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Planck-állandó – Wikipédia

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data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Tartalomjegyzék kinyitása/becsukása" > <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">Tartalomjegyzék kinyitása/becsukása</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"><span class="mw-page-title-main">Planck-állandó</span></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="Ugrás egy más nyelvű szócikkre. Elérhető 79 nyelven" > <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-79" 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">79 nyelv</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Planck_constant" title="Planck constant – angol" lang="en" hreflang="en" data-title="Planck constant" data-language-autonym="English" data-language-local-name="angol" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Konstante_van_Planck" title="Konstante van Planck – afrikaans" lang="af" hreflang="af" data-title="Konstante van Planck" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Constant_de_Planck" title="Constant de Planck – aragonéz" lang="an" hreflang="an" data-title="Constant de Planck" data-language-autonym="Aragonés" data-language-local-name="aragonéz" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AB%D8%A7%D8%A8%D8%AA_%D8%A8%D9%84%D8%A7%D9%86%D9%83" title="ثابت بلانك – arab" lang="ar" hreflang="ar" data-title="ثابت بلانك" data-language-autonym="العربية" data-language-local-name="arab" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%AA%E0%A7%8D%E0%A6%B2%E0%A7%87%E0%A6%82%E0%A6%95%E0%A7%B0_%E0%A6%A7%E0%A7%8D%E0%A7%B0%E0%A7%81%E0%A7%B1%E0%A6%95" title="প্লেংকৰ ধ্ৰুৱক – asszámi" lang="as" hreflang="as" data-title="প্লেংকৰ ধ্ৰুৱক" data-language-autonym="অসমীয়া" data-language-local-name="asszámi" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Constante_de_Planck" title="Constante de Planck – asztúr" lang="ast" hreflang="ast" data-title="Constante de Planck" data-language-autonym="Asturianu" data-language-local-name="asztúr" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Plank_sabiti" title="Plank sabiti – azerbajdzsáni" lang="az" hreflang="az" data-title="Plank sabiti" data-language-autonym="Azərbaycanca" data-language-local-name="azerbajdzsáni" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9F%D0%B0%D1%81%D1%82%D0%B0%D1%8F%D0%BD%D0%BD%D0%B0%D1%8F_%D0%9F%D0%BB%D0%B0%D0%BD%D0%BA%D0%B0" title="Пастаянная Планка – belarusz" lang="be" hreflang="be" data-title="Пастаянная Планка" data-language-autonym="Беларуская" data-language-local-name="belarusz" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D1%81%D1%82%D0%B0%D0%BD%D1%82%D0%B0_%D0%BD%D0%B0_%D0%9F%D0%BB%D0%B0%D0%BD%D0%BA" title="Константа на Планк – bolgár" lang="bg" hreflang="bg" data-title="Константа на Планк" data-language-autonym="Български" data-language-local-name="bolgár" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AA%E0%A7%8D%E0%A6%B2%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%99%E0%A7%8D%E0%A6%95%E0%A7%87%E0%A6%B0_%E0%A6%A7%E0%A7%8D%E0%A6%B0%E0%A7%81%E0%A6%AC%E0%A6%95" title="প্ল্যাঙ্কের ধ্রুবক – bangla" lang="bn" hreflang="bn" data-title="প্ল্যাঙ্কের ধ্রুবক" data-language-autonym="বাংলা" data-language-local-name="bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Planckova_konstanta" title="Planckova konstanta – bosnyák" lang="bs" hreflang="bs" data-title="Planckova konstanta" data-language-autonym="Bosanski" data-language-local-name="bosnyák" 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/Constant_de_Planck" title="Constant de Planck – katalán" lang="ca" hreflang="ca" data-title="Constant de Planck" data-language-autonym="Català" data-language-local-name="katalán" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%86%DB%95%DA%AF%DB%86%DA%95%DB%8C_%D9%BE%D9%84%D8%A7%D9%86%DA%A9" title="نەگۆڕی پلانک – közép-ázsiai kurd" lang="ckb" hreflang="ckb" data-title="نەگۆڕی پلانک" data-language-autonym="کوردی" data-language-local-name="közép-ázsiai kurd" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Planckova_konstanta" title="Planckova konstanta – cseh" lang="cs" hreflang="cs" data-title="Planckova konstanta" data-language-autonym="Čeština" data-language-local-name="cseh" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9F%D0%BB%D0%B0%D0%BD%D0%BA_%D0%BA%D0%BE%D0%BD%D1%81%D1%82%D0%B0%D0%BD%D1%82%D1%82%D0%B8" title="Планк константти – csuvas" lang="cv" hreflang="cv" data-title="Планк константти" data-language-autonym="Чӑвашла" data-language-local-name="csuvas" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Plancks_konstant" title="Plancks konstant – dán" lang="da" hreflang="da" data-title="Plancks konstant" data-language-autonym="Dansk" data-language-local-name="dán" 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/Planck-Konstante" title="Planck-Konstante – német" lang="de" hreflang="de" data-title="Planck-Konstante" data-language-autonym="Deutsch" data-language-local-name="német" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A3%CF%84%CE%B1%CE%B8%CE%B5%CF%81%CE%AC_%CF%84%CE%BF%CF%85_%CE%A0%CE%BB%CE%B1%CE%BD%CE%BA" title="Σταθερά του Πλανκ – görög" lang="el" hreflang="el" data-title="Σταθερά του Πλανκ" data-language-autonym="Ελληνικά" data-language-local-name="görög" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Konstanto_de_Planck" title="Konstanto de Planck – eszperantó" lang="eo" hreflang="eo" data-title="Konstanto de Planck" data-language-autonym="Esperanto" data-language-local-name="eszperantó" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Constante_de_Planck" title="Constante de Planck – spanyol" lang="es" hreflang="es" data-title="Constante de Planck" data-language-autonym="Español" data-language-local-name="spanyol" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Plancki_konstant" title="Plancki konstant – észt" lang="et" hreflang="et" data-title="Plancki konstant" data-language-autonym="Eesti" data-language-local-name="észt" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Plancken_konstantea" title="Plancken konstantea – baszk" lang="eu" hreflang="eu" data-title="Plancken konstantea" data-language-autonym="Euskara" data-language-local-name="baszk" 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%AB%D8%A7%D8%A8%D8%AA_%D9%BE%D9%84%D8%A7%D9%86%DA%A9" title="ثابت پلانک – perzsa" lang="fa" hreflang="fa" data-title="ثابت پلانک" data-language-autonym="فارسی" data-language-local-name="perzsa" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Planckin_vakio" title="Planckin vakio – finn" lang="fi" hreflang="fi" data-title="Planckin vakio" data-language-autonym="Suomi" data-language-local-name="finn" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Constante_de_Planck" title="Constante de Planck – francia" lang="fr" hreflang="fr" data-title="Constante de Planck" data-language-autonym="Français" data-language-local-name="francia" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Planck-taal" title="Planck-taal – északi fríz" lang="frr" hreflang="frr" data-title="Planck-taal" data-language-autonym="Nordfriisk" data-language-local-name="északi fríz" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Tairiseach_Planck" title="Tairiseach Planck – ír" lang="ga" hreflang="ga" data-title="Tairiseach Planck" data-language-autonym="Gaeilge" data-language-local-name="ír" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Constante_de_Planck" title="Constante de Planck – gallego" lang="gl" hreflang="gl" data-title="Constante de Planck" data-language-autonym="Galego" data-language-local-name="gallego" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A7%D7%91%D7%95%D7%A2_%D7%A4%D7%9C%D7%90%D7%A0%D7%A7" title="קבוע פלאנק – héber" lang="he" hreflang="he" data-title="קבוע פלאנק" data-language-autonym="עברית" data-language-local-name="héber" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B2%E0%A5%88%E0%A4%82%E0%A4%95_%E0%A4%B8%E0%A5%8D%E0%A4%A5%E0%A4%BF%E0%A4%B0%E0%A4%BE%E0%A4%82%E0%A4%95" title="प्लैंक स्थिरांक – hindi" lang="hi" hreflang="hi" data-title="प्लैंक स्थिरांक" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Planckova_konstanta" title="Planckova konstanta – horvát" lang="hr" hreflang="hr" data-title="Planckova konstanta" data-language-autonym="Hrvatski" data-language-local-name="horvát" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8A%D5%AC%D5%A1%D5%B6%D5%AF%D5%AB_%D5%B0%D5%A1%D5%BD%D5%BF%D5%A1%D5%BF%D5%B8%D6%82%D5%B6" title="Պլանկի հաստատուն – örmény" lang="hy" hreflang="hy" data-title="Պլանկի հաստատուն" data-language-autonym="Հայերեն" data-language-local-name="örmény" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Konstanta_Planck" title="Konstanta Planck – indonéz" lang="id" hreflang="id" data-title="Konstanta Planck" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonéz" 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/Costante_di_Planck" title="Costante di Planck – olasz" lang="it" hreflang="it" data-title="Costante di Planck" data-language-autonym="Italiano" data-language-local-name="olasz" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%97%E3%83%A9%E3%83%B3%E3%82%AF%E5%AE%9A%E6%95%B0" title="プランク定数 – japán" lang="ja" hreflang="ja" data-title="プランク定数" data-language-autonym="日本語" data-language-local-name="japán" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9E%E1%83%9A%E1%83%90%E1%83%9C%E1%83%99%E1%83%98%E1%83%A1_%E1%83%9B%E1%83%A3%E1%83%93%E1%83%9B%E1%83%98%E1%83%95%E1%83%90" title="პლანკის მუდმივა – grúz" lang="ka" hreflang="ka" data-title="პლანკის მუდმივა" data-language-autonym="ქართული" data-language-local-name="grúz" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9F%D0%BB%D0%B0%D0%BD%D0%BA_%D1%82%D2%B1%D1%80%D0%B0%D2%9B%D1%82%D1%8B%D1%81%D1%8B" title="Планк тұрақтысы – kazah" lang="kk" hreflang="kk" data-title="Планк тұрақтысы" data-language-autonym="Қазақша" data-language-local-name="kazah" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%94%8C%EB%9E%91%ED%81%AC_%EC%83%81%EC%88%98" title="플랑크 상수 – koreai" lang="ko" hreflang="ko" data-title="플랑크 상수" data-language-autonym="한국어" data-language-local-name="koreai" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9F%D0%BB%D0%B0%D0%BD%D0%BA_%D1%82%D1%83%D1%80%D1%83%D0%BA%D1%82%D1%83%D1%83%D0%BB%D1%83%D0%B3%D1%83" title="Планк туруктуулугу – kirgiz" lang="ky" hreflang="ky" data-title="Планк туруктуулугу" data-language-autonym="Кыргызча" data-language-local-name="kirgiz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Constans_Planckiana" title="Constans Planckiana – latin" lang="la" hreflang="la" data-title="Constans Planckiana" data-language-autonym="Latina" data-language-local-name="latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Planko_konstanta" title="Planko konstanta – litván" lang="lt" hreflang="lt" data-title="Planko konstanta" data-language-autonym="Lietuvių" data-language-local-name="litván" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Planka_konstante" title="Planka konstante – lett" lang="lv" hreflang="lv" data-title="Planka konstante" data-language-autonym="Latviešu" data-language-local-name="lett" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9F%D0%BB%D0%B0%D0%BD%D0%BA%D0%BE%D0%B2%D0%B0_%D0%BA%D0%BE%D0%BD%D1%81%D1%82%D0%B0%D0%BD%D1%82%D0%B0" title="Планкова константа – macedón" lang="mk" hreflang="mk" data-title="Планкова константа" data-language-autonym="Македонски" data-language-local-name="macedón" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AA%E0%B5%8D%E0%B4%B2%E0%B4%BE%E0%B4%99%E0%B5%8D%E0%B4%95%E0%B5%8D_%E0%B4%B8%E0%B5%8D%E0%B4%A5%E0%B4%BF%E0%B4%B0%E0%B4%BE%E0%B4%99%E0%B5%8D%E0%B4%95%E0%B4%82" title="പ്ലാങ്ക് സ്ഥിരാങ്കം – malajálam" lang="ml" hreflang="ml" data-title="പ്ലാങ്ക് സ്ഥിരാങ്കം" data-language-autonym="മലയാളം" data-language-local-name="malajálam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%9F%D0%BB%D0%B0%D0%BD%D0%BA%D0%B8%D0%B9%D0%BD_%D1%82%D0%BE%D0%B3%D1%82%D0%BC%D0%BE%D0%BB" title="Планкийн тогтмол – mongol" lang="mn" hreflang="mn" data-title="Планкийн тогтмол" data-language-autonym="Монгол" data-language-local-name="mongol" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B2%E0%A4%BE%E0%A4%82%E0%A4%95%E0%A4%9A%E0%A4%BE_%E0%A4%B8%E0%A5%8D%E0%A4%A5%E0%A4%BF%E0%A4%B0%E0%A4%BE%E0%A4%82%E0%A4%95" title="प्लांकचा स्थिरांक – maráthi" lang="mr" hreflang="mr" data-title="प्लांकचा स्थिरांक" data-language-autonym="मराठी" data-language-local-name="maráthi" 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/Pemalar_Planck" title="Pemalar Planck – maláj" lang="ms" hreflang="ms" data-title="Pemalar Planck" data-language-autonym="Bahasa Melayu" data-language-local-name="maláj" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mzn mw-list-item"><a href="https://mzn.wikipedia.org/wiki/%D9%BE%D9%84%D8%A7%D9%86%DA%A9_%D8%AB%D8%A7%D8%A8%D8%AA" title="پلانک ثابت – mázanderáni" lang="mzn" hreflang="mzn" data-title="پلانک ثابت" data-language-autonym="مازِرونی" data-language-local-name="mázanderáni" class="interlanguage-link-target"><span>مازِرونی</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Constante_van_Planck" title="Constante van Planck – holland" lang="nl" hreflang="nl" data-title="Constante van Planck" data-language-autonym="Nederlands" data-language-local-name="holland" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Planckkonstanten" title="Planckkonstanten – norvég (nynorsk)" lang="nn" hreflang="nn" data-title="Planckkonstanten" data-language-autonym="Norsk nynorsk" data-language-local-name="norvég (nynorsk)" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Plancks_konstant" title="Plancks konstant – norvég (bokmål)" lang="nb" hreflang="nb" data-title="Plancks konstant" data-language-autonym="Norsk bokmål" data-language-local-name="norvég (bokmål)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Constanta_de_Planck" title="Constanta de Planck – okszitán" lang="oc" hreflang="oc" data-title="Constanta de Planck" data-language-autonym="Occitan" data-language-local-name="okszitán" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%AA%E0%A8%B2%E0%A9%88%E0%A8%82%E0%A8%95_%E0%A8%B8%E0%A8%A5%E0%A8%BF%E0%A8%B0%E0%A8%BE%E0%A8%82%E0%A8%95" title="ਪਲੈਂਕ ਸਥਿਰਾਂਕ – pandzsábi" lang="pa" hreflang="pa" data-title="ਪਲੈਂਕ ਸਥਿਰਾਂਕ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="pandzsábi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pcd mw-list-item"><a href="https://pcd.wikipedia.org/wiki/Constante_d%27Planck" title="Constante d&#039;Planck – Picard" lang="pcd" hreflang="pcd" data-title="Constante d&#039;Planck" data-language-autonym="Picard" data-language-local-name="Picard" class="interlanguage-link-target"><span>Picard</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Sta%C5%82a_Plancka" title="Stała Plancka – lengyel" lang="pl" hreflang="pl" data-title="Stała Plancka" data-language-autonym="Polski" data-language-local-name="lengyel" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Costanta_%C3%ABd_Planck" title="Costanta ëd Planck – Piedmontese" lang="pms" hreflang="pms" data-title="Costanta ëd Planck" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D9%BE%D9%84%D8%A7%D9%86%DA%A9_%D9%86%D9%85%D8%A8%D8%B1" title="پلانک نمبر – Western Punjabi" lang="pnb" hreflang="pnb" data-title="پلانک نمبر" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Constante_de_Planck" title="Constante de Planck – portugál" lang="pt" hreflang="pt" data-title="Constante de Planck" data-language-autonym="Português" data-language-local-name="portugál" 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/Constanta_Planck" title="Constanta Planck – román" lang="ro" hreflang="ro" data-title="Constanta Planck" data-language-autonym="Română" data-language-local-name="román" 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%9F%D0%BE%D1%81%D1%82%D0%BE%D1%8F%D0%BD%D0%BD%D0%B0%D1%8F_%D0%9F%D0%BB%D0%B0%D0%BD%D0%BA%D0%B0" title="Постоянная Планка – orosz" lang="ru" hreflang="ru" data-title="Постоянная Планка" data-language-autonym="Русский" data-language-local-name="orosz" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Custanti_di_Planck" title="Custanti di Planck – szicíliai" lang="scn" hreflang="scn" data-title="Custanti di Planck" data-language-autonym="Sicilianu" data-language-local-name="szicíliai" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Planckova_konstanta" title="Planckova konstanta – szerbhorvát" lang="sh" hreflang="sh" data-title="Planckova konstanta" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="szerbhorvát" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Planck_constant" title="Planck constant – Simple English" lang="en-simple" hreflang="en-simple" data-title="Planck constant" 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/Planckova_kon%C5%A1tanta" title="Planckova konštanta – szlovák" lang="sk" hreflang="sk" data-title="Planckova konštanta" data-language-autonym="Slovenčina" data-language-local-name="szlovák" 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/Planckova_konstanta" title="Planckova konstanta – szlovén" lang="sl" hreflang="sl" data-title="Planckova konstanta" data-language-autonym="Slovenščina" data-language-local-name="szlovén" 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%9F%D0%BB%D0%B0%D0%BD%D0%BA%D0%BE%D0%B2%D0%B0_%D0%BA%D0%BE%D0%BD%D1%81%D1%82%D0%B0%D0%BD%D1%82%D0%B0" title="Планкова константа – szerb" lang="sr" hreflang="sr" data-title="Планкова константа" data-language-autonym="Српски / srpski" data-language-local-name="szerb" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Plancks_konstant" title="Plancks konstant – svéd" lang="sv" hreflang="sv" data-title="Plancks konstant" data-language-autonym="Svenska" data-language-local-name="svéd" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%AA%E0%B1%8D%E0%B0%B2%E0%B0%BE%E0%B0%82%E0%B0%95%E0%B1%8D_%E0%B0%B8%E0%B1%8D%E0%B0%A5%E0%B0%BF%E0%B0%B0%E0%B0%BE%E0%B0%82%E0%B0%95%E0%B0%82" title="ప్లాంక్ స్థిరాంకం – telugu" lang="te" hreflang="te" data-title="ప్లాంక్ స్థిరాంకం" data-language-autonym="తెలుగు" data-language-local-name="telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%84%E0%B9%88%E0%B8%B2%E0%B8%84%E0%B8%87%E0%B8%95%E0%B8%B1%E0%B8%A7%E0%B8%82%E0%B8%AD%E0%B8%87%E0%B8%9E%E0%B8%A5%E0%B8%B1%E0%B8%87%E0%B8%84%E0%B9%8C" title="ค่าคงตัวของพลังค์ – thai" lang="th" hreflang="th" data-title="ค่าคงตัวของพลังค์" data-language-autonym="ไทย" data-language-local-name="thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Planck_sabiti" title="Planck sabiti – török" lang="tr" hreflang="tr" data-title="Planck sabiti" data-language-autonym="Türkçe" data-language-local-name="török" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%9F%D0%BB%D0%B0%D0%BD%D0%BA_%D0%B4%D0%B0%D0%B8%D0%BC%D0%B8_%D0%B7%D1%83%D1%80%D0%BB%D1%8B%D0%B3%D1%8B" title="Планк даими зурлыгы – tatár" lang="tt" hreflang="tt" data-title="Планк даими зурлыгы" data-language-autonym="Татарча / tatarça" data-language-local-name="tatár" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D0%BB%D0%B0_%D0%9F%D0%BB%D0%B0%D0%BD%D0%BA%D0%B0" title="Стала Планка – ukrán" lang="uk" hreflang="uk" data-title="Стала Планка" data-language-autonym="Українська" data-language-local-name="ukrán" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%BE%D9%84%D8%A7%D9%86%DA%A9_%DA%A9%D8%A7_%D9%85%D8%B3%D8%AA%D9%82%D9%84%DB%81" title="پلانک کا مستقلہ – urdu" lang="ur" hreflang="ur" data-title="پلانک کا مستقلہ" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Plank_doimiysi" title="Plank doimiysi – üzbég" lang="uz" hreflang="uz" data-title="Plank doimiysi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="üzbég" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/H%E1%BA%B1ng_s%E1%BB%91_Planck" title="Hằng số Planck – vietnámi" lang="vi" hreflang="vi" data-title="Hằng số Planck" data-language-autonym="Tiếng Việt" data-language-local-name="vietnámi" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E5%B8%B8%E6%95%B0" title="普朗克常数 – wu kínai" lang="wuu" hreflang="wuu" data-title="普朗克常数" data-language-autonym="吴语" data-language-local-name="wu kínai" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E5%B8%B8%E6%95%B0" title="普朗克常数 – kínai" lang="zh" hreflang="zh" data-title="普朗克常数" data-language-autonym="中文" data-language-local-name="kínai" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Planck_si%C3%B4ng-s%C3%B2%CD%98" title="Planck siông-sò͘ – min nan kínai" lang="nan" hreflang="nan" data-title="Planck siông-sò͘" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="min nan kínai" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%99%AE%E6%9C%97%E5%85%8B%E5%B8%B8%E6%95%B8" title="普朗克常數 – kantoni" lang="yue" hreflang="yue" data-title="普朗克常數" data-language-autonym="粵語" data-language-local-name="kantoni" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q122894#sitelinks-wikipedia" title="Nyelvközi hivatkozások szerkesztése" class="wbc-editpage">Hivatkozások szerkesztése</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav 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Wikipédiából, a szabad enciklopédiából</div> </div> <div id="contentSub"><div id="mw-content-subtitle"><div id="mw-fr-revision-messages"><div id="mw-fr-revision-details" class="mw-fr-revision-details-dialog" style="display:none;"><div tabindex="0"></div><div class="cdx-dialog cdx-dialog--horizontal-actions"><header class="cdx-dialog__header cdx-dialog__header--default"><div class="cdx-dialog__header__title-group"><h2 class="cdx-dialog__header__title">Változat állapota</h2><p class="cdx-dialog__header__subtitle">Ez a lap egy ellenőrzött változata</p></div><button class="cdx-button cdx-button--action-default cdx-button--weight-quiet&#10;&#9;&#9;&#9;&#9;&#9;&#9;&#9;cdx-button--size-medium cdx-button--icon-only cdx-dialog__header__close-button" aria-label="Close" onclick="document.getElementById(&quot;mw-fr-revision-details&quot;).style.display = &quot;none&quot;;" type="submit"><span class="cdx-icon cdx-icon--medium&#10;&#9;&#9;&#9;&#9;&#9;&#9;&#9;cdx-fr-css-icon--close"></span></button></header><div class="cdx-dialog__body">Ez a <a href="/wiki/Wikip%C3%A9dia:Jel%C3%B6lt_lapv%C3%A1ltozatok" title="Wikipédia:Jelölt lapváltozatok">közzétett változat</a>, <a class="external text" href="https://hu.wikipedia.org/w/index.php?title=Speci%C3%A1lis:Rendszernapl%C3%B3k&amp;type=review&amp;page=Planck-%C3%A1lland%C3%B3">ellenőrizve</a>: <i>2024. június 18.</i><p><table id="mw-fr-revisionratings-box" class="flaggedrevs-color-1" style="margin: auto;" cellpadding="0"><tr><td class="fr-text" style="vertical-align: middle;">Pontosság</td><td class="fr-value40" style="vertical-align: middle;">ellenőrzött</td></tr></table></p></div></div><div tabindex="0"></div></div></div></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="hu" dir="ltr"><p>A <b>Planck-állandó</b> a <a href="/wiki/Kvantummechanika" title="Kvantummechanika">kvantummechanika</a> egyik alapvető állandója. <a href="/wiki/Max_Planck" title="Max Planck">Max Planckról</a>, a kvantummechanikában nagy szerepet játszó fizikusról nevezték el. </p><p>Értéke:<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">&#91;</span>1<span class="cite-bracket">&#93;</span></a></sup> </p> <dl><dd><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 h=6{,}626\,070\,15\cdot 10^{-34}\,{\mbox{J}}\cdot {\mbox{s}}=4{,}135\,667\,667\,696\,{\mbox{eV}}\cdot {\mbox{fs}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> <mo>=</mo> <mn>6,626</mn> <mspace width="thinmathspace" /> <mn>070</mn> <mspace width="thinmathspace" /> <mn>15</mn> <mo>&#x22C5;<!-- ⋅ --></mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>&#x2212;<!-- − --></mo> <mn>34</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>J</mtext> </mstyle> </mrow> <mo>&#x22C5;<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>s</mtext> </mstyle> </mrow> <mo>=</mo> <mn>4,135</mn> <mspace width="thinmathspace" /> <mn>667</mn> <mspace width="thinmathspace" /> <mn>667</mn> <mspace width="thinmathspace" /> <mn>696</mn> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>eV</mtext> </mstyle> </mrow> <mo>&#x22C5;<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>fs</mtext> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h=6{,}626\,070\,15\cdot 10^{-34}\,{\mbox{J}}\cdot {\mbox{s}}=4{,}135\,667\,667\,696\,{\mbox{eV}}\cdot {\mbox{fs}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d506345769c5dd6f68774ec88cbfe893947296d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:54.145ex; height:3.009ex;" alt="{\displaystyle h=6{,}626\,070\,15\cdot 10^{-34}\,{\mbox{J}}\cdot {\mbox{s}}=4{,}135\,667\,667\,696\,{\mbox{eV}}\cdot {\mbox{fs}}}"></span>.</dd></dl> <p>A Planck-állandó <a href="/wiki/M%C3%A9rt%C3%A9kegys%C3%A9g" title="Mértékegység">mértékegysége</a> <a href="/wiki/Energia" title="Energia">energia</a> szorozva <a href="/wiki/Id%C5%91" title="Idő">idővel</a>, amely a <a href="/wiki/Hat%C3%A1selv" title="Hatáselv">hatás</a> egysége. Az egység <a href="/wiki/Lend%C3%BClet" title="Lendület">lendület</a> szorozva <a href="/wiki/T%C3%A1vols%C3%A1g" title="Távolság">távolság</a> formában is felírható (<a href="/wiki/Newton_(m%C3%A9rt%C3%A9kegys%C3%A9g)" title="Newton (mértékegység)">N</a>·<a href="/wiki/M%C3%A9ter" title="Méter">m</a>·<a href="/wiki/M%C3%A1sodperc" title="Másodperc">s</a>), amely a <a href="/wiki/Perd%C3%BClet" title="Perdület">perdület</a> (régebbi nevén impulzusmomentum) egysége. </p><p>Szemléletesen a Planck-állandó az 1 <a href="/wiki/Hz" class="mw-redirect" title="Hz">Hz</a>-es <a href="/wiki/Foton" title="Foton">foton</a> energiáját adja meg. E tulajdonsága miatt 2019. május 20-a óta ez alapján definiálják a kilogramm mértékegységet.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">&#91;</span>2<span class="cite-bracket">&#93;</span></a></sup> </p><p>Sok esetben kényelmesebben használható a <b>redukált Planck-állandó</b>, vagy másik nevén <b>Dirac-állandó</b>: </p> <dl><dd><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 \hbar ={\frac {h}{2\pi }}=1{,}054\,571\,817\cdots \,\cdot 10^{-34}\,{\mbox{J}}\cdot {\mbox{s}}=0{,}658\,211\,9569\cdots \,{\mbox{eV}}\cdot {\mbox{fs}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi class="MJX-variant">&#x210F;<!-- ℏ --></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>h</mi> <mrow> <mn>2</mn> <mi>&#x03C0;<!-- π --></mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>1,054</mn> <mspace width="thinmathspace" /> <mn>571</mn> <mspace width="thinmathspace" /> <mn>817</mn> <mo>&#x22EF;<!-- ⋯ --></mo> <mspace width="thinmathspace" /> <mo>&#x22C5;<!-- ⋅ --></mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>&#x2212;<!-- − --></mo> <mn>34</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>J</mtext> </mstyle> </mrow> <mo>&#x22C5;<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>s</mtext> </mstyle> </mrow> <mo>=</mo> <mn>0,658</mn> <mspace width="thinmathspace" /> <mn>211</mn> <mspace width="thinmathspace" /> <mn>9569</mn> <mo>&#x22EF;<!-- ⋯ --></mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>eV</mtext> </mstyle> </mrow> <mo>&#x22C5;<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>fs</mtext> </mstyle> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \hbar ={\frac {h}{2\pi }}=1{,}054\,571\,817\cdots \,\cdot 10^{-34}\,{\mbox{J}}\cdot {\mbox{s}}=0{,}658\,211\,9569\cdots \,{\mbox{eV}}\cdot {\mbox{fs}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eec33e6a7bd3d79b76a3f12bdbbfcd56902f312a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:66.634ex; height:5.343ex;" alt="{\displaystyle \hbar ={\frac {h}{2\pi }}=1{,}054\,571\,817\cdots \,\cdot 10^{-34}\,{\mbox{J}}\cdot {\mbox{s}}=0{,}658\,211\,9569\cdots \,{\mbox{eV}}\cdot {\mbox{fs}},}"></span></dd></dl> <p>ahol <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 \pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x03C0;<!-- π --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be4ba0bb8df3af72e90a0535fabcc17431e540a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.332ex; height:1.676ex;" alt="{\displaystyle \pi }"></span> a matematika <a href="/wiki/P%C3%AD_(sz%C3%A1m)" class="mw-redirect" title="Pí (szám)">pi</a> állandója. Kiejtése: h-vonás. </p><p>Eredetileg a <a href="/wiki/Feketetest-sug%C3%A1rz%C3%A1s" title="Feketetest-sugárzás">feketetest-sugárzás</a> során vezette be Planck. Feltételeznie kellett, hogy energiaátadás csak kvantumosan (meghatározott adagokban) lehetséges. </p><p>A <a href="/wiki/Fotoeffektus" class="mw-redirect" title="Fotoeffektus">fotoeffektus</a> során is megjelenik. Adott ν frekvenciájú fény adott E energiájú <a href="/wiki/Foton" title="Foton">fotonokból</a> áll: </p> <dl><dd><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 E=h\nu \,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>h</mi> <mi>&#x03BD;<!-- ν --></mi> <mspace width="thinmathspace" /> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=h\nu \,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/624d0c7a0c6c897c79e210a7bca06eff7a545ff0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.479ex; height:2.509ex;" alt="{\displaystyle E=h\nu \,,}"></span></dd></dl> <p>Gyakran kellemesebb ezt az <i>ω=2πν</i> <a href="/wiki/K%C3%B6rfrekvencia" title="Körfrekvencia">körfrekvenciával</a> felírni, melyből </p> <dl><dd><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 E=\hbar \omega \,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi class="MJX-variant">&#x210F;<!-- ℏ --></mi> <mi>&#x03C9;<!-- ω --></mi> <mspace width="thinmathspace" /> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=\hbar \omega \,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6842cc42e4bd82bf1a4d32cebd048e4b86eaff72" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.66ex; height:2.509ex;" alt="{\displaystyle E=\hbar \omega \,,}"></span></dd></dl> <p>Eddig az energia kvantálásáról volt szó. Hasonló elvégezhető más mennyiségekkel is, például a <a href="/wiki/Perd%C3%BClet" title="Perdület">perdülettel</a> is. </p><p>A Planck-állandó megjelenik <a href="/wiki/Werner_Heisenberg" title="Werner Heisenberg">Heisenberg</a> <a href="/wiki/Hat%C3%A1rozatlans%C3%A1gi_rel%C3%A1ci%C3%B3" title="Határozatlansági reláció">határozatlansági relációjában</a> is. A helymérésben fellépő <i>Δx</i> bizonytalanság és az azonos irányban mért <a href="/wiki/Lend%C3%BClet" title="Lendület">lendület</a> <i>Δp</i> bizonytalanságára igaz: </p> <dl><dd><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 \Delta x\Delta p={\begin{matrix}{\frac {1}{2}}\end{matrix}}\hbar }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">&#x0394;<!-- Δ --></mi> <mi>x</mi> <mi mathvariant="normal">&#x0394;<!-- Δ --></mi> <mi>p</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> <mi class="MJX-variant">&#x210F;<!-- ℏ --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta x\Delta p={\begin{matrix}{\frac {1}{2}}\end{matrix}}\hbar }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c75eaefc48bbe53150179edb7ce2356ef8b7e0ac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.968ex; margin-bottom: -0.203ex; width:13.185ex; height:3.509ex;" alt="{\displaystyle \Delta x\Delta p={\begin{matrix}{\frac {1}{2}}\end{matrix}}\hbar }"></span></dd></dl> <p>Hasonlóan igaz több mérhető mennyiségpárra is. </p> <div class="mw-heading mw-heading2"><h2 id="Jegyzetek">Jegyzetek</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Planck-%C3%A1lland%C3%B3&amp;action=edit&amp;section=1" title="Szakasz szerkesztése: Jegyzetek"><span>szerkesztés</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="ref-1col"><div style="-moz-column-count:2; -webkit-column-count:2; column-count:2; -webkit-column-gap: 3em; -moz-column-gap: 3em; column-gap: 3em;"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><span class="citation"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20181119214326/https://www.bipm.org/utils/common/pdf/CGPM-2018/26th-CGPM-Resolutions.pdf"><i>Resolutions of the 26th CGPM</i></a>&#32;(brit angol nyelven).&#32;<i>BIPM </i>, 2018. november 16.&#32;[2018. november 19-i dátummal az <a rel="nofollow" class="external text" href="https://www.bipm.org/utils/common/pdf/CGPM-2018/26th-CGPM-Resolutions.pdf">eredetiből</a> archiválva].&#32;(Hozzáférés: 2018. november 20.)</span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><span class="citation"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20181116215753/https://physicsworld.com/a/kilogram-finally-redefined-as-worlds-metrologists-agree-to-new-formulation-for-si-units/"><i>Kilogram finally redefined as world's metrologists agree to new formulation for SI units – Physics World</i></a>.&#32;<i>web.archive.org</i>, 2018. november 16.&#32;[2018. november 16-i dátummal az <a rel="nofollow" class="external text" href="https://physicsworld.com/a/kilogram-finally-redefined-as-worlds-metrologists-agree-to-new-formulation-for-si-units/">eredetiből</a> archiválva].&#32;(Hozzáférés: 2021. február 25.)</span></span> </li> </ol></div></div><div class="ref-1col"><div style="-moz-column-count:2; -webkit-column-count:2; column-count:2; -webkit-column-gap: 3em; -moz-column-gap: 3em; column-gap: 3em;"></div></div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r26593303">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist 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