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data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Top)</div> </a> </li> <li id="toc-van_der_Waals_volume" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#van_der_Waals_volume"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>van der Waals volume</span> </div> </a> <ul id="toc-van_der_Waals_volume-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Table_of_van_der_Waals_radii" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Table_of_van_der_Waals_radii"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Table of van der Waals radii</span> </div> </a> <ul id="toc-Table_of_van_der_Waals_radii-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Methods_of_determination" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Methods_of_determination"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Methods of determination</span> </div> </a> <button aria-controls="toc-Methods_of_determination-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Methods of determination subsection</span> </button> <ul id="toc-Methods_of_determination-sublist" class="vector-toc-list"> <li id="toc-Van_der_Waals_equation_of_state" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Van_der_Waals_equation_of_state"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Van der Waals equation of state</span> </div> </a> <ul id="toc-Van_der_Waals_equation_of_state-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Crystallographic_measurements" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Crystallographic_measurements"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Crystallographic measurements</span> </div> </a> <ul id="toc-Crystallographic_measurements-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Molar_refractivity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Molar_refractivity"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Molar refractivity</span> </div> </a> <ul id="toc-Molar_refractivity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Polarizability" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Polarizability"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Polarizability</span> </div> </a> <ul id="toc-Polarizability-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading">van der Waals radius</h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 47 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-47" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">47 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Van_der_Waals-radius" title="Van der Waals-radius – Afrikaans" lang="af" hreflang="af" data-title="Van der Waals-radius" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%86%D8%B5%D9%81_%D9%82%D8%B7%D8%B1_%D9%81%D8%A7%D9%86_%D8%AF%D9%8A%D8%B1_%D9%81%D8%A7%D9%84%D8%B3" title="نصف قطر فان دير فالس – Arabic" lang="ar" hreflang="ar" data-title="نصف قطر فان دير فالس" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Radio_de_van_der_Waals" title="Radio de van der Waals – Aragonese" lang="an" hreflang="an" data-title="Radio de van der Waals" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Radiu_de_van_der_Waals" title="Radiu de van der Waals – Asturian" lang="ast" hreflang="ast" data-title="Radiu de van der Waals" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D0%B8%D1%83%D1%81_%D0%BD%D0%B0_%D0%92%D0%B0%D0%BD_%D0%B4%D0%B5%D1%80_%D0%92%D0%B0%D0%B0%D0%BB%D1%81" title="Радиус на Ван дер Ваалс – Bulgarian" lang="bg" hreflang="bg" data-title="Радиус на Ван дер Ваалс" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Van_der_Waalsov_radijus" title="Van der Waalsov radijus – Bosnian" lang="bs" hreflang="bs" data-title="Van der Waalsov radijus" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Radi_de_van_der_Waals" title="Radi de van der Waals – Catalan" lang="ca" hreflang="ca" data-title="Radi de van der Waals" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Van_der_Waals%C5%AFv_polom%C4%9Br" title="Van der Waalsův poloměr – Czech" lang="cs" hreflang="cs" data-title="Van der Waalsův poloměr" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Van_der_Waals-radius" title="Van der Waals-radius – Danish" lang="da" hreflang="da" data-title="Van der Waals-radius" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Van-der-Waals-Radius" title="Van-der-Waals-Radius – German" lang="de" hreflang="de" data-title="Van-der-Waals-Radius" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Radio_de_Van_der_Waals" title="Radio de Van der Waals – Spanish" lang="es" hreflang="es" data-title="Radio de Van der Waals" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Radiuso_de_van_der_Waals" title="Radiuso de van der Waals – Esperanto" lang="eo" hreflang="eo" data-title="Radiuso de van der Waals" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Van_der_Waalsen_erradio" title="Van der Waalsen erradio – Basque" lang="eu" hreflang="eu" data-title="Van der Waalsen erradio" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B4%D8%B9%D8%A7%D8%B9_%D9%88%D8%A7%D9%86%D8%AF%D8%B1%D9%88%D8%A7%D9%84%D8%B3%DB%8C" title="شعاع واندروالسی – Persian" lang="fa" hreflang="fa" data-title="شعاع واندروالسی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Rayon_de_van_der_Waals" title="Rayon de van der Waals – French" lang="fr" hreflang="fr" data-title="Rayon de van der Waals" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Raio_de_van_der_Waals" title="Raio de van der Waals – Galician" lang="gl" hreflang="gl" data-title="Raio de van der Waals" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B0%98%EB%8D%B0%EB%A5%B4%EB%B0%9C%EC%8A%A4_%EB%B0%98%EC%A7%80%EB%A6%84" title="반데르발스 반지름 – Korean" lang="ko" hreflang="ko" data-title="반데르발스 반지름" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B5%E0%A4%BE%E0%A4%A8_%E0%A4%A1%E0%A4%B0_%E0%A4%B5%E0%A4%BE%E0%A4%B2%E0%A5%8D%E0%A4%B8_%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%9C%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="वान डर वाल्स त्रिज्या – Hindi" lang="hi" hreflang="hi" data-title="वान डर वाल्स त्रिज्या" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Jari-jari_van_der_Waals" title="Jari-jari van der Waals – Indonesian" lang="id" hreflang="id" data-title="Jari-jari van der Waals" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Raggio_di_van_der_Waals" title="Raggio di van der Waals – Italian" lang="it" hreflang="it" data-title="Raggio di van der Waals" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A8%D7%93%D7%99%D7%95%D7%A1_%D7%95%D7%90%D7%9F_%D7%93%D7%A8_%D7%95%D7%90%D7%9C%D7%A1" title="רדיוס ואן דר ואלס – Hebrew" lang="he" hreflang="he" data-title="רדיוס ואן דר ואלס" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%92%D0%B0%D0%BD_%D0%B4%D0%B5%D1%80_%D0%92%D0%B0%D0%BB%D1%81%D0%BE%D0%B2_%D0%BF%D0%BE%D0%BB%D1%83%D0%BF%D1%80%D0%B5%D1%87%D0%BD%D0%B8%D0%BA" title="Ван дер Валсов полупречник – Macedonian" lang="mk" hreflang="mk" data-title="Ван дер Валсов полупречник" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B5%E0%A4%BE%E0%A4%A8_%E0%A4%A1%E0%A4%B0_%E0%A4%B5%E0%A4%BE%E0%A4%B2%E0%A5%8D%E0%A4%B8_%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%9C%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="वान डर वाल्स त्रिज्या – Marathi" lang="mr" hreflang="mr" data-title="वान डर वाल्स त्रिज्या" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Jejari_van_der_Waals" title="Jejari van der Waals – Malay" lang="ms" hreflang="ms" data-title="Jejari van der Waals" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Vanderwaalsstraal" title="Vanderwaalsstraal – Dutch" lang="nl" hreflang="nl" data-title="Vanderwaalsstraal" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%95%E3%82%A1%E3%83%B3%E3%83%87%E3%83%AB%E3%83%AF%E3%83%BC%E3%83%AB%E3%82%B9%E5%8D%8A%E5%BE%84" title="ファンデルワールス半径 – Japanese" lang="ja" hreflang="ja" data-title="ファンデルワールス半径" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Rai_de_van_der_Waals" title="Rai de van der Waals – Occitan" lang="oc" hreflang="oc" data-title="Rai de van der Waals" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Promie%C5%84_van_der_Waalsa" title="Promień van der Waalsa – Polish" lang="pl" hreflang="pl" data-title="Promień van der Waalsa" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Raio_de_Van_der_Waals" title="Raio de Van der Waals – Portuguese" lang="pt" hreflang="pt" data-title="Raio de Van der Waals" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Raz%C4%83_van_der_Waals" title="Rază van der Waals – Romanian" lang="ro" hreflang="ro" data-title="Rază van der Waals" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D0%B8%D1%83%D1%81_%D0%92%D0%B0%D0%BD-%D0%B4%D0%B5%D1%80-%D0%92%D0%B0%D0%B0%D0%BB%D1%8C%D1%81%D0%B0" title="Радиус Ван-дер-Ваальса – Russian" lang="ru" hreflang="ru" data-title="Радиус Ван-дер-Ваальса" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Van_der_Waals_radius" title="Van der Waals radius – Scots" lang="sco" hreflang="sco" data-title="Van der Waals radius" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Van_der_Waals_radius" title="Van der Waals radius – Simple English" lang="en-simple" hreflang="en-simple" data-title="Van der Waals radius" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Van_der_Waalsov_polomer" title="Van der Waalsov polomer – Slovak" lang="sk" hreflang="sk" data-title="Van der Waalsov polomer" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Van_der_Waalsov_polmer" title="Van der Waalsov polmer – Slovenian" lang="sl" hreflang="sl" data-title="Van der Waalsov polmer" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%92%D0%B0%D0%BD_%D0%B4%D0%B5%D1%80_%D0%92%D0%B0%D0%BB%D1%81%D0%BE%D0%B2_%D1%80%D0%B0%D0%B4%D0%B8%D1%98%D1%83%D1%81" title="Ван дер Валсов радијус – Serbian" lang="sr" hreflang="sr" data-title="Ван дер Валсов радијус" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Van_der_Valsov_radijus" title="Van der Valsov radijus – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Van der Valsov radijus" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Van_der_Waalsin_s%C3%A4de" title="Van der Waalsin säde – Finnish" lang="fi" hreflang="fi" data-title="Van der Waalsin säde" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Van_der_Waalsradie" title="Van der Waalsradie – Swedish" lang="sv" hreflang="sv" data-title="Van der Waalsradie" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%B5%E0%AE%BE%E0%AE%A3%E0%AF%8D%E0%AE%9F%E0%AF%86%E0%AE%B0%E0%AF%8D%E0%AE%B5%E0%AE%BE%E0%AE%B2%E0%AF%8D%E0%AE%9A%E0%AF%81_%E0%AE%86%E0%AE%B0%E0%AE%AE%E0%AF%8D" title="வாண்டெர்வால்சு ஆரம் – Tamil" lang="ta" hreflang="ta" data-title="வாண்டெர்வால்சு ஆரம்" 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searchaux" style="display:none">Size of an atom's imaginary sphere representing how close other atoms can get</div> <table class="wikitable floatright" align="right"> <caption>van der Waals radii </caption> <tbody><tr> <th>Element</th> <th>radius (<a href="/wiki/Angstrom" title="Angstrom">Å</a>) </th></tr> <tr> <td><a href="/wiki/Hydrogen" title="Hydrogen">Hydrogen</a></td> <td>1.2 (1.09)<sup id="cite_ref-RowlandRS1996_1-0" class="reference"><a href="#cite_note-RowlandRS1996-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td><a href="/wiki/Carbon" title="Carbon">Carbon</a></td> <td>1.7 </td></tr> <tr> <td><a href="/wiki/Nitrogen" title="Nitrogen">Nitrogen</a></td> <td>1.55 </td></tr> <tr> <td><a href="/wiki/Oxygen" title="Oxygen">Oxygen</a></td> <td>1.52 </td></tr> <tr> <td><a href="/wiki/Fluorine" title="Fluorine">Fluorine</a></td> <td>1.47 </td></tr> <tr> <td><a href="/wiki/Phosphorus" title="Phosphorus">Phosphorus</a></td> <td>1.8 </td></tr> <tr> <td><a href="/wiki/Sulfur" title="Sulfur">Sulfur</a></td> <td>1.8 </td></tr> <tr> <td><a href="/wiki/Chlorine" title="Chlorine">Chlorine</a></td> <td>1.75 </td></tr> <tr> <td><a href="/wiki/Copper" title="Copper">Copper</a></td> <td>1.4 </td></tr> <tr> <td colspan="2"><small>van der Waals radii taken from<br />Bondi's compilation (1964).<sup id="cite_ref-Bondi1964_2-0" class="reference"><a href="#cite_note-Bondi1964-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><br />Values from other sources may<br />differ significantly (<i>see text</i>)</small> </td></tr> </tbody></table> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output 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.mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><table class="sidebar nomobile nowraplinks" style="width:auto"><tbody><tr><th class="sidebar-title" style="border-bottom:2px solid; background:#d3d3d3">Types of radii</th></tr><tr><td class="sidebar-content"> <div class="plainlist"> <ul><li><a href="/wiki/Atomic_radius" title="Atomic radius">Atomic radius</a></li> <li><a href="/wiki/Ionic_radius" title="Ionic radius">Ionic radius</a></li> <li><a href="/wiki/Covalent_radius" title="Covalent radius">Covalent radius</a></li> <li><a href="/wiki/Metallic_radius" class="mw-redirect" title="Metallic radius">Metallic radius</a></li> <li><a class="mw-selflink selflink">Van der Waals radius</a></li></ul> </div></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Atomic_radius" title="Template:Atomic radius"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Atomic_radius" title="Template talk:Atomic radius"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Atomic_radius" title="Special:EditPage/Template:Atomic radius"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>The <b>van der Waals radius</b>, <i>r</i><sub>w</sub>, of an <a href="/wiki/Atom" title="Atom">atom</a> is the <a href="/wiki/Radius" title="Radius">radius</a> of an imaginary hard <a href="/wiki/Sphere" title="Sphere">sphere</a> representing the <a href="/wiki/Distance_of_closest_approach" title="Distance of closest approach">distance of closest approach</a> for another atom. It is named after <a href="/wiki/Johannes_Diderik_van_der_Waals" title="Johannes Diderik van der Waals">Johannes Diderik van der Waals</a>, winner of the 1910 <a href="/wiki/Nobel_Prize_in_Physics" title="Nobel Prize in Physics">Nobel Prize in Physics</a>, as he was the first to recognise that atoms were not simply <a href="/wiki/Point_(geometry)" title="Point (geometry)">points</a> and to demonstrate the physical consequences of their size through the <a href="/wiki/Van_der_Waals_equation" title="Van der Waals equation">van der Waals equation of state</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="van_der_Waals_volume">van der Waals volume</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Van_der_Waals_radius&action=edit&section=1" title="Edit section: van der Waals volume"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Van_der_Waals_radius" title="Special:EditPage/Van der Waals radius">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>.</span> <span class="date-container"><i>(<span class="date">June 2015</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>The <b>van der Waals volume</b>, <i>V<sub>w</sub></i>, also called the <b>atomic volume</b> or <b>molecular volume</b>, is the atomic property most directly related to the van der Waals radius.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> It is the volume "occupied" by an individual atom (or molecule). The van der Waals volume may be calculated if the van der Waals radii (and, for molecules, the inter-atomic distances, and angles) are known. For a single atom, it is the volume of a sphere whose radius is the van der Waals radius of the atom:<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{\rm {w}}={4 \over 3}\pi r_{\rm {w}}^{3}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">w</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>4</mn> <mn>3</mn> </mfrac> </mrow> <mi>π</mi> <msubsup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">w</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msubsup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\rm {w}}={4 \over 3}\pi r_{\rm {w}}^{3}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63a0098006f512cfdd277430f12518547e6ff83e" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.317ex; height:5.176ex;" alt="{\displaystyle V_{\rm {w}}={4 \over 3}\pi r_{\rm {w}}^{3}.}"></span> </p><p>For a molecule, it is the volume enclosed by the <a href="/wiki/Van_der_Waals_surface" title="Van der Waals surface">van der Waals surface</a>. The van der Waals volume of a molecule is always smaller than the sum of the van der Waals volumes of the constituent atoms: the atoms can be said to "overlap" when they form <a href="/wiki/Chemical_bond" title="Chemical bond">chemical bonds</a>. </p><p>The van der Waals volume of an atom or molecule may also be determined by experimental measurements on gases, notably from the <a href="/wiki/Van_der_Waals_constant" class="mw-redirect" title="Van der Waals constant">van der Waals constant</a> <i>b</i>, the <a href="/wiki/Polarizability" title="Polarizability">polarizability</a> <i>α</i>, or the <a href="/wiki/Molar_refractivity" title="Molar refractivity">molar refractivity</a> <i>A</i>. In all three cases, measurements are made on macroscopic samples and it is normal to express the results as <a href="/wiki/Mole_(unit)" title="Mole (unit)">molar</a> quantities. To find the van der Waals volume of a single atom or molecule, it is necessary to divide by the <a href="/wiki/Avogadro_constant" title="Avogadro constant">Avogadro constant</a> <i>N</i><sub>A</sub>. </p><p>The molar van der Waals volume should not be confused with the <a href="/wiki/Molar_volume" title="Molar volume">molar volume</a> of the substance. In general, at normal laboratory temperatures and pressures, the atoms or molecules of gas only occupy about <style data-mw-deduplicate="TemplateStyles:r1154941027">.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="frac"><span class="num">1</span>⁄<span class="den"><span class="nowrap"><span data-sort-value="7003100000000000000♠"></span>1000</span></span></span> of the volume of the gas, the rest is empty space. Hence the molar van der Waals volume, which only counts the volume occupied by the atoms or molecules, is usually about <span class="nowrap"><span data-sort-value="7003100000000000000♠"></span>1000</span> times smaller than the molar volume for a gas at <a href="/wiki/Standard_temperature_and_pressure" title="Standard temperature and pressure">standard temperature and pressure</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Table_of_van_der_Waals_radii">Table of van der Waals radii</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Van_der_Waals_radius&action=edit&section=2" title="Edit section: Table of van der Waals radii"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="mw-collapsible collapsed" border="0" cellpadding="0" cellspacing="1" style="text-align:center; background:#f8f8f8; border:1px solid #a9a9a9; width:100%; max-width:1300px; margin:0 auto; padding:2px;"> <tbody><tr> <th colspan="20" style="background:#d8d8d8; padding:2px 4px;"><a class="mw-selflink selflink">Van der Waals radius</a> of the elements in the <a href="/wiki/Periodic_table" title="Periodic table">periodic table</a> </th></tr> <tr style="background:#e8e8e8"> <th width="1.0%"><small><a href="/wiki/Periodic_table_group" class="mw-redirect" title="Periodic table group">Group</a> →</small> </th> <th width="5.4%"><a href="/wiki/Alkali_metal" title="Alkali metal">1</a> </th> <th width="5.4%"><a href="/wiki/Alkaline_earth_metal" title="Alkaline earth metal">2</a> </th> <th width="1.8%"> </th> <th width="5.4%"><a href="/wiki/Group_3_element" title="Group 3 element">3</a> </th> <th width="5.4%"><a href="/wiki/Group_4_element" title="Group 4 element">4</a> </th> <th width="5.4%"><a href="/wiki/Group_5_element" title="Group 5 element">5</a> </th> <th width="5.4%"><a href="/wiki/Group_6_element" title="Group 6 element">6</a> </th> <th width="5.4%"><a href="/wiki/Group_7_element" title="Group 7 element">7</a> </th> <th width="5.4%"><a href="/wiki/Group_8_element" title="Group 8 element">8</a> </th> <th width="5.4%"><a href="/wiki/Group_9_element" title="Group 9 element">9</a> </th> <th width="5.4%"><a href="/wiki/Group_10_element" title="Group 10 element">10</a> </th> <th width="5.4%"><a href="/wiki/Group_11_element" title="Group 11 element">11</a> </th> <th width="5.4%"><a href="/wiki/Group_12_element" title="Group 12 element">12</a> </th> <th width="5.4%"><a href="/wiki/Boron_group" title="Boron group">13</a> </th> <th width="5.4%"><a href="/wiki/Carbon_group" title="Carbon group">14</a> </th> <th width="5.4%"><a href="/wiki/Pnictogen" title="Pnictogen">15</a> </th> <th width="5.4%"><a href="/wiki/Chalcogen" title="Chalcogen">16</a> </th> <th width="5.4%"><a href="/wiki/Halogen" title="Halogen">17</a> </th> <th width="5.4%"><a href="/wiki/Noble_gas" title="Noble gas">18</a> </th></tr> <tr> <th><small>↓ <a href="/wiki/Periodic_table_period" class="mw-redirect" title="Periodic table period">Period</a></small> </th> <td colspan="20"><br /> </td></tr> <tr> <th><a href="/wiki/Period_1_element" title="Period 1 element">1</a> </th> <td title="H , hydrogen" style="text-align:center; padding:0.15em; background:#ff0a00; border:2px solid #6e6e8e;"><a href="/wiki/Hydrogen" title="Hydrogen"><span style="display:block">H </span></a>110<sup id="cite_ref-RowlandRS1996_1-1" class="reference"><a href="#cite_note-RowlandRS1996-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><br />or 120 </td> <td colspan="17"><br /> </td> <td title="He, helium" style="text-align:center; padding:0.15em; background:#ff1e00; border:2px solid #6e6e8e;"><a href="/wiki/Helium" title="Helium"><span style="display:block">He</span></a>140 </td></tr> <tr> <th><a href="/wiki/Period_2_element" title="Period 2 element">2</a> </th> <td title="Li, lithium" style="text-align:center; padding:0.15em; background:#ff4800; border:2px solid #6e6e8e;"><a href="/wiki/Lithium" title="Lithium"><span style="display:block">Li</span></a>182 </td> <td title="Be, beryllium" style="text-align:center; padding:0.15em; background:#ff2b00; border:2px solid #6e6e8e;"><a href="/wiki/Beryllium" title="Beryllium"><span style="display:block">Be</span></a>153<sup id="cite_ref-Mantina_4-0" class="reference"><a href="#cite_note-Mantina-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </td> <td colspan="11"><br /> </td> <td title="B , boron" style="text-align:center; padding:0.15em; background:#ff5200; border:2px solid #6e6e8e;"><a href="/wiki/Boron" title="Boron"><span style="display:block">B </span></a>192<sup id="cite_ref-Mantina_4-1" class="reference"><a href="#cite_note-Mantina-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </td> <td title="C , carbon" style="text-align:center; padding:0.15em; background:#ff3c00; border:2px solid #6e6e8e;"><a href="/wiki/Carbon" title="Carbon"><span style="display:block">C </span></a>170 </td> <td title="N , nitrogen" style="text-align:center; padding:0.15em; background:#ff2d00; border:2px solid #6e6e8e;"><a href="/wiki/Nitrogen" title="Nitrogen"><span style="display:block">N </span></a>155 </td> <td title="O , oxygen" style="text-align:center; padding:0.15em; background:#ff2a00; border:2px solid #6e6e8e;"><a href="/wiki/Oxygen" title="Oxygen"><span style="display:block">O </span></a>152 </td> <td title="F , fluorine" style="text-align:center; padding:0.15em; background:#ff2500; border:2px solid #6e6e8e;"><a href="/wiki/Fluorine" title="Fluorine"><span style="display:block">F </span></a>147 </td> <td title="Ne, neon" style="text-align:center; padding:0.15em; background:#ff2c00; border:2px solid #6e6e8e;"><a href="/wiki/Neon" title="Neon"><span style="display:block">Ne</span></a>154 </td></tr> <tr> <th><a href="/wiki/Period_3_element" title="Period 3 element">3</a> </th> <td title="Na, sodium" style="text-align:center; padding:0.15em; background:#ff7500; border:2px solid #6e6e8e;"><a href="/wiki/Sodium" title="Sodium"><span style="display:block">Na</span></a>227 </td> <td title="Mg, magnesium" style="text-align:center; padding:0.15em; background:#ff3f00; border:2px solid #6e6e8e;"><a href="/wiki/Magnesium" title="Magnesium"><span style="display:block">Mg</span></a>173 </td> <td colspan="11"><br /> </td> <td title="Al, aluminium" style="text-align:center; padding:0.15em; background:#ff4a00; border:2px solid #6e6e8e;"><a href="/wiki/Aluminium" title="Aluminium"><span style="display:block">Al</span></a>184<sup id="cite_ref-Mantina_4-2" class="reference"><a href="#cite_note-Mantina-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </td> <td title="Si, silicon" style="text-align:center; padding:0.15em; background:#ff6400; border:2px solid #6e6e8e;"><a href="/wiki/Silicon" title="Silicon"><span style="display:block">Si</span></a>210 </td> <td title="P , phosphorus" style="text-align:center; padding:0.15em; background:#ff4600; border:2px solid #6e6e8e;"><a href="/wiki/Phosphorus" title="Phosphorus"><span style="display:block">P </span></a>180 </td> <td title="S , sulfur" style="text-align:center; padding:0.15em; background:#ff4600; border:2px solid #6e6e8e;"><a href="/wiki/Sulfur" title="Sulfur"><span style="display:block">S </span></a>180 </td> <td title="Cl, chlorine" style="text-align:center; padding:0.15em; background:#ff4100; border:2px solid #6e6e8e;"><a href="/wiki/Chlorine" title="Chlorine"><span style="display:block">Cl</span></a>175 </td> <td title="Ar, argon" style="text-align:center; padding:0.15em; background:#ff4e00; border:2px solid #6e6e8e;"><a href="/wiki/Argon" title="Argon"><span style="display:block">Ar</span></a>188 </td></tr> <tr> <th><a href="/wiki/Period_4_element" title="Period 4 element">4</a> </th> <td title="K , potassium" style="text-align:center; padding:0.15em; background:#ffa500; border:2px solid #6e6e8e;"><a href="/wiki/Potassium" title="Potassium"><span style="display:block">K </span></a>275 </td> <td title="Ca, calcium" style="text-align:center; padding:0.15em; background:#ff7900; border:2px solid #6e6e8e;"><a href="/wiki/Calcium" title="Calcium"><span style="display:block">Ca</span></a>231<sup id="cite_ref-Mantina_4-3" class="reference"><a href="#cite_note-Mantina-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </td> <td> </td> <td title="Sc, scandium" style="text-align:center; padding:0.15em; background:#ff6400; border:2px solid #6e6e8e;"><a href="/wiki/Scandium" title="Scandium"><span style="display:block">Sc</span></a>211<sup id="cite_ref-Mantina_4-4" class="reference"><a href="#cite_note-Mantina-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </td> <td title="Ti, titanium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Titanium" title="Titanium"><span style="display:block">Ti</span></a>  </td> <td title="V , vanadium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Vanadium" title="Vanadium"><span style="display:block">V </span></a>  </td> <td title="Cr, chromium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Chromium" title="Chromium"><span style="display:block">Cr</span></a>  </td> <td title="Mn, manganese" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Manganese" title="Manganese"><span style="display:block">Mn</span></a>  </td> <td title="Fe, iron" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Iron" title="Iron"><span style="display:block">Fe</span></a>  </td> <td title="Co, cobalt" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Cobalt" title="Cobalt"><span style="display:block">Co</span></a>  </td> <td title="Ni, nickel" style="text-align:center; padding:0.15em; background:#ff3500; border:2px solid #6e6e8e;"><a href="/wiki/Nickel" title="Nickel"><span style="display:block">Ni</span></a>163 </td> <td title="Cu, copper" style="text-align:center; padding:0.15em; background:#ff1e00; border:2px solid #6e6e8e;"><a href="/wiki/Copper" title="Copper"><span style="display:block">Cu</span></a>140 </td> <td title="Zn, zinc" style="text-align:center; padding:0.15em; background:#ff1d00; border:2px solid #6e6e8e;"><a href="/wiki/Zinc" title="Zinc"><span style="display:block">Zn</span></a>139 </td> <td title="Ga, gallium" style="text-align:center; padding:0.15em; background:#ff4d00; border:2px solid #6e6e8e;"><a href="/wiki/Gallium" title="Gallium"><span style="display:block">Ga</span></a>187 </td> <td title="Ge, germanium" style="text-align:center; padding:0.15em; background:#ff6500; border:2px solid #6e6e8e;"><a href="/wiki/Germanium" title="Germanium"><span style="display:block">Ge</span></a>211<sup id="cite_ref-Mantina_4-5" class="reference"><a href="#cite_note-Mantina-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </td> <td title="As, arsenic" style="text-align:center; padding:0.15em; background:#ff4b00; border:2px solid #6e6e8e;"><a href="/wiki/Arsenic" title="Arsenic"><span style="display:block">As</span></a>185 </td> <td title="Se, selenium" style="text-align:center; padding:0.15em; background:#ff5000; border:2px solid #6e6e8e;"><a href="/wiki/Selenium" title="Selenium"><span style="display:block">Se</span></a>190 </td> <td title="Br, bromine" style="text-align:center; padding:0.15em; background:#ff4b00; border:2px solid #6e6e8e;"><a href="/wiki/Bromine" title="Bromine"><span style="display:block">Br</span></a>185 </td> <td title="Kr, krypton" style="text-align:center; padding:0.15em; background:#ff5c00; border:2px solid #6e6e8e;"><a href="/wiki/Krypton" title="Krypton"><span style="display:block">Kr</span></a>202 </td></tr> <tr> <th><a href="/wiki/Period_5_element" title="Period 5 element">5</a> </th> <td title="Rb, rubidium" style="text-align:center; padding:0.15em; background:#ffc100; border:2px solid #6e6e8e;"><a href="/wiki/Rubidium" title="Rubidium"><span style="display:block">Rb</span></a>303<sup id="cite_ref-Mantina_4-6" class="reference"><a href="#cite_note-Mantina-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </td> <td title="Sr, strontium" style="text-align:center; padding:0.15em; background:#ff8b00; border:2px solid #6e6e8e;"><a href="/wiki/Strontium" title="Strontium"><span style="display:block">Sr</span></a>249<sup id="cite_ref-Mantina_4-7" class="reference"><a href="#cite_note-Mantina-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </td> <td> </td> <td title="Y , yttrium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Yttrium" title="Yttrium"><span style="display:block">Y </span></a>  </td> <td title="Zr, zirconium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Zirconium" title="Zirconium"><span style="display:block">Zr</span></a>  </td> <td title="Nb, niobium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Niobium" title="Niobium"><span style="display:block">Nb</span></a>  </td> <td title="Mo, molybdenum" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Molybdenum" title="Molybdenum"><span style="display:block">Mo</span></a>  </td> <td title="Tc, technetium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px dashed #6e6e8e;"><a href="/wiki/Technetium" title="Technetium"><span style="display:block">Tc</span></a>  </td> <td title="Ru, ruthenium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Ruthenium" title="Ruthenium"><span style="display:block">Ru</span></a>  </td> <td title="Rh, rhodium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Rhodium" title="Rhodium"><span style="display:block">Rh</span></a>  </td> <td title="Pd, palladium" style="text-align:center; padding:0.15em; background:#ff3500; border:2px solid #6e6e8e;"><a href="/wiki/Palladium" title="Palladium"><span style="display:block">Pd</span></a>163 </td> <td title="Ag, silver" style="text-align:center; padding:0.15em; background:#ff3e00; border:2px solid #6e6e8e;"><a href="/wiki/Silver" title="Silver"><span style="display:block">Ag</span></a>172 </td> <td title="Cd, cadmium" style="text-align:center; padding:0.15em; background:#ff3000; border:2px solid #6e6e8e;"><a href="/wiki/Cadmium" title="Cadmium"><span style="display:block">Cd</span></a>158 </td> <td title="In, indium" style="text-align:center; padding:0.15em; background:#ff5300; border:2px solid #6e6e8e;"><a href="/wiki/Indium" title="Indium"><span style="display:block">In</span></a>193 </td> <td title="Sn, tin" style="text-align:center; padding:0.15em; background:#ff6b00; border:2px solid #6e6e8e;"><a href="/wiki/Tin" title="Tin"><span style="display:block">Sn</span></a>217 </td> <td title="Sb, antimony" style="text-align:center; padding:0.15em; background:#ff6000; border:2px solid #6e6e8e;"><a href="/wiki/Antimony" title="Antimony"><span style="display:block">Sb</span></a>206<sup id="cite_ref-Mantina_4-8" class="reference"><a href="#cite_note-Mantina-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </td> <td title="Te, tellurium" style="text-align:center; padding:0.15em; background:#ff6000; border:2px solid #6e6e8e;"><a href="/wiki/Tellurium" title="Tellurium"><span style="display:block">Te</span></a>206 </td> <td title="I , iodine" style="text-align:center; padding:0.15em; background:#ff5800; border:2px solid #6e6e8e;"><a href="/wiki/Iodine" title="Iodine"><span style="display:block">I </span></a>198 </td> <td title="Xe, xenon" style="text-align:center; padding:0.15em; background:#ff6a00; border:2px solid #6e6e8e;"><a href="/wiki/Xenon" title="Xenon"><span style="display:block">Xe</span></a>216 </td></tr> <tr> <th><a href="/wiki/Period_6_element" title="Period 6 element">6</a> </th> <td title="Cs, caesium" style="text-align:center; padding:0.15em; background:#ffe900; border:2px solid #6e6e8e;"><a href="/wiki/Caesium" title="Caesium"><span style="display:block">Cs</span></a>343<sup id="cite_ref-Mantina_4-9" class="reference"><a href="#cite_note-Mantina-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </td> <td title="Ba, barium" style="text-align:center; padding:0.15em; background:#ff9e00; border:2px solid #6e6e8e;"><a href="/wiki/Barium" title="Barium"><span style="display:block">Ba</span></a>268<sup id="cite_ref-Mantina_4-10" class="reference"><a href="#cite_note-Mantina-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </td> <td style="text-align:center; vertical-align:middle;"><span class="skin-invert-image" typeof="mw:File"><span><img alt="1 asterisk" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/49/Asterisks_one.svg/16px-Asterisks_one.svg.png" decoding="async" width="16" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/49/Asterisks_one.svg/24px-Asterisks_one.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/49/Asterisks_one.svg/32px-Asterisks_one.svg.png 2x" data-file-width="106" data-file-height="98" /></span></span> </td> <td title="Lu, lutetium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Lutetium" title="Lutetium"><span style="display:block">Lu</span></a>  </td> <td title="Hf, hafnium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Hafnium" title="Hafnium"><span style="display:block">Hf</span></a>  </td> <td title="Ta, tantalum" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Tantalum" title="Tantalum"><span style="display:block">Ta</span></a>  </td> <td title="W , tungsten" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Tungsten" title="Tungsten"><span style="display:block">W </span></a>  </td> <td title="Re, rhenium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Rhenium" title="Rhenium"><span style="display:block">Re</span></a>  </td> <td title="Os, osmium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Osmium" title="Osmium"><span style="display:block">Os</span></a>  </td> <td title="Ir, iridium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Iridium" title="Iridium"><span style="display:block">Ir</span></a>  </td> <td title="Pt, platinum" style="text-align:center; padding:0.15em; background:#ff4100; border:2px solid #6e6e8e;"><a href="/wiki/Platinum" title="Platinum"><span style="display:block">Pt</span></a>175 </td> <td title="Au, gold" style="text-align:center; padding:0.15em; background:#ff3800; border:2px solid #6e6e8e;"><a href="/wiki/Gold" title="Gold"><span style="display:block">Au</span></a>166 </td> <td title="Hg, mercury" style="text-align:center; padding:0.15em; background:#ff2d00; border:2px solid #6e6e8e;"><a href="/wiki/Mercury_(element)" title="Mercury (element)"><span style="display:block">Hg</span></a>155 </td> <td title="Tl, thallium" style="text-align:center; padding:0.15em; background:#ff5600; border:2px solid #6e6e8e;"><a href="/wiki/Thallium" title="Thallium"><span style="display:block">Tl</span></a>196 </td> <td title="Pb, lead" style="text-align:center; padding:0.15em; background:#ff5c00; border:2px solid #6e6e8e;"><a href="/wiki/Lead" title="Lead"><span style="display:block">Pb</span></a>202 </td> <td title="Bi, bismuth" style="text-align:center; padding:0.15em; background:#ff6100; border:2px solid #6e6e8e;"><a href="/wiki/Bismuth" title="Bismuth"><span style="display:block">Bi</span></a>207<sup id="cite_ref-Mantina_4-11" class="reference"><a href="#cite_note-Mantina-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </td> <td title="Po, polonium" style="text-align:center; padding:0.15em; background:#ff5700; border:2px dashed #6e6e8e;"><a href="/wiki/Polonium" title="Polonium"><span style="display:block">Po</span></a>197<sup id="cite_ref-Mantina_4-12" class="reference"><a href="#cite_note-Mantina-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </td> <td title="At, astatine" style="text-align:center; padding:0.15em; background:#ff5c00; border:2px dashed #6e6e8e;"><a href="/wiki/Astatine" title="Astatine"><span style="display:block">At</span></a>202<sup id="cite_ref-Mantina_4-13" class="reference"><a href="#cite_note-Mantina-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </td> <td title="Rn, radon" style="text-align:center; padding:0.15em; background:#ff6e00; border:2px dashed #6e6e8e;"><a href="/wiki/Radon" title="Radon"><span style="display:block">Rn</span></a>220<sup id="cite_ref-Mantina_4-14" class="reference"><a href="#cite_note-Mantina-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <th><a href="/wiki/Period_7_element" title="Period 7 element">7</a> </th> <td title="Fr, francium" style="text-align:center; padding:0.15em; background:#ffee00; border:2px dashed #6e6e8e;"><a href="/wiki/Francium" title="Francium"><span style="display:block">Fr</span></a>348<sup id="cite_ref-Mantina_4-15" class="reference"><a href="#cite_note-Mantina-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </td> <td title="Ra, radium" style="text-align:center; padding:0.15em; background:#ffad00; border:2px dashed #6e6e8e;"><a href="/wiki/Radium" title="Radium"><span style="display:block">Ra</span></a>283<sup id="cite_ref-Mantina_4-16" class="reference"><a href="#cite_note-Mantina-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </td> <td style="text-align:center; vertical-align:middle;"><span class="skin-invert-image" typeof="mw:File"><span><img alt="1 asterisk" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Asterisks_2_%28vertical%29.svg/16px-Asterisks_2_%28vertical%29.svg.png" decoding="async" width="16" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Asterisks_2_%28vertical%29.svg/24px-Asterisks_2_%28vertical%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Asterisks_2_%28vertical%29.svg/32px-Asterisks_2_%28vertical%29.svg.png 2x" data-file-width="106" data-file-height="98" /></span></span> </td> <td title="Lr, lawrencium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px dotted #6e6e8e;"><a href="/wiki/Lawrencium" title="Lawrencium"><span style="display:block">Lr</span></a>  </td> <td title="Rf, rutherfordium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px dotted #6e6e8e;"><a href="/wiki/Rutherfordium" title="Rutherfordium"><span style="display:block">Rf</span></a>  </td> <td title="Db, dubnium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px dotted #6e6e8e;"><a href="/wiki/Dubnium" title="Dubnium"><span style="display:block">Db</span></a>  </td> <td title="Sg, seaborgium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px dotted #6e6e8e;"><a href="/wiki/Seaborgium" title="Seaborgium"><span style="display:block">Sg</span></a>  </td> <td title="Bh, bohrium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px dotted #6e6e8e;"><a href="/wiki/Bohrium" title="Bohrium"><span style="display:block">Bh</span></a>  </td> <td title="Hs, hassium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px dotted #6e6e8e;"><a href="/wiki/Hassium" title="Hassium"><span style="display:block">Hs</span></a>  </td> <td title="Mt, meitnerium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px dotted #6e6e8e;"><a href="/wiki/Meitnerium" title="Meitnerium"><span style="display:block">Mt</span></a>  </td> <td title="Ds, darmstadtium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px dotted #6e6e8e;"><a href="/wiki/Darmstadtium" title="Darmstadtium"><span style="display:block">Ds</span></a>  </td> <td title="Rg, roentgenium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px dotted #6e6e8e;"><a href="/wiki/Roentgenium" title="Roentgenium"><span style="display:block">Rg</span></a>  </td> <td title="Cn, copernicium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px dotted #6e6e8e;"><a href="/wiki/Copernicium" title="Copernicium"><span style="display:block">Cn</span></a>  </td> <td title="Nh, nihonium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px dotted #6e6e8e;"><a href="/wiki/Nihonium" title="Nihonium"><span style="display:block">Nh</span></a>  </td> <td title="Fl, flerovium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px dotted #6e6e8e;"><a href="/wiki/Flerovium" title="Flerovium"><span style="display:block">Fl</span></a>  </td> <td title="Mc, moscovium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px dotted #6e6e8e;"><a href="/wiki/Moscovium" title="Moscovium"><span style="display:block">Mc</span></a>  </td> <td title="Lv, livermorium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px dotted #6e6e8e;"><a href="/wiki/Livermorium" title="Livermorium"><span style="display:block">Lv</span></a>  </td> <td title="Ts, tennessine" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px dotted #6e6e8e;"><a href="/wiki/Tennessine" title="Tennessine"><span style="display:block">Ts</span></a>  </td> <td title="Og, oganesson" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px dotted #6e6e8e;"><a href="/wiki/Oganesson" title="Oganesson"><span style="display:block">Og</span></a>  </td></tr> <tr> <td colspan="22"><br /> </td></tr> <tr> <td colspan="4" style="text-align:right; padding-right:0.5em;; vertical-align:middle;"><span class="skin-invert-image" typeof="mw:File"><span><img alt="1 asterisk" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/49/Asterisks_one.svg/16px-Asterisks_one.svg.png" decoding="async" width="16" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/49/Asterisks_one.svg/24px-Asterisks_one.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/49/Asterisks_one.svg/32px-Asterisks_one.svg.png 2x" data-file-width="106" data-file-height="98" /></span></span> </td> <td title="La, lanthanum" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Lanthanum" title="Lanthanum"><span style="display:block">La</span></a>  </td> <td title="Ce, cerium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Cerium" title="Cerium"><span style="display:block">Ce</span></a>  </td> <td title="Pr, praseodymium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Praseodymium" title="Praseodymium"><span style="display:block">Pr</span></a>  </td> <td title="Nd, neodymium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Neodymium" title="Neodymium"><span style="display:block">Nd</span></a>  </td> <td title="Pm, promethium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px dashed #6e6e8e;"><a href="/wiki/Promethium" title="Promethium"><span style="display:block">Pm</span></a>  </td> <td title="Sm, samarium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Samarium" title="Samarium"><span style="display:block">Sm</span></a>  </td> <td title="Eu, europium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Europium" title="Europium"><span style="display:block">Eu</span></a>  </td> <td title="Gd, gadolinium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Gadolinium" title="Gadolinium"><span style="display:block">Gd</span></a>  </td> <td title="Tb, terbium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Terbium" title="Terbium"><span style="display:block">Tb</span></a>  </td> <td title="Dy, dysprosium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Dysprosium" title="Dysprosium"><span style="display:block">Dy</span></a>  </td> <td title="Ho, holmium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Holmium" title="Holmium"><span style="display:block">Ho</span></a>  </td> <td title="Er, erbium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Erbium" title="Erbium"><span style="display:block">Er</span></a>  </td> <td title="Tm, thulium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Thulium" title="Thulium"><span style="display:block">Tm</span></a>  </td> <td title="Yb, ytterbium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Ytterbium" title="Ytterbium"><span style="display:block">Yb</span></a>  </td></tr> <tr> <td colspan="4" style="text-align:right; padding-right:0.5em;; vertical-align:middle;"><span class="skin-invert-image" typeof="mw:File"><span><img alt="1 asterisk" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Asterisks_2_%28vertical%29.svg/16px-Asterisks_2_%28vertical%29.svg.png" decoding="async" width="16" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Asterisks_2_%28vertical%29.svg/24px-Asterisks_2_%28vertical%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Asterisks_2_%28vertical%29.svg/32px-Asterisks_2_%28vertical%29.svg.png 2x" data-file-width="106" data-file-height="98" /></span></span> </td> <td title="Ac, actinium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px dashed #6e6e8e;"><a href="/wiki/Actinium" title="Actinium"><span style="display:block">Ac</span></a>  </td> <td title="Th, thorium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px solid #6e6e8e;"><a href="/wiki/Thorium" title="Thorium"><span style="display:block">Th</span></a>  </td> <td title="Pa, protactinium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px dashed #6e6e8e;"><a href="/wiki/Protactinium" title="Protactinium"><span style="display:block">Pa</span></a>  </td> <td title="U , uranium" style="text-align:center; padding:0.15em; background:#ff4c00; border:2px solid #6e6e8e;"><a href="/wiki/Uranium" title="Uranium"><span style="display:block">U </span></a>186 </td> <td title="Np, neptunium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px dashed #6e6e8e;"><a href="/wiki/Neptunium" title="Neptunium"><span style="display:block">Np</span></a>  </td> <td title="Pu, plutonium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px dashed #6e6e8e;"><a href="/wiki/Plutonium" title="Plutonium"><span style="display:block">Pu</span></a>  </td> <td title="Am, americium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px dotted #6e6e8e;"><a href="/wiki/Americium" title="Americium"><span style="display:block">Am</span></a>  </td> <td title="Cm, curium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px dotted #6e6e8e;"><a href="/wiki/Curium" title="Curium"><span style="display:block">Cm</span></a>  </td> <td title="Bk, berkelium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px dotted #6e6e8e;"><a href="/wiki/Berkelium" title="Berkelium"><span style="display:block">Bk</span></a>  </td> <td title="Cf, californium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px dotted #6e6e8e;"><a href="/wiki/Californium" title="Californium"><span style="display:block">Cf</span></a>  </td> <td title="Es, einsteinium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px dotted #6e6e8e;"><a href="/wiki/Einsteinium" title="Einsteinium"><span style="display:block">Es</span></a>  </td> <td title="Fm, fermium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px dotted #6e6e8e;"><a href="/wiki/Fermium" title="Fermium"><span style="display:block">Fm</span></a>  </td> <td title="Md, mendelevium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px dotted #6e6e8e;"><a href="/wiki/Mendelevium" title="Mendelevium"><span style="display:block">Md</span></a>  </td> <td title="No, nobelium" style="text-align:center; padding:0.15em; background:#bbbbbb; border:2px dotted #6e6e8e;"><a href="/wiki/Nobelium" title="Nobelium"><span style="display:block">No</span></a>  </td></tr> <tr> <td colspan="19" style="text-align:left;"><b>Legend</b> </td></tr> <tr> <td colspan="19" style="text-align:left;">Values for the van der Waals radii are in <a href="/wiki/Picometers" class="mw-redirect" title="Picometers">picometers</a> (pm or <span class="nowrap"><span data-sort-value="6988100000000000000♠"></span>1<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−12</sup> m</span>) </td></tr> <tr> <td colspan="19" style="text-align:left;">The shade of the box ranges from red to yellow as the radius increases; Gray indicate a lack of data. </td></tr> <tr> <td colspan="19" style="text-align:left;">Unless indicated otherwise, the data is from <i><a href="/wiki/Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a>'</i>s <a rel="nofollow" class="external text" href="https://reference.wolfram.com/language/ref/ElementData.html">ElementData</a> function from <a href="/wiki/Wolfram_Research" title="Wolfram Research">Wolfram Research, Inc.</a><sup id="cite_ref-slater64_5-0" class="reference"><a href="#cite_note-slater64-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td colspan="19"> <div role="presentation" id="periodic-table-legend" style="border: 1px solid #a2a9b1; width:100%; line-height:120%; text-align:center; vertical-align:top; background:#f8f8f8;color:inherit; margin:0;"><div style="padding:0.3em;"> <p><span style="text-align:center;display:inline-block; width:8em; border:2px solid #6e6e8e; background:#e0e0e0;"><a href="/wiki/Primordial_nuclide" title="Primordial nuclide">Primordial</a></span> <span style="text-align:center;display:inline-block; width:8em; border:2px dashed #6e6e8e; background:#e0e0e0;"> <a href="/wiki/Trace_radioisotope" title="Trace radioisotope"><span class="nowrap">From decay</span></a></span> <span style="text-align:center;display:inline-block; width:8em; border:2px dotted #6e6e8e; background:#e0e0e0;"> <a href="/wiki/Synthetic_element" title="Synthetic element">Synthetic</a></span> <span class="nowrap"><b>Border</b> shows natural occurrence of the element</span> </p> </div> </div> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Methods_of_determination">Methods of determination</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Van_der_Waals_radius&action=edit&section=3" title="Edit section: Methods of determination"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Refimprove_science plainlinks metadata ambox ambox-content ambox-Primary_sources" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This scientific article <b>needs additional <a href="/wiki/Wikipedia:Scientific_citation_guidelines" title="Wikipedia:Scientific citation guidelines">citations</a> to <a href="/wiki/Wikipedia:Reliable_sources#Scholarship" title="Wikipedia:Reliable sources">secondary or tertiary sources</a></b>.<span class="hide-when-compact"> Help add sources such as review articles, monographs, or textbooks. Please also establish the relevance for any <a href="/wiki/Wikipedia:No_original_research#Primary,_secondary_and_tertiary_sources" title="Wikipedia:No original research">primary research articles</a> cited. Unsourced or poorly sourced material may be challenged and removed.</span> <span class="date-container"><i>(<span class="date">June 2015</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>Van der Waals radii may be determined from the <a href="/wiki/Mechanics" title="Mechanics">mechanical</a> properties of gases (the original method), from the <a href="/wiki/Critical_point_(thermodynamics)" title="Critical point (thermodynamics)">critical point</a>, from measurements of atomic spacing between pairs of unbonded atoms in <a href="/wiki/Crystal" title="Crystal">crystals</a> or from measurements of electrical or optical properties (the <a href="/wiki/Polarizability" title="Polarizability">polarizability</a> and the <a href="/wiki/Molar_refractivity" title="Molar refractivity">molar refractivity</a>). These various methods give values for the van der Waals radius which are similar (1–2 <a href="/wiki/Angstrom" title="Angstrom">Å</a>, 100–200 <a href="/wiki/Picometre" title="Picometre">pm</a>) but not identical. Tabulated values of van der Waals radii are obtained by taking a <a href="/wiki/Weighted_mean" class="mw-redirect" title="Weighted mean">weighted mean</a> of a number of different experimental values, and, for this reason, different tables will often have different values for the van der Waals radius of the same atom. Indeed, there is no reason to assume that the van der Waals radius is a fixed property of the atom in all circumstances: rather, it tends to vary with the particular chemical environment of the atom in any given case.<sup id="cite_ref-Bondi1964_2-1" class="reference"><a href="#cite_note-Bondi1964-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Van_der_Waals_equation_of_state">Van der Waals equation of state</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Van_der_Waals_radius&action=edit&section=4" title="Edit section: Van der Waals equation of state"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Van_der_Waals_equation" title="Van der Waals equation">Van der Waals equation</a></div> <p>The van der Waals equation of state is the simplest and best-known modification of the <a href="/wiki/Ideal_gas_law" title="Ideal gas law">ideal gas law</a> to account for the behaviour of <a href="/wiki/Real_gas" title="Real gas">real gases</a>: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(p+a\left({\frac {n}{\tilde {V}}}\right)^{2}\right)({\tilde {V}}-nb)=nRT,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow> <mi>p</mi> <mo>+</mo> <mi>a</mi> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>V</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>V</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mo>−</mo> <mi>n</mi> <mi>b</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>n</mi> <mi>R</mi> <mi>T</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(p+a\left({\frac {n}{\tilde {V}}}\right)^{2}\right)({\tilde {V}}-nb)=nRT,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58c0cba318c9cd31cffb525e7183652b4024d472" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:33.776ex; height:7.509ex;" alt="{\displaystyle \left(p+a\left({\frac {n}{\tilde {V}}}\right)^{2}\right)({\tilde {V}}-nb)=nRT,}"></span> where <span class="texhtml mvar" style="font-style:italic;">p</span> is pressure, <span class="texhtml mvar" style="font-style:italic;">n</span> is the number of moles of the gas in question and <span class="texhtml mvar" style="font-style:italic;">a</span> and <span class="texhtml mvar" style="font-style:italic;">b</span> depend on the particular gas, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tilde {V}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>V</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tilde {V}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e85c3b6a767475803068debfbe0e2320d715041d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.676ex;" alt="{\displaystyle {\tilde {V}}}"></span> is the volume, <span class="texhtml mvar" style="font-style:italic;">R</span> is the specific gas constant on a unit mole basis and <span class="texhtml mvar" style="font-style:italic;">T</span> the absolute temperature; <span class="texhtml mvar" style="font-style:italic;">a</span> is a correction for intermolecular forces and <span class="texhtml mvar" style="font-style:italic;">b</span> corrects for finite atomic or molecular sizes; the value of <span class="texhtml mvar" style="font-style:italic;">b</span> equals the van der Waals volume per mole of the gas. <a href="/wiki/Van_der_Waals_constants_(data_page)" title="Van der Waals constants (data page)">Their values</a> vary from gas to gas. </p><p>The van der Waals equation also has a microscopic interpretation: molecules interact with one another. The interaction is strongly repulsive at a very short distance, becomes mildly attractive at the intermediate range, and vanishes at a long distance. The ideal gas law must be corrected when attractive and repulsive forces are considered. For example, the mutual repulsion between molecules has the effect of excluding neighbors from a certain amount of space around each molecule. Thus, a fraction of the total space becomes unavailable to each molecule as it executes random motion. In the equation of state, this volume of exclusion (<span class="texhtml"><i>nb</i></span>) should be subtracted from the volume of the container (<span class="texhtml mvar" style="font-style:italic;">V</span>), thus: (<span class="texhtml"><i>V</i> - <i>nb</i></span>). The other term that is introduced in the van der Waals equation, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle a\left({\frac {n}{\tilde {V}}}\right)^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>a</mi> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>V</mi> <mo stretchy="false">~</mo> </mover> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle a\left({\frac {n}{\tilde {V}}}\right)^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/070676a874de60a45ab6db55dcfd5fcee7f12c79" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.159ex; height:5.176ex;" alt="{\textstyle a\left({\frac {n}{\tilde {V}}}\right)^{2}}"></span>, describes a weak attractive force among molecules (known as the <a href="/wiki/Van_der_Waals_force" title="Van der Waals force">van der Waals force</a>), which increases when <span class="texhtml mvar" style="font-style:italic;">n</span> increases or <span class="texhtml mvar" style="font-style:italic;">V</span> decreases and molecules become more crowded together. </p> <table class="wikitable floatright" align="right"> <tbody><tr> <th>Gas </th> <th><i>d</i> (<a href="/wiki/%C3%85ngstr%C3%B6m" class="mw-redirect" title="Ångström">Å</a>) </th> <th><i>b</i> (cm<sup>3</sup>mol<sup>–1</sup>) </th> <th><i>V</i><sub>w</sub> (Å<sup>3</sup>) </th> <th><i>r</i><sub>w</sub> (Å) </th></tr> <tr> <td><a href="/wiki/Hydrogen" title="Hydrogen">Hydrogen</a> </td> <td>0.74611 </td> <td align="center">26.61 </td> <td>34.53 </td> <td>2.02 </td></tr> <tr> <td><a href="/wiki/Nitrogen" title="Nitrogen">Nitrogen</a> </td> <td>1.0975 </td> <td align="center">39.13 </td> <td>47.71 </td> <td>2.25 </td></tr> <tr> <td><a href="/wiki/Oxygen" title="Oxygen">Oxygen</a> </td> <td>1.208 </td> <td align="center">31.83 </td> <td>36.62 </td> <td>2.06 </td></tr> <tr> <td><a href="/wiki/Chlorine" title="Chlorine">Chlorine</a> </td> <td>1.988 </td> <td align="center">56.22 </td> <td>57.19 </td> <td>2.39 </td></tr> <tr> <td colspan="5"><small>van der Waals radii <i>r</i><sub>w</sub> in Å (or in 100 picometers) calculated from the <a href="/wiki/Van_der_Waals_constant" class="mw-redirect" title="Van der Waals constant">van der Waals constants</a><br />of some diatomic gases. Values of <i>d</i> and <i>b</i> from Weast (1981).</small> </td></tr></tbody></table> <p>The <a href="/wiki/Van_der_Waals_constant" class="mw-redirect" title="Van der Waals constant">van der Waals constant</a> <i>b</i> volume can be used to calculate the van der Waals volume of an atom or molecule with experimental data derived from measurements on gases. </p><p>For <a href="/wiki/Helium" title="Helium">helium</a>,<sup id="cite_ref-CRC_6-0" class="reference"><a href="#cite_note-CRC-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> <i>b</i> = 23.7 cm<sup>3</sup>/mol. Helium is a <a href="/wiki/Monatomic_gas" title="Monatomic gas">monatomic gas</a>, and each mole of helium contains <span class="nowrap"><span data-sort-value="7023602200000000000♠"></span>6.022<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>23</sup></span> atoms (the <a href="/wiki/Avogadro_constant" title="Avogadro constant">Avogadro constant</a>, <i>N</i><sub>A</sub>): <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{\rm {w}}={b \over {N_{\rm {A}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">w</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\rm {w}}={b \over {N_{\rm {A}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb731530c6bb28b191fd733dd9b18b92ba47f6e8" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:10.04ex; height:5.843ex;" alt="{\displaystyle V_{\rm {w}}={b \over {N_{\rm {A}}}}}"></span> Therefore, the van der Waals volume of a single atom <i>V</i><sub>w</sub> = 39.36 Å<sup>3</sup>, which corresponds to <i>r</i><sub>w</sub> = 2.11 Å (≈ 200 picometers). This method may be extended to diatomic gases by approximating the molecule as a rod with rounded ends where the diameter is <span class="texhtml">2<i>r</i><sub>w</sub></span> and the internuclear distance is <span class="texhtml mvar" style="font-style:italic;">d</span>. The algebra is more complicated, but the relation <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{\rm {w}}={4 \over 3}\pi r_{\rm {w}}^{3}+\pi r_{\rm {w}}^{2}d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">w</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>4</mn> <mn>3</mn> </mfrac> </mrow> <mi>π</mi> <msubsup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">w</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msubsup> <mo>+</mo> <mi>π</mi> <msubsup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">w</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\rm {w}}={4 \over 3}\pi r_{\rm {w}}^{3}+\pi r_{\rm {w}}^{2}d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dcb26d4360a2f3054e0121aa99376df696127608" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:19.526ex; height:5.176ex;" alt="{\displaystyle V_{\rm {w}}={4 \over 3}\pi r_{\rm {w}}^{3}+\pi r_{\rm {w}}^{2}d}"></span> can be solved by the normal methods for <a href="/wiki/Cubic_functions" class="mw-redirect" title="Cubic functions">cubic functions</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Crystallographic_measurements">Crystallographic measurements</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Van_der_Waals_radius&action=edit&section=5" title="Edit section: Crystallographic measurements"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The molecules in a <a href="/wiki/Molecular_crystal" class="mw-redirect" title="Molecular crystal">molecular crystal</a> are held together by <a href="/wiki/Van_der_Waals_force" title="Van der Waals force">van der Waals forces</a> rather than <a href="/wiki/Chemical_bond" title="Chemical bond">chemical bonds</a>. In principle, the closest that two atoms belonging to <i>different</i> molecules can approach one another is given by the sum of their van der Waals radii. By examining a large number of structures of molecular crystals, it is possible to find a minimum radius for each type of atom such that other non-bonded atoms do not encroach any closer. This approach was first used by <a href="/wiki/Linus_Pauling" title="Linus Pauling">Linus Pauling</a> in his seminal work <i>The Nature of the Chemical Bond</i>.<sup id="cite_ref-Pauling1945_7-0" class="reference"><a href="#cite_note-Pauling1945-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Arnold Bondi also conducted a study of this type, published in 1964,<sup id="cite_ref-Bondi1964_2-2" class="reference"><a href="#cite_note-Bondi1964-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> although he also considered other methods of determining the van der Waals radius in coming to his final estimates. Some of Bondi's figures are given in the table at the top of this article, and they remain the most widely used "consensus" values for the van der Waals radii of the elements. Scott Rowland and Robin Taylor re-examined these 1964 figures in the light of more recent crystallographic data: on the whole, the agreement was very good, although they recommend a value of 1.09 Å for the van der Waals radius of <a href="/wiki/Hydrogen" title="Hydrogen">hydrogen</a> as opposed to Bondi's 1.20 Å.<sup id="cite_ref-RowlandRS1996_1-2" class="reference"><a href="#cite_note-RowlandRS1996-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> A more recent analysis of the <a href="/wiki/Cambridge_Structural_Database" title="Cambridge Structural Database">Cambridge Structural Database</a>, carried out by Santiago Alvareza, provided a new set of values for 93 naturally occurring elements.<sup id="cite_ref-Alvarez2013_8-0" class="reference"><a href="#cite_note-Alvarez2013-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>A simple example of the use of crystallographic data (here <a href="/wiki/Neutron_diffraction" title="Neutron diffraction">neutron diffraction</a>) is to consider the case of solid helium, where the atoms are held together only by van der Waals forces (rather than by <a href="/wiki/Covalent_bond" title="Covalent bond">covalent</a> or <a href="/wiki/Metallic_bond" class="mw-redirect" title="Metallic bond">metallic bonds</a>) and so the distance between the nuclei can be considered to be equal to twice the van der Waals radius. The density of solid helium at 1.1 K and 66 <a href="/wiki/Atmosphere_(unit)" class="mw-redirect" title="Atmosphere (unit)">atm</a> is <span class="nowrap"><span data-sort-value="7002214000000000000♠"></span>0.214(6) g/cm<sup>3</sup></span>,<sup id="cite_ref-Henshaw1958_9-0" class="reference"><a href="#cite_note-Henshaw1958-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> corresponding to a <a href="/wiki/Molar_volume" title="Molar volume">molar volume</a> <i>V</i><sub>m</sub> = <span class="nowrap"><span data-sort-value="6995186999999999999♠"></span>18.7<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−6</sup> m<sup>3</sup>/mol</span>. The van der Waals volume is given by <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{\rm {w}}={\frac {\pi V_{\rm {m}}}{N_{\rm {A}}{\sqrt {18}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">w</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>π</mi> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mrow> </msub> </mrow> <mrow> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>18</mn> </msqrt> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\rm {w}}={\frac {\pi V_{\rm {m}}}{N_{\rm {A}}{\sqrt {18}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9cdaa564afaeed7e6a9981e5a973fb01cbb3a637" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:14.3ex; height:6.176ex;" alt="{\displaystyle V_{\rm {w}}={\frac {\pi V_{\rm {m}}}{N_{\rm {A}}{\sqrt {18}}}}}"></span> where the factor of π/√18 arises from the <a href="/wiki/Sphere_packing" title="Sphere packing">packing of spheres</a>: <i>V</i><sub>w</sub> = <span class="nowrap"><span data-sort-value="6971229999999999999♠"></span>2.30<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−29</sup> m<sup>3</sup></span> = 23.0 Å<sup>3</sup>, corresponding to a van der Waals radius <i>r</i><sub>w</sub> = 1.76 Å. </p> <div class="mw-heading mw-heading3"><h3 id="Molar_refractivity">Molar refractivity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Van_der_Waals_radius&action=edit&section=6" title="Edit section: Molar refractivity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Molar_refractivity" title="Molar refractivity">molar refractivity</a> <span class="texhtml mvar" style="font-style:italic;">A</span> of a gas is related to its <a href="/wiki/Refractive_index" title="Refractive index">refractive index</a> <span class="texhtml mvar" style="font-style:italic;">n</span> by the <a href="/wiki/Lorentz%E2%80%93Lorenz_equation" class="mw-redirect" title="Lorentz–Lorenz equation">Lorentz–Lorenz equation</a>: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A={\frac {RT(n^{2}-1)}{3p}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>R</mi> <mi>T</mi> <mo stretchy="false">(</mo> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> <mrow> <mn>3</mn> <mi>p</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A={\frac {RT(n^{2}-1)}{3p}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/065c266b8623f8e85265e788d7b4dcbcaa4535f7" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:17.339ex; height:6.343ex;" alt="{\displaystyle A={\frac {RT(n^{2}-1)}{3p}}}"></span> The refractive index of helium <i>n</i> = <span class="nowrap"><span data-sort-value="7000100003500000000♠"></span>1.000<span style="margin-left:.25em;">0350</span></span> at 0 °C and 101.325 kPa,<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> which corresponds to a molar refractivity <i>A</i> = <span class="nowrap"><span data-sort-value="6993523000000000000♠"></span>5.23<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−7</sup> m<sup>3</sup>/mol</span>. Dividing by the Avogadro constant gives <i>V</i><sub>w</sub> = <span class="nowrap"><span data-sort-value="6969868500000000000♠"></span>8.685<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−31</sup> m<sup>3</sup></span> = 0.8685 Å<sup>3</sup>, corresponding to <i>r</i><sub>w</sub> = 0.59 Å. </p> <div class="mw-heading mw-heading3"><h3 id="Polarizability">Polarizability</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Van_der_Waals_radius&action=edit&section=7" title="Edit section: Polarizability"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Polarizability" title="Polarizability">polarizability</a> <i>α</i> of a gas is related to its <a href="/wiki/Electric_susceptibility" title="Electric susceptibility">electric susceptibility</a> <i>χ</i><sub>e</sub> by the relation <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha ={\varepsilon _{0}k_{\rm {B}}T \over p}\chi _{\rm {e}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mi>T</mi> </mrow> <mi>p</mi> </mfrac> </mrow> <msub> <mi>χ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha ={\varepsilon _{0}k_{\rm {B}}T \over p}\chi _{\rm {e}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e391e9dd468ba655967e8b91d9e06923a5f4edac" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:14.221ex; height:5.843ex;" alt="{\displaystyle \alpha ={\varepsilon _{0}k_{\rm {B}}T \over p}\chi _{\rm {e}}}"></span> and the electric susceptibility may be calculated from tabulated values of the <a href="/wiki/Permittivity" title="Permittivity">relative permittivity</a> <i>ε</i><sub>r</sub> using the relation <i>χ</i><sub>e</sub> = <i>ε</i><sub>r</sub> − 1. The electric susceptibility of helium <i>χ</i><sub>e</sub> = <span class="nowrap"><span data-sort-value="6995700000000000000♠"></span>7<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−5</sup></span> at 0 °C and 101.325 kPa,<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> which corresponds to a polarizability <i>α</i> = <span class="nowrap"><span data-sort-value="6959230700000000000♠"></span>2.307<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−41</sup> C⋅m<sup>2</sup>/V</span>. The polarizability is related the van der Waals volume by the relation <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{\rm {w}}={1 \over {4\pi \varepsilon _{0}}}\alpha ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">w</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> <mi>π</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mi>α</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\rm {w}}={1 \over {4\pi \varepsilon _{0}}}\alpha ,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bac11aa9a64f7de5a3e34e4a69caf02bc0edc408" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:13.475ex; height:5.676ex;" alt="{\displaystyle V_{\rm {w}}={1 \over {4\pi \varepsilon _{0}}}\alpha ,}"></span> so the van der Waals volume of helium <i>V</i><sub>w</sub> = <span class="nowrap"><span data-sort-value="6969207300000000000♠"></span>2.073<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−31</sup> m<sup>3</sup></span> = 0.2073 Å<sup>3</sup> by this method, corresponding to <i>r</i><sub>w</sub> = 0.37 Å. </p><p>When the atomic polarizability is quoted in units of volume such as Å<sup>3</sup>, as is often the case, it is equal to the van der Waals volume. However, the term "atomic polarizability" is preferred as polarizability is a precisely defined (and measurable) <a href="/wiki/Physical_quantity" title="Physical quantity">physical quantity</a>, whereas "van der Waals volume" can have any number of definitions depending on the method of measurement. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Van_der_Waals_radius&action=edit&section=8" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Atomic_radii_of_the_elements_(data_page)" title="Atomic radii of the elements (data page)">Atomic radii of the elements (data page)</a></li> <li><a href="/wiki/Van_der_Waals_force" title="Van der Waals force">van der Waals force</a></li> <li><a href="/wiki/Van_der_Waals_molecule" title="Van der Waals molecule">van der Waals molecule</a></li> <li><a href="/wiki/Van_der_Waals_strain" title="Van der Waals strain">van der Waals strain</a></li> <li><a href="/wiki/Van_der_Waals_surface" title="Van der Waals surface">van der Waals surface</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Van_der_Waals_radius&action=edit&section=9" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-RowlandRS1996-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-RowlandRS1996_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-RowlandRS1996_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-RowlandRS1996_1-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output 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a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and 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Ithaca, NY: Cornell University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8014-0333-0" title="Special:BookSources/978-0-8014-0333-0"><bdi>978-0-8014-0333-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Nature+of+the+Chemical+Bond&rft.place=Ithaca%2C+NY&rft.pub=Cornell+University+Press&rft.date=1945&rft.isbn=978-0-8014-0333-0&rft.aulast=Pauling&rft.aufirst=Linus&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVan+der+Waals+radius" class="Z3988"></span></span> </li> <li id="cite_note-Alvarez2013-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-Alvarez2013_8-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAlvareza2013" class="citation journal cs1">Alvareza, Santiago (2013). <a rel="nofollow" class="external text" href="https://doi.org/10.1039%2FC3DT50599E">"A cartography of the van der Waals territories"</a>. <i><a href="/wiki/Dalton_Trans." class="mw-redirect" title="Dalton Trans.">Dalton Trans.</a></i> <b>42</b> (24): <span class="nowrap">8617–</span>36. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1039%2FC3DT50599E">10.1039/C3DT50599E</a></span>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/2445%2F48823">2445/48823</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/23632803">23632803</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Dalton+Trans.&rft.atitle=A+cartography+of+the+van+der+Waals+territories&rft.volume=42&rft.issue=24&rft.pages=%3Cspan+class%3D%22nowrap%22%3E8617-%3C%2Fspan%3E36&rft.date=2013&rft_id=info%3Ahdl%2F2445%2F48823&rft_id=info%3Apmid%2F23632803&rft_id=info%3Adoi%2F10.1039%2FC3DT50599E&rft.aulast=Alvareza&rft.aufirst=Santiago&rft_id=https%3A%2F%2Fdoi.org%2F10.1039%252FC3DT50599E&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVan+der+Waals+radius" class="Z3988"></span></span> </li> <li id="cite_note-Henshaw1958-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-Henshaw1958_9-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHenshaw1958" class="citation journal cs1">Henshaw, D.G. (1958). "Structure of Solid Helium by Neutron Diffraction". <i><a href="/wiki/Physical_Review" title="Physical Review">Physical Review</a></i>. <b>109</b> (2): <span class="nowrap">328–</span>330. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1958PhRv..109..328H">1958PhRv..109..328H</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRev.109.328">10.1103/PhysRev.109.328</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review&rft.atitle=Structure+of+Solid+Helium+by+Neutron+Diffraction&rft.volume=109&rft.issue=2&rft.pages=%3Cspan+class%3D%22nowrap%22%3E328-%3C%2Fspan%3E330&rft.date=1958&rft_id=info%3Adoi%2F10.1103%2FPhysRev.109.328&rft_id=info%3Abibcode%2F1958PhRv..109..328H&rft.aulast=Henshaw&rft.aufirst=D.G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVan+der+Waals+radius" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text">Kaye & Laby Tables, <a rel="nofollow" class="external text" href="http://www.kayelaby.npl.co.uk/general_physics/2_5/2_5_7.html">Refractive index of gases</a>.</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">Kaye & Laby Tables, <a rel="nofollow" class="external text" href="http://www.kayelaby.npl.co.uk/general_physics/2_6/2_6_5.html">Dielectric Properties of Materials</a>.</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Van_der_Waals_radius&action=edit&section=10" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHuheeyKeiterKeiter1997" class="citation book cs1">Huheey, James E.; Keiter, Ellen A.; Keiter, Richard L. (1997). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/inorganicchemist00huhe_0"><i>Inorganic Chemistry: Principles of Structure and Reactivity</i></a></span> (4th ed.). New York: Prentice Hall. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-06-042995-9" title="Special:BookSources/978-0-06-042995-9"><bdi>978-0-06-042995-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Inorganic+Chemistry%3A+Principles+of+Structure+and+Reactivity&rft.place=New+York&rft.edition=4th&rft.pub=Prentice+Hall&rft.date=1997&rft.isbn=978-0-06-042995-9&rft.aulast=Huheey&rft.aufirst=James+E.&rft.au=Keiter%2C+Ellen+A.&rft.au=Keiter%2C+Richard+L.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Finorganicchemist00huhe_0&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVan+der+Waals+radius" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Van_der_Waals_radius&action=edit&section=11" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://periodictable.com/Properties/A/VanDerWaalsRadius.v.html">van der Waals Radius of the elements</a> at PeriodicTable.com</li> <li><a rel="nofollow" class="external text" href="http://www.webelements.com/periodicity/van_der_waals_radius/">van der Waals Radius – Periodicity</a> at WebElements.com</li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Van_der_Waals_radius&oldid=1259471377">https://en.wikipedia.org/w/index.php?title=Van_der_Waals_radius&oldid=1259471377</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Chemical_properties" title="Category:Chemical properties">Chemical properties</a></li><li><a href="/wiki/Category:Intermolecular_forces" title="Category:Intermolecular forces">Intermolecular forces</a></li><li><a href="/wiki/Category:Johannes_Diderik_van_der_Waals" title="Category:Johannes Diderik van der Waals">Johannes Diderik van der Waals</a></li><li><a href="/wiki/Category:Atomic_radius" title="Category:Atomic radius">Atomic radius</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li><li><a href="/wiki/Category:Articles_needing_additional_references_from_June_2015" title="Category:Articles needing additional references from June 2015">Articles needing additional references from June 2015</a></li><li><a href="/wiki/Category:All_articles_needing_additional_references" title="Category:All articles needing additional references">All articles needing additional references</a></li><li><a href="/wiki/Category:Articles_lacking_reliable_references_from_June_2015" title="Category:Articles lacking reliable references from June 2015">Articles lacking reliable references from June 2015</a></li><li><a href="/wiki/Category:All_articles_lacking_reliable_references" title="Category:All articles lacking reliable references">All articles lacking reliable references</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 25 November 2024, at 10:02<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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