2011), https://www-s.nist.gov/srmors/certificates/951a.pdf (accessed Jan 25, 2021).Search in Google Scholar">20</a>] is <em>A</em><sub>r</sub>(B, SRM 951a) = 10.8118 ± 0.0001 (<em>k</em> = 2).</p> <p>This span of atomic weight values in normal materials is termed “interval”. The interval [<em>a</em>, <em>b</em>] is the set of values <em>x</em> for which <em>a</em> ≤ <em>x</em> ≤ <em>b</em>, where <em>a</em> < <em>b</em> and where <em>a</em> and <em>b</em> are the lower and upper bounds of the interval [<a href="#j_pac-2019-0603_ref_021" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_021" data-bs-toggle="tooltip" title="21. 
 Joint Committee for Guides in Metrology. International vocabulary of metrology – Basic and general concepts and associated terms (VIM)International Bureau of Weights and Measures (BIPM), Sèvres, France, 3rd ed. (2012), URLBIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP and OIML, JCGM 200:2012 (2008 version with minor corrections), https://www.bipm.org/en/committees/jc/jcgm/publications (accessed Jan 25, 2021).Search in Google Scholar">21</a>]. Lower bounds are rounded downward and upper bounds are rounded upward. Each bound is a considered decision by the Commission determined from the lowest and highest atomic weight based on professional evaluation and judgment of published, peer reviewed data with consideration of measurement uncertainties.</p> <p>The range of an interval [<em>a</em>, <em>b</em>] is the difference between its upper and lower bounds, that is <em>b</em> − <em>a</em> [<a href="#j_pac-2019-0603_ref_021" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_021" data-bs-toggle="tooltip" title="21. 
 Joint Committee for Guides in Metrology. International vocabulary of metrology – Basic and general concepts and associated terms (VIM)International Bureau of Weights and Measures (BIPM), Sèvres, France, 3rd ed. (2012), URLBIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP and OIML, JCGM 200:2012 (2008 version with minor corrections), https://www.bipm.org/en/committees/jc/jcgm/publications (accessed Jan 25, 2021).Search in Google Scholar">21</a>]. Thus, the range of the standard atomic weight interval of carbon is calculated as 12.0116 − 12.0096 = 0.0020. The interval does not imply any statistical distribution of atomic weight values between the lower and upper bound (<em>e.g.</em> the arithmetic mean of <em>a</em> and <em>b</em> is not necessarily the most likely value). Similarly, the interval does not convey a simple statistical representation of uncertainty. The probability density function may differ case by case, due to varying sources and their proportions may need to be considered. If no additional information is available or utilized, the probability density function associated with the standard atomic weights can be considered as uniform (rectangular). Information on the range of standard atomic weights expressed in interval notation is available for argon in <a href="#j_pac-2019-0603_fig_003" class="link link-fig" data-bs-target="j_pac-2019-0603_fig_003">Figs. 3</a><a href="#j_pac-2019-0603_fig_004" class="link link-fig" data-bs-target="j_pac-2019-0603_fig_004"></a>–<a href="#j_pac-2019-0603_fig_005" class="link link-fig" data-bs-target="j_pac-2019-0603_fig_005">5</a>, for lead in <a href="#j_pac-2019-0603_fig_006" class="link link-fig" data-bs-target="j_pac-2019-0603_fig_006">Figs. 6</a><a href="#j_pac-2019-0603_fig_007" class="link link-fig" data-bs-target="j_pac-2019-0603_fig_007"></a><a href="#j_pac-2019-0603_fig_008" class="link link-fig" data-bs-target="j_pac-2019-0603_fig_008"></a>–<a href="#j_pac-2019-0603_fig_009" class="link link-fig" data-bs-target="j_pac-2019-0603_fig_009">9</a> and for the other 12 such elements in the papers of Meija et al. [<a href="#j_pac-2019-0603_ref_002" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_002" data-bs-toggle="tooltip" title="2. J. Meija, T. B. Coplen, M. Berglund, W. A. Brand, P. De Bièvre, M. Gröning, N. E. Holden, J. Irrgeher, R. D. Loss, T. Walczyk, T. Prohaska. Pure Appl. Chem.88, 265 (2016).10.1515/pac-2015-0305Search in Google Scholar">2</a>] and Coplen and Shrestha [<a href="#j_pac-2019-0603_ref_022" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_022" data-bs-toggle="tooltip" title="22. T. B. Coplen, Y. Shrestha. Pure Appl. Chem.88, 1203 (2016).10.1515/pac-2016-0302Search in Google Scholar">22</a>], [<a href="#j_pac-2019-0603_ref_023" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_023" data-bs-toggle="tooltip" title="23. T. B. Coplen, Y. Shrestha. Pure Appl. Chem.91, 173 (2019).Search in Google Scholar">23</a>], [<a href="#j_pac-2019-0603_ref_024" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_024" data-bs-toggle="tooltip" title="24. T. B. Coplen, Y. Shrestha. Tables and Charts for Isotope-Abundance Variations and Atomic Weights of Selected Elements: 2016 (Ver. 1.1, May 2018), U.S. Geological Survey Data Release (2018).10.1515/pac-2018-0504Search in Google Scholar">24</a>]. These ranges have to be interpreted as uniform probability density functions because there is no information available on the relative probability of encountering any specific value in the ranges displayed.</p> </section> <section id="j_pac-2019-0603_s_005"> <h2 class="subheading">5 Isotope delta measurements</h2> <p>Commonly, isotope delta measurements are the basis for the determination of the atomic weight [<a href="#j_pac-2019-0603_ref_025" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_025" data-bs-toggle="tooltip" title="25. T. B. Coplen. Rapid Commun. Mass Spectrom. 2011 25, 2538 (2011).10.1002/rcm.5129Search in Google Scholar
 PubMed
 ">25</a>], [<a href="#j_pac-2019-0603_ref_026" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_026" data-bs-toggle="tooltip" title="26. R. Gonfiantini. Nature271, 534 (1978).10.1038/271534a0Search in Google Scholar">26</a>], [<a href="#j_pac-2019-0603_ref_027" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_027" data-bs-toggle="tooltip" title="27. T. B. Coplen, J. K. Böhlke, P. De Bievre, T. Ding, N. E. Holden, J. A. Hopple, H. R. Krouse, A. Lamberty, H. S. Peiser, K. Revesz, S. E. Rieder, K. J. R. Rosman, E. Roth, P. D. P. Taylor, R. D. Vockejr., Y. K. Xiao. Pure Appl. Chem.74, 1987 (2002).10.1351/pac200274101987Search in Google Scholar">27</a>]. The isotope delta is obtained from the isotope number ratio <em>R</em>(<sup><em>i</em>/<em>j</em></sup>E) in a substance P:</p><div class="formula" id="j_pac-2019-0603_eq_003"><span class="label">(3)</span><span class="alternatives"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mml:mrow><mml:mi>R</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mmultiscripts><mml:mtext>E</mml:mtext><mml:mprescripts></mml:mprescripts><mml:none></mml:none><mml:mrow><mml:mi>i</mml:mi><mml:mo>/</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:mmultiscripts><mml:mo>,</mml:mo><mml:mtext> P</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mrow><mml:mi>N</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mmultiscripts><mml:mtext>E</mml:mtext><mml:mprescripts></mml:mprescripts><mml:none></mml:none><mml:mi>i</mml:mi></mml:mmultiscripts><mml:mo>,</mml:mo><mml:mtext> P</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mi>N</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mmultiscripts><mml:mtext>E</mml:mtext><mml:mprescripts></mml:mprescripts><mml:none></mml:none><mml:mi>j</mml:mi></mml:mmultiscripts><mml:mo>,</mml:mo><mml:mtext> P</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mrow></mml:math></span></div><p>where <em>N</em>(<sup><em>i</em></sup>E, P) and <em>N</em>(<sup><em>j</em></sup>E, P) are the numbers of atoms of each isotope, and <sup><em>i</em></sup>E denotes in general the higher (superscript <em>i</em>) and <sup><em>j</em></sup>E the lower (superscript <em>j</em>) atomic mass numbers of the isotopes of the chemical element E in substance P. <sup><em>j</em></sup>E represents the reference isotope which is not necessarily the isotope with the lowest atomic mass number. The isotope delta value (symbol <em>δ</em>), also called the relative isotope ratio difference, is a differential measurement obtained from isotope number ratios of substance P and a scale represented by a reference material [<a href="#j_pac-2019-0603_ref_028" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_028" data-bs-toggle="tooltip" title="28. W. A. Brand, T. B. Coplen, J. Vogl, M. Rosner, T. Prohaska. Pure Appl. Chem. 2014 86, 425 (2014).10.1515/pac-2013-1023Search in Google Scholar">28</a>].</p><div class="formula" id="j_pac-2019-0603_eq_004"><span class="label">(4)</span><span class="alternatives"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mml:mrow><mml:msub><mml:mi>δ</mml:mi><mml:mtext>Ref</mml:mtext></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mmultiscripts><mml:mtext>E</mml:mtext><mml:mprescripts></mml:mprescripts><mml:none></mml:none><mml:mrow><mml:mi>i</mml:mi><mml:mo>/</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:mmultiscripts><mml:mo>,</mml:mo><mml:mtext> P</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mrow><mml:mi>R</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mmultiscripts><mml:mtext>E</mml:mtext><mml:mprescripts></mml:mprescripts><mml:none></mml:none><mml:mrow><mml:mi>i</mml:mi><mml:mo>/</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:mmultiscripts><mml:mo>,</mml:mo><mml:mtext> P</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mi>R</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mmultiscripts><mml:mtext>E</mml:mtext><mml:mprescripts></mml:mprescripts><mml:none></mml:none><mml:mrow><mml:mi>i</mml:mi><mml:mo>/</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:mmultiscripts><mml:mo>,</mml:mo><mml:mtext> Ref</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:mrow></mml:mrow></mml:math></span></div> <p>Isotope delta values are small numbers and therefore frequently presented in multiples of 10<sup>−3</sup> or per mil (symbol ‰). To match an isotope delta scale of an element to an isotope amount scale, a substance is needed whose isotopic abundances and whose isotope delta value is also well known relative to the isotope delta scale. Commonly this substance is an isotopic reference material [<a href="#j_pac-2019-0603_ref_028" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_028" data-bs-toggle="tooltip" title="28. W. A. Brand, T. B. Coplen, J. Vogl, M. Rosner, T. Prohaska. Pure Appl. Chem. 2014 86, 425 (2014).10.1515/pac-2013-1023Search in Google Scholar">28</a>] that has served as the “best measurement” material for the determination of isotopic abundances [<a href="#j_pac-2019-0603_ref_013" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_013" data-bs-toggle="tooltip" title="13. J. Meija, T. B. Coplen, M. Berglund, W. A. Brand, P. De Bièvre, M. Gröning, N. E. Holden, J. Irrgeher, R. D. Loss, T. Walczyk, T. Prohaska. Pure Appl. Chem.88, 293 (2016).10.1515/pac-2015-0503Search in Google Scholar">13</a>]. For carbon, as an example, the <em>x</em>(<sup>13</sup>C) abundance scale is matched to the <em>δ</em><sub>VPDB</sub>(<sup>13/12</sup>C) scale through the measurement of the isotopic reference material NBS 19 (calcium carbonate), which has been assigned the consensus <em>δ</em><sub>VPDB</sub>(<sup>13/12</sup>C, NBS 19) value of +1.95 ‰. The carbon isotope number ratio of NBS 19 was measured by Zhang and Li [<a href="#j_pac-2019-0603_ref_029" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_029" data-bs-toggle="tooltip" title="29. Q. Zhang, W. Li. Chin. Sci. Bull.35, 290 (1990).10.1360/csb1990-35-22-1759-xSearch in Google Scholar">29</a>] and is <em>R</em>(<sup>13/12</sup>C, NBS 19) = 0.011 202 ± 0.000 028. This measurement serves as the “best measurement” of a single terrestrial source [<a href="#j_pac-2019-0603_ref_013" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_013" data-bs-toggle="tooltip" title="13. J. Meija, T. B. Coplen, M. Berglund, W. A. Brand, P. De Bièvre, M. Gröning, N. E. Holden, J. Irrgeher, R. D. Loss, T. Walczyk, T. Prohaska. Pure Appl. Chem.88, 293 (2016).10.1515/pac-2015-0503Search in Google Scholar">13</a>]. Vienna Peedee belemnite (VPDB) is the zero point on the carbon isotope-delta scale and therefore <em>δ</em><sub>VPDB</sub>(<sup>13/12</sup>C, VPDB) = 0. Since 1 ‰ = 0.001, it follows:</p><div class="formula" id="j_pac-2019-0603_eq_005"><span class="label">(5)</span><span class="alternatives"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mml:mrow><mml:mi>R</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mmultiscripts><mml:mtext>C</mml:mtext><mml:mprescripts></mml:mprescripts><mml:none></mml:none><mml:mrow><mml:mn>13</mml:mn><mml:mo>/</mml:mo><mml:mn>12</mml:mn></mml:mrow></mml:mmultiscripts><mml:mo>,</mml:mo><mml:mtext> VPDB</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mrow><mml:mn>0.011</mml:mn><mml:mtext> </mml:mtext><mml:mn>202</mml:mn></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>1.95</mml:mn><mml:mo>×</mml:mo><mml:mn>0.001</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mn>0.011</mml:mn><mml:mtext> </mml:mtext><mml:mn>180</mml:mn></mml:mrow></mml:math></span></div> <p>Therefore, ignoring the uncertainty, the relation between carbon isotope delta values (<em>δ</em>) and <sup>13</sup>C amount fractions (<em>x</em>) of a material P is:</p><div class="formula" id="j_pac-2019-0603_eq_006"><span class="label">(6)</span><span class="alternatives"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mml:mrow><mml:mi>x</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mmultiscripts><mml:mtext>C</mml:mtext><mml:mprescripts></mml:mprescripts><mml:none></mml:none><mml:mn>13</mml:mn></mml:mmultiscripts><mml:mo>,</mml:mo><mml:mtext> P</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mi>R</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mmultiscripts><mml:mtext>C</mml:mtext><mml:mprescripts></mml:mprescripts><mml:none></mml:none><mml:mrow><mml:mn>13</mml:mn><mml:mo>/</mml:mo><mml:mn>12</mml:mn></mml:mrow></mml:mmultiscripts><mml:mo>,</mml:mo><mml:mtext> VPDB</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>×</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:msub><mml:mi>δ</mml:mi><mml:mtext>VPDB</mml:mtext></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mmultiscripts><mml:mtext>C</mml:mtext><mml:mprescripts></mml:mprescripts><mml:none></mml:none><mml:mn>13</mml:mn></mml:mmultiscripts><mml:mo>,</mml:mo><mml:mtext> P</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></span></div> <p>For example, consider the material with the lowest measured isotopic abundance of carbon-13, crocetane (2,6,11,15-tetramethylhexadecane), produced at cold seeps of the eastern Aleutian subduction zone. The material has a published <em>δ</em><sub>VPDB</sub>(<sup>13</sup>C) value of (−130.3 ± 0.3) ‰ (<em>k</em> = 1) [<a href="#j_pac-2019-0603_ref_030" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_030" data-bs-toggle="tooltip" title="30. M. Elvert, E. Suess, J. Greinert, M. J. Whiticar. Org. Geochem.31, 1175 (2000).10.1016/S0146-6380(00)00111-XSearch in Google Scholar">30</a>]. The isotopic abundance of carbon-13 of this specimen is determined using <a href="#j_pac-2019-0603_eq_005" class="link link-disp-formula" data-bs-target="j_pac-2019-0603_eq_005">eq. (5)</a> and is <em>x</em>(<sup>13</sup>C) = 0.009 630 ± 0.000 003. Likewise, the isotopic abundance of carbon-12 is <em>x</em>(<sup>12</sup>C) = 1 − <em>x</em>(<sup>13</sup>C). The atomic weight of carbon in this specimen is determined using the carbon isotope number ratio of VPDB as calculated in <a href="#j_pac-2019-0603_eq_002" class="link link-disp-formula" data-bs-target="j_pac-2019-0603_eq_002">eq. (2)</a>, the isotopic abundances of carbon-12 and carbon-13, and the atomic weight values of carbon-12 and carbon-13 isotopes (<em>A</em><sub>r</sub>(<sup>12</sup>C) = 12 and <em>A</em><sub>r</sub>(<sup>13</sup>C) = 13.003 354 835 ± 0.000 000 002). For this material, <em>A</em><sub>r</sub>(C) = 12.009 662 ± 0.000 003 (<em>k</em> = 1).</p> <p>If material P is the normal material having the lowest atomic weight of element E, then the lower bound is <em>A</em><sub>r</sub>(E, P) − <em>U</em>[<em>A</em><sub>r</sub>(E, P)] where <em>U</em>[<em>A</em><sub>r</sub>(E, P)] is the expanded uncertainty that incorporates the uncertainty in the measurement of the delta value of material P and the uncertainty in relating the delta-value scale to the isotope amount fraction and atomic weight scales. The latter is the uncertainty in relating an isotope delta scale to an atomic weight scale.</p> <p>The expanded uncertainty <em>U</em> is obtained by multiplying the combined standard uncertainty of a quantity <em>y</em>, <em>u</em><sub>c</sub>(<em>y</em>), by a coverage factor <em>k</em>, <em>U</em> = <em>k</em> × <em>u</em><sub>c</sub>(<em>y</em>). The value of <em>k</em> varies between elements and is at least 2.</p> </section> <section id="j_pac-2019-0603_s_006"> <h2 class="subheading">6 Uncertainty of standard atomic weights</h2> <p>Uncertainties of standard atomic weights are estimated by the Commission through evaluation of the relevant published literature. The atomic weight of any element is expected to be within the interval indicated by the uncertainty of the standard atomic weight (or within the explicit standard atomic weight interval for 14 elements) at great certitude for normal materials which have been investigated at the time of the compilation of the data. The values are the result of a decision reached after consideration of the relevant data [<a href="#j_pac-2019-0603_ref_031" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_031" data-bs-toggle="tooltip" title="31. T. B. Coplen, H. S. Peiser. Pure Appl. Chem.70, 237 (1998).10.1351/pac199870010237Search in Google Scholar">31</a>, <a href="#j_pac-2019-0603_ref_032" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_032" data-bs-toggle="tooltip" title="32. J. Meija, A. Possolo. Metrologia54, 229 (2017).10.1088/1681-7575/aa634dSearch in Google Scholar">32</a>], which includes the quality of the measurements [<a href="#j_pac-2019-0603_ref_002" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_002" data-bs-toggle="tooltip" title="2. J. Meija, T. B. Coplen, M. Berglund, W. A. Brand, P. De Bièvre, M. Gröning, N. E. Holden, J. Irrgeher, R. D. Loss, T. Walczyk, T. Prohaska. Pure Appl. Chem.88, 265 (2016).10.1515/pac-2015-0305Search in Google Scholar">2</a>, <a href="#j_pac-2019-0603_ref_033" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_033" data-bs-toggle="tooltip" title="33. M. E. Wieser, M. Berglund. Pure Appl. Chem.81, 2131 (2009).10.1351/PAC-REP-09-08-03Search in Google Scholar">33</a>]. The intervals, in which the atomic weight values of elements in normal materials are expected, are either given by the reported <em>A</em><sub>r</sub>°(E) values and their uncertainties <em>U</em>[<em>A</em><sub>r</sub>°(E)] (<a href="#j_pac-2019-0603_tab_003" class="link link-table" data-bs-target="j_pac-2019-0603_tab_003">Table 1</a>, columns 4 and 5) or as explicit intervals (for 14 elements, see <a href="#j_pac-2019-0603_tab_003" class="link link-table" data-bs-target="j_pac-2019-0603_tab_003">Table 1</a>, column 4).</p> <div class="table-wrap mb-4" id="j_pac-2019-0603_tab_003" position="float"> <div class="table-label h3">Table 1:</div> <div class="caption mb-3"> <p> <strong>Standard atomic weights of the elements (Table of Standard Atomic Weights 2021).</strong> Standard atomic weights, <em>A</em><sub>r</sub>°(E), are listed in increasing atomic number (column 3) with the element name (column 1) and element symbol (column 2). Commonly used alternative spellings for aluminium and caesium are aluminum and cesium. Standard atomic weights are given as single values (column 4) with uncertainties (column 5) or as intervals (column 4). Standard atomic weights are expressed as the ratio of the average mass of the atom to the unified atomic mass unit. The stated uncertainties (column 5) are uncertainties for normal materials and include evaluations of measurement uncertainty and natural variability. The footnotes (column 6) to this table elaborate the types of variations that may occur for individual elements and that may lie outside the values listed.</p> <p>Standard atomic weight intervals are given in column 4 with the symbol [a, b] to denote the set of atomic weight values in normal materials for 14 elements (<em>a</em> ≤ <em>A</em><sub>r</sub>(E) ≤ <em>b</em> for element E). For these 14 elements, abridged atomic weight values including a +/− value corresponding to the smallest symmetric number in order to cover the standard atomic weight interval are given in column 7 and 8. These values replace the previously published conventional atomic weights, except that for hydrogen, which was 1.008, and has been expanded to 1.0080 to provide a lower value in column 8.</p> </div> <table xmlns:env="http://degruyter.com/resources/metadata" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:dgror="http://degruyter.com/resources/fetched-ror-id" xmlns:m="http://degruyter.com/resources/metadata" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:tei="http://www.tei-c.org/ns/1.0" rules="groups" frame="hsides" class="content-table"> <colgroup> <col align="left"></col> <col align="left"></col> <col align="right"></col> <col align="right"></col> <col align="left"></col> <col align="left"></col> <col align="right"></col> <col align="right"></col> </colgroup> <thead> <tr> <th style="text-align: left">1</th> <th style="text-align: left">2</th> <th style="text-align: right">3</th> <th style="text-align: right">4</th> <th style="text-align: left">5</th> <th style="text-align: left">6</th> <th style="text-align: right">7</th> <th style="text-align: right">8</th> </tr> <tr> <th style="text-align: left" colspan="8"> <hr></hr> </th> </tr> <tr> <th style="text-align: left" rowspan="2">Element</th> <th style="text-align: left" rowspan="2">Symbol</th> <th style="text-align: right" rowspan="2">Atomic number</th> <th style="text-align: right" colspan="2">Standard atomic weight</th> <th style="text-align: left" rowspan="2">Foot-note</th> <th style="text-align: left" colspan="2">Abridged standard atomic weight</th> </tr> <tr> <th style="text-align: left">Value</th> <th style="text-align: left">Uncertainty<sup>b</sup></th> <th style="text-align: right">Value</th> <th style="text-align: right">+/−</th> </tr> </thead> <tbody> <tr> <td style="text-align: left">hydrogen</td> <td style="text-align: left">H</td> <td style="text-align: right">1</td> <td style="text-align: right">[1.007 84, 1.008 11]</td> <td style="text-align: left"></td> <td style="text-align: left">m</td> <td style="text-align: right">1.0080</td> <td style="text-align: right">0.0002</td> </tr> <tr> <td style="text-align: left">helium</td> <td style="text-align: left">He</td> <td style="text-align: right">2</td> <td style="text-align: right">4.002 602</td> <td style="text-align: left">0.000 002</td> <td style="text-align: left">g r</td> <td style="text-align: right">4.0026</td> <td style="text-align: right">0.0001</td> </tr> <tr> <td style="text-align: left">lithium</td> <td style="text-align: left">Li</td> <td style="text-align: right">3</td> <td style="text-align: right">[6.938, 6.997]</td> <td style="text-align: left"></td> <td style="text-align: left">m</td> <td style="text-align: right">6.94</td> <td style="text-align: right">0.06</td> </tr> <tr> <td style="text-align: left">beryllium</td> <td style="text-align: left">Be</td> <td style="text-align: right">4</td> <td style="text-align: right">9.012 1831</td> <td style="text-align: left">0.000 0005</td> <td style="text-align: left"></td> <td style="text-align: right">9.0122</td> <td style="text-align: right">0.0001</td> </tr> <tr> <td style="text-align: left">boron</td> <td style="text-align: left">B</td> <td style="text-align: right">5</td> <td style="text-align: right">[10.806, 10.821]</td> <td style="text-align: left"></td> <td style="text-align: left">m</td> <td style="text-align: right">10.81</td> <td style="text-align: right">0.02</td> </tr> <tr> <td style="text-align: left">carbon</td> <td style="text-align: left">C</td> <td style="text-align: right">6</td> <td style="text-align: right">[12.0096, 12.0116]</td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">12.011</td> <td style="text-align: right">0.002</td> </tr> <tr> <td style="text-align: left">nitrogen</td> <td style="text-align: left">N</td> <td style="text-align: right">7</td> <td style="text-align: right">[14.006 43, 14.007 28]</td> <td style="text-align: left"></td> <td style="text-align: left">m</td> <td style="text-align: right">14.007</td> <td style="text-align: right">0.001</td> </tr> <tr> <td style="text-align: left">oxygen</td> <td style="text-align: left">O</td> <td style="text-align: right">8</td> <td style="text-align: right">[15.999 03, 15.999 77]</td> <td style="text-align: left"></td> <td style="text-align: left">m</td> <td style="text-align: right">15.999</td> <td style="text-align: right">0.001</td> </tr> <tr> <td style="text-align: left">fluorine</td> <td style="text-align: left">F</td> <td style="text-align: right">9</td> <td style="text-align: right">18.998 403 162</td> <td style="text-align: left">0.000 000 005</td> <td style="text-align: left"></td> <td style="text-align: right">18.998</td> <td style="text-align: right">0.001</td> </tr> <tr> <td style="text-align: left">neon</td> <td style="text-align: left">Ne</td> <td style="text-align: right">10</td> <td style="text-align: right">20.1797</td> <td style="text-align: left">0.0006</td> <td style="text-align: left">g m</td> <td style="text-align: right">20.180</td> <td style="text-align: right">0.001</td> </tr> <tr> <td style="text-align: left">sodium</td> <td style="text-align: left">Na</td> <td style="text-align: right">11</td> <td style="text-align: right">22.989 769 28</td> <td style="text-align: left">0.000 000 02</td> <td style="text-align: left"></td> <td style="text-align: right">22.990</td> <td style="text-align: right">0.001</td> </tr> <tr> <td style="text-align: left">magnesium</td> <td style="text-align: left">Mg</td> <td style="text-align: right">12</td> <td style="text-align: right">[24.304, 24.307]</td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">24.305</td> <td style="text-align: right">0.002</td> </tr> <tr> <td style="text-align: left">aluminium</td> <td style="text-align: left">Al</td> <td style="text-align: right">13</td> <td style="text-align: right">26.981 5384</td> <td style="text-align: left">0.000 0003</td> <td style="text-align: left"></td> <td style="text-align: right">26.982</td> <td style="text-align: right">0.001</td> </tr> <tr> <td style="text-align: left">silicon</td> <td style="text-align: left">Si</td> <td style="text-align: right">14</td> <td style="text-align: right">[28.084, 28.086]</td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">28.085</td> <td style="text-align: right">0.001</td> </tr> <tr> <td style="text-align: left">phosphorus</td> <td style="text-align: left">P</td> <td style="text-align: right">15</td> <td style="text-align: right">30.973 761 998</td> <td style="text-align: left">0.000 000 005</td> <td style="text-align: left"></td> <td style="text-align: right">30.974</td> <td style="text-align: right">0.001</td> </tr> <tr> <td style="text-align: left">sulfur</td> <td style="text-align: left">S</td> <td style="text-align: right">16</td> <td style="text-align: right">[32.059, 32.076]</td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">32.06</td> <td style="text-align: right">0.02</td> </tr> <tr> <td style="text-align: left">chlorine</td> <td style="text-align: left">Cl</td> <td style="text-align: right">17</td> <td style="text-align: right">[35.446, 35.457]</td> <td style="text-align: left"></td> <td style="text-align: left">m</td> <td style="text-align: right">35.45</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">argon</td> <td style="text-align: left">Ar</td> <td style="text-align: right">18</td> <td style="text-align: right">[39.792, 39.963]</td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">39.95</td> <td style="text-align: right">0.16</td> </tr> <tr> <td style="text-align: left">potassium</td> <td style="text-align: left">K</td> <td style="text-align: right">19</td> <td style="text-align: right">39.0983</td> <td style="text-align: left">0.0001</td> <td style="text-align: left"></td> <td style="text-align: right">39.098</td> <td style="text-align: right">0.001</td> </tr> <tr> <td style="text-align: left">calcium</td> <td style="text-align: left">Ca</td> <td style="text-align: right">20</td> <td style="text-align: right">40.078</td> <td style="text-align: left">0.004</td> <td style="text-align: left">g</td> <td style="text-align: right">40.078</td> <td style="text-align: right">0.004</td> </tr> <tr> <td style="text-align: left">scandium</td> <td style="text-align: left">Sc</td> <td style="text-align: right">21</td> <td style="text-align: right">44.955 907</td> <td style="text-align: left">0.000 004</td> <td style="text-align: left"></td> <td style="text-align: right">44.956</td> <td style="text-align: right">0.001</td> </tr> <tr> <td style="text-align: left">titanium</td> <td style="text-align: left">Ti</td> <td style="text-align: right">22</td> <td style="text-align: right">47.867</td> <td style="text-align: left">0.001</td> <td style="text-align: left"></td> <td style="text-align: right">47.867</td> <td style="text-align: right">0.001</td> </tr> <tr> <td style="text-align: left">vanadium</td> <td style="text-align: left">V</td> <td style="text-align: right">23</td> <td style="text-align: right">50.9415</td> <td style="text-align: left">0.0001</td> <td style="text-align: left"></td> <td style="text-align: right">50.942</td> <td style="text-align: right">0.001</td> </tr> <tr> <td style="text-align: left">chromium</td> <td style="text-align: left">Cr</td> <td style="text-align: right">24</td> <td style="text-align: right">51.9961</td> <td style="text-align: left">0.0006</td> <td style="text-align: left"></td> <td style="text-align: right">51.996</td> <td style="text-align: right">0.001</td> </tr> <tr> <td style="text-align: left">manganese</td> <td style="text-align: left">Mn</td> <td style="text-align: right">25</td> <td style="text-align: right">54.938 043</td> <td style="text-align: left">0.000 002</td> <td style="text-align: left"></td> <td style="text-align: right">54.938</td> <td style="text-align: right">0.001</td> </tr> <tr> <td style="text-align: left">iron</td> <td style="text-align: left">Fe</td> <td style="text-align: right">26</td> <td style="text-align: right">55.845</td> <td style="text-align: left">0.002</td> <td style="text-align: left"></td> <td style="text-align: right">55.845</td> <td style="text-align: right">0.002</td> </tr> <tr> <td style="text-align: left">cobalt</td> <td style="text-align: left">Co</td> <td style="text-align: right">27</td> <td style="text-align: right">58.933 194</td> <td style="text-align: left">0.000 003</td> <td style="text-align: left"></td> <td style="text-align: right">58.933</td> <td style="text-align: right">0.001</td> </tr> <tr> <td style="text-align: left">nickel</td> <td style="text-align: left">Ni</td> <td style="text-align: right">28</td> <td style="text-align: right">58.6934</td> <td style="text-align: left">0.0004</td> <td style="text-align: left">r</td> <td style="text-align: right">58.693</td> <td style="text-align: right">0.001</td> </tr> <tr> <td style="text-align: left">copper</td> <td style="text-align: left">Cu</td> <td style="text-align: right">29</td> <td style="text-align: right">63.546</td> <td style="text-align: left">0.003</td> <td style="text-align: left">r</td> <td style="text-align: right">63.546</td> <td style="text-align: right">0.003</td> </tr> <tr> <td style="text-align: left">zinc</td> <td style="text-align: left">Zn</td> <td style="text-align: right">30</td> <td style="text-align: right">65.38</td> <td style="text-align: left">0.02</td> <td style="text-align: left">r</td> <td style="text-align: right">65.38</td> <td style="text-align: right">0.02</td> </tr> <tr> <td style="text-align: left">gallium</td> <td style="text-align: left">Ga</td> <td style="text-align: right">31</td> <td style="text-align: right">69.723</td> <td style="text-align: left">0.001</td> <td style="text-align: left"></td> <td style="text-align: right">69.723</td> <td style="text-align: right">0.001</td> </tr> <tr> <td style="text-align: left">germanium</td> <td style="text-align: left">Ge</td> <td style="text-align: right">32</td> <td style="text-align: right">72.630</td> <td style="text-align: left">0.008</td> <td style="text-align: left"></td> <td style="text-align: right">72.630</td> <td style="text-align: right">0.008</td> </tr> <tr> <td style="text-align: left">arsenic</td> <td style="text-align: left">As</td> <td style="text-align: right">33</td> <td style="text-align: right">74.921 595</td> <td style="text-align: left">0.000 006</td> <td style="text-align: left"></td> <td style="text-align: right">74.922</td> <td style="text-align: right">0.001</td> </tr> <tr> <td style="text-align: left">selenium</td> <td style="text-align: left">Se</td> <td style="text-align: right">34</td> <td style="text-align: right">78.971</td> <td style="text-align: left">0.008</td> <td style="text-align: left">r</td> <td style="text-align: right">78.971</td> <td style="text-align: right">0.008</td> </tr> <tr> <td style="text-align: left">bromine</td> <td style="text-align: left">Br</td> <td style="text-align: right">35</td> <td style="text-align: right">[79.901, 79.907]</td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">79.904</td> <td style="text-align: right">0.003</td> </tr> <tr> <td style="text-align: left">krypton</td> <td style="text-align: left">Kr</td> <td style="text-align: right">36</td> <td style="text-align: right">83.798</td> <td style="text-align: left">0.002</td> <td style="text-align: left">g m</td> <td style="text-align: right">83.798</td> <td style="text-align: right">0.002</td> </tr> <tr> <td style="text-align: left">rubidium</td> <td style="text-align: left">Rb</td> <td style="text-align: right">37</td> <td style="text-align: right">85.4678</td> <td style="text-align: left">0.0003</td> <td style="text-align: left">g</td> <td style="text-align: right">85.468</td> <td style="text-align: right">0.001</td> </tr> <tr> <td style="text-align: left">strontium</td> <td style="text-align: left">Sr</td> <td style="text-align: right">38</td> <td style="text-align: right">87.62</td> <td style="text-align: left">0.01</td> <td style="text-align: left">g r</td> <td style="text-align: right">87.62</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">yttrium</td> <td style="text-align: left">Y</td> <td style="text-align: right">39</td> <td style="text-align: right">88.905 838</td> <td style="text-align: left">0.000 002</td> <td style="text-align: left"></td> <td style="text-align: right">88.906</td> <td style="text-align: right">0.001</td> </tr> <tr> <td style="text-align: left">zirconium</td> <td style="text-align: left">Zr</td> <td style="text-align: right">40</td> <td style="text-align: right">91.224</td> <td style="text-align: left">0.002</td> <td style="text-align: left">g</td> <td style="text-align: right">91.224</td> <td style="text-align: right">0.002</td> </tr> <tr> <td style="text-align: left">niobium</td> <td style="text-align: left">Nb</td> <td style="text-align: right">41</td> <td style="text-align: right">92.906 37</td> <td style="text-align: left">0.000 01</td> <td style="text-align: left"></td> <td style="text-align: right">92.906</td> <td style="text-align: right">0.001</td> </tr> <tr> <td style="text-align: left">molybdenum</td> <td style="text-align: left">Mo</td> <td style="text-align: right">42</td> <td style="text-align: right">95.95</td> <td style="text-align: left">0.01</td> <td style="text-align: left">g</td> <td style="text-align: right">95.95</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">technetium<sup>a</sup></td> <td style="text-align: left">Tc</td> <td style="text-align: right">43</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">ruthenium</td> <td style="text-align: left">Ru</td> <td style="text-align: right">44</td> <td style="text-align: right">101.07</td> <td style="text-align: left">0.02</td> <td style="text-align: left">g</td> <td style="text-align: right">101.07</td> <td style="text-align: right">0.02</td> </tr> <tr> <td style="text-align: left">rhodium</td> <td style="text-align: left">Rh</td> <td style="text-align: right">45</td> <td style="text-align: right">102.905 49</td> <td style="text-align: left">0.000 02</td> <td style="text-align: left"></td> <td style="text-align: right">102.91</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">palladium</td> <td style="text-align: left">Pd</td> <td style="text-align: right">46</td> <td style="text-align: right">106.42</td> <td style="text-align: left">0.01</td> <td style="text-align: left">g</td> <td style="text-align: right">106.42</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">silver</td> <td style="text-align: left">Ag</td> <td style="text-align: right">47</td> <td style="text-align: right">107.8682</td> <td style="text-align: left">0.0002</td> <td style="text-align: left">g</td> <td style="text-align: right">107.87</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">cadmium</td> <td style="text-align: left">Cd</td> <td style="text-align: right">48</td> <td style="text-align: right">112.414</td> <td style="text-align: left">0.004</td> <td style="text-align: left">g</td> <td style="text-align: right">112.41</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">indium</td> <td style="text-align: left">In</td> <td style="text-align: right">49</td> <td style="text-align: right">114.818</td> <td style="text-align: left">0.001</td> <td style="text-align: left"></td> <td style="text-align: right">114.82</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">tin</td> <td style="text-align: left">Sn</td> <td style="text-align: right">50</td> <td style="text-align: right">118.710</td> <td style="text-align: left">0.007</td> <td style="text-align: left">g</td> <td style="text-align: right">118.71</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">antimony</td> <td style="text-align: left">Sb</td> <td style="text-align: right">51</td> <td style="text-align: right">121.760</td> <td style="text-align: left">0.001</td> <td style="text-align: left">g</td> <td style="text-align: right">121.76</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">tellurium</td> <td style="text-align: left">Te</td> <td style="text-align: right">52</td> <td style="text-align: right">127.60</td> <td style="text-align: left">0.03</td> <td style="text-align: left">g</td> <td style="text-align: right">127.60</td> <td style="text-align: right">0.03</td> </tr> <tr> <td style="text-align: left">iodine</td> <td style="text-align: left">I</td> <td style="text-align: right">53</td> <td style="text-align: right">126.904 47</td> <td style="text-align: left">0.000 03</td> <td style="text-align: left"></td> <td style="text-align: right">126.90</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">xenon</td> <td style="text-align: left">Xe</td> <td style="text-align: right">54</td> <td style="text-align: right">131.293</td> <td style="text-align: left">0.006</td> <td style="text-align: left">g m</td> <td style="text-align: right">131.29</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">caesium</td> <td style="text-align: left">Cs</td> <td style="text-align: right">55</td> <td style="text-align: right">132.905 451 96</td> <td style="text-align: left">0.000 000 06</td> <td style="text-align: left"></td> <td style="text-align: right">132.91</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">barium</td> <td style="text-align: left">Ba</td> <td style="text-align: right">56</td> <td style="text-align: right">137.327</td> <td style="text-align: left">0.007</td> <td style="text-align: left"></td> <td style="text-align: right">137.33</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">lanthanum</td> <td style="text-align: left">La</td> <td style="text-align: right">57</td> <td style="text-align: right">138.905 47</td> <td style="text-align: left">0.000 07</td> <td style="text-align: left">g</td> <td style="text-align: right">138.91</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">cerium</td> <td style="text-align: left">Ce</td> <td style="text-align: right">58</td> <td style="text-align: right">140.116</td> <td style="text-align: left">0.001</td> <td style="text-align: left">g</td> <td style="text-align: right">140.12</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">praseodymium</td> <td style="text-align: left">Pr</td> <td style="text-align: right">59</td> <td style="text-align: right">140.907 66</td> <td style="text-align: left">0.000 01</td> <td style="text-align: left"></td> <td style="text-align: right">140.91</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">neodymium</td> <td style="text-align: left">Nd</td> <td style="text-align: right">60</td> <td style="text-align: right">144.242</td> <td style="text-align: left">0.003</td> <td style="text-align: left">g</td> <td style="text-align: right">144.24</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">promethium<sup>a</sup></td> <td style="text-align: left">Pm</td> <td style="text-align: right">61</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">samarium</td> <td style="text-align: left">Sm</td> <td style="text-align: right">62</td> <td style="text-align: right">150.36</td> <td style="text-align: left">0.02</td> <td style="text-align: left">g</td> <td style="text-align: right">150.36</td> <td style="text-align: right">0.02</td> </tr> <tr> <td style="text-align: left">europium</td> <td style="text-align: left">Eu</td> <td style="text-align: right">63</td> <td style="text-align: right">151.964</td> <td style="text-align: left">0.001</td> <td style="text-align: left">g</td> <td style="text-align: right">151.96</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">gadolinium</td> <td style="text-align: left">Gd</td> <td style="text-align: right">64</td> <td style="text-align: right">157.25</td> <td style="text-align: left">0.03</td> <td style="text-align: left">g</td> <td style="text-align: right">157.25</td> <td style="text-align: right">0.03</td> </tr> <tr> <td style="text-align: left">terbium</td> <td style="text-align: left">Tb</td> <td style="text-align: right">65</td> <td style="text-align: right">158.925 354</td> <td style="text-align: left">0.000 007</td> <td style="text-align: left"></td> <td style="text-align: right">158.93</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">dysprosium</td> <td style="text-align: left">Dy</td> <td style="text-align: right">66</td> <td style="text-align: right">162.500</td> <td style="text-align: left">0.001</td> <td style="text-align: left">g</td> <td style="text-align: right">162.50</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">holmium</td> <td style="text-align: left">Ho</td> <td style="text-align: right">67</td> <td style="text-align: right">164.930 329</td> <td style="text-align: left">0.000 005</td> <td style="text-align: left"></td> <td style="text-align: right">164.93</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">erbium</td> <td style="text-align: left">Er</td> <td style="text-align: right">68</td> <td style="text-align: right">167.259</td> <td style="text-align: left">0.003</td> <td style="text-align: left">g</td> <td style="text-align: right">167.26</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">thulium</td> <td style="text-align: left">Tm</td> <td style="text-align: right">69</td> <td style="text-align: right">168.934 219</td> <td style="text-align: left">0.000 005</td> <td style="text-align: left"></td> <td style="text-align: right">168.93</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">ytterbium</td> <td style="text-align: left">Yb</td> <td style="text-align: right">70</td> <td style="text-align: right">173.045</td> <td style="text-align: left">0.010</td> <td style="text-align: left">g</td> <td style="text-align: right">173.05</td> <td style="text-align: right">0.02</td> </tr> <tr> <td style="text-align: left">lutetium</td> <td style="text-align: left">Lu</td> <td style="text-align: right">71</td> <td style="text-align: right">174.9668</td> <td style="text-align: left">0.0001</td> <td style="text-align: left">g</td> <td style="text-align: right">174.97</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">hafnium</td> <td style="text-align: left">Hf</td> <td style="text-align: right">72</td> <td style="text-align: right">178.486</td> <td style="text-align: left">0.006</td> <td style="text-align: left">g</td> <td style="text-align: right">178.49</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">tantalum</td> <td style="text-align: left">Ta</td> <td style="text-align: right">73</td> <td style="text-align: right">180.947 88</td> <td style="text-align: left">0.000 02</td> <td style="text-align: left"></td> <td style="text-align: right">180.95</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">tungsten</td> <td style="text-align: left">W</td> <td style="text-align: right">74</td> <td style="text-align: right">183.84</td> <td style="text-align: left">0.01</td> <td style="text-align: left"></td> <td style="text-align: right">183.84</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">rhenium</td> <td style="text-align: left">Re</td> <td style="text-align: right">75</td> <td style="text-align: right">186.207</td> <td style="text-align: left">0.001</td> <td style="text-align: left"></td> <td style="text-align: right">186.21</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">osmium</td> <td style="text-align: left">Os</td> <td style="text-align: right">76</td> <td style="text-align: right">190.23</td> <td style="text-align: left">0.03</td> <td style="text-align: left">g</td> <td style="text-align: right">190.23</td> <td style="text-align: right">0.03</td> </tr> <tr> <td style="text-align: left">iridium</td> <td style="text-align: left">Ir</td> <td style="text-align: right">77</td> <td style="text-align: right">192.217</td> <td style="text-align: left">0.002</td> <td style="text-align: left"></td> <td style="text-align: right">192.22</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">platinum</td> <td style="text-align: left">Pt</td> <td style="text-align: right">78</td> <td style="text-align: right">195.084</td> <td style="text-align: left">0.009</td> <td style="text-align: left"></td> <td style="text-align: right">195.08</td> <td style="text-align: right">0.02</td> </tr> <tr> <td style="text-align: left">gold</td> <td style="text-align: left">Au</td> <td style="text-align: right">79</td> <td style="text-align: right">196.966 570</td> <td style="text-align: left">0.000 004</td> <td style="text-align: left"></td> <td style="text-align: right">196.97</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">mercury</td> <td style="text-align: left">Hg</td> <td style="text-align: right">80</td> <td style="text-align: right">200.592</td> <td style="text-align: left">0.003</td> <td style="text-align: left"></td> <td style="text-align: right">200.59</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">thallium</td> <td style="text-align: left">Tl</td> <td style="text-align: right">81</td> <td style="text-align: right">[204.382, 204.385]</td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">204.38</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">lead</td> <td style="text-align: left">Pb</td> <td style="text-align: right">82</td> <td style="text-align: right">[206.14, 207.94]</td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">207.2</td> <td style="text-align: right">1.1</td> </tr> <tr> <td style="text-align: left">bismuth<sup>a</sup></td> <td style="text-align: left">Bi</td> <td style="text-align: right">83</td> <td style="text-align: right">208.980 40</td> <td style="text-align: left">0.000 01</td> <td style="text-align: left"></td> <td style="text-align: right">208.98</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">polonium<sup>a</sup></td> <td style="text-align: left">Po</td> <td style="text-align: right">84</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">astatine<sup>a</sup></td> <td style="text-align: left">At</td> <td style="text-align: right">85</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">radon<sup>a</sup></td> <td style="text-align: left">Rn</td> <td style="text-align: right">86</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">francium<sup>a</sup></td> <td style="text-align: left">Fr</td> <td style="text-align: right">87</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">radium<sup>a</sup></td> <td style="text-align: left">Ra</td> <td style="text-align: right">88</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">actinium<sup>a</sup></td> <td style="text-align: left">Ac</td> <td style="text-align: right">89</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">thorium<sup>a</sup></td> <td style="text-align: left">Th</td> <td style="text-align: right">90</td> <td style="text-align: right">232.0377</td> <td style="text-align: left">0.0004</td> <td style="text-align: left">g</td> <td style="text-align: right">232.04</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">protactinium<sup>a</sup></td> <td style="text-align: left">Pa</td> <td style="text-align: right">91</td> <td style="text-align: right">231.035 88</td> <td style="text-align: left">0.000 01</td> <td style="text-align: left"></td> <td style="text-align: right">231.04</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">uranium<sup>a</sup></td> <td style="text-align: left">U</td> <td style="text-align: right">92</td> <td style="text-align: right">238.028 91</td> <td style="text-align: left">0.000 03</td> <td style="text-align: left">g m</td> <td style="text-align: right">238.03</td> <td style="text-align: right">0.01</td> </tr> <tr> <td style="text-align: left">neptunium<sup>a</sup></td> <td style="text-align: left">Np</td> <td style="text-align: right">93</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">plutonium<sup>a</sup></td> <td style="text-align: left">Pu</td> <td style="text-align: right">94</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">americium<sup>a</sup></td> <td style="text-align: left">Am</td> <td style="text-align: right">95</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">curium<sup>a</sup></td> <td style="text-align: left">Cm</td> <td style="text-align: right">96</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">berkelium<sup>a</sup></td> <td style="text-align: left">Bk</td> <td style="text-align: right">97</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">californium<sup>a</sup></td> <td style="text-align: left">Cf</td> <td style="text-align: right">98</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">einsteinium<sup>a</sup></td> <td style="text-align: left">Es</td> <td style="text-align: right">99</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">fermium<sup>a</sup></td> <td style="text-align: left">Fm</td> <td style="text-align: right">100</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">mendelevium<sup>a</sup></td> <td style="text-align: left">Md</td> <td style="text-align: right">101</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">nobelium<sup>a</sup></td> <td style="text-align: left">No</td> <td style="text-align: right">102</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">lawrencium<sup>a</sup></td> <td style="text-align: left">Lr</td> <td style="text-align: right">103</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">rutherfordium<sup>a</sup></td> <td style="text-align: left">Rf</td> <td style="text-align: right">104</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">dubnium<sup>a</sup></td> <td style="text-align: left">Db</td> <td style="text-align: right">105</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">seaborgium<sup>a</sup></td> <td style="text-align: left">Sg</td> <td style="text-align: right">106</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">bohrium<sup>a</sup></td> <td style="text-align: left">Bh</td> <td style="text-align: right">107</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">hassium<sup>a</sup></td> <td style="text-align: left">Hs</td> <td style="text-align: right">108</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">meitnerium<sup>a</sup></td> <td style="text-align: left">Mt</td> <td style="text-align: right">109</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">darmstadtium<sup>a</sup></td> <td style="text-align: left">Ds</td> <td style="text-align: right">110</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">roentgenium<sup>a</sup></td> <td style="text-align: left">Rg</td> <td style="text-align: right">111</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">copernicium<sup>a</sup></td> <td style="text-align: left">Cn</td> <td style="text-align: right">112</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">nihonium<sup>a</sup></td> <td style="text-align: left">Nh</td> <td style="text-align: right">113</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">flerovium<sup>a</sup></td> <td style="text-align: left">Fl</td> <td style="text-align: right">114</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">moscovium<sup>a</sup></td> <td style="text-align: left">Mc</td> <td style="text-align: right">115</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">livermorium<sup>a</sup></td> <td style="text-align: left">Lv</td> <td style="text-align: right">116</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">tennessine<sup>a</sup></td> <td style="text-align: left">Ts</td> <td style="text-align: right">117</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> <tr> <td style="text-align: left">oganesson<sup>a</sup></td> <td style="text-align: left">Og</td> <td style="text-align: right">118</td> <td style="text-align: right"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right"></td> <td style="text-align: right"></td> </tr> </tbody> </table> <div class="table-wrap-foot"> <ol class="footnote-group" id=""> <li class="footnote footnote-noLabel" id="j_pac-2019-0603_fn_002" fn-type="other"> <p> <sup>a</sup>Element has no stable isotope, only radioactive isotopes. For four elements (Bi, Th, Pa, and U) a standard atomic weight is tabulated because these elements have a characteristic terrestrial isotopic composition; for the other 34 elements a standard atomic weight cannot be determined.</p> <p> <sup>b</sup> <em>A</em> <sub>r</sub>°(E) values and their uncertainties are given for normal materials and include evaluations of measurement uncertainty as well as natural variations in atomic weight where applicable. The atomic weight of a normal material is expected to lie within the lower and upper endpoints of the standard atomic weight at the current status of knowledge. If the uncertainty in <em>A</em><sub>r</sub>°(E) is considered too large for a user’s purpose for an element with measurable variations in atomic weight, a value of <em>A</em><sub>r</sub>(E) with a lower uncertainty might be obtained by measurement of an individual specimen.</p> <p>g Geological and biological materials are known in which the element has an isotopic composition outside the limits for normal material. The difference between the atomic weight of the element in such materials and that given in the table may exceed the stated uncertainty.</p> <p>m Modified isotopic compositions may be found in commercially available material because the material has been subjected to some undisclosed or inadvertent isotopic fractionation. Substantial deviations in atomic weight of the element from that given in the table can occur.</p> <p>r Range in isotopic composition of normal terrestrial material prevents a more precise standard atomic weight being given; the tabulated value and uncertainty should be applicable to normal material.</p> </li> </ol> </div> </div> <p>The reported uncertainties of the standard atomic weights, <em>U</em>[<em>A</em><sub>r</sub>°(E)], are such that the atomic weight values of normal materials are expected to lie between <em>A</em><sub>r</sub>°(E) − <em>U</em>[<em>A</em><sub>r</sub>°(E)] and <em>A</em><sub>r</sub>°(E) + <em>U</em>[<em>A</em><sub>r</sub>°(E)] with great certitude. Hence, for example, the standard atomic weight of iridium, 192.217 ± 0.002, indicates that atomic weight values of iridium in normal materials are expected to be equal to or higher than 192.215 and equal to or lower than 192.219.</p> <p>The uniform distribution on these intervals (specified either as the uncertainty <em>U</em>[<em>A</em><sub>r</sub>°(E)] or as an explicit interval) can be used as a simple and practically useful model for a complex reality [<a href="#j_pac-2019-0603_ref_034" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_034" data-bs-toggle="tooltip" title="34. A. Possolo, A. M. H. van der Veen, J. Meija, D. B. Hibbert. Pure Appl. Chem.90, 395 (2018).10.1515/pac-2016-0402Search in Google Scholar">34</a>]. The interpretation of a standard atomic weight in terms of a uniform distribution, concentrated either on the given interval itself or on the interval determined by that uncertainty, serves to summarize the knowledge about the natural variability of atomic weight values while disregarding the anatomy of this variability among the vast collection of all normal materials [<a href="#j_pac-2019-0603_ref_034" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_034" data-bs-toggle="tooltip" title="34. A. Possolo, A. M. H. van der Veen, J. Meija, D. B. Hibbert. Pure Appl. Chem.90, 395 (2018).10.1515/pac-2016-0402Search in Google Scholar">34</a>]. Other statistical models may be more appropriate and can provide a better representation of this anatomy.</p> <p>With improvements in analytical instrumentation during the last three decades, documented variations in atomic weight values of some elements in normal materials exceed the uncertainty of the atomic weight determined from a “best measurement”. These elements are given footnote “r” in the IUPAC Table of Standard Atomic Weights (<a href="#j_pac-2019-0603_tab_003" class="link link-table" data-bs-target="j_pac-2019-0603_tab_003">Table 1</a>) to indicate that the range of the isotopic composition of normal material prevents the assignment of a lower uncertainty value for the standard atomic weight of these elements (unless they are assigned intervals for their standard atomic-weight values).</p> </section> <section id="j_pac-2019-0603_s_007"> <h2 class="subheading">7 The Table of Standard Atomic Weights</h2> <p>The Table of Standard Atomic Weights is given in the order of increasing atomic number (<a href="#j_pac-2019-0603_tab_003" class="link link-table" data-bs-target="j_pac-2019-0603_tab_003">Table 1</a>). The Table of Standard Atomic Weights is intended to apply to all normal terrestrial materials with minor exceptions covered by footnotes. Standard atomic weights do not apply to extraterrestrial materials nor do they apply to materials with deliberately altered isotopic composition with the exception of lithium, for which artificially <sup>6</sup>Li-depleted substances have been included in the determination of its <em>A</em><sub>r</sub>° value. Standard atomic weights are given as a single value with uncertainties or as an interval (<a href="#j_pac-2019-0603_tab_003" class="link link-table" data-bs-target="j_pac-2019-0603_tab_003">Table 1</a>, columns 4 and 5).</p> <p>During the review of the last Commission report [<a href="#j_pac-2019-0603_ref_002" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_002" data-bs-toggle="tooltip" title="2. J. Meija, T. B. Coplen, M. Berglund, W. A. Brand, P. De Bièvre, M. Gröning, N. E. Holden, J. Irrgeher, R. D. Loss, T. Walczyk, T. Prohaska. Pure Appl. Chem.88, 265 (2016).10.1515/pac-2015-0305Search in Google Scholar">2</a>], it was noted that the expression of uncertainty of standard atomic weights was not in compliance with the GUM (Guide to the Expression of Uncertainty in Measurement) [<a href="#j_pac-2019-0603_ref_035" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_035" data-bs-toggle="tooltip" title="35. 
 Joint Committee for Guides in Metrology. Evaluation of measurement data – Supplement 2 to the “Guide to the expression of uncertainty in measurement” – Extension to any number of output quantities, International Bureau of Weights and Measures (BIPM), Sèvres, France (2011), URLBIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP and OIML, JCGM 102:2011, https://www.bipm.org/en/committees/jc/jcgm/publications (accessed Jan 25, 2021).Search in Google Scholar">35</a>]. For example, the standard atomic weight of iridium, which is 192.217, having an uncertainty of ±0.002, would be tabulated as 192.217(2). However, this format does not comply with the expression of uncertainty in the GUM [<a href="#j_pac-2019-0603_ref_035" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_035" data-bs-toggle="tooltip" title="35. 
 Joint Committee for Guides in Metrology. Evaluation of measurement data – Supplement 2 to the “Guide to the expression of uncertainty in measurement” – Extension to any number of output quantities, International Bureau of Weights and Measures (BIPM), Sèvres, France (2011), URLBIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP and OIML, JCGM 102:2011, https://www.bipm.org/en/committees/jc/jcgm/publications (accessed Jan 25, 2021).Search in Google Scholar">35</a>] as this format suggests that the stated uncertainty is a standard uncertainty. Based on the work of the Subcommittee on Natural Assessment of Fundamental Understanding of Isotopes [<a href="#j_pac-2019-0603_ref_017" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_017" data-bs-toggle="tooltip" title="17. T. B. Coplen, N. E. Holden, T. Ding, H. A. J. Meijer, J. Vogl, X. Zhu. Rapid Commun. Mass Spectrom., e8864 (2020).Search in Google Scholar">17</a>], the Commission selected the format in which the uncertainty value is delineated with the symbol “±”; <em>e.g.</em>, the standard atomic weight of iridium is now expressed as 192.217 ± 0.002. In the Table of Standard Atomic Weights 2021 the uncertainty is tabulated in a new column, or in interval notation. In addition, based on a collaboration between the Subcommittee and the Commission, a new footnote with the symbol double dagger (‡) was added to the Table of Standard Atomic Weights (<a href="#j_pac-2019-0603_tab_003" class="link link-table" data-bs-target="j_pac-2019-0603_tab_003">Table 1</a>) to emphasize that an atomic-weight uncertainty is a consensus based on expert judgement [<a href="#j_pac-2019-0603_ref_017" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_017" data-bs-toggle="tooltip" title="17. T. B. Coplen, N. E. Holden, T. Ding, H. A. J. Meijer, J. Vogl, X. Zhu. Rapid Commun. Mass Spectrom., e8864 (2020).Search in Google Scholar">17</a>, <a href="#j_pac-2019-0603_ref_031" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_031" data-bs-toggle="tooltip" title="31. T. B. Coplen, H. S. Peiser. Pure Appl. Chem.70, 237 (1998).10.1351/pac199870010237Search in Google Scholar">31</a>, <a href="#j_pac-2019-0603_ref_036" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_036" data-bs-toggle="tooltip" title="36. P. De Bièvre, H. H Ku, H. S. Peiser. J. Phys. Chem. Ref. Data. 23, 509 (1994).10.1063/1.555946Search in Google Scholar">36</a>].</p> <p>The detail and number of significant digits reported in the Table of Standard Atomic Weights (<a href="#j_pac-2019-0603_tab_003" class="link link-table" data-bs-target="j_pac-2019-0603_tab_003">Table 1</a>) exceeds in many cases the needs of users and in some cases, a single value is needed for further calculations considering interval elements. Therefore, tables of abridged standard atomic weights have been published since 1981 with the expectation that revisions of these abridged values will be minimal if changes to the corresponding standard atomic weights should become necessary. Additionally, a table abridged to four significant digits was published along with the standard atomic weight table and a table with conventional atomic-weight values for interval elements.</p> <p>In order to provide clearer recommendations to serve the needs of commerce, education, industry and research, the Commission has decided in its 2015, 2017 and 2019 meetings to provide a single table containing both standard atomic weights and abridged standard atomic weights for general use. The CIAAW acknowledges that standard atomic weights might provide too many details. For this purpose, abridged atomic weights are quoted to five significant figures (<a href="#j_pac-2019-0603_tab_003" class="link link-table" data-bs-target="j_pac-2019-0603_tab_003">Table 1</a>, column 7) unless such precision cannot be attained due to the variability of isotopic composition in normal materials or due to the limitations of the measurement capability. A conservative +/− value (<a href="#j_pac-2019-0603_tab_003" class="link link-table" data-bs-target="j_pac-2019-0603_tab_003">Table 1</a>, column 8) is given as a simplified measure of the reliability of the abridged values.</p> <p>The “conventional atomic weights” of previous reports for interval elements were included in this column in order to provide a single table for further usage. The previous “conventional atomic weights” can be extracted from this column except that for hydrogen, which was 1.008, and has been expanded to 1.0080 to provide a lower uncertainty value in column 8. The columns 7 and 8 provide a single atomic weight value (column 7) including an uncertainty (column 8) for all elements having a standard atomic weight value or standard atomic weight interval according to the following rules:<ol type="1" class="list " id="j_pac-2019-0603_list_003" list-type="simple"><li class="listItem ps-2" id="j_pac-2019-0603_li_008" style="list-style-type:'i)';"><div class="listItem-contents"><p>For elements that do not have a standard atomic weight expressed as an interval and have a standard atomic weight value expressed with five or fewer significant digits, the value in column 7 (abridged standard atomic weight) corresponds to the value in column 4. The uncertainty (column 8) corresponds to the uncertainty in column 5 (<a href="#j_pac-2019-0603_tab_003" class="link link-table" data-bs-target="j_pac-2019-0603_tab_003">Table 1</a>).</p></div></li><li class="listItem ps-2" id="j_pac-2019-0603_li_009" style="list-style-type:'ii)';"><div class="listItem-contents"><p>For elements that do not have their standard atomic weight expressed as an interval and have a standard atomic weight with more than 5 significant digits, the standard atomic weight value is abridged to 5 significant digits in column 7. The conservative uncertainty value given in column 8 for these elements corresponds to the place value of the last rounded and thus least significant digit of the value in column 8 providing the reliability of the abridged values.</p></div></li><li class="listItem ps-2" id="j_pac-2019-0603_li_010" style="list-style-type:'iii)';"><div class="listItem-contents"><p>For 14 elements (argon, boron, bromine, carbon, chlorine, hydrogen, lead, lithium, magnesium, nitrogen, oxygen, silicon, sulfur, and thallium) the standard atomic weight is given as an atomic weight interval in column 4 (<a href="#j_pac-2019-0603_tab_003" class="link link-table" data-bs-target="j_pac-2019-0603_tab_003">Table 1</a>). For these elements, a single value is provided in column 7, replacing the former conventional atomic weights for education, trade and commerce published in a “Table of Conventional Atomic Weights” in previous reports [<a href="#j_pac-2019-0603_ref_002" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_002" data-bs-toggle="tooltip" title="2. J. Meija, T. B. Coplen, M. Berglund, W. A. Brand, P. De Bièvre, M. Gröning, N. E. Holden, J. Irrgeher, R. D. Loss, T. Walczyk, T. Prohaska. Pure Appl. Chem.88, 265 (2016).10.1515/pac-2015-0305Search in Google Scholar">2</a>, <a href="#j_pac-2019-0603_ref_018" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_018" data-bs-toggle="tooltip" title="18. M. E. Wieser, T. B. Coplen. Pure Appl. Chem.83, 359 (2011). http://dx.doi.org/10.1351/PAC-REP-10-09-1410.1351/PAC-REP-10-09-14Search in Google Scholar">18</a>, <a href="#j_pac-2019-0603_ref_019" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_019" data-bs-toggle="tooltip" title="19. M. E. Wieser, N. E. Holden, T. B. Coplen, J. K. Böhlke, M. Berglund, W. A. Brand, P. De Bièvre, M. Gröning, R. D. Loss, J. Meija, T. Hirata, T. Prohaska, R. Schoenberg, G. O’Connor, T. Walczyk, S. Yoneda, X. Zhu. Pure Appl. Chem.85, 1047 (2013).10.1351/PAC-REP-13-03-02Search in Google Scholar">19</a>]. These values can be used if a single atomic-weight value is required and the significant numbers of digits are sufficient for further use. The value provided in column 7 for these elements does not correspond necessarily to the midpoints of the intervals (in case of Li, Mg, S, Ar and Pb), and many correspond to the <em>A</em><sub>r</sub> values of frequently used reference materials (<em>e.g.</em> NIST SRM 981 for Pb; argon in tropospheric air for Ar). A corresponding conservative +/− value is provided in column 8 which corresponds to the smallest symmetric number in order to cover the standard atomic weight interval. The significant numbers of digits after the decimal point of the abridged atomic weights corresponds to the significant numbers of digits after the decimal point of this value.</p></div></li></ol></p> </section> <section id="j_pac-2019-0603_s_008"> <h2 class="subheading">8 Comments on standard atomic weights of selected elements</h2> <p>Since the inaugural International Atomic Weights report, published in 1902, the Commission has provided rationale for the changes in the reported atomic weights. This description is accompanied by the historical list of reported values. Brief descriptions of the changes to the standard atomic weights resulting from the Commission meetings in 2015, 2017, 2019, and 2021 are provided below.</p> <section id="j_pac-2019-0603_s_009"> <h3 class="subheading">8.1 Argon</h3> <p>The isotopic composition of argon is variable in terrestrial materials. Those variations are a source of uncertainty in the assignment of standard properties for argon, but they provide useful information in many areas of science [<a href="#j_pac-2019-0603_ref_015" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_015" data-bs-toggle="tooltip" title="15. J. K. Böhlke. Pure Appl. Chem.86, 1421 (2014).10.1515/pac-2013-0918Search in Google Scholar">15</a>]. Variations in the stable isotopic composition and atomic weight of argon are caused by several different processes, including (1) isotope production from other elements by radioactive decay (radiogenic isotopes) or other nuclear transformations (nucleogenic isotopes), and (2) isotopic fractionation by physical–chemical processes such as diffusion or phase equilibration. The latter physical–chemical processes cause correlated mass-dependent variations in the argon isotope-amount ratios <em>n</em>(<sup>40</sup>Ar)/<em>n</em>(<sup>36</sup>Ar) and <em>n</em>(<sup>38</sup>Ar)/<em>n</em>(<sup>36</sup>Ar), where the relative variation in the <em>n</em>(<sup>40</sup>Ar)/<em>n</em>(<sup>36</sup>Ar) is about twice the variation in <em>n</em>(<sup>38</sup>Ar)/<em>n</em>(<sup>36</sup>Ar) because of the factor of two difference in the isotope masses. In contrast, nuclear transformation processes cause variations that do not follow this pattern. For example, a process producing <sup>40</sup>Ar would change the <em>n</em>(<sup>40</sup>Ar)/<em>n</em>(<sup>36</sup>Ar) amount ratio, but not <em>n</em>(<sup>38</sup>Ar)/<em>n</em>(<sup>36</sup>Ar); a process producing <sup>36</sup>Ar would lead to equal relative changes in both <em>n</em>(<sup>40</sup>Ar)/<em>n</em>(<sup>36</sup>Ar) and <em>n</em>(<sup>38</sup>Ar)/<em>n</em>(<sup>36</sup>Ar).</p> <p>While atmospheric argon can serve as an abundant and homogeneous isotopic reference, deviations from the atmospheric isotopic ratios in other argon sources limit the precision with which a standard atomic weight can be given for argon. Published data indicate variation of argon atomic weights in normal terrestrial materials between 39.792 and 39.963 [<a href="#j_pac-2019-0603_ref_015" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_015" data-bs-toggle="tooltip" title="15. J. K. Böhlke. Pure Appl. Chem.86, 1421 (2014).10.1515/pac-2013-0918Search in Google Scholar">15</a>]. The upper endpoint of this interval corresponds to the atomic weight (relative atomic mass) of argon-40, as some K-rich mineral samples contain almost pure radiogenic argon-40 [<a href="#j_pac-2019-0603_ref_015" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_015" data-bs-toggle="tooltip" title="15. J. K. Böhlke. Pure Appl. Chem.86, 1421 (2014).10.1515/pac-2013-0918Search in Google Scholar">15</a>]. The atomic weight of pure argon-40, <em>A</em><sub>r</sub>(<sup>40</sup>Ar) = 39.962 383, was rounded up to 39.963 to obtain the upper bound for the standard atomic weight of argon. The lower bound of the standard atomic weight of argon is from a sample of pitchblende (U ore from Saskatchewan, Canada) containing large amounts of nucleogenic isotopes <sup>36</sup>Ar and <sup>38</sup>Ar [<a href="#j_pac-2019-0603_ref_037" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_037" data-bs-toggle="tooltip" title="37. J. Eikenberg, P. Signer, R. Wieler. Geochem. Cosmochim. Acta. 57, 1053 (1993).10.1016/0016-7037(93)90040-4Search in Google Scholar">37</a>]. These measurements were calibrated against atmospheric argon. Conservatively, assuming both isotope ratios as independent and having 0.5 % expanded relative uncertainty to align with the Commission-recommended (2007) value of the isotope ratio in atmospheric argon [<a href="#j_pac-2019-0603_ref_033" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_033" data-bs-toggle="tooltip" title="33. M. E. Wieser, M. Berglund. Pure Appl. Chem.81, 2131 (2009).10.1351/PAC-REP-09-08-03Search in Google Scholar">33</a>, <a href="#j_pac-2019-0603_ref_038" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_038" data-bs-toggle="tooltip" title="38. J. Y. Lee, K. Marti, J. P. Severinghaus, K. Kawamura, H. S. Yoo, J. B. Lee, J. S. Kim. Geochem. Cosmochim. Acta70, 4507 (2006).10.1016/j.gca.2006.06.1563Search in Google Scholar">38</a>], we obtain isotope ratios <em>R</em>(<sup>38</sup>Ar/<sup>36</sup>Ar) = 2.09 ± 0.01 and <em>R</em>(<sup>40</sup>Ar/<sup>36</sup>Ar) = 45.2 ± 0.22 and the atomic weight <em>A</em><sub>r</sub>(Ar) = 39.7931 ± 0.0009 (<em>k</em> = 2) thus giving the lower endpoint of the standard atomic weight of argon 39.7931 − 0.0009 = 39.792 (rounded down). Within the standard atomic weight interval of argon, measurements of different isotope ratios, <em>R</em>(<sup>40</sup>Ar/<sup>36</sup>Ar) or <em>R</em>(<sup>38</sup>Ar/<sup>36</sup>Ar) at various levels of precision are widely used for studies in geochronology, water-rock interaction, atmospheric evolution, and other fields [<a href="#j_pac-2019-0603_ref_014" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_014" data-bs-toggle="tooltip" title="14. T. B. Coplen, N. E. Holden, M. E. Wieser, J. K. Böhlke. Pure Appl. Chem.90, 1221 (2018).10.1515/pac-2017-0301Search in Google Scholar">14</a>]. If a single atomic-weight value is needed, the Commission recommends using 39.95 ± 0.16, which corresponds to the argon in air with an uncertainty covering normal materials. Reported historical values of the standard atomic weight of argon have been [<a href="#j_pac-2019-0603_ref_031" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_031" data-bs-toggle="tooltip" title="31. T. B. Coplen, H. S. Peiser. Pure Appl. Chem.70, 237 (1998).10.1351/pac199870010237Search in Google Scholar">31</a>, <a href="#j_pac-2019-0603_ref_039" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_039" data-bs-toggle="tooltip" title="39. T. B. Coplen, H. S. Peiser. Pure Appl. Chem.79, 953 (2007).10.1351/pac200779050953Search in Google Scholar">39</a>]: 1902, 39.9; 1911, 39.88; 1920, 39.9; 1925, 39.91; 1931, 39.944; 1961, 39.948; 1969, 39.948 ± 0.003; and 1979, 39.948 ± 0.001. The proposed element cell for argon for the IUPAC Periodic Table of the Elements and Isotopes [<a href="#j_pac-2019-0603_ref_006" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_006" data-bs-toggle="tooltip" title="6. N. E. Holden, T. B. Coplen, J. K. Böhlke, L. V. Tarbox, J. Benefield, J. R. de Laeter, P. G. Mahaffy, G. O’Connor, E. Roth, D. H. Tepper, T. Walczyk, M. E. Wieser, S. Yoneda. Pure Appl. Chem.90, 1833 (2018).10.1515/pac-2015-0703Search in Google Scholar">6</a>] is given in <a href="#j_pac-2019-0603_fig_001" class="link link-fig" data-bs-target="j_pac-2019-0603_fig_001">Fig. 1</a>.</p> <div class="figure-wrapper" id="j_pac-2019-0603_fig_001"><div class="figure w-100"><div class="graphic"><img loading="lazy" src="/document/doi/10.1515/pac-2019-0603/asset/graphic/j_pac-2019-0603_fig_011.jpg" alt="Fig. 1: 
 
 Proposed element cell for argon for the IUPAC Periodic Table of the Elements and Isotopes [6]. The pink background designates an element for which (1) two or more isotopes are used to determine the standard atomic weight and (2) the isotopic abundances and atomic weights vary in normal materials, and these variations exceed measurement uncertainty and are well known. The standard atomic weight value, “[39.792, 39.963]”, is given as a lower and upper bounds within square brackets “[ ]”. The single atomic-weight value for education, commerce, and industry of 39.95, corresponding to previously published conventional atomic-weight values [2, 18, 19], is shown in white.
 "></img></div><div class="figure-description mb-3"><div class="figure-label h3"><span class="label">Fig. 1:</span></div><div class="figure-caption mb-2"><span class="caption"><p> <strong>Proposed element cell for argon for the IUPAC Periodic Table of the Elements and Isotopes</strong> [<a href="#j_pac-2019-0603_ref_006" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_006" data-bs-toggle="tooltip" title="6. N. E. Holden, T. B. Coplen, J. K. Böhlke, L. V. Tarbox, J. Benefield, J. R. de Laeter, P. G. Mahaffy, G. O’Connor, E. Roth, D. H. Tepper, T. Walczyk, M. E. Wieser, S. Yoneda. Pure Appl. Chem.90, 1833 (2018).10.1515/pac-2015-0703Search in Google Scholar">6</a>]<strong>.</strong> The pink background designates an element for which (1) two or more isotopes are used to determine the standard atomic weight and (2) the isotopic abundances and atomic weights vary in normal materials, and these variations exceed measurement uncertainty and are well known. The standard atomic weight value, “[39.792, 39.963]”, is given as a lower and upper bounds within square brackets “[ ]”. The single atomic-weight value for education, commerce, and industry of 39.95, corresponding to previously published conventional atomic-weight values [<a href="#j_pac-2019-0603_ref_002" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_002" data-bs-toggle="tooltip" title="2. J. Meija, T. B. Coplen, M. Berglund, W. A. Brand, P. De Bièvre, M. Gröning, N. E. Holden, J. Irrgeher, R. D. Loss, T. Walczyk, T. Prohaska. Pure Appl. Chem.88, 265 (2016).10.1515/pac-2015-0305Search in Google Scholar">2</a>, <a href="#j_pac-2019-0603_ref_018" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_018" data-bs-toggle="tooltip" title="18. M. E. Wieser, T. B. Coplen. Pure Appl. Chem.83, 359 (2011). http://dx.doi.org/10.1351/PAC-REP-10-09-1410.1351/PAC-REP-10-09-14Search in Google Scholar">18</a>, <a href="#j_pac-2019-0603_ref_019" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_019" data-bs-toggle="tooltip" title="19. M. E. Wieser, N. E. Holden, T. B. Coplen, J. K. Böhlke, M. Berglund, W. A. Brand, P. De Bièvre, M. Gröning, R. D. Loss, J. Meija, T. Hirata, T. Prohaska, R. Schoenberg, G. O’Connor, T. Walczyk, S. Yoneda, X. Zhu. Pure Appl. Chem.85, 1047 (2013).10.1351/PAC-REP-13-03-02Search in Google Scholar">19</a>], is shown in white.</p></span></div></div></div></div> </section> <section id="j_pac-2019-0603_s_010"> <h3 class="subheading">8.2 Ytterbium</h3> <p>One of the last rare earth elements to be discovered, ytterbium was first obtained in a pure state just about 50 years ago. To date, only two calibrated measurements of its isotopic composition have been made: TIMS measurements by de Laeter et al. [<a href="#j_pac-2019-0603_ref_040" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_040" data-bs-toggle="tooltip" title="40. J. R. de Laeter, N. Bukilic. Int. J. Mass Spectrom.252, 222 (2006).10.1016/j.ijms.2006.03.011Search in Google Scholar">40</a>] and recent work by Wang et al. [<a href="#j_pac-2019-0603_ref_041" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_041" data-bs-toggle="tooltip" title="41. J. Wang, T. Ren, H. Lu, T. Zhou, Y. Zhou. J. Anal. At. Spectrom.30, 1377 (2015).10.1039/C5JA00054HSearch in Google Scholar">41</a>] who reported measurements for natural ytterbium samples and the reference material GBW 04623 employing both total evaporation TIMS (thermal ionization mass spectrometry) and MC ICP-MS (multi collector inductively coupled plasma mass spectrometry). While many other measurements of ytterbium isotopic compositions are available, they do not cover all ytterbium isotopes or they rely on assumed conventional values of certain isotope ratios. These measurements differ from one another significantly and ytterbium therefore exemplifies the situation that is also true for many other elements: well-documented isotope ratio measurements are still needed.</p> <p>While both studies employed fractionated ytterbium isotopes to calibrate isotope ratios, both measurements were only partially calibrated for the instrumental isotope ratio fractionation because only two or three separated near-pure isotopes (out of seven stable isotopes) were employed for calibrating the mass spectrometers. The uncertainties of such measurement results are expanded by a factor of <em>k</em> = 6 but the Commission adopted a larger-than-usual uncertainty expansion factor (<em>k</em> = 9) to the small uncertainty estimates reported by Wang et al. [<a href="#j_pac-2019-0603_ref_041" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_041" data-bs-toggle="tooltip" title="41. J. Wang, T. Ren, H. Lu, T. Zhou, Y. Zhou. J. Anal. At. Spectrom.30, 1377 (2015).10.1039/C5JA00054HSearch in Google Scholar">41</a>], especially for the uncertainty contribution due to weighing of isotope mixtures. Nonetheless, the work of Wang et al. [<a href="#j_pac-2019-0603_ref_041" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_041" data-bs-toggle="tooltip" title="41. J. Wang, T. Ren, H. Lu, T. Zhou, Y. Zhou. J. Anal. At. Spectrom.30, 1377 (2015).10.1039/C5JA00054HSearch in Google Scholar">41</a>] is reported as the new IUPAC “best measurement” for Yb isotopic composition. Evaluated results from these studies are as follows:<div class="table-wrap mb-4" id="j_pac-2019-0603_tab_004" position="anchor" orientation="portrait"><table rules="groups" frame="hsides" class="content-table"><colgroup><col align="left"></col><col align="left"></col></colgroup><tbody><tr><td style="text-align: left">de Laeter et al. (2006) [<a href="#j_pac-2019-0603_ref_040" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_040" data-bs-toggle="tooltip" title="40. J. R. de Laeter, N. Bukilic. Int. J. Mass Spectrom.252, 222 (2006).10.1016/j.ijms.2006.03.011Search in Google Scholar">40</a>]:</td><td style="text-align: left"><em>A</em><sub>r</sub>(Yb) = 173.0542 (<em>u</em> = 0.0008, <em>k</em> = 1)</td></tr><tr><td style="text-align: left">Wang et al. (2015) [<a href="#j_pac-2019-0603_ref_041" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_041" data-bs-toggle="tooltip" title="41. J. Wang, T. Ren, H. Lu, T. Zhou, Y. Zhou. J. Anal. At. Spectrom.30, 1377 (2015).10.1039/C5JA00054HSearch in Google Scholar">41</a>]:</td><td style="text-align: left"><em>A</em><sub>r</sub>(Yb) = 173.0417 (<em>u</em> = 0.0002, <em>k</em> = 1)</td></tr></tbody></table></div></p> <p>The Commission combined these results using the multivariate random effects model as implemented in the R package CIAAWconsensus [<a href="#j_pac-2019-0603_ref_032" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_032" data-bs-toggle="tooltip" title="32. J. Meija, A. Possolo. Metrologia54, 229 (2017).10.1088/1681-7575/aa634dSearch in Google Scholar">32</a>] for calculating the standard atomic weight. For this, a priori uncertainty expansion factor of <em>k</em> = 6 was used for isotope ratios reported by de Laeter et al. [<a href="#j_pac-2019-0603_ref_040" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_040" data-bs-toggle="tooltip" title="40. J. R. de Laeter, N. Bukilic. Int. J. Mass Spectrom.252, 222 (2006).10.1016/j.ijms.2006.03.011Search in Google Scholar">40</a>] and a factor of <em>k</em> = 9 for isotope ratios reported by Wang et al. [<a href="#j_pac-2019-0603_ref_041" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_041" data-bs-toggle="tooltip" title="41. J. Wang, T. Ren, H. Lu, T. Zhou, Y. Zhou. J. Anal. At. Spectrom.30, 1377 (2015).10.1039/C5JA00054HSearch in Google Scholar">41</a>]. This resulted in the revised standard atomic weight of ytterbium <em>A</em><sub>r</sub>°(Yb) = 173.045 ± 0.010 where 0.010 is the expanded uncertainty (<em>k</em> ≈ 3). Reported historical values of standard atomic weight of ytterbium have been [<a href="#j_pac-2019-0603_ref_031" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_031" data-bs-toggle="tooltip" title="31. T. B. Coplen, H. S. Peiser. Pure Appl. Chem.70, 237 (1998).10.1351/pac199870010237Search in Google Scholar">31</a>, <a href="#j_pac-2019-0603_ref_039" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_039" data-bs-toggle="tooltip" title="39. T. B. Coplen, H. S. Peiser. Pure Appl. Chem.79, 953 (2007).10.1351/pac200779050953Search in Google Scholar">39</a>]: 1902, 173.0; 1909, 172.0; 1916, 173.5; 1925, 173.6; 1931, 173.5; 1934, 173.04; 1969, 173.04 ± 0.03; and 2007, 173.054 ± 0.005.</p> </section> <section id="j_pac-2019-0603_s_011"> <h3 class="subheading">8.3 Hafnium</h3> <p>Prior to 2019, the standard atomic weight of hafnium was set as the average result from three uncalibrated isotope ratio measurements published in the 1940s and 50s [<a href="#j_pac-2019-0603_ref_042" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_042" data-bs-toggle="tooltip" title="42. J. H. Reynolds. Phys. Rev.90, 1047 (1953).10.1103/PhysRev.90.1047Search in Google Scholar">42</a>], [<a href="#j_pac-2019-0603_ref_043" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_043" data-bs-toggle="tooltip" title="43. F. White, T. Collins, F. Rourke. Phys. Rev.101, 1786 (1956).10.1103/PhysRev.101.1786Search in Google Scholar">43</a>], [<a href="#j_pac-2019-0603_ref_044" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_044" data-bs-toggle="tooltip" title="44. J. Vervoort. Encyclopedia of Scientific Dating Methods, p. 379, Springer Netherlands (2015).10.1007/978-94-007-6304-3_46Search in Google Scholar">44</a>]. The recent work of Tong et al. has provided a new measurement on the JMC-475 standard material which is used in nearly all studies concerning measurements of the isotopic composition of hafnium [<a href="#j_pac-2019-0603_ref_045" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_045" data-bs-toggle="tooltip" title="45. S. Tong, J. Meija, L. Zhou, Z. Mester, L. Yang. Metrologia56, 044008 (2019).10.1088/1681-7575/ab2995Search in Google Scholar">45</a>]. This work measured the isotopic composition of hafnium in the JMC-475 standard using MC ICP-MS. The isotope ratio measurements were calibrated using the regression method which has been classified by the Commission as a new IUPAC best measurement of hafnium isotopic composition (the Commission considers this a ‘partially’ calibrated measurement). The atomic weight of hafnium in JMC-475 is 178.4864 with standard uncertainty 0.0004. With this, it is possible now to re-evaluate its atomic weight while considering the well-documented variations of the radiogenic <sup>176</sup>Hf/<sup>177</sup>Hf isotope ratio in normal materials [<a href="#j_pac-2019-0603_ref_046" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_046" data-bs-toggle="tooltip" title="46. E. Belousova, Y. Kostitsyn, W. L. Griffin, G. C. Begg, S. Y. O’Reilly, N. J. Pearson. Lithos119, 457 (2010).10.1016/j.lithos.2010.07.024Search in Google Scholar">46</a>].</p> <p>The radioactive decay of lutetium alters the isotopic composition of hafnium by producing the light isotope of hafnium-176. The majority of geological samples have <sup>176</sup>Hf/<sup>177</sup>Hf isotope ratios between 0.2797 and 0.2848 which corresponds to the isotope delta <em>δ</em>(<sup>176</sup>Hf/<sup>177</sup>Hf) from −8 ‰ to +10 ‰ relative to JMC-475 with lutetium-free materials providing the lowest <sup>176</sup>Hf/<sup>177</sup>Hf ratios [<a href="#j_pac-2019-0603_ref_046" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_046" data-bs-toggle="tooltip" title="46. E. Belousova, Y. Kostitsyn, W. L. Griffin, G. C. Begg, S. Y. O’Reilly, N. J. Pearson. Lithos119, 457 (2010).10.1016/j.lithos.2010.07.024Search in Google Scholar">46</a>], [<a href="#j_pac-2019-0603_ref_047" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_047" data-bs-toggle="tooltip" title="47. V. J. Salters, A. Zindler. Earth Planet Sci. Lett.129, 13 (1995).10.1016/0012-821X(94)00234-PSearch in Google Scholar">47</a>], [<a href="#j_pac-2019-0603_ref_048" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_048" data-bs-toggle="tooltip" title="48. M. Garçon, R. Carlson, S. Shirey, N. Arndt, M. Horan, T. Mock. Geochem. Cosmochim. Acta, 216 (2017).10.1016/j.gca.2017.03.006Search in Google Scholar">48</a>]. Given that this is the first re-evaluation of the isotopic composition of hafnium since the 1950s, we conservatively adopt the interval <em>δ</em>(<sup>176</sup>Hf/<sup>177</sup>Hf) from −20 ‰ to +20 ‰ relative to JMC-475 to cover the variations in <sup>176</sup>Hf/<sup>177</sup>Hf isotope ratios in natural materials. The standard atomic weight of hafnium is centered on the best estimate corresponding to JMC-475 and the calculation of the uncertainty associated with the standard atomic weight of hafnium (and the associated isotopic composition) was obtained as follows:<ol type="1" class="list " id="j_pac-2019-0603_list_004" list-type="order"><li class="listItem" id="j_pac-2019-0603_li_011"><div class="listItem-contents"><p>Measurement uncertainty associated with the isotope ratios is taken from the IUPAC Best Measurement [<a href="#j_pac-2019-0603_ref_045" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_045" data-bs-toggle="tooltip" title="45. S. Tong, J. Meija, L. Zhou, Z. Mester, L. Yang. Metrologia56, 044008 (2019).10.1088/1681-7575/ab2995Search in Google Scholar">45</a>] whereas uncertainty of the isotope masses is taken from the AME2016 [<a href="#j_pac-2019-0603_ref_049" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_049" data-bs-toggle="tooltip" title="49. M. Wang, G. Audi, F. G. Kondev, W. J. Huang, S. Naimi, X. Xu. Chin. Phys. C41, 030003 (2017).10.1088/1674-1137/41/3/030003Search in Google Scholar">49</a>], both taken with additional coverage factor <em>k</em> = 6 following the CIAAW practices.</p></div></li><li class="listItem" id="j_pac-2019-0603_li_012"><div class="listItem-contents"><p>We take a conservative estimate of mass-dependent natural variations in <sup>180</sup>Hf/<sup>177</sup>Hf ratio as ±1 ‰ relative to JMC-475 (corresponding two times the interval observed by Tong et al. [<a href="#j_pac-2019-0603_ref_045" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_045" data-bs-toggle="tooltip" title="45. S. Tong, J. Meija, L. Zhou, Z. Mester, L. Yang. Metrologia56, 044008 (2019).10.1088/1681-7575/ab2995Search in Google Scholar">45</a>] from four commercial reagents). Changes in all other isotope ratios were modelled according to the mass-dependent behavior: <em>δ</em>(<sup>179</sup>Hf/<sup>177</sup>Hf) = (2/3) × <em>δ</em>(<sup>180</sup>Hf/<sup>177</sup>Hf), <em>δ</em>(<sup>178</sup>Hf/<sup>177</sup>Hf) = (1/3) × <em>δ</em>(<sup>180</sup>Hf/<sup>177</sup>Hf), and <em>δ</em>(<sup>174</sup>Hf/<sup>177</sup>Hf) = −<em>δ</em>(<sup>180</sup>Hf/<sup>177</sup>Hf).</p></div></li><li class="listItem" id="j_pac-2019-0603_li_013"><div class="listItem-contents"><p>Natural variations of the radiogenic <sup>176</sup>Hf/<sup>177</sup>Hf isotope ratio of hafnium are modeled independent of all other ratios and are very conservatively modelled as ±20 ‰ relative to JMC-475 (uniform distribution).</p></div></li></ol></p> <p>Together, the effect of these isotope-ratio variations was evaluated using the Monte Carlo method and the resulting standard uncertainty of the atomic weight of hafnium was <em>u</em> = 0.0026. Applying a probability coverage factor of <em>k</em> = 2 for expanded uncertainty leads to the value 0.0052, which, when rounded to 0.006, effectively corresponds to coverage factor <em>k</em> = 2.3. This resulted in the revised standard atomic weight of hafnium <em>A</em><sub>r</sub>°(Hf) = 178.486 ± 0.006. Reported historical values of standard atomic weight of hafnium have been [<a href="#j_pac-2019-0603_ref_031" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_031" data-bs-toggle="tooltip" title="31. T. B. Coplen, H. S. Peiser. Pure Appl. Chem.70, 237 (1998).10.1351/pac199870010237Search in Google Scholar">31</a>, <a href="#j_pac-2019-0603_ref_039" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_039" data-bs-toggle="tooltip" title="39. T. B. Coplen, H. S. Peiser. Pure Appl. Chem.79, 953 (2007).10.1351/pac200779050953Search in Google Scholar">39</a>]: 1931, 178.6; 1955, 178.50; 1961, 178.49; 1969, 178.49 ± 0.03; and 1985, 178.49 ± 0.02.</p> <p>We also recognize that anomalous geological samples are known to have <sup>176</sup>Hf/<sup>177</sup>Hf values well outside the standard atomic weight which necessitates the footnote “g” in the Table of Standard Atomic Weights. One of the most radiogenic isotopic compositions of hafnium ever measured for terrestrial rocks is reported in Barberton sedimentary Chert (South Africa) with <em>R</em>(<sup>176</sup>Hf/<sup>177</sup>Hf) = 0.3657, <em>δ</em>(<sup>176</sup>Hf/<sup>177</sup>Hf) = +296 ‰ relative to JMC 475 having <em>A</em><sub>r</sub>(Hf) = 178.447 [<a href="#j_pac-2019-0603_ref_046" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_046" data-bs-toggle="tooltip" title="46. E. Belousova, Y. Kostitsyn, W. L. Griffin, G. C. Begg, S. Y. O’Reilly, N. J. Pearson. Lithos119, 457 (2010).10.1016/j.lithos.2010.07.024Search in Google Scholar">46</a>].</p> </section> <section id="j_pac-2019-0603_s_012"> <h3 class="subheading">8.4 Iridium</h3> <p>In 1993, the Commission changed the reported value for the standard atomic weight of iridium to <em>A</em><sub>r</sub>°(Ir) = 192.217 ± 0.003 based on high-precision measurements using both positive and negative thermal ionization mass spectrometry (TIMS). This value was reaffirmed in 2017 with the work of Zhu et al. using MC ICP-MS [<a href="#j_pac-2019-0603_ref_050" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_050" data-bs-toggle="tooltip" title="50. Z. Zhu, J. Meija, A. Zheng, Z. Mester, L. Yang. Anal. Chem.89, 9375 (2017).10.1021/acs.analchem.7b02206Search in Google Scholar
 PubMed
 ">50</a>]. Zhu et al. employed a regression-based calibration method for the isotope ratios of iridium with NIST-certified isotopic reference materials of rhenium and thallium as primary standards. This measurement was classified by the Commission as partially calibrated because the regression model is still a relatively novel technique with its full potential and limitations still to be studied. Nevertheless, the measurement of Zhu et al. represents a significant improvement in the precision of the isotopic composition and atomic weight of iridium and is reported as the new IUPAC best measurement.</p> <p>The Commission considered the results of three studies for calculating the standard atomic weight of iridium:<div class="table-wrap mb-4" id="j_pac-2019-0603_tab_005" position="anchor" orientation="portrait"><table rules="groups" frame="hsides" class="content-table"><colgroup><col align="left"></col><col align="left"></col></colgroup><tbody><tr><td style="text-align: left">Chang et al. (1992) [<a href="#j_pac-2019-0603_ref_051" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_051" data-bs-toggle="tooltip" title="51. T. L. Chang, Y. K. Xiao. Chin. Chem. Lett.3, 731 (1992).Search in Google Scholar">51</a>]:</td><td style="text-align: left"><em>R</em><sub>191/193</sub> = 0.593 99 (<em>u</em> = 0.001 03, <em>k</em> = 1)</td></tr><tr><td style="text-align: left">Walczyk et al. (1993) [<a href="#j_pac-2019-0603_ref_052" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_052" data-bs-toggle="tooltip" title="52. T. Walczyk, K. G. Heumann. Int. J. Mass Spectrom.123, 139 (1993).10.1016/0168-1176(93)87008-GSearch in Google Scholar">52</a>]:</td><td style="text-align: left"><em>R</em><sub>191/193</sub> = 0.594 18 (<em>u</em> = 0.000 37, <em>k</em> = 1)</td></tr><tr><td style="text-align: left">Zhu et al. (2017) [<a href="#j_pac-2019-0603_ref_050" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_050" data-bs-toggle="tooltip" title="50. Z. Zhu, J. Meija, A. Zheng, Z. Mester, L. Yang. Anal. Chem.89, 9375 (2017).10.1021/acs.analchem.7b02206Search in Google Scholar
 PubMed
 ">50</a>]:</td><td style="text-align: left"><em>R</em><sub>191/193</sub> = 0.592 90 (<em>u</em> = 0.000 21, <em>k</em> = 1)</td></tr></tbody></table></div></p> <p>These three independent results were combined using the random effects statistical model and DerSimonian and Laird estimator [<a href="#j_pac-2019-0603_ref_053" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_053" data-bs-toggle="tooltip" title="53. D. Böhning, U. Malzahn, E. Dietz, P. Schlattmann, C. Viwatwongkasem, A. Biggeri. Biostatistics3, 445 (2002).Search in Google Scholar">53</a>]. For this, the uncertainties of the isotope ratios reported from the individual studies were a priori expanded by coverage factors <em>k</em> = 6 (Chang et al. [<a href="#j_pac-2019-0603_ref_051" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_051" data-bs-toggle="tooltip" title="51. T. L. Chang, Y. K. Xiao. Chin. Chem. Lett.3, 731 (1992).Search in Google Scholar">51</a>]), <em>k</em> = 9 (Walczyk et al. [<a href="#j_pac-2019-0603_ref_052" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_052" data-bs-toggle="tooltip" title="52. T. Walczyk, K. G. Heumann. Int. J. Mass Spectrom.123, 139 (1993).10.1016/0168-1176(93)87008-GSearch in Google Scholar">52</a>]), and <em>k</em> = 6 (Zhu et al. [<a href="#j_pac-2019-0603_ref_050" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_050" data-bs-toggle="tooltip" title="50. Z. Zhu, J. Meija, A. Zheng, Z. Mester, L. Yang. Anal. Chem.89, 9375 (2017).10.1021/acs.analchem.7b02206Search in Google Scholar
 PubMed
 ">50</a>]) which follows the practice of the Commission whereby uncertainties of calibrated, partially-calibrated, and non-calibrated measurement results are expanded by a factor of 3, 6, or 9, respectively [<a href="#j_pac-2019-0603_ref_032" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_032" data-bs-toggle="tooltip" title="32. J. Meija, A. Possolo. Metrologia54, 229 (2017).10.1088/1681-7575/aa634dSearch in Google Scholar">32</a>]. This resulted in the revised standard atomic weight of iridium, <em>A</em><sub>r</sub>°(Ir) = 192.217 ± 0.002 where 0.002 is the expanded uncertainty (<em>k</em> = 2). Reported historical values of standard atomic weight of iridium have been [<a href="#j_pac-2019-0603_ref_031" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_031" data-bs-toggle="tooltip" title="31. T. B. Coplen, H. S. Peiser. Pure Appl. Chem.70, 237 (1998).10.1351/pac199870010237Search in Google Scholar">31</a>, <a href="#j_pac-2019-0603_ref_039" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_039" data-bs-toggle="tooltip" title="39. T. B. Coplen, H. S. Peiser. Pure Appl. Chem.79, 953 (2007).10.1351/pac200779050953Search in Google Scholar">39</a>]: 1902, 193.0; 1909, 193.1; 1953, 192.2; 1969, 192.22 ± 0.03; and 1993, 192.217 ± 0.003.</p> </section> <section id="j_pac-2019-0603_s_013"> <h3 class="subheading">8.5 Lead</h3> <p>The isotopic composition and atomic weight of lead are variable in terrestrial materials because its three heaviest stable isotopes are stable end-products of the radioactive decay of uranium (<sup>238</sup>U to <sup>206</sup>Pb and <sup>235</sup>U to <sup>207</sup>Pb) and thorium (<sup>232</sup>Th to <sup>208</sup>Pb). These variations in isotope ratios and atomic weights provide useful information in many areas of science, including geochronology, archaeology, environmental studies, and forensic science. While elemental lead can serve as an abundant and homogeneous isotopic reference, deviations from the isotope ratios in other lead occurrences limit the accuracy with which a standard atomic weight can be given for lead.</p> <p>In a comprehensive review of several hundred publications and analyses of more than 8000 samples [<a href="#j_pac-2019-0603_ref_016" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_016" data-bs-toggle="tooltip" title="16. X. K. Zhu, J. Benefield, T. B. Coplen, Z. Gao, N. Holden. Pure Appl. Chem.93, 155 (2021).10.1515/pac-2018-0916Search in Google Scholar">16</a>], published isotope data indicate that the lowest reported lead atomic weight of a normal terrestrial material is 206.1462 ± 0.0028 (<em>k</em> = 2), determined for a growth of the phosphate mineral monazite from the Lewisian complex in north-western Scotland, which contains mostly <sup>206</sup>Pb and almost no <sup>204</sup>Pb [<a href="#j_pac-2019-0603_ref_054" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_054" data-bs-toggle="tooltip" title="54. X. K. Zhu, R. K. O’Nions, N. S. Belshaw, A. J. Gibb. Chem. Geol.136, 205 (1997).10.1016/S0009-2541(96)00143-XSearch in Google Scholar">54</a>]. The highest published lead atomic weight 207.9351 ± 0.0005 (<em>k</em> = 2) is for monazite from a micro-inclusion. The material is also from the Lewisian complex in north-western Scotland containing almost pure radiogenic <sup>208</sup>Pb [<a href="#j_pac-2019-0603_ref_054" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_054" data-bs-toggle="tooltip" title="54. X. K. Zhu, R. K. O’Nions, N. S. Belshaw, A. J. Gibb. Chem. Geol.136, 205 (1997).10.1016/S0009-2541(96)00143-XSearch in Google Scholar">54</a>]. Assigning the aforementioned lead atomic weights as the lower and upper bounds of the interval, the standard atomic weight of lead is <em>A</em><sub>r</sub><sup>o</sup>(Pb) = [206.14, 207.94]. If a single atomic-weight value is needed, the Commission recommends using 207.2 ± 1.1, which corresponds to the common lead with a symmetric uncertainty covering normal materials. The proposed cell for lead for the IUPAC Periodic Table of Elements and Isotopes is shown in <a href="#j_pac-2019-0603_fig_002" class="link link-fig" data-bs-target="j_pac-2019-0603_fig_002">Fig. 2</a> with the conventional atomic-weight value of 207.2 shown in white. Reported historical values of the standard atomic weight of lead have been [<a href="#j_pac-2019-0603_ref_031" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_031" data-bs-toggle="tooltip" title="31. T. B. Coplen, H. S. Peiser. Pure Appl. Chem.70, 237 (1998).10.1351/pac199870010237Search in Google Scholar">31</a>, <a href="#j_pac-2019-0603_ref_039" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_039" data-bs-toggle="tooltip" title="39. T. B. Coplen, H. S. Peiser. Pure Appl. Chem.79, 953 (2007).10.1351/pac200779050953Search in Google Scholar">39</a>]: 1902, 206.9; 1909, 207.10; 1916, 207.20; 1937, 207.21; 1961, 207.19; and 1969, 207.2 ± 0.1.</p> <div class="figure-wrapper" id="j_pac-2019-0603_fig_002"><div class="figure w-100"><div class="graphic"><img loading="lazy" src="/document/doi/10.1515/pac-2019-0603/asset/graphic/j_pac-2019-0603_fig_012.jpg" alt="Fig. 2: 
 
 Proposed element cell for lead for the IUPAC Periodic Table of the Elements and Isotopes [6]. The pink background designates an element for which (1) two or more isotopes are used to determine the standard atomic weight and (2) the isotopic abundances and atomic weights vary in normal materials, and these variations exceed measurement uncertainty and are well known. The standard atomic weight value, “[206.14, 207.94]”, is given as a lower and upper bounds within square brackets [ ]. The single atomic-weight value for education, commerce, and industry of 207.2, corresponding to previously published conventional atomic-weight values [2, 18, 19], is shown in white.
 "></img></div><div class="figure-description mb-3"><div class="figure-label h3"><span class="label">Fig. 2:</span></div><div class="figure-caption mb-2"><span class="caption"><p> <strong>Proposed element cell for lead for the IUPAC Periodic Table of the Elements and Isotopes</strong> [<a href="#j_pac-2019-0603_ref_006" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_006" data-bs-toggle="tooltip" title="6. N. E. Holden, T. B. Coplen, J. K. Böhlke, L. V. Tarbox, J. Benefield, J. R. de Laeter, P. G. Mahaffy, G. O’Connor, E. Roth, D. H. Tepper, T. Walczyk, M. E. Wieser, S. Yoneda. Pure Appl. Chem.90, 1833 (2018).10.1515/pac-2015-0703Search in Google Scholar">6</a>]<strong>.</strong> The pink background designates an element for which (1) two or more isotopes are used to determine the standard atomic weight and (2) the isotopic abundances and atomic weights vary in normal materials, and these variations exceed measurement uncertainty and are well known. The standard atomic weight value, “[206.14, 207.94]”, is given as a lower and upper bounds within square brackets [ ]. The single atomic-weight value for education, commerce, and industry of 207.2, corresponding to previously published conventional atomic-weight values [<a href="#j_pac-2019-0603_ref_002" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_002" data-bs-toggle="tooltip" title="2. J. Meija, T. B. Coplen, M. Berglund, W. A. Brand, P. De Bièvre, M. Gröning, N. E. Holden, J. Irrgeher, R. D. Loss, T. Walczyk, T. Prohaska. Pure Appl. Chem.88, 265 (2016).10.1515/pac-2015-0305Search in Google Scholar">2</a>, <a href="#j_pac-2019-0603_ref_018" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_018" data-bs-toggle="tooltip" title="18. M. E. Wieser, T. B. Coplen. Pure Appl. Chem.83, 359 (2011). http://dx.doi.org/10.1351/PAC-REP-10-09-1410.1351/PAC-REP-10-09-14Search in Google Scholar">18</a>, <a href="#j_pac-2019-0603_ref_019" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_019" data-bs-toggle="tooltip" title="19. M. E. Wieser, N. E. Holden, T. B. Coplen, J. K. Böhlke, M. Berglund, W. A. Brand, P. De Bièvre, M. Gröning, R. D. Loss, J. Meija, T. Hirata, T. Prohaska, R. Schoenberg, G. O’Connor, T. Walczyk, S. Yoneda, X. Zhu. Pure Appl. Chem.85, 1047 (2013).10.1351/PAC-REP-13-03-02Search in Google Scholar">19</a>], is shown in white.</p></span></div></div></div></div> </section> </section> <section id="j_pac-2019-0603_s_014"> <h2 class="subheading">9 Elements with revised atomic mass values (aluminium, cobalt, fluorine, gold, holmium, manganese, niobium, praseodymium, protactinium, rhodium, scandium, terbium, thulium, and yttrium)</h2> <p>In normal materials, the standard atomic weight of 19 elements is determined by only one isotope, which is stable (non-radioactive). Thus, the standard atomic weight for these elements is invariant. These elements are: Be, F, Na, Al, P, Sc, Mn, Co, As, Y, Nb, Rh, I, Cs, Pr, Tb, Ho, Tm, and Au. In addition, two elements, Bi and Pa, have only one isotope that contributes to the standard atomic weight, but that isotope is radioactive. The standard atomic weights of these 21 elements are derived directly from their atomic masses.</p> <p>The two recent Atomic Mass Evaluation reports (AME2016 and AME2020) contain many advances in the measurement science of atomic masses [<a href="#j_pac-2019-0603_ref_011" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_011" data-bs-toggle="tooltip" title="11. M. Wang, W. J. Huang, F. G. Kondev, G. Audi, S. Naimi. Chin. Phys. C45, 030003 (2021).10.1088/1674-1137/abddafSearch in Google Scholar">11</a>, <a href="#j_pac-2019-0603_ref_049" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_049" data-bs-toggle="tooltip" title="49. M. Wang, G. Audi, F. G. Kondev, W. J. Huang, S. Naimi, X. Xu. Chin. Phys. C41, 030003 (2017).10.1088/1674-1137/41/3/030003Search in Google Scholar">49</a>]. The most notable increase in the reported precision of the nuclide masses is the significant reduction in the uncertainty of the atomic masses of boron, ytterbium, strontium, and zirconium in AME2016 or hydrogen in AME2020. With respect to the consistency between the values of AME2012 and AME2016, the atomic mass of only two nuclides contributing to the standard atomic weights are inconsistent at the 3-sigma level of precision (helium-4 and palladium-102) compared to seven nuclides between the 2003 and 2012 evaluations. Similarly, atomic mass estimates of only two nuclides (hydrogen-1 and helium-3) differ by more than 3-sigma between AME2016 and AME2020.</p> <p>The coverage factor for the uncertainty of the <em>A</em><sub>r</sub>° value of monoisotopic elements is <em>k</em> = 6 (for AME masses). Revised standard atomic weights are provided for 12 elements in 2017 (Al, Au, Co, Ho, Mn, Nb, Pr, Pa, Rh, Tb, Tm, and Y) and for 6 elements in 2021 (F, Ho, Sc, Tb, Tm, Y) for which improvements in the measurement precision of the atomic-mass values have been reported.</p> </section> <section id="j_pac-2019-0603_s_015"> <h2 class="subheading">10 Plots of the natural variation of atomic weights</h2> <p>IUPAC published plots of natural variations in isotopic abundances and atomic weights for 15 elements, 12 of which had standard atomic weights expressed as an interval [<a href="#j_pac-2019-0603_ref_006" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_006" data-bs-toggle="tooltip" title="6. N. E. Holden, T. B. Coplen, J. K. Böhlke, L. V. Tarbox, J. Benefield, J. R. de Laeter, P. G. Mahaffy, G. O’Connor, E. Roth, D. H. Tepper, T. Walczyk, M. E. Wieser, S. Yoneda. Pure Appl. Chem.90, 1833 (2018).10.1515/pac-2015-0703Search in Google Scholar">6</a>]. These plots provide information on the likely atomic-weight values of an element in a given substance [<a href="#j_pac-2019-0603_ref_022" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_022" data-bs-toggle="tooltip" title="22. T. B. Coplen, Y. Shrestha. Pure Appl. Chem.88, 1203 (2016).10.1515/pac-2016-0302Search in Google Scholar">22</a>, <a href="#j_pac-2019-0603_ref_023" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_023" data-bs-toggle="tooltip" title="23. T. B. Coplen, Y. Shrestha. Pure Appl. Chem.91, 173 (2019).Search in Google Scholar">23</a>] and are available in Excel worksheets [<a href="#j_pac-2019-0603_ref_024" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_024" data-bs-toggle="tooltip" title="24. T. B. Coplen, Y. Shrestha. Tables and Charts for Isotope-Abundance Variations and Atomic Weights of Selected Elements: 2016 (Ver. 1.1, May 2018), U.S. Geological Survey Data Release (2018).10.1515/pac-2018-0504Search in Google Scholar">24</a>]. Additionally, the Commission provides plots of natural variations in isotopic abundances and atomic weights for elements whose standard atomic weight is expressed as an interval [<a href="#j_pac-2019-0603_ref_002" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_002" data-bs-toggle="tooltip" title="2. J. Meija, T. B. Coplen, M. Berglund, W. A. Brand, P. De Bièvre, M. Gröning, N. E. Holden, J. Irrgeher, R. D. Loss, T. Walczyk, T. Prohaska. Pure Appl. Chem.88, 265 (2016).10.1515/pac-2015-0305Search in Google Scholar">2</a>, <a href="#j_pac-2019-0603_ref_019" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_019" data-bs-toggle="tooltip" title="19. M. E. Wieser, N. E. Holden, T. B. Coplen, J. K. Böhlke, M. Berglund, W. A. Brand, P. De Bièvre, M. Gröning, R. D. Loss, J. Meija, T. Hirata, T. Prohaska, R. Schoenberg, G. O’Connor, T. Walczyk, S. Yoneda, X. Zhu. Pure Appl. Chem.85, 1047 (2013).10.1351/PAC-REP-13-03-02Search in Google Scholar">19</a>] which can be downloaded from the Commission’s website [<a href="#j_pac-2019-0603_ref_055" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_055" data-bs-toggle="tooltip" title="55. 
 CIAAW. Natural variations of isotopic abundances, https://ciaaw.org/natural-variations.htm (accessed Jan 25, 2021).Search in Google Scholar">55</a>] or via the online IUPAC Periodic Table of the Elements and Isotopes [<a href="#j_pac-2019-0603_ref_008" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_008" data-bs-toggle="tooltip" title="8. 
 Isotopes Matter, https://www.isotopesmatter.com (accessed Jan 25, 2021).Search in Google Scholar">8</a>]. Argon was assigned an interval standard atomic weight at the 2017 Commission meeting based on the report by Böhlke [<a href="#j_pac-2019-0603_ref_015" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_015" data-bs-toggle="tooltip" title="15. J. K. Böhlke. Pure Appl. Chem.86, 1421 (2014).10.1515/pac-2013-0918Search in Google Scholar">15</a>] and the corresponding new graphs are displayed in <a href="#j_pac-2019-0603_fig_003" class="link link-fig" data-bs-target="j_pac-2019-0603_fig_003">Figs. 3</a><a href="#j_pac-2019-0603_fig_004" class="link link-fig" data-bs-target="j_pac-2019-0603_fig_004"></a>–<a href="#j_pac-2019-0603_fig_005" class="link link-fig" data-bs-target="j_pac-2019-0603_fig_005">5</a>. Lead was assigned an interval standard atomic weight by the Commission in 2020, via correspondence, based on the report by Zhu et al. [<a href="#j_pac-2019-0603_ref_016" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_016" data-bs-toggle="tooltip" title="16. X. K. Zhu, J. Benefield, T. B. Coplen, Z. Gao, N. Holden. Pure Appl. Chem.93, 155 (2021).10.1515/pac-2018-0916Search in Google Scholar">16</a>] and the corresponding new graphs are displayed in <a href="#j_pac-2019-0603_fig_006" class="link link-fig" data-bs-target="j_pac-2019-0603_fig_006">Figs. 6</a><a href="#j_pac-2019-0603_fig_007" class="link link-fig" data-bs-target="j_pac-2019-0603_fig_007"></a><a href="#j_pac-2019-0603_fig_008" class="link link-fig" data-bs-target="j_pac-2019-0603_fig_008"></a>–<a href="#j_pac-2019-0603_fig_009" class="link link-fig" data-bs-target="j_pac-2019-0603_fig_009">9</a>.</p> <div class="figure-wrapper" id="j_pac-2019-0603_fig_003"><div class="figure w-100"><div class="graphic"><img loading="lazy" src="/document/doi/10.1515/pac-2019-0603/asset/graphic/j_pac-2019-0603_fig_013.jpg" alt="Fig. 3: 
 
 Variation in atomic weight (black lines) of argon, A
 
 r
 
 (Ar), with amount fraction (pink lines) of
 
 36
 
 Ar, x(
 
 36
 
 Ar), of selected argon-bearing materials. Because argon has three isotopes whose variations are not mass-dependent, the changes in the Ar(Ar) and x(36Ar) values are not superimposed. Each horizontal line spans the minimum and maximum values observed for the corresponding class of materials (data from [15]).
 "></img></div><div class="figure-description mb-3"><div class="figure-label h3"><span class="label">Fig. 3:</span></div><div class="figure-caption mb-2"><span class="caption"><p> <strong>Variation in atomic weight (black lines) of argon, <em>A</em></strong> <sub> <strong>r</strong> </sub> <strong>(Ar), with amount fraction (pink lines) of</strong> <sup> <strong>36</strong> </sup> <strong>Ar, <em>x</em>(</strong> <sup> <strong>36</strong> </sup> <strong>Ar), of selected argon-bearing materials</strong>. Because argon has three isotopes whose variations are not mass-dependent, the changes in the <em>A</em><sub>r</sub>(Ar) and <em>x</em>(<sup>36</sup>Ar) values are not superimposed. Each horizontal line spans the minimum and maximum values observed for the corresponding class of materials (data from [<a href="#j_pac-2019-0603_ref_015" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_015" data-bs-toggle="tooltip" title="15. J. K. Böhlke. Pure Appl. Chem.86, 1421 (2014).10.1515/pac-2013-0918Search in Google Scholar">15</a>]).</p></span></div></div></div></div> <div class="figure-wrapper" id="j_pac-2019-0603_fig_004"><div class="figure w-100"><div class="graphic"><img loading="lazy" src="/document/doi/10.1515/pac-2019-0603/asset/graphic/j_pac-2019-0603_fig_014.jpg" alt="Fig. 4: 
 
 Variation in atomic weight (black lines) of argon, A
 
 r
 
 (Ar), with amount fraction (green lines) of
 
 38
 
 Ar, x(
 
 38
 
 Ar), of selected argon-bearing materials. Because argon has three isotopes whose variations are not mass-dependent, the changes in the Ar(Ar) and x(38Ar) values are not superimposed. Each horizontal line spans the minimum and maximum values observed for the corresponding class of materials (data from [15]).
 "></img></div><div class="figure-description mb-3"><div class="figure-label h3"><span class="label">Fig. 4:</span></div><div class="figure-caption mb-2"><span class="caption"><p> <strong>Variation in atomic weight (black lines) of argon, <em>A</em></strong> <sub> <strong>r</strong> </sub> <strong>(Ar), with amount fraction (green lines) of</strong> <sup> <strong>38</strong> </sup> <strong>Ar, <em>x</em>(</strong> <sup> <strong>38</strong> </sup> <strong>Ar), of selected argon-bearing materials.</strong> Because argon has three isotopes whose variations are not mass-dependent, the changes in the <em>A</em><sub>r</sub>(Ar) and <em>x</em>(<sup>38</sup>Ar) values are not superimposed. Each horizontal line spans the minimum and maximum values observed for the corresponding class of materials (data from [<a href="#j_pac-2019-0603_ref_015" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_015" data-bs-toggle="tooltip" title="15. J. K. Böhlke. Pure Appl. Chem.86, 1421 (2014).10.1515/pac-2013-0918Search in Google Scholar">15</a>]).</p></span></div></div></div></div> <div class="figure-wrapper" id="j_pac-2019-0603_fig_005"><div class="figure w-100"><div class="graphic"><img loading="lazy" src="/document/doi/10.1515/pac-2019-0603/asset/graphic/j_pac-2019-0603_fig_015.jpg" alt="Fig. 5: 
 
 Variation in atomic weight (black lines) of argon, A
 
 r
 
 (Ar), with amount fraction (blue lines) of
 
 40
 
 Ar, x(
 
 40
 
 Ar), of selected argon-bearing materials. Because argon has three isotopes whose variations are not mass-dependent, the changes in the Ar(Ar) and x(40Ar) values are not superimposed. Each horizontal line spans the minimum and maximum values observed for the corresponding class of materials (data from [15]).
 "></img></div><div class="figure-description mb-3"><div class="figure-label h3"><span class="label">Fig. 5:</span></div><div class="figure-caption mb-2"><span class="caption"><p> <strong>Variation in atomic weight (black lines) of argon, <em>A</em></strong> <sub> <strong>r</strong> </sub> <strong>(Ar), with amount fraction (blue lines) of</strong> <sup> <strong>40</strong> </sup> <strong>Ar, <em>x</em>(</strong> <sup> <strong>40</strong> </sup> <strong>Ar), of selected argon-bearing materials.</strong> Because argon has three isotopes whose variations are not mass-dependent, the changes in the <em>A</em><sub>r</sub>(Ar) and <em>x</em>(<sup>40</sup>Ar) values are not superimposed. Each horizontal line spans the minimum and maximum values observed for the corresponding class of materials (data from [<a href="#j_pac-2019-0603_ref_015" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_015" data-bs-toggle="tooltip" title="15. J. K. Böhlke. Pure Appl. Chem.86, 1421 (2014).10.1515/pac-2013-0918Search in Google Scholar">15</a>]).</p></span></div></div></div></div> <div class="figure-wrapper" id="j_pac-2019-0603_fig_006"><div class="figure w-100"><div class="graphic"><img loading="lazy" src="/document/doi/10.1515/pac-2019-0603/asset/graphic/j_pac-2019-0603_fig_016.jpg" alt="Fig. 6: 
 
 Variation in atomic weight (black lines) of lead, A
 
 r
 
 (Pb), with amount fraction (orange lines) of
 
 204
 
 Pb, x(
 
 204
 
 Pb), of selected lead-bearing materials. Because lead has four isotopes whose variations are not mass-dependent, the changes in the Ar(Pb) and x(204Pb) values are not superimposed. Each horizontal line spans the minimum and maximum values observed for the corresponding class of materials (data from [16]).
 "></img></div><div class="figure-description mb-3"><div class="figure-label h3"><span class="label">Fig. 6:</span></div><div class="figure-caption mb-2"><span class="caption"><p> <strong>Variation in atomic weight (black lines) of lead, <em>A</em></strong> <sub> <strong>r</strong> </sub> <strong>(Pb), with amount fraction (orange lines) of</strong> <sup> <strong>204</strong> </sup> <strong>Pb, <em>x</em>(</strong> <sup> <strong>204</strong> </sup> <strong>Pb), of selected lead-bearing materials.</strong> Because lead has four isotopes whose variations are not mass-dependent, the changes in the <em>A</em><sub>r</sub>(Pb) and <em>x</em>(<sup>204</sup>Pb) values are not superimposed. Each horizontal line spans the minimum and maximum values observed for the corresponding class of materials (data from [<a href="#j_pac-2019-0603_ref_016" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_016" data-bs-toggle="tooltip" title="16. X. K. Zhu, J. Benefield, T. B. Coplen, Z. Gao, N. Holden. Pure Appl. Chem.93, 155 (2021).10.1515/pac-2018-0916Search in Google Scholar">16</a>]).</p></span></div></div></div></div> <div class="figure-wrapper" id="j_pac-2019-0603_fig_007"><div class="figure w-100"><div class="graphic"><img loading="lazy" src="/document/doi/10.1515/pac-2019-0603/asset/graphic/j_pac-2019-0603_fig_017.jpg" alt="Fig. 7: 
 
 Variation in atomic weight (black lines) of lead, A
 
 r
 
 (Pb), with amount fraction (green lines) of
 
 206
 
 Pb, x(
 
 206
 
 Pb), of selected lead-bearing materials. Because lead has four isotopes whose variations are not mass-dependent, the changes in the Ar(Pb) and x(206Pb) values are not superimposed. Each horizontal line spans the minimum and maximum values observed for the corresponding class of materials (data from [16]).
 "></img></div><div class="figure-description mb-3"><div class="figure-label h3"><span class="label">Fig. 7:</span></div><div class="figure-caption mb-2"><span class="caption"><p> <strong>Variation in atomic weight (black lines) of lead, <em>A</em></strong> <sub> <strong>r</strong> </sub> <strong>(Pb), with amount fraction (green lines) of</strong> <sup> <strong>206</strong> </sup> <strong>Pb, <em>x</em>(</strong> <sup> <strong>206</strong> </sup> <strong>Pb), of selected lead-bearing materials.</strong> Because lead has four isotopes whose variations are not mass-dependent, the changes in the <em>A</em><sub>r</sub>(Pb) and <em>x</em>(<sup>206</sup>Pb) values are not superimposed. Each horizontal line spans the minimum and maximum values observed for the corresponding class of materials (data from [<a href="#j_pac-2019-0603_ref_016" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_016" data-bs-toggle="tooltip" title="16. X. K. Zhu, J. Benefield, T. B. Coplen, Z. Gao, N. Holden. Pure Appl. Chem.93, 155 (2021).10.1515/pac-2018-0916Search in Google Scholar">16</a>]).</p></span></div></div></div></div> <div class="figure-wrapper" id="j_pac-2019-0603_fig_008"><div class="figure w-100"><div class="graphic"><img loading="lazy" src="/document/doi/10.1515/pac-2019-0603/asset/graphic/j_pac-2019-0603_fig_018.jpg" alt="Fig. 8: 
 
 Variation in atomic weight (black lines) of lead, A
 
 r
 
 (Pb), with amount fraction (blue lines) of
 
 207
 
 Pb, x(
 
 207
 
 Pb), of selected lead-bearing materials. Because lead has four isotopes whose variations are not mass-dependent, the changes in the Ar(Pb) and x(207Pb) values are not superimposed. Each horizontal line spans the minimum and maximum values observed for the corresponding class of materials (data from [16]).
 "></img></div><div class="figure-description mb-3"><div class="figure-label h3"><span class="label">Fig. 8:</span></div><div class="figure-caption mb-2"><span class="caption"><p> <strong>Variation in atomic weight (black lines) of lead, <em>A</em></strong> <sub> <strong>r</strong> </sub> <strong>(Pb), with amount fraction (blue lines) of</strong> <sup> <strong>207</strong> </sup> <strong>Pb, <em>x</em>(</strong> <sup> <strong>207</strong> </sup> <strong>Pb), of selected lead-bearing materials.</strong> Because lead has four isotopes whose variations are not mass-dependent, the changes in the <em>A</em><sub>r</sub>(Pb) and <em>x</em>(<sup>207</sup>Pb) values are not superimposed. Each horizontal line spans the minimum and maximum values observed for the corresponding class of materials (data from [<a href="#j_pac-2019-0603_ref_016" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_016" data-bs-toggle="tooltip" title="16. X. K. Zhu, J. Benefield, T. B. Coplen, Z. Gao, N. Holden. Pure Appl. Chem.93, 155 (2021).10.1515/pac-2018-0916Search in Google Scholar">16</a>]).</p></span></div></div></div></div> <div class="figure-wrapper" id="j_pac-2019-0603_fig_009"><div class="figure w-100"><div class="graphic"><img loading="lazy" src="/document/doi/10.1515/pac-2019-0603/asset/graphic/j_pac-2019-0603_fig_019.jpg" alt="Fig. 9: 
 
 Variation in atomic weight (black lines) of lead, A
 
 r
 
 (Pb), with amount fraction (pink lines) of
 
 208
 
 Pb, x(
 
 208
 
 Pb), of selected lead-bearing materials. Because lead has four isotopes whose variations are not mass-dependent, the changes in the Ar(Pb) and x(208Pb) values are not superimposed. Each horizontal line spans the minimum and maximum values observed for the corresponding class of materials (data from [16]).
 "></img></div><div class="figure-description mb-3"><div class="figure-label h3"><span class="label">Fig. 9:</span></div><div class="figure-caption mb-2"><span class="caption"><p> <strong>Variation in atomic weight (black lines) of lead, <em>A</em></strong> <sub> <strong>r</strong> </sub> <strong>(Pb), with amount fraction (pink lines) of</strong> <sup> <strong>208</strong> </sup> <strong>Pb, <em>x</em>(</strong> <sup> <strong>208</strong> </sup> <strong>Pb), of selected lead-bearing materials.</strong> Because lead has four isotopes whose variations are not mass-dependent, the changes in the <em>A</em><sub>r</sub>(Pb) and <em>x</em>(<sup>208</sup>Pb) values are not superimposed. Each horizontal line spans the minimum and maximum values observed for the corresponding class of materials (data from [<a href="#j_pac-2019-0603_ref_016" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_016" data-bs-toggle="tooltip" title="16. X. K. Zhu, J. Benefield, T. B. Coplen, Z. Gao, N. Holden. Pure Appl. Chem.93, 155 (2021).10.1515/pac-2018-0916Search in Google Scholar">16</a>]).</p></span></div></div></div></div> </section> <section id="j_pac-2019-0603_s_016"> <h2 class="subheading">11 Discontinuance of LSVEC as an isotopic reference material for carbon isotope delta measurements</h2> <p>The Commission notes that the international isotopic reference material LSVEC lithium carbonate which (together with NBS 19) has been used to define the carbon isotope-delta scale (VPDB), is able to absorb carbon dioxide from air [<a href="#j_pac-2019-0603_ref_056" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_056" data-bs-toggle="tooltip" title="56. S. Assonov. Rapid Commun. Mass Spectrom.32, 827 (2018).10.1002/rcm.8102Search in Google Scholar
 PubMed
 ">56</a>]. This process changes the carbon isotopic composition of LSVEC with time. As a consequence, LSVEC is unsuitable as an isotopic reference material for carbon isotope ratio analysis. Therefore, its use as carbon isotopic reference material is no longer recommended. The carbon isotope-delta scale is defined by the virtual material Vienna Peedee belemnite (VPDB). Since 2005, the VPDB scale has been defined by assigning consensus values of −46.6 ‰ to LSVEC lithium carbonate and +1.95 ‰ to NBS 19 calcium carbonate [<a href="#j_pac-2019-0603_ref_057" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_057" data-bs-toggle="tooltip" title="57. T. B. Coplen, W. A. Brand, M. Gehre, M. Gröning, H. A. J. Meijer, B. Toman, R. M. Verkouteren. Anal. Chem.78, 2439 (2006).10.1021/ac052027cSearch in Google Scholar
 PubMed
 ">57</a>, <a href="#j_pac-2019-0603_ref_058" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_058" data-bs-toggle="tooltip" title="58. T. B. Coplen, W. A. Brand, M. Gehre, M. Gröning, H. A. J. Meijer, B. Toman, R. M. Verkouteren. Rapid Commun. Mass Spectrom.20, 3165 (2006).10.1002/rcm.2727Search in Google Scholar
 PubMed
 ">58</a>]. Before a proper replacement material for LSVEC is identified, the Commission gives the following recommendations:<ol type="1" class="list " id="j_pac-2019-0603_list_005" list-type="order"><li class="listItem" id="j_pac-2019-0603_li_014"><div class="listItem-contents"><p>Users should refrain from using LSVEC as a carbon isotope-delta reference material.</p></div></li><li class="listItem" id="j_pac-2019-0603_li_015"><div class="listItem-contents"><p>Carbon isotope-delta measurements should still be normalized to the VPDB scale using at least two suitable international reference materials selected as appropriate by the users. The applied values should be published with the measurement results. The most recent recommended values are those of Brand et al. [<a href="#j_pac-2019-0603_ref_028" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_028" data-bs-toggle="tooltip" title="28. W. A. Brand, T. B. Coplen, J. Vogl, M. Rosner, T. Prohaska. Pure Appl. Chem. 2014 86, 425 (2014).10.1515/pac-2013-1023Search in Google Scholar">28</a>].</p></div></li></ol></p> <p>The Commission also notes the recommendation of the 2016 IAEA Technical Meeting on Stable Isotope Reference Materials [<a href="#j_pac-2019-0603_ref_059" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_059" data-bs-toggle="tooltip" title="59. 
 IAEA. Report of a Technical Meeting on “Development of IAEA Stable Isotope Reference Products, held 21-25 Nov 2016 in Vienna, Austria”, p. 37, https://nucleus.iaea.org/sites/ReferenceMaterials/Shared%20Documents/Publications/SI_meetings/StabIso_TM_REPORT_2016.pdf (accessed Apr 26, 2019).Search in Google Scholar">59</a>], which proposed the material IAEA-603 as the future replacement of the quarantined NBS 19. The formal change of both VPDB scale-realizing materials – NBS 19 and LSVEC – will be considered by the Commission when the replacement for LSVEC is agreed upon.</p> </section> <section id="j_pac-2019-0603_s_017"> <h2 class="subheading">12 New definition of the mole</h2> <p>The General Conference on Weights and Measures has adopted revised definitions of the kilogram, mole, ampere, and kelvin at its 26th meeting based on fundamental constants (Planck constant, Avogadro constant, elementary charge, and Boltzmann constant). These changes took effect on 20 May 2019. Of particular interest is the new definition of the mole in terms of the exact stipulated value for the Avogadro constant [<a href="#j_pac-2019-0603_ref_060" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_060" data-bs-toggle="tooltip" title="60. R. Marquardt, J. Meija, Z. Mester, M. Towns, R. Weir, R. Davis, J. Stohner. Pure Appl. Chem.89, 951 (2017).10.1515/pac-2016-0808Search in Google Scholar">60</a>, <a href="#j_pac-2019-0603_ref_061" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_061" data-bs-toggle="tooltip" title="61. R. Marquardt, J. Meija, Z. Mester, M. Towns, R. Weir, R. Davis, J. Stohner. Pure Appl. Chem.90, 175 (2018).10.1515/pac-2017-0106Search in Google Scholar">61</a>] “One mole contains exactly 6.022 140 76 × 10<sup>23</sup> elementary entities.” While this revision of the International System of Units has no practical effect on the atomic weights of the elements, calculation of molar masses to very high-precision will be affected by this change. Most notably, the molar mass of unbound carbon-12 atoms will no longer be 12 g mol<sup>−1</sup> exactly. Rather, it will acquire a small uncertainty of less than one part in 10<sup>9</sup>, which is of no consequence to chemists. This small change will arise because the 1971 definition of the mole was linked to carbon-12 whereas this is no longer the case in the new definition of the mole (meanwhile, the atomic mass unit remains linked to carbon-12). Hence, molar masses of elementary entities (in g mol<sup>−1</sup>) were numerically identical to their atomic masses (in Da). Also note that the 1971 definition of the mole, as clarified by the International Committee for Weights and Measures (CIPM) in 1980, refers to unbound carbon-12 atoms. In contrast, 12 g of pure carbon-12 bound in a substance such as diamond or graphite contains slightly more than 1 mol because an additional number of atoms is needed in order to make 12 g of substance compared to 12 g of unbound atoms as a result of mass loss (Δ<em>m</em> = Δ<em>E</em>/<em>c</em><sup>2</sup>) due to energy that is necessary to bind the atoms. The order of magnitude of this effect is one part in 10<sup>9</sup>.</p> </section> <section id="j_pac-2019-0603_s_018"> <h2 class="subheading">13 Atomic masses and half-lives of selected radioactive isotopes</h2> <p>For elements that have no stable or long-lived isotopes, data on radioactive half-lives and atomic-mass values for selected isotopes of interest are available from dedicated evaluations published in full detail elsewhere [<a href="#j_pac-2019-0603_ref_011" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_011" data-bs-toggle="tooltip" title="11. M. Wang, W. J. Huang, F. G. Kondev, G. Audi, S. Naimi. Chin. Phys. C45, 030003 (2021).10.1088/1674-1137/abddafSearch in Google Scholar">11</a>, <a href="#j_pac-2019-0603_ref_062" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_062" data-bs-toggle="tooltip" title="62. F. G. Kondev, M. Wang, W. J. Huang, S. Naimi, G. Augi. Chin. Phys. C. 45, 030001 (2021).10.1088/1674-1137/abddaeSearch in Google Scholar">62</a>], and a selection of the reported values is listed in <a href="#j_pac-2019-0603_tab_006" class="link link-table" data-bs-target="j_pac-2019-0603_tab_006">Table 2</a>. There is no general agreement on which of the various isotopes of radioactive elements are, or are likely to be judged, important. Various criteria such as longest half-life, production in quantity, and commercial relevance have been applied in the past. This table contains information about selected radioactive nuclides which will enable the calculation of atomic weights of radioactive materials with a variety of isotopic compositions. Nuclide masses are taken from the AME2020 report [<a href="#j_pac-2019-0603_ref_011" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_011" data-bs-toggle="tooltip" title="11. M. Wang, W. J. Huang, F. G. Kondev, G. Audi, S. Naimi. Chin. Phys. C45, 030003 (2021).10.1088/1674-1137/abddafSearch in Google Scholar">11</a>] whereas the half-life values are from the NUBASE2020 report [<a href="#j_pac-2019-0603_ref_062" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_062" data-bs-toggle="tooltip" title="62. F. G. Kondev, M. Wang, W. J. Huang, S. Naimi, G. Augi. Chin. Phys. C. 45, 030001 (2021).10.1088/1674-1137/abddaeSearch in Google Scholar">62</a>]. Uncertainties of these values are omitted for brevity and are available in the aforementioned reports.</p> <div class="table-wrap mb-4" id="j_pac-2019-0603_tab_006" position="float"> <div class="table-label h3">Table 2:</div> <div class="caption mb-3"> <p> <strong>Atomic masses and half-lives of selected radioactive nuclides.</strong> Data are transcribed from AME2020 [<a href="#j_pac-2019-0603_ref_011" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_011" data-bs-toggle="tooltip" title="11. M. Wang, W. J. Huang, F. G. Kondev, G. Audi, S. Naimi. Chin. Phys. C45, 030003 (2021).10.1088/1674-1137/abddafSearch in Google Scholar">11</a>] and NUBASE2020 [<a href="#j_pac-2019-0603_ref_062" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_062" data-bs-toggle="tooltip" title="62. F. G. Kondev, M. Wang, W. J. Huang, S. Naimi, G. Augi. Chin. Phys. C. 45, 030001 (2021).10.1088/1674-1137/abddaeSearch in Google Scholar">62</a>] with uncertainties omitted. (Note: Element names and symbols are according to current nomenclature).</p> </div> <table xmlns:env="http://degruyter.com/resources/metadata" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:dgror="http://degruyter.com/resources/fetched-ror-id" xmlns:m="http://degruyter.com/resources/metadata" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:tei="http://www.tei-c.org/ns/1.0" rules="groups" frame="hsides" class="content-table"> <colgroup> <col align="left"></col> <col align="left"></col> <col align="left"></col> <col align="right"></col> <col align="right"></col> <col align="left"></col> </colgroup> <thead> <tr> <th style="text-align: left">Atomic number</th> <th style="text-align: left">Element</th> <th style="text-align: left">Symbol</th> <th style="text-align: right">Mass number<sup>a</sup></th> <th style="text-align: right">Atomic mass (Da)<sup>b</sup></th> <th style="text-align: left">Half-life</th> </tr> </thead> <tbody> <tr> <td style="text-align: left">19</td> <td style="text-align: left">potassium</td> <td style="text-align: left">K</td> <td style="text-align: right">40*</td> <td style="text-align: right">39.964 00</td> <td style="text-align: left">1.248 × 10<sup>9</sup> a</td> </tr> <tr> <td style="text-align: left">20</td> <td style="text-align: left">calcium</td> <td style="text-align: left">Ca</td> <td style="text-align: right">48*</td> <td style="text-align: right">47.952 52</td> <td style="text-align: left">5.6 × 10<sup>19</sup> a</td> </tr> <tr> <td style="text-align: left">23</td> <td style="text-align: left">vanadium</td> <td style="text-align: left">V</td> <td style="text-align: right">50*</td> <td style="text-align: right">49.947 16</td> <td style="text-align: left">2.7 × 10<sup>17</sup> a</td> </tr> <tr> <td style="text-align: left">32</td> <td style="text-align: left">germanium</td> <td style="text-align: left">Ge</td> <td style="text-align: right">76*</td> <td style="text-align: right">75.921 40</td> <td style="text-align: left">1.88 × 10<sup>21</sup> a</td> </tr> <tr> <td style="text-align: left">34</td> <td style="text-align: left">selenium</td> <td style="text-align: left">Se</td> <td style="text-align: right">82*</td> <td style="text-align: right">81.916 70</td> <td style="text-align: left">8.76 × 10<sup>19</sup> a</td> </tr> <tr> <td style="text-align: left">37</td> <td style="text-align: left">rubidium</td> <td style="text-align: left">Rb</td> <td style="text-align: right">87*</td> <td style="text-align: right">86.909 18</td> <td style="text-align: left">4.97 × 10<sup>10</sup> a</td> </tr> <tr> <td style="text-align: left">40</td> <td style="text-align: left">zirconium</td> <td style="text-align: left">Zr</td> <td style="text-align: right">96*</td> <td style="text-align: right">95.908 28</td> <td style="text-align: left">2.34 × 10<sup>19</sup> a</td> </tr> <tr> <td style="text-align: left">42</td> <td style="text-align: left">molybdenum</td> <td style="text-align: left">Mo</td> <td style="text-align: right">100*</td> <td style="text-align: right">99.907 47</td> <td style="text-align: left">7.07 × 10<sup>18</sup> a</td> </tr> <tr> <td style="text-align: left">43</td> <td style="text-align: left">technetium</td> <td style="text-align: left">Tc</td> <td style="text-align: right">97</td> <td style="text-align: right">96.906 36</td> <td style="text-align: left">4.21 × 10<sup>6</sup> a</td> </tr> <tr> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">98</td> <td style="text-align: right">97.907 21</td> <td style="text-align: left">4.2 × 10<sup>6</sup> a</td> </tr> <tr> <td style="text-align: left">48</td> <td style="text-align: left">cadmium</td> <td style="text-align: left">Cd</td> <td style="text-align: right">113*</td> <td style="text-align: right">112.904 41</td> <td style="text-align: left">8.04 × 10<sup>15</sup> a</td> </tr> <tr> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">116*</td> <td style="text-align: right">115.904 76</td> <td style="text-align: left">2.69 × 10<sup>19</sup> a</td> </tr> <tr> <td style="text-align: left">49</td> <td style="text-align: left">indium</td> <td style="text-align: left">In</td> <td style="text-align: right">115*</td> <td style="text-align: right">114.903 88</td> <td style="text-align: left">4.41 × 10<sup>14</sup> a</td> </tr> <tr> <td style="text-align: left">52</td> <td style="text-align: left">tellurium</td> <td style="text-align: left">Te</td> <td style="text-align: right">128*</td> <td style="text-align: right">127.904 46</td> <td style="text-align: left">2.25 × 10<sup>24</sup> a</td> </tr> <tr> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">130*</td> <td style="text-align: right">129.906 22</td> <td style="text-align: left">7.91 × 10<sup>20</sup> a</td> </tr> <tr> <td style="text-align: left">54</td> <td style="text-align: left">xenon</td> <td style="text-align: left">Xe</td> <td style="text-align: right">136*</td> <td style="text-align: right">135.907 21</td> <td style="text-align: left">2.18 × 10<sup>21</sup> a</td> </tr> <tr> <td style="text-align: left">56</td> <td style="text-align: left">barium</td> <td style="text-align: left">Ba</td> <td style="text-align: right">130*</td> <td style="text-align: right">129.906 33</td> <td style="text-align: left">1 × 10<sup>21</sup> a</td> </tr> <tr> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">132*</td> <td style="text-align: right">131.905 06</td> <td style="text-align: left">>3.00 × 10<sup>20</sup> a</td> </tr> <tr> <td style="text-align: left">57</td> <td style="text-align: left">lanthanum</td> <td style="text-align: left">La</td> <td style="text-align: right">138*</td> <td style="text-align: right">137.907 12</td> <td style="text-align: left">1.03 × 10<sup>11</sup> a</td> </tr> <tr> <td style="text-align: left">60</td> <td style="text-align: left">neodymium</td> <td style="text-align: left">Nd</td> <td style="text-align: right">144*</td> <td style="text-align: right">143.910 09</td> <td style="text-align: left">2.29 × 10<sup>15</sup> a</td> </tr> <tr> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">150*</td> <td style="text-align: right">149.920 90</td> <td style="text-align: left">9.3 × 10<sup>18</sup> a</td> </tr> <tr> <td style="text-align: left">61</td> <td style="text-align: left">promethium</td> <td style="text-align: left">Pm</td> <td style="text-align: right">145</td> <td style="text-align: right">144.912 76</td> <td style="text-align: left">17.7 a</td> </tr> <tr> <td style="text-align: left">62</td> <td style="text-align: left">samarium</td> <td style="text-align: left">Sm</td> <td style="text-align: right">147*</td> <td style="text-align: right">146.914 90</td> <td style="text-align: left">1.066 × 10<sup>11</sup> a</td> </tr> <tr> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">148*</td> <td style="text-align: right">147.914 83</td> <td style="text-align: left">6.3 × 10<sup>15</sup> a</td> </tr> <tr> <td style="text-align: left">63</td> <td style="text-align: left">europium</td> <td style="text-align: left">Eu</td> <td style="text-align: right">151*</td> <td style="text-align: right">150.919 86</td> <td style="text-align: left">4.6 × 10<sup>18</sup> a</td> </tr> <tr> <td style="text-align: left">71</td> <td style="text-align: left">lutetium</td> <td style="text-align: left">Lu</td> <td style="text-align: right">176*</td> <td style="text-align: right">175.942 69</td> <td style="text-align: left">3.70 × 10<sup>10</sup> a</td> </tr> <tr> <td style="text-align: left">72</td> <td style="text-align: left">hafnium</td> <td style="text-align: left">Hf</td> <td style="text-align: right">174*</td> <td style="text-align: right">173.940 05</td> <td style="text-align: left">2.0 × 10<sup>15</sup> a</td> </tr> <tr> <td style="text-align: left">74</td> <td style="text-align: left">tungsten</td> <td style="text-align: left">W</td> <td style="text-align: right">180*</td> <td style="text-align: right">179.946 71</td> <td style="text-align: left">1.59 × 10<sup>18</sup> a</td> </tr> <tr> <td style="text-align: left">75</td> <td style="text-align: left">rhenium</td> <td style="text-align: left">Re</td> <td style="text-align: right">187*</td> <td style="text-align: right">186.955 75</td> <td style="text-align: left">4.16 × 10<sup>10</sup> a</td> </tr> <tr> <td style="text-align: left">76</td> <td style="text-align: left">osmium</td> <td style="text-align: left">Os</td> <td style="text-align: right">184*</td> <td style="text-align: right">183.952 49</td> <td style="text-align: left">1.12 × 10<sup>13</sup> a</td> </tr> <tr> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">186*</td> <td style="text-align: right">185.953 84</td> <td style="text-align: left">2.0 × 10<sup>15</sup> a</td> </tr> <tr> <td style="text-align: left">78</td> <td style="text-align: left">platinum</td> <td style="text-align: left">Pt</td> <td style="text-align: right">190*</td> <td style="text-align: right">189.959 95</td> <td style="text-align: left">4.83 × 10<sup>11</sup> a</td> </tr> <tr> <td style="text-align: left">83</td> <td style="text-align: left">bismuth</td> <td style="text-align: left">Bi</td> <td style="text-align: right">209*</td> <td style="text-align: right">208.980 40</td> <td style="text-align: left">2.01 × 10<sup>19</sup> a</td> </tr> <tr> <td style="text-align: left">84</td> <td style="text-align: left">polonium</td> <td style="text-align: left">Po</td> <td style="text-align: right">209</td> <td style="text-align: right">208.982 43</td> <td style="text-align: left">124 a</td> </tr> <tr> <td style="text-align: left">85</td> <td style="text-align: left">astatine</td> <td style="text-align: left">At</td> <td style="text-align: right">210</td> <td style="text-align: right">209.987 15</td> <td style="text-align: left">8.1 h</td> </tr> <tr> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">211</td> <td style="text-align: right">210.987 50</td> <td style="text-align: left">7.214 h</td> </tr> <tr> <td style="text-align: left">86</td> <td style="text-align: left">radon</td> <td style="text-align: left">Rn</td> <td style="text-align: right">210</td> <td style="text-align: right">209.989 69</td> <td style="text-align: left">2.4 h</td> </tr> <tr> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">211</td> <td style="text-align: right">210.990 60</td> <td style="text-align: left">14.6 h</td> </tr> <tr> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">222</td> <td style="text-align: right">222.017 58</td> <td style="text-align: left">3.8215 d</td> </tr> <tr> <td style="text-align: left">87</td> <td style="text-align: left">francium</td> <td style="text-align: left">Fr</td> <td style="text-align: right">212</td> <td style="text-align: right">211.996 23</td> <td style="text-align: left">20.0 min</td> </tr> <tr> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">222</td> <td style="text-align: right">222.017 58</td> <td style="text-align: left">14.2 min</td> </tr> <tr> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">223</td> <td style="text-align: right">223.019 73</td> <td style="text-align: left">22.00 min</td> </tr> <tr> <td style="text-align: left">88</td> <td style="text-align: left">radium</td> <td style="text-align: left">Ra</td> <td style="text-align: right">226</td> <td style="text-align: right">226.025 41</td> <td style="text-align: left">1.600 × 10<sup>3</sup> a</td> </tr> <tr> <td style="text-align: left">89</td> <td style="text-align: left">actinium</td> <td style="text-align: left">Ac</td> <td style="text-align: right">227</td> <td style="text-align: right">227.027 75</td> <td style="text-align: left">21.772 a</td> </tr> <tr> <td style="text-align: left">90</td> <td style="text-align: left">thorium</td> <td style="text-align: left">Th</td> <td style="text-align: right">230*</td> <td style="text-align: right">230.033 13</td> <td style="text-align: left">7.54 × 10<sup>4</sup> a</td> </tr> <tr> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">232*</td> <td style="text-align: right">232.038 05</td> <td style="text-align: left">1.40 × 10<sup>10</sup> a</td> </tr> <tr> <td style="text-align: left">91</td> <td style="text-align: left">protactinium</td> <td style="text-align: left">Pa</td> <td style="text-align: right">231*</td> <td style="text-align: right">231.035 88</td> <td style="text-align: left">3.265 × 10<sup>4</sup> a</td> </tr> <tr> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">233</td> <td style="text-align: right">233.040 25</td> <td style="text-align: left">26.975 d</td> </tr> <tr> <td style="text-align: left">92</td> <td style="text-align: left">uranium</td> <td style="text-align: left">U</td> <td style="text-align: right">233</td> <td style="text-align: right">233.039 63</td> <td style="text-align: left">1.592 × 10<sup>5</sup> a</td> </tr> <tr> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">234*</td> <td style="text-align: right">234.040 95</td> <td style="text-align: left">2.455 × 10<sup>5</sup> a</td> </tr> <tr> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">235*</td> <td style="text-align: right">235.043 93</td> <td style="text-align: left">7.04 × 10<sup>8</sup> a</td> </tr> <tr> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">236</td> <td style="text-align: right">236.045 57</td> <td style="text-align: left">2.342 × 10<sup>7</sup> a</td> </tr> <tr> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">238*</td> <td style="text-align: right">238.050 79</td> <td style="text-align: left">4.463 × 10<sup>9</sup> a</td> </tr> <tr> <td style="text-align: left">93</td> <td style="text-align: left">neptunium</td> <td style="text-align: left">Np</td> <td style="text-align: right">237</td> <td style="text-align: right">237.048 17</td> <td style="text-align: left">2.144 × 10<sup>6</sup> a</td> </tr> <tr> <td style="text-align: left">94</td> <td style="text-align: left">plutonium</td> <td style="text-align: left">Pu</td> <td style="text-align: right">244</td> <td style="text-align: right">244.064 20</td> <td style="text-align: left">8.13 × 10<sup>7</sup> a</td> </tr> <tr> <td style="text-align: left">95</td> <td style="text-align: left">americium</td> <td style="text-align: left">Am</td> <td style="text-align: right">243</td> <td style="text-align: right">243.061 38</td> <td style="text-align: left">7.350 × 10<sup>3</sup> a</td> </tr> <tr> <td style="text-align: left">96</td> <td style="text-align: left">curium</td> <td style="text-align: left">Cm</td> <td style="text-align: right">247</td> <td style="text-align: right">247.070 35</td> <td style="text-align: left">1.56 × 10<sup>7</sup> a</td> </tr> <tr> <td style="text-align: left">97</td> <td style="text-align: left">berkelium</td> <td style="text-align: left">Bk</td> <td style="text-align: right">247</td> <td style="text-align: right">247.070 31</td> <td style="text-align: left">1.38 × 10<sup>3</sup> a</td> </tr> <tr> <td style="text-align: left">98</td> <td style="text-align: left">californium</td> <td style="text-align: left">Cf</td> <td style="text-align: right">251</td> <td style="text-align: right">251.079 59</td> <td style="text-align: left">898 a</td> </tr> <tr> <td style="text-align: left">99</td> <td style="text-align: left">einsteinium</td> <td style="text-align: left">Es</td> <td style="text-align: right">252</td> <td style="text-align: right">252.082 98</td> <td style="text-align: left">471.7 d</td> </tr> <tr> <td style="text-align: left">100</td> <td style="text-align: left">fermium</td> <td style="text-align: left">Fm</td> <td style="text-align: right">257</td> <td style="text-align: right">257.095 11</td> <td style="text-align: left">100.5 d</td> </tr> <tr> <td style="text-align: left">101</td> <td style="text-align: left">mendelevium</td> <td style="text-align: left">Md</td> <td style="text-align: right">258</td> <td style="text-align: right">258.098 43</td> <td style="text-align: left">51.6 d</td> </tr> <tr> <td style="text-align: left">102</td> <td style="text-align: left">nobelium</td> <td style="text-align: left">No</td> <td style="text-align: right">259</td> <td style="text-align: right">259.101 00</td> <td style="text-align: left">58 min</td> </tr> <tr> <td style="text-align: left">103</td> <td style="text-align: left">lawrencium</td> <td style="text-align: left">Lr</td> <td style="text-align: right">262</td> <td style="text-align: right">262.109 62</td> <td style="text-align: left">4 h</td> </tr> <tr> <td style="text-align: left">104</td> <td style="text-align: left">rutherfordium</td> <td style="text-align: left">Rf</td> <td style="text-align: right">267</td> <td style="text-align: right">267.121 79</td> <td style="text-align: left">2.5 h</td> </tr> <tr> <td style="text-align: left">105</td> <td style="text-align: left">dubnium</td> <td style="text-align: left">Db</td> <td style="text-align: right">268</td> <td style="text-align: right">268.125 67</td> <td style="text-align: left">29 h</td> </tr> <tr> <td style="text-align: left">106</td> <td style="text-align: left">seaborgium</td> <td style="text-align: left">Sg</td> <td style="text-align: right">269</td> <td style="text-align: right">269.128 50</td> <td style="text-align: left">5 min</td> </tr> <tr> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">271</td> <td style="text-align: right">271.133 78</td> <td style="text-align: left">2.2 min</td> </tr> <tr> <td style="text-align: left">107</td> <td style="text-align: left">bohrium</td> <td style="text-align: left">Bh</td> <td style="text-align: right">270</td> <td style="text-align: right">270.133 37</td> <td style="text-align: left">3.8 min</td> </tr> <tr> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">274</td> <td style="text-align: right">274.143 60</td> <td style="text-align: left">57 s</td> </tr> <tr> <td style="text-align: left">108</td> <td style="text-align: left">hassium</td> <td style="text-align: left">Hs</td> <td style="text-align: right">269</td> <td style="text-align: right">269.133 65</td> <td style="text-align: left">15 s</td> </tr> <tr> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">270</td> <td style="text-align: right">270.134 31</td> <td style="text-align: left">9 s</td> </tr> <tr> <td style="text-align: left">109</td> <td style="text-align: left">meitnerium</td> <td style="text-align: left">Mt</td> <td style="text-align: right">277</td> <td style="text-align: right">277.153 53</td> <td style="text-align: left">9 s</td> </tr> <tr> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">278</td> <td style="text-align: right">278.156 49</td> <td style="text-align: left">6 s</td> </tr> <tr> <td style="text-align: left">110</td> <td style="text-align: left">darmstadtium</td> <td style="text-align: left">Ds</td> <td style="text-align: right">281</td> <td style="text-align: right">281.164 55</td> <td style="text-align: left">14 s</td> </tr> <tr> <td style="text-align: left">111</td> <td style="text-align: left">roentgenium</td> <td style="text-align: left">Rg</td> <td style="text-align: right">282</td> <td style="text-align: right">282.169 34</td> <td style="text-align: left">130 s</td> </tr> <tr> <td style="text-align: left">112</td> <td style="text-align: left">copernicium</td> <td style="text-align: left">Cn</td> <td style="text-align: right">285</td> <td style="text-align: right">285.177 23</td> <td style="text-align: left">30 s</td> </tr> <tr> <td style="text-align: left">113</td> <td style="text-align: left">nihonium</td> <td style="text-align: left">Nh</td> <td style="text-align: right">285</td> <td style="text-align: right">285.180 11</td> <td style="text-align: left">4.6 s</td> </tr> <tr> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">286</td> <td style="text-align: right">286.182 46</td> <td style="text-align: left">12 s</td> </tr> <tr> <td style="text-align: left">114</td> <td style="text-align: left">flerovium</td> <td style="text-align: left">Fl</td> <td style="text-align: right">289</td> <td style="text-align: right">289.190 52</td> <td style="text-align: left">2.1 s</td> </tr> <tr> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">290</td> <td style="text-align: right">290.191 88</td> <td style="text-align: left">80 s</td> </tr> <tr> <td style="text-align: left">115</td> <td style="text-align: left">moscovium</td> <td style="text-align: left">Mc</td> <td style="text-align: right">288</td> <td style="text-align: right">288.192 88</td> <td style="text-align: left">177 ms</td> </tr> <tr> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">289</td> <td style="text-align: right">289.193 97</td> <td style="text-align: left">410 ms</td> </tr> <tr> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">290</td> <td style="text-align: right">290.196 24</td> <td style="text-align: left">840 ms</td> </tr> <tr> <td style="text-align: left">116</td> <td style="text-align: left">livermorium</td> <td style="text-align: left">Lv</td> <td style="text-align: right">291</td> <td style="text-align: right">291.201 01</td> <td style="text-align: left">26 ms</td> </tr> <tr> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">292</td> <td style="text-align: right">292.201 97</td> <td style="text-align: left">16 ms</td> </tr> <tr> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: left"></td> <td style="text-align: right">293</td> <td style="text-align: right">293.204 58</td> <td style="text-align: left">70 ms</td> </tr> <tr> <td style="text-align: left">117</td> <td style="text-align: left">tennessine</td> <td style="text-align: left">Ts</td> <td style="text-align: right">294</td> <td style="text-align: right">294.210 84</td> <td style="text-align: left">70 ms</td> </tr> <tr> <td style="text-align: left">118</td> <td style="text-align: left">oganesson</td> <td style="text-align: left">Og</td> <td style="text-align: right">294</td> <td style="text-align: right">294.213 98</td> <td style="text-align: left">0.7 ms</td> </tr> </tbody> </table> <div class="table-wrap-foot"> <ol class="footnote-group" id=""> <li class="footnote footnote-noLabel" id="j_pac-2019-0603_fn_003" fn-type="other"> <p> <sup>a</sup>Long-lived radioactive isotopes of elements with a characteristic terrestrial isotopic composition that contribute to the standard atomic weight determinations are marked with an asterisk (*). <sup>b</sup>IUPAC-recommended symbols are used for units of time: year (a), day (d), minute (min), second (s), millisecond (ms).</p> </li> </ol> </div> </div> </section> <section id="j_pac-2019-0603_s_019"> <h2 class="subheading">14 IUPAC Periodic Table of the Elements and Isotopes</h2> <p>The Periodic Table of the Elements, developed independently by Mendeleev and Meyer in 1869, represents a remarkable achievement leading to improved understanding of the electronic structure of the atoms and the chemical and physical properties of the elements. In recognition of this milestone, the United Nations General Assembly proclaimed 2019 as the International Year of the Periodic Table of Chemical Elements during its 74th Plenary Meeting. Traditionally, the Periodic Table includes the standard atomic weights of the elements. With the introduction of intervals to represent the standard atomic weights for elements that have large variations in isotopic abundance from which atomic weights are calculated, members of the Commission together with assistance from the IUPAC Committee on Chemistry Education developed a Periodic Table of the Isotopes [<a href="#j_pac-2019-0603_ref_006" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_006" data-bs-toggle="tooltip" title="6. N. E. Holden, T. B. Coplen, J. K. Böhlke, L. V. Tarbox, J. Benefield, J. R. de Laeter, P. G. Mahaffy, G. O’Connor, E. Roth, D. H. Tepper, T. Walczyk, M. E. Wieser, S. Yoneda. Pure Appl. Chem.90, 1833 (2018).10.1515/pac-2015-0703Search in Google Scholar">6</a>, <a href="#j_pac-2019-0603_ref_008" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_008" data-bs-toggle="tooltip" title="8. 
 Isotopes Matter, https://www.isotopesmatter.com (accessed Jan 25, 2021).Search in Google Scholar">8</a>, <a href="#j_pac-2019-0603_ref_063" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_063" data-bs-toggle="tooltip" title="63. N. E. Holden, T. B. Coplen, J. K. Böhlke, M. E. Wieser, G. Singleton T. R. Walczyk, S. Yoneda, P. G. Mahaffy, L. V. Tarbox. Chem. Int.33(4), 20 (2011), https://doi.org/10.1515/ci.2011.33.4.20c.Search in Google Scholar">63</a>], which has now been published as the IUPAC Periodic Table of Elements and Isotopes [<a href="#j_pac-2019-0603_ref_006" class="link link-bibr" data-bs-target="j_pac-2019-0603_ref_006" data-bs-toggle="tooltip" title="6. N. E. Holden, T. B. Coplen, J. K. Böhlke, L. V. Tarbox, J. Benefield, J. R. de Laeter, P. G. Mahaffy, G. O’Connor, E. Roth, D. H. Tepper, T. Walczyk, M. E. Wieser, S. Yoneda. Pure Appl. Chem.90, 1833 (2018).10.1515/pac-2015-0703Search in Google Scholar">6</a>]. One goal of this IUPAC-sponsored project was to produce learner-oriented materials on an interactive periodic table to emphasize the existence of isotopes, the role of isotopic abundances in the determination of atomic weights, and applications of isotopes in science and industry.</p> <p>In August 2016, IUPAC launched an interactive electronic version of the Periodic Table of the Elements and Isotopes. These new resources are created for educators and students at secondary and post-secondary levels, and they inform the public about the many uses of isotopes in our lives. They are based on educational practices that encourage engaged and active learning by students. The IUPAC Interactive Electronic Periodic Table and accompanying resources can be accessed at <a href="http://www.isotopesmatter.com" class="link link-external" rel="noopener noreferrer nofollow" target="_blank">www.isotopesmatter.com</a>.</p> </section> <section id="j_pac-2019-0603_s_020"> <h2 class="subheading">15 Membership of sponsoring bodies</h2> <p>Membership of the Inorganic Chemistry Division Committee for the period 2020–2021 was as follows:</p> <p> <strong>President:</strong> L. Öhrström (Sweden); <strong>Vice President:</strong> L. Armelao (Italy); <strong>Secretary:</strong> D. Rabinovich (USA); <strong>Titular members:</strong> J. Colón (Puerto Rico), M. Hasegawa (Japan), P. Knauth (France), M.H. Lim (South Korea), R. Macaluso (USA), J. Meija (Canada), X.K. Zhu (China/Beijing); <strong>Associate members:</strong> M. Diop (Senegal), J. Galamba Correia (Portugal), Pilar Gómez-Sal (Spain), P. Karen (Norway), A. Powell (Germany), T. Walczyk (Singapore); <strong>National representatives:</strong> F. Abdul Aziz (Malaysia), Y. Gorbunova (Russia), M. Gruden-Pavlovic (Serbia), P.J. Kulesza (Poland), G. J. Leigh (UK), O. Metin (Turkey), K. Sakai (Japan), V. Stilinović (Coratia), Yi-Chou Tsai (China/Taipei), and Michael Wieser (Canada).</p> <p>Membership of the Inorganic Chemistry Division Committee for the period 2018–2019 was as follows:</p> <p> <strong>President:</strong> L. Öhrström (Sweden); <strong>Vice President:</strong> J. Garcia Martinez (Spain); <strong>Secretary:</strong> M. Leskelä (Finland); <strong>Titular members:</strong> J. Reedijk (The Netherlands); X.K. Zhu (China); L. Armelao (Italy); P. Karen (Norway), R. Macaluso (USA); M. Hasegawa (Japan), M. Drabik (Slovakia); <strong>Associate members:</strong> A. Powell (Germany), L. Meesuk (Thailand), F. Abdul Aziz (Malaysia), J. Colón (Puerto Rico), T. Walczyk (Singapore), D. Rabinovich<em>;</em><strong>National representatives:</strong> J. Galamba Correia (Portugal), S. Kalmykov (Russia), P. Knauth (France), K. Yoon (South Korea), M. Diop (Senegal), J. Leigh (UK), K. Sakai (Japan), N. Trendafilova (Bulgaria), V. Stilinović (Coratia), O. Metin (Turkey), M.H. Lim (South Korea), P.J. Kulesza (Poland).</p> <p>Membership of the Inorganic Chemistry Division Committee for the period 2016–2017 was as follows:</p> <p> <strong>President:</strong> J. Reedijk (The Netherlands); <strong>Secretary:</strong> M. Leskelä (Finland); <strong>Vice President:</strong> L. Öhrström (Sweden); <strong>Titular Members:</strong> R. D. Loss (Australia); L. Armelao (Italy); T. Ding (China); P. Karen (Norway); D. Rabinovich (USA); T. Walczyk (Singapore); M. E. Wieser (Canada); <strong>Associate Members:</strong> M. Drábik (Slovakia); K. Sakai (Japan); N. Trendafilova (Bulgaria); L. M. Meesuk (Thailand); F. Abdul Aziz (Malaysia); J. Colon (Puerto Rico); <strong>National Representatives:</strong> J. Galamba Correia (Portugal); S. N. Kalmykov (Russia); S. Mathur (Germany); A. Kilic (Turkey); M. Hasegawa (Japan); P. Knauth (France); K. B. Yoon (South Korea); M. Diop (Senegal); J. Darkwa (South Africa); J. Leigh (UK).</p> <p>Membership of the Inorganic Chemistry Division Committee for the period 2014–2015 was as follows:</p> <p> <strong>President:</strong> J. Reedijk (The Netherlands); <strong>Secretary:</strong> M. Leskelä (Finland); <strong>Vice President:</strong> L. R. Öhrström (Sweden); <strong>Titular Members:</strong> R. D. Loss (Australia); T. Ding (China); M. Drábik (Slovakia); E. Y. Tshuva (Israel); D. Rabinovich (USA); T. Walczyk (Singapore); M. E. Wieser (Canada); <strong>Associate Members:</strong> J. Garcia-Martinez (Spain); P. Karen (Norway); A. Kilic (Turkey); R. N. Vannier (France); J. Buchweshaija (Tanzania); K. Sakai (Japan); <strong>National Representatives:</strong> L. Armaleo (Italy); F. Abdul Aziz (Malaysia); A. Badshah (Pakistan); V. Chandrasekhar (India); J. Galamba Correia (Portugal); S. N. Kalmykov (Russia); S. Mathur (Germany); L. M. Meesuk (Thailand); B. Prugovecki (Croatia); N. Trendafilova (Bulgaria).</p> <p>Membership of the Commission on Isotopic Abundances and Atomic Weights for the period 2020–2021 was as follows:</p> <p> <strong>Chair:</strong> J. Meija (Canada); <strong>Secretary:</strong> T. Prohaska (Austria); <strong>Titular Members:</strong> M. Gröning (Austria), J. Irrgeher (Austria), J. Vogl (Germany), H. Meijer (The Netherlands); <strong>Associate Members:</strong> P. Dunn (UK), H. Moossen (Germany), A. Possolo (USA), Y. Takahashi (Japan), and Jun Wang (China/Beijing).</p> <p>Membership of the Commission on Isotopic Abundances and Atomic Weights for the period 2018–2019 was as follows:</p> <p> <strong>Chair:</strong> J. Meija (Canada); <strong>Secretary:</strong> T. Prohaska (Austria); <strong>Titular Members:</strong> M. Gröning (Austria); J. Irrgeher (Austria); J. Vogl (Germany); H. Meijer (The Netherlands); <strong>Associate Members:</strong> A. Possolo (USA); J. Wang (China), P. Dunn (UK).</p> <p>Membership of the Commission on Isotopic Abundances and Atomic Weights for the period 2016–2017 was as follows:</p> <p> <strong>Chair:</strong> J. Meija (Canada); <strong>Secretary:</strong> T. Prohaska (Austria); <strong>Titular Members:</strong> M. Gröning (Austria); J. Irrgeher (Germany); J. Vogl (Germany); X. K. Zhu (China); <strong>Associate Members:</strong> L. Chesson (USA), A. Possolo (USA); H. Meijer (The Netherlands). <strong>National Representatives:</strong> P. De Bièvre (Belgium).</p> <p>Membership of the Commission on Isotopic Abundances and Atomic Weights for the period 2014–2015 was as follows:</p> <p> <strong>Chair:</strong> J. Meija (Canada); <strong>Secretary:</strong> T. Prohaska (Austria); <strong>Titular Members:</strong> W. A. Brand (Germany); M. Gröning (Austria); R. Schönberg (Germany); X. K. Zhu (China); <strong>Associate Members:</strong> T. Hirata (Japan); J. Vogl (Germany); J. Irrgeher (Germany); <strong>National Representatives:</strong> T. B. Coplen (USA); P. De Bièvre (Belgium).</p> </section> <section id="j_pac-2019-0603_s_021"> <h2 class="subheading">16 In memoriam: Paul De Bièvre (1933–2016)</h2> <p>The Commission notes the death of the inaugural Chairman of the Subcommittee on Isotopic Abundance Measurements, Dr. Paul De Bièvre. Paul Jan De Bièvre (<a href="#j_pac-2019-0603_fig_010" class="link link-fig" data-bs-target="j_pac-2019-0603_fig_010">Fig. 10</a>) was born on 7 July 1933 in Blankenberge (Belgium) and passed away on 14 April 2016 in Leuven (Belgium) at the age of 82.</p> <div class="figure-wrapper" id="j_pac-2019-0603_fig_010"><div class="figure w-100"><div class="graphic"><img loading="lazy" src="/document/doi/10.1515/pac-2019-0603/asset/graphic/j_pac-2019-0603_fig_020.jpg" alt="Fig. 10: 
 Paul De Bièvre at the 2007 Commission meeting in Pisa, Italy (Courtesy of Michael E. Wieser).
 "></img></div><div class="figure-description mb-3"><div class="figure-label h3"><span class="label">Fig. 10:</span></div><div class="figure-caption mb-2"><span class="caption"><p>Paul De Bièvre at the 2007 Commission meeting in Pisa, Italy (Courtesy of Michael E. Wieser).</p></span></div></div></div></div> <p>He obtained his PhD from Gent University in 1959 where he continued to work as a lecturer until 1961. In 1961 he joined the Central Bureau for Nuclear Measurements of the European Commission (later renamed Institute for Reference Materials and Measurements, IRMM). Paul attended his first Commission meeting in Washington, D.C. (1971) and was elected Associate Member. He remained an active member of the Commission throughout the next five decades. At the 1973 Munich meeting, Paul (and Norman E. Holden) proposed to form a Working Party to review the data on isotopic abundance measurements and their impact on atomic weights. This started an eight-year project for IUPAC on the assessment of our knowledge of the isotopic composition of the elements and led to what is now known as the Subcommittee on Isotopic Abundance Measurements with Paul as its inaugural Chairman.</p> <p>Paul’s early work in the Central Bureau for Nuclear Measurements focused on the isotope dilution method and he pioneered the uncertainty analysis in this area. From the 1980s, he directed IRMM work on the improved measurements of the Avogadro constant through the single crystal route. This work, now led by the Physikalisch-Technische Bundesanstalt (PTB, Germany), formed an integral part of the new International System of Units (SI), which was changed in 2019.</p> <p>Paul was very active in the international activities of chemistry and he was a charter member of many international chemistry organizations, including the Consultative Committee on the Amount of Substance (CCQM). He was co-founder (1989) and President (1993–1995) of Eurachem and co-founder (1992) of CITAC (“Co-operation on International Traceability in Analytical Chemistry”). In 1988 he was elected President of the National Committee on Chemistry of the Royal Academies of Belgium (1988–2006), he represented IUPAC to the Joint Committee for Guides in Metrology and was an active contributor to the 1998–2008 revision of the International Vocabulary of Metrology.</p> <p>Paul had a penchant for philosophy of science and he believed that great measurements start with great thinking. His writings on metrology in chemistry appeared frequently in <em>Accreditation and Quality Assurance</em> (Springer) of which he was the Founding Editor-in-Chief (1995). He was a straightforward, cheerful person and his colleagues fondly remember his passion for science. Talking science for hours in the rain at a bus stop was not unusual for those who were fortunate enough to have met him. He was an inspiration to generations of analytical chemists and his passion for the highest quality measurements and accuracy in communication will be lasting memories. Paul loved a good debate and this quality placed him at the center of the decade-long discussions on the redefinition of the SI unit for the amount of substance, the mole. Fittingly, he lived only 10 km away from the city called Mol.</p> </section> </div><section class="frontNote"><hr></hr> <p> <strong>Dedicated to</strong> Paul de Bièvre (1933–2016), a long-serving member of the CIAAW and the inaugural Chairman of its Subcommittee on Isotopic Abundance Measurements.</p> <hr></hr></section><section class="authorNotes"><hr></hr> <div class="correspondingAuthor">Corresponding author: <strong>Thomas Prohaska</strong>, <span class="institution" content-type="university">Montanuniversität Leoben</span>, <span class="city">Leoben</span>, <span class="country" country="AT">Austria</span>; and <span class="institution" content-type="university">University of Calgary</span>, <span class="city">Calgary</span>, <span class="country" country="CA">Canada</span>, e-mail: <span xmlns:xlink="http://www.w3.org/1999/xlink" class="email" xlink:href="mailto:thomas.prohaska@unileoben.ac.at">thomas.prohaska@unileoben.ac.at</span></div> <div class="authorNotesFootnote" id="j_pac-2019-0603_fn_001" fn-type="other"> <p> <strong>Article note:</strong> Sponsoring body: IUPAC (International Union of Pure and Applied Chemistry) Inorganic Chemistry Division Committee. See more details on page 596.</p> </div> <hr></hr></section><div class="contrib-group"></div><div class="back"> <div class="acknowledgements" id="j_pac-2019-0603_ack_001"> <h2 class="subheading">Acknowledgments</h2> <p>We acknowledge the valuable comments and contributions of Jan Kaiser and other anonymous reviewers for supporting a substantial improvement of the manuscript.</p> </div> <ol class="footnote-group" id=""> <li class="footnote footnote-noLabel" id="j_pac-2019-0603_fn_004" fn-type="financial-disclosure"> <p> <strong>Research funding:</strong> We gratefully acknowledge the support of the IUPAC and its funding bodies. 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H., Gröning, Manfred, Holden, Norman E., Meijer, Harro A. J., Moossen, Heiko, Possolo, Antonio, Takahashi, Yoshio, Vogl, Jochen, Walczyk, Thomas, Wang, Jun, Wieser, Michael E., Yoneda, Shigekazu, Zhu, Xiang-Kun and Meija, Juris. "Standard atomic weights of the elements 2021 (IUPAC Technical Report)" <i>Pure and Applied Chemistry</i>, vol. 94, no. 5, 2022, pp. 573-600. <a href='https://doi.org/10.1515/pac-2019-0603'>https://doi.org/10.1515/pac-2019-0603</a></div> <div class="tab-pane fade " id="APA" role="tabpanel" aria-labelledby="APA-tab">Prohaska, T., Irrgeher, J., Benefield, J., Böhlke, J., Chesson, L., Coplen, T., Ding, T., Dunn, P., Gröning, M., Holden, N., Meijer, H., Moossen, H., Possolo, A., Takahashi, Y., Vogl, J., Walczyk, T., Wang, J., Wieser, M., Yoneda, S., Zhu, X. & Meija, J. (2022). Standard atomic weights of the elements 2021 (IUPAC Technical Report). <i>Pure and Applied Chemistry</i>, <i>94</i>(5), 573-600. <a href='https://doi.org/10.1515/pac-2019-0603'>https://doi.org/10.1515/pac-2019-0603</a></div> <div class="tab-pane fade " id="Harvard" role="tabpanel" aria-labelledby="Harvard-tab">Prohaska, T., Irrgeher, J., Benefield, J., Böhlke, J., Chesson, L., Coplen, T., Ding, T., Dunn, P., Gröning, M., Holden, N., Meijer, H., Moossen, H., Possolo, A., Takahashi, Y., Vogl, J., Walczyk, T., Wang, J., Wieser, M., Yoneda, S., Zhu, X. and Meija, J. (2022) Standard atomic weights of the elements 2021 (IUPAC Technical Report). Pure and Applied Chemistry, Vol. 94 (Issue 5), pp. 573-600. <a href='https://doi.org/10.1515/pac-2019-0603'>https://doi.org/10.1515/pac-2019-0603</a></div> <div class="tab-pane fade " id="Chicago" role="tabpanel" aria-labelledby="Chicago-tab">Prohaska, Thomas, Irrgeher, Johanna, Benefield, Jacqueline, Böhlke, John K., Chesson, Lesley A., Coplen, Tyler B., Ding, Tiping, Dunn, Philip J. H., Gröning, Manfred, Holden, Norman E., Meijer, Harro A. J., Moossen, Heiko, Possolo, Antonio, Takahashi, Yoshio, Vogl, Jochen, Walczyk, Thomas, Wang, Jun, Wieser, Michael E., Yoneda, Shigekazu, Zhu, Xiang-Kun and Meija, Juris. "Standard atomic weights of the elements 2021 (IUPAC Technical Report)" <i>Pure and Applied Chemistry</i> 94, no. 5 (2022): 573-600. <a href='https://doi.org/10.1515/pac-2019-0603'>https://doi.org/10.1515/pac-2019-0603</a></div> <div class="tab-pane fade " id="Vancouver" role="tabpanel" aria-labelledby="Vancouver-tab">Prohaska T, Irrgeher J, Benefield J, Böhlke J, Chesson L, Coplen T, Ding T, Dunn P, Gröning M, Holden N, Meijer H, Moossen H, Possolo A, Takahashi Y, Vogl J, Walczyk T, Wang J, Wieser M, Yoneda S, Zhu X, Meija J. Standard atomic weights of the elements 2021 (IUPAC Technical Report). <i>Pure and Applied Chemistry</i>. 2022;94(5): 573-600. <a href='https://doi.org/10.1515/pac-2019-0603'>https://doi.org/10.1515/pac-2019-0603</a></div> <div class="d-flex justify-content-center"><span id="citationCopied" aria-hidden="true">Copied to clipboard</span></div> </div> <div class="d-flex justify-content-between mt-2"> <div><a href="#" id="citationCopy" class="font-size-14">Copy to clipboard</a></div> <div> <span class="font-size-14">Download:</span> <a title='Download in BibTeX format' aria-label='Download in BibTeX format' class="ms-1 font-size-14" href="/document/doi/10.1515/pac-2019-0603/machineReadableCitation/BibTeX">BibTeX</a> <a title='Download in EndNote format' aria-label='Download in EndNote format' class="ms-1 font-size-14" href="/document/doi/10.1515/pac-2019-0603/machineReadableCitation/EndNote">EndNote</a> <a title='Download in RIS format' aria-label='Download in RIS format' class="ms-1 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Standard atomic weights of the elements 2021 (IUPAC Technical Report)