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Spin | Nuclear Structure, Electron Configurations & Magnetic Moments | Britannica

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class="drawer d-flex flex-column open"> <div class="left-rail-section-content"> <div class="topic-left-rail-header text-truncate bg-gray-50 position-relative text-right d-flex align-items-center"> <div class="tlr-title px-20 py-15 text-left"> <em class="material-icons text-gray-400 d-lg-none" data-icon="toc"></em> <a class="font-serif font-weight-bold text-black link-blue" href="https://www.britannica.com/science/spin-atomic-physics">spin</a> </div> <button aria-label="Close" class="js-sections-close-button btn-link btn-sm btn d-lg-none position-absolute top-0 p-10 right-0" > <em class="material-icons font-26" data-icon="close"></em> </button> </div> <div class="section-content pl-10 pr-20 pl-sm-50 pr-sm-60 pl-lg-5 pr-lg-10 pt-10 pt-lg-0 bg-gray-50 clear-catfish-ad"> <div class="toc mb-20"> <div class="font-serif font-14 font-weight-bold mx-15 mb-15 mt-20"> Table of Contents </div> <span class="toc-extra-link selected link-gray-900 mt-15"> Introduction </span> <a class="toc-extra-link link-gray-900" href="https://www.britannica.com/science/spin-atomic-physics/additional-info">References &amp; Edit History</a> <a class="toc-extra-link link-gray-900" href="/facts/spin-atomic-physics">Quick Facts & Related Topics</a> </div> <div class="mb-30 tlr-related-questions"> <div class="text-gray-900 p-5 pb-0 font-serif font-14 font-weight-bold mx-10 mb-15"> Related Questions </div> <ul> <li class="link-gray-900 mb-15"><a class="" href="/question/How-is-the-atomic-number-of-an-atom-defined">How is the atomic number of an atom defined?</a> </li> </ul> </div> <div class="mb-30 tlr-discover"> <div class="text-gray-900 p-5 font-serif font-14 font-weight-bold mx-10 mb-10"> Discover </div> <div class="imagelink-with-image-on-the-side card card-horizontal tlr-img-with-side-link ml-15 link-gray-900 mb-10" > <div class="position-relative card-media" style="flex: 0;"> <a class="ilf-image position-relative" href="/list/10-of-the-worlds-most-dangerous-fish"> <img loading="lazy" src="https://cdn.britannica.com/96/173996-131-3DDAD81A/Fish-Lionfish-Lion-fish-Turkey-fish-Red-lionfish.jpg?w=200&h=200&c=crop" alt="Fish. Lionfish. Lion-fish. Turkey fish. Fire-fish. Red lionfish. Pterois volitans. Venomous fin spines. Coral reefs. Underwater. Ocean. Red lionfish swims by seaweed." width="200" height="200" /> </a> </div> <div class="card-body ilf-content"> <a class="font-weight-semi-bold d-block mb-5 font-16 ilf-title" href="/list/10-of-the-worlds-most-dangerous-fish" >10 of the World’s Most Dangerous Fish</a> </div> </div> <div class="imagelink-with-image-on-the-side card card-horizontal tlr-img-with-side-link ml-15 link-gray-900 mb-10" > <div class="position-relative card-media" style="flex: 0;"> <a class="ilf-image position-relative" href="/story/nikola-teslas-weird-obsession-with-pigeons"> <img loading="lazy" src="https://cdn.britannica.com/13/173513-131-C6E1BD52/mourning-dove-North-America.jpg?w=200&h=200&c=crop" alt="bird. mourning dove. pigeon and dove. 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Homepage 2010, arts and entertainment, history and society" width="200" height="200" /> </a> </div> <div class="card-body ilf-content"> <a class="font-weight-semi-bold d-block mb-5 font-16 ilf-title" href="/list/the-10-greatest-basketball-players-of-all-time" >The 10 Greatest Basketball Players of All Time</a> </div> </div> <div class="imagelink-with-image-on-the-side card card-horizontal tlr-img-with-side-link ml-15 link-gray-900 mb-10" > <div class="position-relative card-media" style="flex: 0;"> <a class="ilf-image position-relative" href="/list/6-of-the-worlds-deadliest-natural-disasters"> <img loading="lazy" src="https://cdn.britannica.com/16/234616-131-50959175/Damage-Balakot-Pakistan-due-to-earthquake-October-8-2005-Kashmir.jpg?w=200&h=200&c=crop" alt="In this aerial photo, structures are damaged and destroyed October 15, 2005 in Balakot, Pakistan. It is estimated that 90% of the city of Balakot was leveled by the earthquake. The death toll in the 7.6 magnitude earthquake that struck northern Pakistan on October 8, 2005 is believed to be 38,000 with at least 1,300 more dead in Indian Kashmir. SEE CONTENT NOTES." width="200" height="200" /> </a> </div> <div class="card-body ilf-content"> <a class="font-weight-semi-bold d-block mb-5 font-16 ilf-title" href="/list/6-of-the-worlds-deadliest-natural-disasters" >6 of the World’s Deadliest Natural Disasters</a> </div> </div> <div class="imagelink-with-image-on-the-side card card-horizontal tlr-img-with-side-link ml-15 link-gray-900 mb-10" > <div class="position-relative card-media" style="flex: 0;"> <a class="ilf-image position-relative" href="/list/6-deadliest-earthquakes"> <img loading="lazy" src="https://cdn.britannica.com/41/166941-131-E27FD3A6/Yingxiu-school-China-Sichuan-earthquake-May-2008.jpg?w=200&h=200&c=crop" alt="earthquake. Heavily damaged school in the town of Yingxiu after a major earthquake struck China's Sichuan Province on May 12, 2008." width="200" height="200" /> </a> </div> <div class="card-body ilf-content"> <a class="font-weight-semi-bold d-block mb-5 font-16 ilf-title" href="/list/6-deadliest-earthquakes" >The 6 Deadliest Earthquakes Since 1950</a> </div> </div> <div class="imagelink-with-image-on-the-side card card-horizontal tlr-img-with-side-link ml-15 link-gray-900 mb-10" > <div class="position-relative card-media" style="flex: 0;"> <a class="ilf-image position-relative" href="/story/the-lost-colony-of-roanoke"> <img loading="lazy" src="https://cdn.britannica.com/39/191439-131-59FE0A72/John-White-word-tree-CROATOAN-Roanoke-Island-1590.jpg?w=200&h=200&c=crop" alt="The Lost Colony of Roanoke, North Carolina, where 115 people mysteriously disappeared c. 1590. John White discovers the word Croatoan carved onto a tree upon his return to the deserted Roanoke Colony in 1590" width="200" height="200" /> </a> </div> <div class="card-body ilf-content"> <a class="font-weight-semi-bold d-block mb-5 font-16 ilf-title" href="/story/the-lost-colony-of-roanoke" >The Lost Colony of Roanoke</a> </div> </div> <div class="imagelink-with-image-on-the-side card card-horizontal tlr-img-with-side-link ml-15 link-gray-900 mb-10" > <div class="position-relative card-media" style="flex: 0;"> <a class="ilf-image position-relative" href="/story/which-waters-do-you-pass-through-when-you-sail-the-seven-seas"> <img loading="lazy" src="https://cdn.britannica.com/97/196697-131-0155C802/Sailboat-landscape.jpg?w=200&h=200&c=crop" alt="Sailboat against a beautiful landscape" width="200" height="200" /> </a> </div> <div class="card-body ilf-content"> <a class="font-weight-semi-bold d-block mb-5 font-16 ilf-title" href="/story/which-waters-do-you-pass-through-when-you-sail-the-seven-seas" >Which Waters Do You Pass Through When You “Sail the Seven Seas”?</a> </div> </div> </div> </div> </div> </div> <button class="drawerToggle btn position-sticky border btn-xs btn-white btn-circle rounded-sm d-none d-lg-flex " type="button" aria-label="Toggle Drawer"> <em class="material-icons font-18 text-blue" data-icon="keyboard_arrow_left"></em> </button> </div> </div> <div class="col"> <div class="h-100 ml-0 pr-lg-0 "> <div class="h-100 grid gx-0 gx-lg-20"> <div class="h-100 col-sm"> <div class="h-100 infinite-pagination-container d-flex flex-column position-relative"> <div class="position-absolute top-0 h-100 w-100"> <div class="toc-sticky-header d-none d-lg-none bg-gray-50 px-10 px-sm-30 position-sticky w-100 "> <div class="toc-sticky-header-inner-container align-items-center d-flex mx-auto h-100 w-100"> <button class="d-flex d-lg-none btn btn-sm btn-white text-blue border-2 border-gray-100 gtm-mobile-toc-header-button js-sections-button d-lg-none p-10"> <em class="material-icons my-n5 md-icon" data-icon="toc"></em> Contents </button> <div class="header-ai-simplify-button-placeholder"></div> <div class="header-ai-ask-button-placeholder"></div> </div> </div> </div> <div class="grey-box w-100 grey-box-top grey-box-bottom"> <div class="grey-box-content mx-auto w-100"> <script type="application/ld+json"> { "@context" : "https://schema.org", "@type" : "BreadcrumbList", "itemListElement" : [ { "@type" : "ListItem", "position" : 1, "item" : { "@id" : "https://www.britannica.com/browse/Science", "name": "Science" } } , { "@type" : "ListItem", "position" : 2, "item" : { "@id" : "https://www.britannica.com/browse/Physics", "name": "Physics" } } , { "@type" : "ListItem", "position" : 3, "item" : { "@id" : "https://www.britannica.com/browse/Matter-Energy", "name": "Matter &amp; 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They write new content and verify and edit content received from contributors.</div> </a> <div data-popper-arrow></div> </div> <span class="btn btn-link editor-link p-0 qa-byline-link gtm-byline font-12 byline-contributor text-decoration-underline"> The Editors of Encyclopaedia Britannica</span></div> <div class="last-updated font-12 font-serif"> <span class="text-gray-700"> Last Updated: <time datetime="2025-01-26T00:00:00CST" >Jan 26, 2025</time> •</span> <a class="byline-edit-history" href="https://www.britannica.com/science/spin-atomic-physics/additional-info#history" rel="nofollow">Article History</a> </div></div> </div> <button class="d-flex d-lg-none btn btn-outline-blue border rounded-sm shadow-sm mobile-toc-button gtm-mobile-toc-inline-button d-none d-sm-block js-sections-inline-button module-spacing btn d-lg-none"> <em class="material-icons mr-5 ml-n10 my-n5 md-icon" data-icon="toc"></em> Table of Contents </button> <div class="d-flex d-sm-none flex-row"> <button class="d-flex d-lg-none btn btn-outline-blue border rounded-sm shadow-sm mobile-toc-button gtm-mobile-toc-inline-button js-sections-inline-button module-spacing"> <em class="material-icons mr-5 ml-n10 my-n5 md-icon" data-icon="toc"></em> Table of Contents </button> <button class="ai-ask-button btn btn-sm border-2 btn-outline-red-400 border-red-400 module-spacing js-inline-ai-ask-button p-10 ml-5"> Ask the Chatbot </button> </div> <div class="js-qf-module qf-module px-40 px-sm-20 py-15 mx-auto module-spacing font-14 bg-gray-50 rounded"> <div class="facts-list mt-10"> <div class=""> <div class="js-fact mb-10 line-clamp clamp-3"> <dl> <dt>Key People: </dt> <dd><a href="/biography/Maurice-Goldhaber" topicid="237857">Maurice Goldhaber</a></dd> </dl> <button class="js-more-btn d-none btn btn-unstyled font-12 bg-gray-50" aria-label="Toggle more/less fact data"> <em class="js-content link-blue">(Show&nbsp;more)</em> </button> </div> </div> <div class=""> <div class="js-fact mb-10 line-clamp clamp-3"> <dl> <dt>Related Topics: </dt> <dd><a href="/science/total-spin-angular-momentum" topicid="600424">total spin angular momentum</a></dd> <dd><a href="/science/quantization-axis" topicid="486154">quantization axis</a></dd> <dd><a href="/science/electron-spin" topicid="183658">electron spin</a></dd> <dd><a href="/science/Dirac-h" topicid="164813">Dirac h</a></dd> <dd><a href="/science/spin-quantum-number" topicid="560006">spin quantum number</a></dd> </dl> <button class="js-more-btn d-none btn btn-unstyled font-12 bg-gray-50" aria-label="Toggle more/less fact data"> <em class="js-content link-blue">(Show&nbsp;more)</em> </button> </div> </div> <div class=""> <div class="js-fact mb-10 line-clamp clamp-3"> <dl> <dt>On the Web: </dt> <dd><a href="https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=5fe904ba14488aa3894e0f4fcb92fdbf658ac4e7" target="_blank">CiteSeerX - https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=5fe904ba14488aa3894e0f4fcb92fdbf658ac4e7 (PDF)</a> (Jan. 26, 2025)</dd> </dl> <button class="js-more-btn d-none btn btn-unstyled font-12 bg-gray-50" aria-label="Toggle more/less fact data"> <em class="js-content link-blue">(Show&nbsp;more)</em> </button> </div> <div class="text-center"> <a class="btn btn-sm btn-link p-0" href="/facts/spin-atomic-physics"> See all related content </a> </div> </div> </div> </div><!--[BEFORE-ARTICLE]--><span class="marker before-article"></span><section data-level="1" id="ref1"><!--[PREMOD1]--><span class="marker PREMOD1 mod-inline"></span><p class="topic-paragraph"><strong><span id="ref122400"></span>spin</strong>, in <a href="https://www.britannica.com/science/physics-science" class="md-crosslink autoxref " data-show-preview="true">physics</a>, the amount of <a href="https://www.britannica.com/science/angular-momentum" class="md-crosslink autoxref " data-show-preview="true">angular momentum</a> associated with a <span id="ref894610"></span><a href="https://www.britannica.com/science/subatomic-particle" class="md-crosslink " data-show-preview="true">subatomic particle</a> or <span id="ref894611"></span><a href="https://www.britannica.com/science/atomic-nucleus" class="md-crosslink ">nucleus</a> and measured in multiples of a unit called the <span id="ref122401"></span>Dirac <em>h,</em> or <em>h</em>-bar (ℏ), equal to the <a href="https://www.britannica.com/science/Plancks-constant" class="md-crosslink autoxref " data-show-preview="true">Planck constant</a> divided by 2π. For electrons, neutrons, and protons, the multiple is 0.5; pions have zero spin. The total angular momentum of nuclei more complex than the proton is the vector sum of the orbital angular momenta and <a class="md-dictionary-link md-dictionary-tt-off mw" data-term="intrinsic" href="https://www.merriam-webster.com/dictionary/intrinsic" data-type="MW">intrinsic</a> spins of the <a class="md-dictionary-link md-dictionary-tt-off mw" data-term="constituent" href="https://www.merriam-webster.com/dictionary/constituent" data-type="MW">constituent</a> nucleons. For nuclei of even <a href="https://www.britannica.com/science/mass-number" class="md-crosslink autoxref " data-show-preview="true">mass number</a>, the multiple is an integer; for those of odd mass number, the multiple is a half-integer. All nuclei with even numbers of neutrons and protons have spin zero in their ground states.</p><!--[MOD1]--><span class="marker MOD1 mod-inline"></span></section> <span class="md-signature font-12">This article was most recently revised and updated by <a href="/editor/William-L-Hosch/6481">William L. 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