Atomic Theory III | Chemistry

<!DOCTYPE html> <html lang="en" dir="ltr"> <head>  <meta http-equiv="X-UA-Compatible" content="ie=edge"> <meta charset="utf-8"> <base href="https://www.visionlearning.com"> <title>Atomic Theory III | Chemistry | Visionlearning</title> <link rel="canonical" href="https://www.visionlearning.com/en/library/chemistry/1/atomic-theory-iii/223"> <meta name="description" content="The 20th century was a period rich in advancing our knowledge of quantum mechanics, shaping modern physics. Tracing developments during this time, this module covers ideas and refinements that built on Bohr’s groundbreaking work in quantum theory. Contributions by many scientists highlight how theoretical insights and experimental results revolutionized our understanding of the atom. Concepts include the Schrödinger equation, Born’s three-dimensional probability maps, the Heisenberg uncertainty principle, and electron spin."> <meta name="keywords" content="atomic theory, physics, quantum mechanics, momentum, uncertainty"> <meta name="viewport" content="width=device-width, initial-scale=1.0, shrink-to-fit=no"> <meta name="msvalidate.01" content="D8E20F39AD48052260032E56DE409970"> <script type="application/ld+json"> { "@context": "http://schema.org/", "@type": "Article", "mainEntityOfPage": { "@type": "WebPage", "@id": "https://visionlearning.com/en/library/chemistry/1/atomic-theory-iii/223" }, "name": "Atomic Theory III", "headline": "Atomic Theory III: Wave-particle duality and the electron", "author": [ { "@type": "Person", "name": "Adrian Dingle, B.Sc." } , { "@type": "Person", "name": "Anthony Carpi, Ph.D." }], "datePublished": "2015-09-14 01:29:09", "dateModified": "2017-02-12T08:30:00+05:00", "image": { "@type": "ImageObject", "url": "/img/library/moduleImages/featured_image_223-23061209064501.jpeg", "width": 696, "height": 464 }, "publisher": { "@type": "Organization", "name": "Visionlearning, Inc.", "logo": { "@type": "ImageObject", "url": "http://visionlearning.com/images/logo.png", "width": 278, "height": 60 } }, "description": "The 20th century was a period rich in advancing our knowledge of quantum mechanics, shaping modern physics. Tracing developments during this time, this module covers ideas and refinements that built on Bohr’s groundbreaking work in quantum theory. Contributions by many scientists highlight how theoretical insights and experimental results revolutionized our understanding of the atom. Concepts include the Schrödinger equation, Born’s three-dimensional probability maps, the Heisenberg uncertainty principle, and electron spin.", "keywords": "atomic theory, physics, quantum mechanics, momentum, uncertainty", "inLanguage": { "@type": "Language", "name": "English", "alternateName": "en" }, "copyrightHolder": { "@type": "Organization", "name": "Visionlearning, Inc." }, "copyrightYear": "2015"} </script> <meta property="og:url" content="https://visionlearning.com/en/library/chemistry/1/atomic-theory-iii/223"> <meta property="og:title" content="Atomic Theory III | Chemistry | Visionlearning" /> <meta property="og:type" content="website"> <meta property="og:site_name" content="Visionlearning"> <meta property="og:description" content="The 20th century was a period rich in advancing our knowledge of quantum mechanics, shaping modern physics. Tracing developments during this time, this module covers ideas and refinements that built on Bohr’s groundbreaking work in quantum theory. Contributions by many scientists highlight how theoretical insights and experimental results revolutionized our understanding of the atom. 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class="accordion__button" id="acc-button-environmental-science" data-accordion="button" aria-controls="acc-panel-environmental-science" aria-expanded="false"> <span class="accordion__button__label"> Environmental Science </span> </button> <div class="accordion__panel" id="acc-panel-environmental-science" data-accordion="panel" aria-labelledby="acc-button-environmental-science" role="region"> <div class="accordion accordion--secondary"> <button class="accordion__button" id="acc-button-ecology" data-accordion="button" aria-controls="acc-panel-ecology" aria-expanded="false"> <span class="accordion__button__label"> Ecology </span> </button> <div class="accordion__panel" id="acc-panel-ecology" data-accordion="panel" aria-labelledby="acc-button-ecology" role="region"> <ul class="nav text-color-link"> <li><a href="/en/library/environmental-science/61/biodiversity-i/276">Biodiversity I</a></li> <li><a href="/en/library/environmental-science/61/biodiversity-ii/281">Biodiversity II</a></li> <li><a href="/en/library/environmental-science/61/ecosystem-services/279">Ecosystem Services</a></li> <li><a href="/en/library/environmental-science/61/population-biology/287">Population Biology</a></li> </ul> </div> <button class="accordion__button" id="acc-button-earth-cycles" data-accordion="button" aria-controls="acc-panel-earth-cycles" aria-expanded="false"> <span class="accordion__button__label"> Earth Cycles </span> </button> <div class="accordion__panel" id="acc-panel-earth-cycles" data-accordion="panel" aria-labelledby="acc-button-earth-cycles" role="region"> <ul class="nav text-color-link"> <li><a href="/en/library/environmental-science/61/the-nitrogen-cycle/98">The Nitrogen Cycle</a></li> <li><a href="/en/library/environmental-science/61/the-carbon-cycle/95">The Carbon Cycle</a></li> <li><a href="/en/library/environmental-science/61/the-phosphorus-cycle/197">The Phosphorus Cycle</a></li> </ul> </div> <button class="accordion__button" id="acc-button-scientific-research" data-accordion="button" aria-controls="acc-panel-scientific-research" aria-expanded="false"> <span class="accordion__button__label"> Scientific Research </span> </button> <div class="accordion__panel" id="acc-panel-scientific-research" data-accordion="panel" aria-labelledby="acc-button-scientific-research" role="region"> <ul class="nav text-color-link"> <li><a href="/en/library/environmental-science/61/collaborative-research-in-the-arctic-towards-understanding-climate-change/183">Collaborative Research in the Arctic Towards Understanding Climate Change</a></li> <li><a href="/en/library/environmental-science/61/atmospheric-chemistry-research-that-changed-global-policy/211">Atmospheric Chemistry Research that Changed Global Policy</a></li> </ul> </div> </div> </div> <button class="accordion__button" id="acc-button-general-science" data-accordion="button" aria-controls="acc-panel-general-science" aria-expanded="false"> <span class="accordion__button__label"> General Science </span> </button> <div class="accordion__panel" id="acc-panel-general-science" data-accordion="panel" aria-labelledby="acc-button-general-science" role="region"> <div class="accordion accordion--secondary"> <button class="accordion__button" id="acc-button-methods" data-accordion="button" aria-controls="acc-panel-methods" aria-expanded="false"> <span class="accordion__button__label"> Methods </span> </button> <div class="accordion__panel" id="acc-panel-methods" data-accordion="panel" aria-labelledby="acc-button-methods" role="region"> <ul class="nav text-color-link"> <li><a href="/en/library/general-science/3/the-scientific-method/45">The Scientific Method</a></li> </ul> </div> <button class="accordion__button" id="acc-button-measurement" data-accordion="button" aria-controls="acc-panel-measurement" aria-expanded="false"> <span class="accordion__button__label"> Measurement </span> </button> <div class="accordion__panel" id="acc-panel-measurement" data-accordion="panel" aria-labelledby="acc-button-measurement" role="region"> <ul class="nav text-color-link"> <li><a href="/en/library/general-science/3/the-metric-system/47">The Metric System</a></li> </ul> </div> <button class="accordion__button" id="acc-button-physical-properties" data-accordion="button" aria-controls="acc-panel-physical-properties" aria-expanded="false"> <span class="accordion__button__label"> Physical Properties </span> </button> <div class="accordion__panel" id="acc-panel-physical-properties" data-accordion="panel" aria-labelledby="acc-button-physical-properties" role="region"> <ul class="nav text-color-link"> <li><a href="/en/library/general-science/3/temperature/48">Temperature</a></li> <li><a href="/en/library/general-science/3/density-and-buoyancy/37">Density and Buoyancy</a></li> </ul> </div> </div> </div> <button class="accordion__button" id="acc-button-math-in-science" data-accordion="button" aria-controls="acc-panel-math-in-science" aria-expanded="false"> <span class="accordion__button__label"> Math in Science </span> </button> <div class="accordion__panel" id="acc-panel-math-in-science" data-accordion="panel" aria-labelledby="acc-button-math-in-science" role="region"> <div class="accordion accordion--secondary"> <button class="accordion__button" id="acc-button-equations" data-accordion="button" aria-controls="acc-panel-equations" aria-expanded="false"> <span class="accordion__button__label"> Equations </span> </button> <div class="accordion__panel" id="acc-panel-equations" data-accordion="panel" aria-labelledby="acc-button-equations" role="region"> <ul class="nav text-color-link"> <li><a href="/en/library/math-in-science/62/unit-conversion/144">Unit Conversion</a></li> <li><a href="/en/library/math-in-science/62/linear-equations/194">Linear Equations</a></li> <li><a href="/en/library/math-in-science/62/exponential-equations-i/206">Exponential Equations I</a></li> <li><a href="/en/library/math-in-science/62/exponential-equations-ii/210">Exponential Equations II</a></li> <li><a href="/en/library/math-in-science/62/scientific-notation/250">Scientific Notation</a></li> <li><a href="/en/library/math-in-science/62/measurement/257">Measurement</a></li> </ul> </div> <button class="accordion__button" id="acc-button-statistics" data-accordion="button" aria-controls="acc-panel-statistics" aria-expanded="false"> <span class="accordion__button__label"> Statistics </span> </button> <div class="accordion__panel" id="acc-panel-statistics" data-accordion="panel" aria-labelledby="acc-button-statistics" role="region"> <ul class="nav text-color-link"> <li><a href="/en/library/math-in-science/62/introduction-to-descriptive-statistics/218">Introduction to Descriptive Statistics</a></li> <li><a href="/en/library/math-in-science/62/introduction-to-inferential-statistics/224">Introduction to Inferential Statistics</a></li> <li><a href="/en/library/math-in-science/62/statistical-techniques/239">Statistical Techniques</a></li> </ul> </div> <button class="accordion__button" id="acc-button-trigonometric-functions" data-accordion="button" aria-controls="acc-panel-trigonometric-functions" aria-expanded="false"> <span class="accordion__button__label"> Trigonometric Functions </span> </button> <div class="accordion__panel" id="acc-panel-trigonometric-functions" data-accordion="panel" aria-labelledby="acc-button-trigonometric-functions" role="region"> <ul class="nav text-color-link"> <li><a href="/en/library/math-in-science/62/wave-mathematics/131">Wave Mathematics</a></li> </ul> </div> </div> </div> <button class="accordion__button" id="acc-button-physics" data-accordion="button" aria-controls="acc-panel-physics" aria-expanded="false"> <span class="accordion__button__label"> Physics </span> </button> <div class="accordion__panel" id="acc-panel-physics" data-accordion="panel" aria-labelledby="acc-button-physics" role="region"> <div class="accordion accordion--secondary"> <button class="accordion__button" id="acc-button-light-and-optics" data-accordion="button" aria-controls="acc-panel-light-and-optics" aria-expanded="false"> <span class="accordion__button__label"> Light and Optics </span> </button> <div class="accordion__panel" id="acc-panel-light-and-optics" data-accordion="panel" aria-labelledby="acc-button-light-and-optics" role="region"> <ul class="nav text-color-link"> <li><a href="/en/library/physics/24/the-nature-of-light/132">The Nature of Light</a></li> <li><a href="/en/library/physics/24/electromagnetism-and-light/138">Electromagnetism and Light</a></li> </ul> </div> <button class="accordion__button" id="acc-button-mechanics" data-accordion="button" aria-controls="acc-panel-mechanics" aria-expanded="false"> <span class="accordion__button__label"> Mechanics </span> </button> <div class="accordion__panel" id="acc-panel-mechanics" data-accordion="panel" aria-labelledby="acc-button-mechanics" role="region"> <ul class="nav text-color-link"> <li><a href="/en/library/physics/24/defining-energy/199">Defining Energy</a></li> <li><a href="/en/library/physics/24/waves-and-wave-motion/102">Waves and Wave Motion</a></li> <li><a href="/en/library/physics/24/gravity/118">Gravity</a></li> <li><a href="/en/library/physics/24/thermodynamics-i/200">Thermodynamics I</a></li> </ul> </div> </div> </div> <button class="accordion__button" id="acc-button-process-of-science" data-accordion="button" aria-controls="acc-panel-process-of-science" aria-expanded="false"> <span class="accordion__button__label"> Process of Science </span> </button> <div class="accordion__panel" id="acc-panel-process-of-science" data-accordion="panel" aria-labelledby="acc-button-process-of-science" role="region"> <div class="accordion accordion--secondary"> <button class="accordion__button" id="acc-button-introduction" data-accordion="button" aria-controls="acc-panel-introduction" aria-expanded="false"> <span class="accordion__button__label"> Introduction </span> </button> <div class="accordion__panel" id="acc-panel-introduction" data-accordion="panel" aria-labelledby="acc-button-introduction" role="region"> <ul class="nav text-color-link"> <li><a href="/en/library/process-of-science/49/the-process-of-science/176">The Process of Science</a></li> </ul> </div> <button class="accordion__button" id="acc-button-the-culture-of-science" data-accordion="button" aria-controls="acc-panel-the-culture-of-science" aria-expanded="false"> <span class="accordion__button__label"> The Culture of Science </span> </button> <div class="accordion__panel" id="acc-panel-the-culture-of-science" data-accordion="panel" aria-labelledby="acc-button-the-culture-of-science" role="region"> <ul class="nav text-color-link"> <li><a href="/en/library/process-of-science/49/the-nature-of-scientific-knowledge/185">The Nature of Scientific Knowledge</a></li> <li><a href="/en/library/process-of-science/49/scientists-and-the-scientific-community/172">Scientists and the Scientific Community</a></li> <li><a href="/en/library/process-of-science/49/scientific-ethics/161">Scientific Ethics</a></li> <li><a href="/en/library/process-of-science/49/scientific-institutions-and-societies/162">Scientific Institutions and Societies</a></li> </ul> </div> <button class="accordion__button" id="acc-button-ideas-in-science" data-accordion="button" aria-controls="acc-panel-ideas-in-science" aria-expanded="false"> <span class="accordion__button__label"> Ideas in Science </span> </button> <div class="accordion__panel" id="acc-panel-ideas-in-science" data-accordion="panel" aria-labelledby="acc-button-ideas-in-science" role="region"> <ul class="nav text-color-link"> <li><a href="/en/library/process-of-science/49/theories-hypotheses-and-laws/177">Theories, Hypotheses, and Laws</a></li> <li><a href="/en/library/process-of-science/49/scientific-controversy/181">Scientific Controversy</a></li> <li><a href="/en/library/process-of-science/49/creativity-in-science/182">Creativity in Science</a></li> </ul> </div> <button class="accordion__button" id="acc-button-research-methods" data-accordion="button" aria-controls="acc-panel-research-methods" aria-expanded="false"> <span class="accordion__button__label"> Research Methods </span> </button> <div class="accordion__panel" id="acc-panel-research-methods" data-accordion="panel" aria-labelledby="acc-button-research-methods" role="region"> <ul class="nav text-color-link"> <li><a href="/en/library/process-of-science/49/the-practice-of-science/148">The Practice of Science</a></li> <li><a href="/en/library/process-of-science/49/experimentation-in-scientific-research/150">Experimentation in Scientific Research</a></li> <li><a href="/en/library/process-of-science/49/description-in-scientific-research/151">Description in Scientific Research</a></li> <li><a href="/en/library/process-of-science/49/comparison-in-scientific-research/152">Comparison in Scientific Research</a></li> <li><a href="/en/library/process-of-science/49/modeling-in-scientific-research/153">Modeling in Scientific Research</a></li> </ul> </div> <button class="accordion__button" id="acc-button-data" data-accordion="button" aria-controls="acc-panel-data" aria-expanded="false"> <span class="accordion__button__label"> Data </span> </button> <div class="accordion__panel" id="acc-panel-data" data-accordion="panel" aria-labelledby="acc-button-data" role="region"> <ul class="nav text-color-link"> <li><a href="/en/library/process-of-science/49/data-analysis-and-interpretation/154">Data Analysis and Interpretation</a></li> <li><a href="/en/library/process-of-science/49/uncertainty-error-and-confidence/157">Uncertainty, Error, and Confidence</a></li> <li><a href="/en/library/process-of-science/49/statistics-in-science/155">Statistics in Science</a></li> <li><a href="/en/library/process-of-science/49/using-graphs-and-visual-data-in-science/156">Using Graphs and Visual Data in Science</a></li> </ul> </div> <button class="accordion__button" id="acc-button-scientific-communication" data-accordion="button" aria-controls="acc-panel-scientific-communication" aria-expanded="false"> <span class="accordion__button__label"> Scientific Communication </span> </button> <div class="accordion__panel" id="acc-panel-scientific-communication" data-accordion="panel" aria-labelledby="acc-button-scientific-communication" role="region"> <ul class="nav text-color-link"> <li><a href="/en/library/process-of-science/49/understanding-scientific-journals-and-articles/158">Understanding Scientific Journals and Articles</a></li> <li><a href="/en/library/process-of-science/49/utilizing-the-scientific-literature/173">Utilizing the Scientific Literature</a></li> <li><a href="/en/library/process-of-science/49/peer-review-in-scientific-publishing/159">Peer Review in Scientific Publishing</a></li> <li><a href="/en/library/process-of-science/49/the-how-and-why-of-scientific-meetings/186">The How and Why of Scientific Meetings</a></li> </ul> </div> </div> </div> <button class="accordion__button" id="acc-button-scientists-and-research" data-accordion="button" aria-controls="acc-panel-scientists-and-research" aria-expanded="false"> <span class="accordion__button__label"> Scientists and Research </span> </button> <div class="accordion__panel" id="acc-panel-scientists-and-research" data-accordion="panel" aria-labelledby="acc-button-scientists-and-research" role="region"> <div class="accordion accordion--secondary"> <button class="accordion__button" id="acc-button-scientific-research" data-accordion="button" aria-controls="acc-panel-scientific-research" aria-expanded="false"> <span class="accordion__button__label"> Scientific Research </span> </button> <div class="accordion__panel" id="acc-panel-scientific-research" data-accordion="panel" aria-labelledby="acc-button-scientific-research" role="region"> <ul class="nav text-color-link"> <li><a href="/en/library/scientists-and-research/58/collaborative-research-in-the-arctic-towards-understanding-climate-change/183">Collaborative Research in the Arctic Towards Understanding Climate Change</a></li> <li><a href="/en/library/scientists-and-research/58/from-stable-chromosomes-to-jumping-genes/184">From Stable Chromosomes to Jumping Genes</a></li> <li><a href="/en/library/scientists-and-research/58/an-elegant-experiment-to-test-the-process-of-dna-replication/187">An Elegant Experiment to Test the Process of DNA Replication</a></li> <li><a href="/en/library/scientists-and-research/58/the-founding-of-neuroscience/233">The Founding of Neuroscience</a></li> <li><a href="/en/library/scientists-and-research/58/tracking-endangered-jaguars-across-the-border/189">Tracking Endangered Jaguars across the Border</a></li> <li><a href="/en/library/scientists-and-research/58/atmospheric-chemistry-research-that-changed-global-policy/211">Atmospheric Chemistry Research that Changed Global Policy</a></li> <li><a href="/en/library/scientists-and-research/58/revolutionizing-medicine-with-monoclonal-antibodies/220">Revolutionizing Medicine with Monoclonal Antibodies</a></li> <li><a href="/en/library/scientists-and-research/58/uncovering-the-mysteries-of-chronic-mountain-sickness/238">Uncovering the Mysteries of Chronic Mountain Sickness</a></li> </ul> </div> <button class="accordion__button" id="acc-button-profiles-in-science" data-accordion="button" aria-controls="acc-panel-profiles-in-science" aria-expanded="false"> <span class="accordion__button__label"> Profiles in Science </span> </button> <div class="accordion__panel" id="acc-panel-profiles-in-science" data-accordion="panel" aria-labelledby="acc-button-profiles-in-science" role="region"> <ul class="nav text-color-link"> <li><a href="/en/library/scientists-and-research/58/luis-e.-miramontes/232">Luis E. Miramontes</a></li> <li><a href="/en/library/scientists-and-research/58/bernardo-houssay/237">Bernardo Houssay</a></li> <li><a href="/en/library/scientists-and-research/58/craig-lee/256">Craig Lee</a></li> <li><a href="/en/library/scientists-and-research/58/david-ho/241">David Ho</a></li> <li><a href="/en/library/scientists-and-research/58/louis-tompkins-wright/244">Louis Tompkins Wright</a></li> <li><a href="/en/library/scientists-and-research/58/carlos-j.-finlay/217">Carlos J. Finlay</a></li> <li><a href="/en/library/scientists-and-research/58/cecilia-payne/290">Cecilia Payne</a></li> <li><a href="/en/library/scientists-and-research/58/jazmin-scarlett/291">Jazmin Scarlett</a></li> <li><a href="/en/library/scientists-and-research/58/ramari-stewart/292">Ramari Stewart</a></li> <li><a href="/en/library/scientists-and-research/58/johnson-cerda/300">Johnson Cerda</a></li> <li><a href="/en/library/scientists-and-research/58/ellen-ochoa/201">Ellen Ochoa</a></li> <li><a href="/en/library/scientists-and-research/58/ruth-benerito/205">Ruth Benerito</a></li> <li><a href="/en/library/scientists-and-research/58/franklin-chang-díaz/219">Franklin Chang Díaz</a></li> <li><a href="/en/library/scientists-and-research/58/percy-lavon-julian/221">Percy Lavon Julian</a></li> <li><a href="/en/library/scientists-and-research/58/luis-walter-alvarez/229">Luis Walter Alvarez</a></li> <li><a href="/en/library/scientists-and-research/58/france-anne-dominic-córdova/230">France Anne-Dominic Córdova</a></li> </ul> </div> </div> </div> </div> </div> </li> <li>  <button class="button" data-toggle="dropdown">Chemistry </button> <div class="nav__dropdown box-shadow-1 padding-1"> <div class="accordion accordion--secondary font-size-sm"> <div class="accordion accordion--secondary"> <button class="accordion__button" id="acc-sub-button-atomic-theory-and-structure" data-accordion="button" aria-controls="acc-sub-panel-atomic-theory-and-structure" aria-expanded="false"> <span class="accordion__button__label"> Atomic Theory and Structure </span> </button> <div class="accordion__panel" id="acc-sub-panel-atomic-theory-and-structure" data-accordion="panel" aria-labelledby="acc-sub-button-atomic-theory-and-structure" role="region"> <ul class="nav text-color-link"> <li><a href="/en/library/chemistry/1/early-ideas-about-matter/49">Early Ideas about Matter</a></li> <li><a href="/en/library/chemistry/1/the-periodic-table-of-elements-i/52">The Periodic Table of Elements I</a></li> <li><a href="/en/library/chemistry/1/the-periodic-table-of-elements-ii/296">The Periodic Table of Elements II</a></li> <li><a href="/en/library/chemistry/1/the-periodic-table-of-elements-iii/297">The Periodic Table of Elements III</a></li> <li><a href="/en/library/chemistry/1/the-periodic-table-of-elements-iv/298">The Periodic Table of Elements IV</a></li> <li><a href="/en/library/chemistry/1/the-periodic-table-of-elements-v/299">The Periodic Table of Elements V</a></li> <li><a href="/en/library/chemistry/1/atomic-theory-i/50">Atomic Theory I</a></li> <li><a href="/en/library/chemistry/1/atomic-theory-ii/51">Atomic Theory II</a></li> <li class="current">Atomic Theory III</li> <li><a href="/en/library/chemistry/1/atomic-theory-iv/231">Atomic Theory IV</a></li> <li><a href="/en/library/chemistry/1/the-mole-and-atomic-mass/53">The Mole and Atomic Mass</a></li> </ul> </div> <button class="accordion__button" id="acc-sub-button-physical-states-and-properties" data-accordion="button" 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id="skip-header-content"> <div class="margin-bottom-5"> <article class="container wide module"> <header class="grid grid--sidebar-right module__header"> <div class="module__header__title"> <span class="subcategory"> <strong><em>Atomic Theory and Structure</em></strong> </span> <h1>Atomic Theory III: <sub><em>Wave-particle duality and the electron</em></sub></h1> <p class="byline">by Adrian Dingle, B.Sc., Anthony Carpi, Ph.D.</p> <nav class="module__header__tabs"> <ul class="tabs-nav tabs-nav--horizontal library"> <li> <a href="/en/library/chemistry/1/atomic-theory-iii/223/reading" aria-current="page" >Reading</a> </li> <li> <a href="/en/library/chemistry/1/atomic-theory-iii/223/quiz">Quiz</a> </li> <li> <a href="/en/library/chemistry/1/atomic-theory-iii/223/resources">Teach with this</a> </li> </ul> </nav> </div> <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "AudioObject", "contentUrl": 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Tracing developments during this time, this module covers ideas and refinements that built on Bohr’s groundbreaking work in quantum theory. Contributions by many scientists highlight how theoretical insights and experimental results revolutionized our understanding of the atom. Concepts include the Schrödinger equation, Born’s three-dimensional probability maps, the Heisenberg uncertainty principle, and electron spin.", "encodingFormat": "mp3", "name": "module_223.mp3" } </script> <div class="module_header_audio"> <div class="audio-player border border-radius"> <audio id="audio"> <source src="https://www.visionlearning.com/img/library/moduleAudio/module_223.mp3" type="audio/mpeg"> Your browser does not support the audio element. </audio> <div class="audio-player__title"> <p>Listen to this reading</p> <span class="audio-player__timestamp" id="timestamp"> 00:00 </span> </div> <div class="audio-player__controls" id="controls"> <button class="button button--icon-only" id="play-pause-button"> <span class="icon icon-play" aria-hidden="true"></span> </button> <div class="audio-player__progress" id="progress-bar" tabindex="0" aria-valuemin="0" aria-valuemax="100" aria-valuenow="0" aria-label="Use arrow keys to forward or rewind the audio" role="slider"> <div class="audio-player__progress__fill"> <span class="audio-player__thumb"></span> </div> </div> <div class="audio-player__volume-container"> <button id="mute-button"> <span class="icon icon-volume"></span> </button> <div class="audio-player__volume" tabindex="0" aria-valuemin="0" aria-valuemax="100" aria-valuenow="100" aria-label="Use arrow keys to adjust volume" role="slider"> <div class="audio-player__volume__fill"> <span class="audio-player__thumb"></span> </div> </div> </div> </div> </div> </div> </header> <hr class="divider"/>   <div class="grid grid--sidebar-right grid--divider"> <div class="order-2 order-1--lg module__main"> <div class="narrow margin-x-auto margin-y-5"> <div class="accordion margin-bottom-5">  <button class="accordion__button" id="acc-button-key-concepts" data-accordion="button" aria-controls="acc-panel-key-concepts" aria-expanded="true" tabindex="0"> Did you know? </button> <div class="accordion__panel shown show" id="acc-panel-key-concepts" data-accordion="panel" aria-labelledby="acc-button-key-concepts" role="region"> <div class="accordion__panel__content"> <p>Did you know that atoms could not be described accurately until quantum theory as developed? Quantum theory offered a fresh way of thinking about the universe at the atomic level. After tremendous advances in quantum mechanics in the last century, the position of electrons and other infinitesimal particles can be predicted with confidence.</p> </div> </div>  <button class="accordion__button" id="acc-button-table-of-contents" data-accordion="button" aria-controls="acc-panel-table-of-contents" aria-expanded="false" tabindex="0"> Key concepts </button> <div class="accordion__panel" id="acc-panel-table-of-contents" data-accordion="panel" aria-labelledby="acc-button-table-of-contents" role="region" aria-hidden="true"> <div class="accordion__panel__content"> <ul class="bulleted"> <li><p>Electrons, like light, have been shown to be wave-particles, exhibiting the behavior of both waves and particles.</p></li> <li><p>The Schrödinger equation describes how the wave function of a wave-particle changes with time in a similar fashion to the way Newton’s second law describes the motion of a classic particle. Using quantum numbers, one can write the wave function, and find a solution to the equation that helps to define the most likely position of an electron within an atom.</p></li> <li><p>Max Born’s interpretation of the Schrödinger equation allows for the construction of three-dimensional probability maps of where electrons may be found around an atom. These ‘maps’ have come to be known as the <em>s, p, d,</em> and <em>f</em> orbitals.</p></li> <li><p>The Heisenberg Uncertainty Principle establishes that an electron’s position and momentum cannot be precisely known together, instead we can only calculate statistical likelihood of an electron’s location.</p></li> <li><p>The discovery of electron spin defines a fourth quantum number independent of the electron orbital but unique to an electron. The Pauli exclusion principle states that no two electrons with the same spin can occupy the same orbital.</p></li> </ul> </div> </div>  <button class="accordion__button" id="acc-button-terms-you-should-know" data-accordion="button" aria-controls="acc-panel-terms-you-should-know" aria-expanded="false" tabindex="0"> Terms you should know </button> <div class="accordion__panel" id="acc-panel-terms-you-should-know" data-accordion="panel" aria-labelledby="acc-button-terms-you-should-know" role="region" aria-hidden="true"> <div class="accordion__panel__content"> <dl> <dt>momentum </dt> <dd> the force that an object has because of its mass and motion. </dd> <dt>quantum number </dt> <dd> Numbers that describe the coordinates of the atomic orbital, including its size (<em>n</em>, the principal quantum number), shape (<em>l</em>, the angular quantum number), orientation in space (<em>m</em>, the magnetic quantum number), and electron direction (<em>s</em>, the spin quantum number). </dd> <dt>spin </dt> <dd> the angular momentum possessed by individual electrons based on their orientation. </dd> <dt><a href="/en/glossary/view/uncertainty">uncertainty </a></dt> <dd> the difference between the calculated value and the true value in any measurement; the numerical value assigned to an estimation of error; a measure of the variability that is inherent when measuring any data.</dd> </dl> </div> </div> </div> <hr class="border-color-dark" /> <section> <div class="container narrow"> <p>As discussed in our <a href="/library/module_viewer.php?mid=51">Atomic Theory II module</a>, at the end of 1913 <mark class="term" data-term="Niels Bohr" data-term-def="Danish physicist born in Copenhagen (1885-1962). Bohr's research was mainly theoretical in nature, including an investigation into the absorption of alpha&hellip;" data-term-url="/en/glossary/view/Bohr%2C+Niels/4521">Niels Bohr</mark> facilitated the leap to a new paradigm of atomic <mark class="term" data-term="theory" data-term-def="A scientific theory is an explanation inferred from multiple lines of evidence for some broad aspect of the natural world and&hellip;" data-term-url="/en/glossary/view/theory/4854">theory</mark> – <mark class="term" data-term="quantum mechanics" data-term-def="The mathematical model that describes the behavior of subatomic particles, beyond classical particle models, by incorporating the quantization of energy and&hellip;" data-term-url="/en/glossary/view/quantum+mechanics/8715">quantum mechanics</mark>. Bohr’s new idea that <mark class="term" data-term="electron" data-term-def="A subatomic particle with a negative charge of 1.60 × 10<sup>-19</sup> coulombs and a mass of 9.11 × 10<sup>-31</sup> kg. Electrons&hellip;" data-term-url="/en/glossary/view/electron/852">electrons</mark> could only be found in specified, <mark class="term" data-term="quantized" data-term-def="The application of only certain, specific values to systems, thus allowing only certain, discrete magnitudes to be associated with them." data-term-url="/en/glossary/view/quantized/9060">quantized</mark> orbits was revolutionary (Bohr, 1913). As is consistent with all new scientific discoveries, a fresh way of thinking about the <mark class="term" data-term="universe" data-term-def="The cosmos and everything that exists in it." data-term-url="/en/glossary/view/universe/5288">universe</mark> at the atomic level would only lead to more questions, the need for additional experimentation and collection of <mark class="term" data-term="evidence" data-term-def="Support for an idea, opinion, or hypothesis." data-term-url="/en/glossary/view/evidence/8243">evidence</mark>, and the <mark class="term" data-term="development" data-term-def="The gradual exposure to stimuli in the early-developmental stages that influences the size, shape, and function of animal once mature." data-term-url="/en/glossary/view/development/13147">development</mark> of expanded <mark class="term" data-term="theory" data-term-url="/en/glossary/view/theory" data-term-def="A scientific theory is an explanation inferred from multiple lines of evidence for some broad aspect of the natural world and&hellip;">theories</mark>. As such, at the beginning of the second decade of the 20<sup>th</sup> century, another rich vein of scientific work was about to be mined.</p> <p><section id="toc_1" class=""> <h2>Periodic trends lead to the distribution of electrons</h2></p> <p><mark id="ngss-405" class="ngss"> In the late 19<sup>th</sup> century, the father of the periodic table, Russian chemist <mark class="term" data-term="Dmitri Mendeleev" data-term-def="Russian inventor and chemist born in Tobolsk, Siberia (1834-1907). Mendeleev's most famous work is the development of the periodic table of&hellip;" data-term-url="/en/glossary/view/Mendeleev%2C+Dmitri/4522">Dmitri Mendeleev</mark>, had already determined that the <mark class="term" data-term="element" data-term-def="One of fewer than 118 pure chemical substances. An element is a substance composed of atoms with identical atomic number." data-term-url="/en/glossary/view/element/1510">elements</mark> could be grouped together in a manner that showed gradual changes in their observed properties. (This is discussed in more detail in our module <a href="/library/module_viewer.php?mid=52">The Periodic Table of Elements</a>.) By the early 1920s, other periodic trends, such as atomic <mark class="term" data-term="volume" data-term-def="The amount of space taken up by matter, commonly expressed in cubic centimeters (cm<sup>3</sup>) or milliliters (ml)." data-term-url="/en/glossary/view/volume/8515">volume</mark> and ionization <mark class="term" data-term="energy" data-term-def="An abstract property defined as the capacity to do work. The basic forms of energy include chemical, electrical, mechanical, nuclear, and&hellip;" data-term-url="/en/glossary/view/energy/1497">energy</mark>, were also well established.</mark></p><div class="figure"><figure class="full centered"> <a class="ajax" href="/library/animations/periodic_table/index.html" title="The Periodic Table of Elements"> <span class="fa fa-search-plus"></span> <img src="/images/figure-images/52-a.jpg" alt="The Periodic Table of Elements"> </a> <figcaption><strong>The Periodic Table of Elements</strong> </figcaption> </figure></div><p><mark id="ngss-406" class="ngss">The German physicist <mark class="term" data-term="Wolfgang Pauli" data-term-def="Austrian born theoretical physicist and pioneer in the quantum physics field. Known particularly for the Pauli exclusion principle, for which he&hellip;" data-term-url="/en/glossary/view/Pauli%2C+Wolfgang/8716">Wolfgang Pauli</mark> made a quantum leap by realizing that in order for there to be differences in ionization energies and atomic <mark class="term" data-term="volume" data-term-def="The amount of space taken up by matter, commonly expressed in cubic centimeters (cm<sup>3</sup>) or milliliters (ml)." data-term-url="/en/glossary/view/volume/8515">volumes</mark> among <mark class="term" data-term="atom" data-term-def="The smallest unit of an element that retains the chemical properties of the element. Atoms can exist alone or in&hellip;" data-term-url="/en/glossary/view/atom/1509">atoms</mark> with many <mark class="term" data-term="electron" data-term-def="A subatomic particle with a negative charge of 1.60 × 10<sup>-19</sup> coulombs and a mass of 9.11 × 10<sup>-31</sup> kg. Electrons&hellip;" data-term-url="/en/glossary/view/electron/852">electrons</mark>, there had to be a way that the electrons were not all placed in the lowest <mark class="term" data-term="energy" data-term-def="An abstract property defined as the capacity to do work. The basic forms of energy include chemical, electrical, mechanical, nuclear, and&hellip;" data-term-url="/en/glossary/view/energy/1497">energy</mark> levels. If multi-electron atoms did have all of their electrons placed in the lowest energy levels, then very different periodic patterns would have resulted from what was actually observed. However, before we reach Pauli and his work, we need to establish a number of more fundamental ideas.</mark></p></section> <section id="toc_2"> <h2>Wave-particle duality</h2><p>The <mark class="term" data-term="development" data-term-def="The gradual exposure to stimuli in the early-developmental stages that influences the size, shape, and function of animal once mature." data-term-url="/en/glossary/view/development/13147">development</mark> of early quantum <mark class="term" data-term="theory" data-term-def="A scientific theory is an explanation inferred from multiple lines of evidence for some broad aspect of the natural world and&hellip;" data-term-url="/en/glossary/view/theory/4854">theory</mark> leaned heavily on the concept of <mark class="term" data-term="wave-particle duality" data-term-def="The concept that predicts that every elementary particle will exhibit the characteristics and properties of both a wave and a particle." data-term-url="/en/glossary/view/wave~particle+duality/8717">wave-particle duality</mark>. This simultaneously simple and complex idea is that <mark class="term" data-term="light" data-term-def="A form of electromagnetic radiation. Visible light is that associated with stimulating the organs of sight, which for normal human&hellip;" data-term-url="/en/glossary/view/light/1498">light</mark> (as well as other particles) has properties that are consistent with both <mark class="term" data-term="waves" data-term-def="The motion of rising and falling in curves; undulation." data-term-url="/en/glossary/view/waves/8274">waves</mark> <em>and</em> <mark class="term" data-term="particle" data-term-def="A tiny piece of matter." data-term-url="/en/glossary/view/particle/8259">particles</mark>. The idea had been first seriously hinted at in relation to light in the late 17<sup>th</sup> century. <mark id="ngss-407" class="ngss">Two camps formed over the nature of light: one in favor of light as a particle and one in favor of light as a wave. (See our <a href="/library/module_viewer.php?mid=132">Light I: Particle or Wave?</a> module for more details.) Although both groups presented effective arguments supported by <mark class="term" data-term="data" data-term-def="(plural form of <b>datum</b>) A collection of pieces of information, generally taking the form of numbers, text, bits, or facts, that&hellip;" data-term-url="/en/glossary/view/data/3729">data</mark>, it wasn’t until some two hundred years later that the <mark class="term" data-term="debate" data-term-def="A reasoned discussion of opposing points in an argument." data-term-url="/en/glossary/view/debate/8242">debate</mark> was settled.</mark></p> <a class="interactive-animation" href="https://www.visionlearning.com/library/animations/Periodic/Periodic_main.html" target="_blank"> <img class="interactive-animation__image" src="/images/anim-snaps/ia-periodic.jpg" width="200" alt="Atomic and ionic structure of the first 12 elements" /> <p class="interactive-animation__title"> <em>Interactive Animation:</em> <strong class="link-new-window"> <span class="link__text">Atomic and ionic structure of the first 12 elements</span> </strong> </p> </a> <p><mark id="ngss-408" class="ngss">At the end of the 19<sup>th</sup> century the wave-particle <mark class="term" data-term="debate" data-term-def="A reasoned discussion of opposing points in an argument." data-term-url="/en/glossary/view/debate/8242">debate</mark> continued. <mark class="term" data-term="James Clerk Maxwell" data-term-def="Scottish theoretical physicist and mathematician born in Edinburgh (1831-1879). Maxwell developed the classical electromagnetic theory, which synthesized previously unrelated observations, experiments,&hellip;" data-term-url="/en/glossary/view/Maxwell%2C+James+Clerk/4558">James Clerk Maxwell</mark>, a Scottish physicist, developed a series of equations that accurately described the behavior of <mark class="term" data-term="light" data-term-def="A form of electromagnetic radiation. Visible light is that associated with stimulating the organs of sight, which for normal human&hellip;" data-term-url="/en/glossary/view/light/1498">light</mark> as an electromagnetic wave, seemingly tipping the debate in favor of <mark class="term" data-term="waves" data-term-def="The motion of rising and falling in curves; undulation." data-term-url="/en/glossary/view/waves/8274">waves</mark>. </mark><mark id="ngss-474" class="ngss">However, at the beginning of the 20<sup>th</sup> century, both <mark class="term" data-term="Max Planck" data-term-def="Theoretical physicist, born in Kiel, Germany (1858–1947), who won the Nobel Prize in Physics in 1918 for his research on quantum&hellip;" data-term-url="/en/glossary/view/Planck%2C+Max/8894">Max Planck</mark> and <mark class="term" data-term="Albert Einstein" data-term-def="Theoretical physicist, born in Württemberg, Germany (1879–1955), who became an American citizen in 1940. While working as a patent clerk in&hellip;" data-term-url="/en/glossary/view/Einstein%2C+Albert/4458">Albert Einstein</mark> conceived of <mark class="term" data-term="experiment" data-term-def="A test or trial carried out under controlled conditions so that specific actions can be performed and the results can be observed." data-term-url="/en/glossary/view/experiment/8292">experiments</mark> which demonstrated that light exhibited behavior that was consistent with it being a <mark class="term" data-term="particle" data-term-def="A tiny piece of matter." data-term-url="/en/glossary/view/particle/8259">particle</mark>. In fact, they developed <mark class="term" data-term="theory" data-term-url="/en/glossary/view/theory" data-term-def="A scientific theory is an explanation inferred from multiple lines of evidence for some broad aspect of the natural world and&hellip;">theories</mark> that suggested that light was a wave-particle – a hybrid of the two properties. By the time of Bohr’s watershed papers, the time was right for the expansion of this new idea of wave–particle duality in the context of quantum <mark class="term" data-term="theory" data-term-def="A scientific theory is an explanation inferred from multiple lines of evidence for some broad aspect of the natural world and&hellip;" data-term-url="/en/glossary/view/theory/4854">theory</mark>, and in stepped French physicist <mark class="term" data-term="Louis de Broglie" data-term-def="French physicist whose PhD thesis first suggested the wave nature of electrons, leading to the establishment of wave-particle duality in quantum&hellip;" data-term-url="/en/glossary/view/de+Broglie%2C+Louis/9052">Louis de Broglie</mark>.</mark></p></section> <section id="toc_3"> <h2>de Broglie says electrons can act like waves</h2><p>In 1924, de Broglie published his PhD thesis (de Broglie, 1924). <mark id="ngss-409" class="ngss">He proposed the extension of the <mark class="term" data-term="wave-particle duality" data-term-def="The concept that predicts that every elementary particle will exhibit the characteristics and properties of both a wave and a particle." data-term-url="/en/glossary/view/wave~particle+duality/8717">wave-particle duality</mark> of <mark class="term" data-term="light" data-term-def="A form of electromagnetic radiation. Visible light is that associated with stimulating the organs of sight, which for normal human&hellip;" data-term-url="/en/glossary/view/light/1498">light</mark> to all <mark class="term" data-term="matter" data-term-def="The substance that makes up physical objects." data-term-url="/en/glossary/view/matter/8264">matter</mark>, but in particular to <mark class="term" data-term="electron" data-term-def="A subatomic particle with a negative charge of 1.60 × 10<sup>-19</sup> coulombs and a mass of 9.11 × 10<sup>-31</sup> kg. Electrons&hellip;" data-term-url="/en/glossary/view/electron/852">electrons</mark>. The starting point for de Broglie was Einstein’s equation that described the dual nature of photons, and he used an analogy, backed up by mathematics, to derive an equation that came to be known as the “de Broglie wavelength”</mark> (see Figure 1 for a visual representation of the wavelength).</p><p>The <mark class="term" data-term="de Broglie wavelength" data-term-def="the wavelength (&#955;) associated with a fundamental particle, that is related to Planck’s constant (<em>h</em>) and momentum (&#961;), via the equation,&hellip;" data-term-url="/en/glossary/view/de+Broglie+wavelength/9053">de Broglie wavelength</mark> equation is, in the grand scheme of things, a profoundly simple one that relates two <mark class="term" data-term="variable" data-term-def="In math, an expression that can be assigned any set of values. Variables are written as symbols, such as x, y&hellip;" data-term-url="/en/glossary/view/variable/3797">variables</mark> and a constant: momentum, <mark class="term" data-term="wavelength" data-term-def="The distance between corresponding points on two successive waves, generally measured from crest to crest." data-term-url="/en/glossary/view/wavelength/1500">wavelength</mark>, and Planck's <mark class="term" data-term="constant" data-term-def="In mathematics, a quantity that has a fixed value; something that does not vary." data-term-url="/en/glossary/view/constant/8557">constant</mark>. There was support for de Broglie’s idea since it made theoretical sense, but the very nature of science demands that good ideas be tested and ultimately demonstrated by <mark class="term" data-term="experiment" data-term-def="A test or trial carried out under controlled conditions so that specific actions can be performed and the results can be observed." data-term-url="/en/glossary/view/experiment/8292">experiment</mark>. Unfortunately, de Broglie did not have any experimental <mark class="term" data-term="data" data-term-def="(plural form of <b>datum</b>) A collection of pieces of information, generally taking the form of numbers, text, bits, or facts, that&hellip;" data-term-url="/en/glossary/view/data/3729">data</mark>, so his idea remained unconfirmed for a number of years.</p> <div class="figure"> <figure> <button class="lightbox-button lightbox-button--icon" data-lightbox="" data-lightbox-src="/img/library/large_images/image_8898.jpg"> <img src="/img/library/modules/mid223/Image/VLObject-8898-150913110958.jpg" alt="Figure 1: Two representations of a de Broglie wavelength (the blue line) using a hydrogen atom: a radial view (A) and a 3D view (B)." /> </button> <figcaption> <p><strong>Figure 1</strong>: Two representations of a de Broglie wavelength (the blue line) using a hydrogen atom: a radial view (A) and a 3D view (B).</p> </figcaption> </figure> </div> <p>It wasn’t until 1927 that de Broglie’s <mark class="term" data-term="hypothesis" data-term-def="From the Greek word <em>hypothesis</em> meaning assumption or the basis of an argument, a hypothesis is a proposal intended to explain&hellip;" data-term-url="/en/glossary/view/hypothesis/3727">hypothesis</mark> was demonstrated via the <mark class="term" data-term="Davisson-Germer experiment" data-term-def="An experiment carried out in the 1920’s by American physicists Clinton Davisson and Lester Germer, it produced data that confirmed de&hellip;" data-term-url="/en/glossary/view/Davisson~Germer+experiment/9054">Davisson-Germer experiment</mark> (Davisson, 1928). <mark id="ngss-410" class="ngss">In their <mark class="term" data-term="experiment" data-term-def="A test or trial carried out under controlled conditions so that specific actions can be performed and the results can be observed." data-term-url="/en/glossary/view/experiment/8292">experiment</mark>, Clinton Davisson and Lester Germer fired <mark class="term" data-term="electron" data-term-def="A subatomic particle with a negative charge of 1.60 × 10<sup>-19</sup> coulombs and a mass of 9.11 × 10<sup>-31</sup> kg. Electrons&hellip;" data-term-url="/en/glossary/view/electron/852">electrons</mark> at a piece of nickel metal and collected <mark class="term" data-term="data" data-term-def="(plural form of <b>datum</b>) A collection of pieces of information, generally taking the form of numbers, text, bits, or facts, that&hellip;" data-term-url="/en/glossary/view/data/3729">data</mark> on the <mark class="term" data-term="diffraction" data-term-def="The bending or spreading of waves when they meet an obstruction." data-term-url="/en/glossary/view/diffraction/3606">diffraction</mark> patterns observed (Figure 2). The diffraction pattern of the electrons was entirely consistent with the pattern already measured for <mark class="term" data-term="X-ray" data-term-def="A form of electromagnetic radiation with higher frequency and energy than any other electromagnetic radiation besides gamma rays. X-rays have various&hellip;" data-term-url="/en/glossary/view/X~ray/7573">X-rays</mark> and, since X-rays were known to be <mark class="term" data-term="electromagnetic radiation" data-term-def="A series of waves that are propagated by simultaneous, periodic variations of electrical and magnetic fields. Examples of electromagnetic radiation include&hellip;" data-term-url="/en/glossary/view/electromagnetic+radiation/1501">electromagnetic radiation</mark> (i.e., waves), the experiment confirmed that electrons had a wave component. This confirmation meant that de Broglie’s hypothesis was correct.</mark></p> <div class="figure"> <figure> <button class="lightbox-button lightbox-button--icon" data-lightbox="" data-lightbox-src="/img/library/large_images/image_8895.png"> <img src="/img/library/modules/mid223/Image/VLObject-8895-150909040932.png" alt="Figure 2: A drawing of the experiment conducted by Davisson and Germer where they fired electrons at a piece of nickel metal and observed the diffraction patterns." /> </button> <figcaption> <p><strong>Figure 2</strong>: A drawing of the experiment conducted by Davisson and Germer where they fired electrons at a piece of nickel metal and observed the diffraction patterns.</p> <span class="credit">image ©Roshan220195</span> </figcaption> </figure> </div> <p>Interestingly, it was the (experimental) efforts of others (Davisson and Germer), that led to de Broglie winning the <mark class="term" data-term="Nobel Prize" data-term-def="Awards made annually, beginning in 1901, from funds originally established by Alfred B. Nobel for outstanding achievement in physics, chemistry, medicine&hellip;" data-term-url="/en/glossary/view/Nobel+Prize/3843">Nobel Prize</mark> in Physics in 1929 for his theoretical discovery of the wave-nature of <mark class="term" data-term="electron" data-term-def="A subatomic particle with a negative charge of 1.60 × 10<sup>-19</sup> coulombs and a mass of 9.11 × 10<sup>-31</sup> kg. Electrons&hellip;" data-term-url="/en/glossary/view/electron/852">electrons</mark>. Without the proof that the <mark class="term" data-term="Davisson-Germer experiment" data-term-def="An experiment carried out in the 1920’s by American physicists Clinton Davisson and Lester Germer, it produced data that confirmed de&hellip;" data-term-url="/en/glossary/view/Davisson~Germer+experiment/9054">Davisson-Germer experiment</mark> provided, de Broglie’s 1924 <mark class="term" data-term="hypothesis" data-term-def="From the Greek word <em>hypothesis</em> meaning assumption or the basis of an argument, a hypothesis is a proposal intended to explain&hellip;" data-term-url="/en/glossary/view/hypothesis/3727">hypothesis</mark> would have remained just that – a hypothesis. This sequence of events is a quintessential example of a <mark class="term" data-term="theory" data-term-def="A scientific theory is an explanation inferred from multiple lines of evidence for some broad aspect of the natural world and&hellip;" data-term-url="/en/glossary/view/theory/4854">theory</mark> being corroborated by experimental <mark class="term" data-term="data" data-term-def="(plural form of <b>datum</b>) A collection of pieces of information, generally taking the form of numbers, text, bits, or facts, that&hellip;" data-term-url="/en/glossary/view/data/3729">data</mark>.</p> <div class="comprehension-checkpoint margin-y-4"> <h6 class="comprehension-checkpoint__header"> <span> <span class="icon icon-question"></span> </span> Comprehension Checkpoint </h6> <form class="" name="cc8849"> <div class="form-entry"> <div class="form-entry__field"> <span class="form-entry__field__label">Theories must be backed up by</span> <div class="form-entry__option"> <div class="form-entry__option__radio" data-answer="correct"> <label> <input id="q1-8849-0-option-a" name="quiz-option-8849" type="radio" value="experimental data." > <span class="option__label"> <span class="screen-reader-only">a.</span> experimental data. </span> </label> <span class="quiz__response" id="response-8849-0"> <strong>Correct!</strong> </span> </div> <div class="form-entry__option__radio" data-answer="incorrect"> <label> <input id="q1-8849-1-option-b" name="quiz-option-8849" type="radio" value="the opinions of important scientists." > <span class="option__label"> <span class="screen-reader-only">b.</span> the opinions of important scientists. </span> </label> <span class="quiz__response" id="response-8849-1"> <strong>Incorrect.</strong> </span> </div> </div> </div> </div> </form> </div> </section> <section id="toc_4"> <h2>Schrödinger does the math</h2><p>In 1926, <mark class="term" data-term="Erwin Schrödinger" data-term-def="Austrian physicist instrumental in the development of quantum theory and for his known for the Schrödinger equation. 1933 Nobel Prize winner&hellip;" data-term-url="/en/glossary/view/Schr%C3%B6dinger%2C+Erwin/9056">Erwin Schrödinger</mark> derived his now famous equation (Schrödinger, 1926). For approximately 200 years prior to Schrödinger’s work, the infinitely simpler <em>F = ma</em> (Newton’s second law) had been used to describe the motion of <mark class="term" data-term="particle" data-term-def="A tiny piece of matter." data-term-url="/en/glossary/view/particle/8259">particles</mark> in classical mechanics. <mark id="ngss-411" class="ngss">With the advent of <mark class="term" data-term="quantum mechanics" data-term-def="The mathematical model that describes the behavior of subatomic particles, beyond classical particle models, by incorporating the quantization of energy and&hellip;" data-term-url="/en/glossary/view/quantum+mechanics/8715">quantum mechanics</mark>, a completely new equation was required to describe the properties of subatomic particles. Since these particles were no longer thought of as classical particles but as particle-waves, Schrödinger’s partial <mark class="term" data-term="differential equation" data-term-def="An equation relating a variable that changes over time (referred to as a <i>function</i>), to its rate of change (referred to&hellip;" data-term-url="/en/glossary/view/differential+equation/3902">differential equation</mark> was the answer. In the simplest terms, just as Newton’s second <mark class="term" data-term="law" data-term-def="In science, a principle that describes a phenomenon, often mathematically." data-term-url="/en/glossary/view/law/8686">law</mark> describes how the motion of physical objects changes with changing conditions, the <mark class="term" data-term="Schrödinger's equation" data-term-url="/en/glossary/view/Schr%C3%B6dinger%27s+equation" data-term-def="A partial differential equation developed by Erwin Schrodinger that describes the change of the quantum state of a physical system over&hellip;">Schrödinger equation</mark> describes how the wave <mark class="term" data-term="function" data-term-def="Adaptations that influence how the animal interacts with other species. For example, animal function typically serves genetic and reproductive success." data-term-url="/en/glossary/view/function/13151">function</mark> (Ψ) of a quantum <mark class="term" data-term="system" data-term-def="A group of interacting, interrelated or interdependent components that form a complex whole. The size of the system is defined for&hellip;" data-term-url="/en/glossary/view/system/3904">system</mark> changes over time (Equation 1). The Schrödinger equation was found to be consistent with the description of the <mark class="term" data-term="electron" data-term-def="A subatomic particle with a negative charge of 1.60 × 10<sup>-19</sup> coulombs and a mass of 9.11 × 10<sup>-31</sup> kg. Electrons&hellip;" data-term-url="/en/glossary/view/electron/852">electron</mark> as a wave, and to correctly predict the <mark class="term" data-term="parameter" data-term-def="In statistics, a parameter is a numerical value that represents a characteristic of a statistical population. Contrast with statistic." data-term-url="/en/glossary/view/parameter/9481">parameters</mark> of the <mark class="term" data-term="energy" data-term-def="An abstract property defined as the capacity to do work. The basic forms of energy include chemical, electrical, mechanical, nuclear, and&hellip;" data-term-url="/en/glossary/view/energy/1497">energy</mark> levels of the hydrogen <mark class="term" data-term="atom" data-term-def="The smallest unit of an element that retains the chemical properties of the element. Atoms can exist alone or in&hellip;" data-term-url="/en/glossary/view/atom/1509">atom</mark> that Bohr had proposed.</mark></p><div class="figure"><figure> $${i\hslash} \left( \frac { \partial } { \partial{t}} \right) {\Psi} = {\hat{H}\Psi} $$ <figcaption> <p><strong>Equation 1:</strong> The Schrödinger equation.</p> </figcaption> </figure></div><p>Schrödinger’s equation is perhaps most commonly used to define a three-dimensional area of space where a given <mark class="term" data-term="electron" data-term-def="A subatomic particle with a negative charge of 1.60 × 10<sup>-19</sup> coulombs and a mass of 9.11 × 10<sup>-31</sup> kg. Electrons&hellip;" data-term-url="/en/glossary/view/electron/852">electron</mark> is most likely to be found. Each area of space is known as an atomic orbital and is characterized by a set of three <mark class="term" data-term="quantum numbers" data-term-def="A set of four numbers that are commonly used to describe the position of an electron within an atom. These include:&hellip;" data-term-url="/en/glossary/view/quantum+numbers/9066">quantum numbers</mark>. These numbers represent <mark class="term" data-term="value" data-term-def="A number that is assigned based on measurement or a calculation. In mathematics, an unknown value that is commonly represented by&hellip;" data-term-url="/en/glossary/view/value/8254">values</mark> that describe the coordinates of the atomic orbital: including its size (<em>n</em>, the principal quantum number), shape (<em>l</em>, the angular or azimuthal quantum number), and orientation in space (<em>m</em>, the magnetic quantum number). There is also a fourth <mark class="term" data-term="quantum numbers" data-term-url="/en/glossary/view/quantum+numbers" data-term-def="A set of four numbers that are commonly used to describe the position of an electron within an atom. These include:&hellip;">quantum number</mark> that is exclusive to a particular electron rather than a particular orbital (<em>s</em>, the spin quantum number; see below for more information). </p><p>Schrödinger’s equation allows the calculation of each of these three <mark class="term" data-term="quantum numbers" data-term-def="A set of four numbers that are commonly used to describe the position of an electron within an atom. These include:&hellip;" data-term-url="/en/glossary/view/quantum+numbers/9066">quantum numbers</mark>. This equation was a critical piece in the <mark class="term" data-term="quantum mechanics" data-term-def="The mathematical model that describes the behavior of subatomic particles, beyond classical particle models, by incorporating the quantization of energy and&hellip;" data-term-url="/en/glossary/view/quantum+mechanics/8715">quantum mechanics</mark> puzzle, since it brought quantum <mark class="term" data-term="theory" data-term-def="A scientific theory is an explanation inferred from multiple lines of evidence for some broad aspect of the natural world and&hellip;" data-term-url="/en/glossary/view/theory/4854">theory</mark> into sharp focus via what amounted to a mathematical demonstration of Bohr’s fundamental quantum idea. The Schrödinger wave equation is important since it bridges the gap between classical Newtonian physics (which breaks down at the atomic level) and quantum mechanics.</p><p>The <mark class="term" data-term="Schrödinger's equation" data-term-url="/en/glossary/view/Schr%C3%B6dinger%27s+equation" data-term-def="A partial differential equation developed by Erwin Schrodinger that describes the change of the quantum state of a physical system over&hellip;">Schrödinger equation</mark> is rightfully considered to be a monumental contribution to the advancement and understanding of quantum <mark class="term" data-term="theory" data-term-def="A scientific theory is an explanation inferred from multiple lines of evidence for some broad aspect of the natural world and&hellip;" data-term-url="/en/glossary/view/theory/4854">theory</mark>, but there are three additional considerations, detailed below, that must also be understood. Without these, we would have an incomplete picture of our <mark class="term" data-term="non-relativistic" data-term-def="A physical system where relativistic effects (those involving the theory of relativity) are small enough to be ignored. Usually, this is&hellip;" data-term-url="/en/glossary/view/non~relativistic/8712">non-relativistic</mark> understanding of <mark class="term" data-term="electron" data-term-def="A subatomic particle with a negative charge of 1.60 × 10<sup>-19</sup> coulombs and a mass of 9.11 × 10<sup>-31</sup> kg. Electrons&hellip;" data-term-url="/en/glossary/view/electron/852">electrons</mark> in <mark class="term" data-term="atom" data-term-def="The smallest unit of an element that retains the chemical properties of the element. Atoms can exist alone or in&hellip;" data-term-url="/en/glossary/view/atom/1509">atoms</mark>.</p></section> <section id="toc_5"> <h2>Max Born further interprets the Schrödinger equation</h2><p><mark id="ngss-412" class="ngss">German mathematician and physicist <mark class="term" data-term="Max Born" data-term-def="German physicist instrumental in the development of quantum mechanics for which he won the Nobel Prize in physics in 1954 for,&hellip;" data-term-url="/en/glossary/view/Born%2C+Max/9068">Max Born</mark> made a very specific and crucially important contribution to <mark class="term" data-term="quantum mechanics" data-term-def="The mathematical model that describes the behavior of subatomic particles, beyond classical particle models, by incorporating the quantization of energy and&hellip;" data-term-url="/en/glossary/view/quantum+mechanics/8715">quantum mechanics</mark> relating to the <mark class="term" data-term="Schrödinger's equation" data-term-url="/en/glossary/view/Schr%C3%B6dinger%27s+equation" data-term-def="A partial differential equation developed by Erwin Schrodinger that describes the change of the quantum state of a physical system over&hellip;">Schrödinger equation</mark>. Born took the wave <mark class="term" data-term="function" data-term-def="Adaptations that influence how the animal interacts with other species. For example, animal function typically serves genetic and reproductive success." data-term-url="/en/glossary/view/function/13151">functions</mark> that Schrödinger produced, and said that the solutions to the equation could be interpreted as three-dimensional <mark class="term" data-term="probability" data-term-def="The likelihood that a given event will occur. In statistics, probability is often expressed as a ratio of the number of&hellip;" data-term-url="/en/glossary/view/probability/3913">probability</mark> “maps” of where an <mark class="term" data-term="electron" data-term-def="A subatomic particle with a negative charge of 1.60 × 10<sup>-19</sup> coulombs and a mass of 9.11 × 10<sup>-31</sup> kg. Electrons&hellip;" data-term-url="/en/glossary/view/electron/852">electron</mark> may most likely be found around an <mark class="term" data-term="atom" data-term-def="The smallest unit of an element that retains the chemical properties of the element. Atoms can exist alone or in&hellip;" data-term-url="/en/glossary/view/atom/1509">atom</mark> (Born, 1926). These maps have come to be known as the <em>s, p, d</em>, and <em>f</em> orbitals (Figure 3).</mark></p> <div class="figure"> <figure> <button class="lightbox-button lightbox-button--icon" data-lightbox="" data-lightbox-src="/img/library/large_images/image_8897.jpg"> <img src="/img/library/modules/mid223/Image/VLObject-8897-150913070903.jpg" alt="Figure 3: Based on Born's theories, these are representations of the three-dimensional probabilities of an electron's location around an atom. The four orbitals, in increasing complexity, are: s, p, d, and f. Additional information is given about the orbital's magnetic quantum number (m)." /> </button> <figcaption> <p><mark id="ngss-413" class="ngss"><strong>Figure 3</strong>: Based on Born's theories, these are representations of the three-dimensional probabilities of an electron's location around an atom. The four orbitals, in increasing complexity, are: <em>s, p, d, </em>and <em>f</em>. Additional information is given about the orbital's magnetic quantum number (<em>m</em>).</mark></p> <span class="credit">image ©UC Davis/ChemWiki</span> </figcaption> </figure> </div> </section> <section id="toc_6"> <h2>Werner Heisenberg’s Uncertainty Principle</h2><p><mark id="ngss-414" class="ngss">In the year following the publication of Schrödinger’s work, the German physicist <mark class="term" data-term="Werner Heisenberg" data-term-def="German physicist instrumental in the development of quantum mechanics for which he won the Nobel Prize in 1932 in physics for,&hellip;" data-term-url="/en/glossary/view/Heisenberg%2C+Werner/9069">Werner Heisenberg</mark> published a paper that outlined his <mark class="term" data-term="uncertainty" data-term-def="The quantitative estimation of error, which indicates the precision of a measurement or value. All measurements include some amount of uncertainty&hellip;" data-term-url="/en/glossary/view/uncertainty/5219">uncertainty</mark> <mark class="term" data-term="principle" data-term-def="In the sciences, a principle is a fundamental, primary, or general law or truth. For instance, one of the most basic&hellip;" data-term-url="/en/glossary/view/principle/5289">principle</mark> (Heisenberg, 1927). He realized that there were limitations on the extent to which the momentum of an <mark class="term" data-term="electron" data-term-def="A subatomic particle with a negative charge of 1.60 × 10<sup>-19</sup> coulombs and a mass of 9.11 × 10<sup>-31</sup> kg. Electrons&hellip;" data-term-url="/en/glossary/view/electron/852">electron</mark> and its position could be described. The <mark class="term" data-term="Heisenberg Uncertainty Principle" data-term-def="A mathematical assertion in quantum mechanics, that states that both the position and momentum of a particle cannot be simultaneously, accurately&hellip;" data-term-url="/en/glossary/view/Heisenberg+Uncertainty+Principle/9070">Heisenberg Uncertainty Principle</mark> places a limit on the <mark class="term" data-term="accuracy" data-term-def="In science, the term accuracy describes how well a measurement approximates the theoretically correct value of that measurement, for example, how&hellip;" data-term-url="/en/glossary/view/accuracy/4222">accuracy</mark> of simultaneously knowing the position and momentum of a particle: As the certainty of one increases, then the uncertainty of other also increases.</mark></p><p><mark id="ngss-415" class="ngss">The crucial thing about the <mark class="term" data-term="uncertainty" data-term-def="The quantitative estimation of error, which indicates the precision of a measurement or value. All measurements include some amount of uncertainty&hellip;" data-term-url="/en/glossary/view/uncertainty/5219">uncertainty</mark> <mark class="term" data-term="principle" data-term-def="In the sciences, a principle is a fundamental, primary, or general law or truth. For instance, one of the most basic&hellip;" data-term-url="/en/glossary/view/principle/5289">principle</mark> is that it fits with the quantum <mark class="term" data-term="mechanical" data-term-def="Involving physical force or motion." data-term-url="/en/glossary/view/mechanical/8516">mechanical</mark> <mark class="term" data-term="model" data-term-def="A representation, pattern, or mathematical description that can help scientists replicate a system." data-term-url="/en/glossary/view/model/8236">model</mark> in which <mark class="term" data-term="electron" data-term-def="A subatomic particle with a negative charge of 1.60 × 10<sup>-19</sup> coulombs and a mass of 9.11 × 10<sup>-31</sup> kg. Electrons&hellip;" data-term-url="/en/glossary/view/electron/852">electrons</mark> are not found in very specific, planetary-like orbits – the original Bohr model – and it also dovetails with Born’s <mark class="term" data-term="probability" data-term-def="The likelihood that a given event will occur. In statistics, probability is often expressed as a ratio of the number of&hellip;" data-term-url="/en/glossary/view/probability/3913">probability</mark> maps. The two contributions (Born and Heisenberg’s) taken together with the solution to the <mark class="term" data-term="Schrödinger's equation" data-term-url="/en/glossary/view/Schr%C3%B6dinger%27s+equation" data-term-def="A partial differential equation developed by Erwin Schrodinger that describes the change of the quantum state of a physical system over&hellip;">Schrödinger equation</mark>, reveal that the position of the electron in an <mark class="term" data-term="atom" data-term-def="The smallest unit of an element that retains the chemical properties of the element. Atoms can exist alone or in&hellip;" data-term-url="/en/glossary/view/atom/1509">atom</mark> can only be accurately predicted in a statistical way. That is to say, we know where the electron is most <em>likely</em> to be found in the atom, but we can never be absolutely sure of its exact position.</mark></p> <div class="comprehension-checkpoint margin-y-4"> <h6 class="comprehension-checkpoint__header"> <span> <span class="icon icon-question"></span> </span> Comprehension Checkpoint </h6> <form class="" name="cc8864"> <div class="form-entry"> <div class="form-entry__field"> <span class="form-entry__field__label">The Heisenberg uncertainty principle concerning the position and momentum of a particle states that as the certainty of one increases, the _____ of the other increases.</span> <div class="form-entry__option"> <div class="form-entry__option__radio" data-answer="incorrect"> <label> <input id="q1-8864-0-option-a" name="quiz-option-8864" type="radio" value="certainty" > <span class="option__label"> <span class="screen-reader-only">a.</span> certainty </span> </label> <span class="quiz__response" id="response-8864-0"> <strong>Incorrect.</strong> </span> </div> <div class="form-entry__option__radio" data-answer="correct"> <label> <input id="q1-8864-1-option-b" name="quiz-option-8864" type="radio" value="uncertainty" > <span class="option__label"> <span class="screen-reader-only">b.</span> uncertainty </span> </label> <span class="quiz__response" id="response-8864-1"> <strong>Correct!</strong> </span> </div> </div> </div> </div> </form> </div> </section> <section id="toc_7"> <h2>Angular momentum, or "Spin"</h2><p><mark id="ngss-416" class="ngss">In 1922 German physicists <mark class="term" data-term="Otto Stern" data-term-def="German physicist and 1943 Nobel Prize winner in physics, noted for his work with Walther Gerlach in establishing the spin-quantization of electrons." data-term-url="/en/glossary/view/Stern%2C+Otto/9071">Otto Stern</mark>, an assistant of Born’s, and <mark class="term" data-term="Walther Gerlach" data-term-def="German physicist noted for his work with Otto Stern in establishing the spin-quantization of electrons." data-term-url="/en/glossary/view/Gerlach%2C+Walther/9072">Walther Gerlach</mark> conducted an <mark class="term" data-term="experiment" data-term-def="A test or trial carried out under controlled conditions so that specific actions can be performed and the results can be observed." data-term-url="/en/glossary/view/experiment/8292">experiment</mark> in which they passed silver <mark class="term" data-term="atom" data-term-def="The smallest unit of an element that retains the chemical properties of the element. Atoms can exist alone or in&hellip;" data-term-url="/en/glossary/view/atom/1509">atoms</mark> through a magnetic field and observed the deflection pattern. In simple terms, the results yielded two distinct possibilities related to the single, 5s <mark class="term" data-term="valence" data-term-def="The number of single bonds an atom can form, also measured as the number of hydrogen atoms that typically bond to&hellip;" data-term-url="/en/glossary/view/valence/1563">valence</mark> <mark class="term" data-term="electron" data-term-def="A subatomic particle with a negative charge of 1.60 × 10<sup>-19</sup> coulombs and a mass of 9.11 × 10<sup>-31</sup> kg. Electrons&hellip;" data-term-url="/en/glossary/view/electron/852">electron</mark> in each atom. This was an unexpected <mark class="term" data-term="observation" data-term-def="1. The act of noticing something. 2. A record of that which has been noticed." data-term-url="/en/glossary/view/observation/8255">observation</mark>, and implied that a single electron could take on two, very distinct states. At the time, nobody could explain the phenomena that the experiment had demonstrated, and it took a number of scientists, working both independently and in unison with earlier experimental observations, to work it out over a period of several years.</mark></p><p>In the early 1920s, Bohr’s quantum <mark class="term" data-term="model" data-term-def="A representation, pattern, or mathematical description that can help scientists replicate a system." data-term-url="/en/glossary/view/model/8236">model</mark> and various spectra that had been produced could be adequately described by the use of only three <mark class="term" data-term="quantum numbers" data-term-def="A set of four numbers that are commonly used to describe the position of an electron within an atom. These include:&hellip;" data-term-url="/en/glossary/view/quantum+numbers/9066">quantum numbers</mark>. However, there were experimental <mark class="term" data-term="observation" data-term-def="1. The act of noticing something. 2. A record of that which has been noticed." data-term-url="/en/glossary/view/observation/8255">observations</mark> that could not be explained via only three mathematical <mark class="term" data-term="parameter" data-term-def="In statistics, a parameter is a numerical value that represents a characteristic of a statistical population. Contrast with statistic." data-term-url="/en/glossary/view/parameter/9481">parameters</mark>. In particular, as far back as 1896, the Dutch physicist Pieter Zeeman noted that the single <mark class="term" data-term="valence" data-term-def="The number of single bonds an atom can form, also measured as the number of hydrogen atoms that typically bond to&hellip;" data-term-url="/en/glossary/view/valence/1563">valence</mark> <mark class="term" data-term="electron" data-term-def="A subatomic particle with a negative charge of 1.60 × 10<sup>-19</sup> coulombs and a mass of 9.11 × 10<sup>-31</sup> kg. Electrons&hellip;" data-term-url="/en/glossary/view/electron/852">electron</mark> present in the sodium <mark class="term" data-term="atom" data-term-def="The smallest unit of an element that retains the chemical properties of the element. Atoms can exist alone or in&hellip;" data-term-url="/en/glossary/view/atom/1509">atom</mark> could yield two different <mark class="term" data-term="spectral lines" data-term-def="See line spectra." data-term-url="/en/glossary/view/spectral+lines/9073">spectral lines</mark> in the presence of a magnetic field. This same phenomenon was observed with other atoms with odd numbers of <mark class="term" data-term="valence electron" data-term-def="Electrons that can be actively involved in chemical change; usually electrons in the shell with the highest value of n (electrons&hellip;" data-term-url="/en/glossary/view/valence+electron/851">valence electrons</mark>. These observations were problematic since they failed to fit the working model. </p><p><mark id="ngss-417" class="ngss">In 1925, Dutch physicist George Uhlenbeck and his graduate student Samuel Goudsmit proposed that these odd <mark class="term" data-term="observation" data-term-def="1. The act of noticing something. 2. A record of that which has been noticed." data-term-url="/en/glossary/view/observation/8255">observations</mark> could be explained if <mark class="term" data-term="electron" data-term-def="A subatomic particle with a negative charge of 1.60 × 10<sup>-19</sup> coulombs and a mass of 9.11 × 10<sup>-31</sup> kg. Electrons&hellip;" data-term-url="/en/glossary/view/electron/852">electrons</mark> possessed <mark class="term" data-term="angular momentum" data-term-def="The momentum possessed by an object in rotation around a point, it is the analog to linear momentum. In physics, one&hellip;" data-term-url="/en/glossary/view/angular+momentum/8713">angular momentum</mark>, a concept that <mark class="term" data-term="Wolfgang Pauli" data-term-def="Austrian born theoretical physicist and pioneer in the quantum physics field. Known particularly for the Pauli exclusion principle, for which he&hellip;" data-term-url="/en/glossary/view/Pauli%2C+Wolfgang/8716">Wolfgang Pauli</mark> later called “spin.” As a result, the existence of a fourth <mark class="term" data-term="quantum numbers" data-term-url="/en/glossary/view/quantum+numbers" data-term-def="A set of four numbers that are commonly used to describe the position of an electron within an atom. These include:&hellip;">quantum number</mark> was revealed, one that was independent of the orbital in which the electron resides, but unique to an individual electron.</mark></p><p><mark id="ngss-418" class="ngss">By considering spin, the <mark class="term" data-term="observation" data-term-def="1. The act of noticing something. 2. A record of that which has been noticed." data-term-url="/en/glossary/view/observation/8255">observations</mark> by Stern and Gerlach made sense. If an <mark class="term" data-term="electron" data-term-def="A subatomic particle with a negative charge of 1.60 × 10<sup>-19</sup> coulombs and a mass of 9.11 × 10<sup>-31</sup> kg. Electrons&hellip;" data-term-url="/en/glossary/view/electron/852">electron</mark> could be thought of as a rotating, electrically-charged body, it would create its own <mark class="term" data-term="magnetic moment" data-term-def="A measure of an object's interaction with an external magnetic field. A magnet, an electron, and a planet all have magnetic&hellip;" data-term-url="/en/glossary/view/magnetic+moment/8714">magnetic moment</mark>. If the electron had two different orientations (one right-handed and one left-handed), it would produce two different ‘spins,’ and these two different states would explain the anomalous behavior noted by Zeeman. This observation meant that there was a need for a fourth <mark class="term" data-term="quantum numbers" data-term-url="/en/glossary/view/quantum+numbers" data-term-def="A set of four numbers that are commonly used to describe the position of an electron within an atom. These include:&hellip;">quantum number</mark>, ultimately known as the “spin quantum number,” to fully describe electrons. Later it was determined that the spin number was indeed needed, but for a different reason – either way, a fourth quantum number was required.</mark></p> <div class="comprehension-checkpoint margin-y-4"> <h6 class="comprehension-checkpoint__header"> <span> <span class="icon icon-question"></span> </span> Comprehension Checkpoint </h6> <form class="" name="cc8902"> <div class="form-entry"> <div class="form-entry__field"> <span class="form-entry__field__label">Some experimental observations could not be explained mathematically using three parameters because</span> <div class="form-entry__option"> <div class="form-entry__option__radio" data-answer="incorrect"> <label> <input id="q1-8902-0-option-a" name="quiz-option-8902" type="radio" value="scientists had recorded their data incorrectly." > <span class="option__label"> <span class="screen-reader-only">a.</span> scientists had recorded their data incorrectly. </span> </label> <span class="quiz__response" id="response-8902-0"> <strong>Incorrect.</strong> </span> </div> <div class="form-entry__option__radio" data-answer="correct"> <label> <input id="q1-8902-1-option-b" name="quiz-option-8902" type="radio" value="a fourth quantum number was needed." > <span class="option__label"> <span class="screen-reader-only">b.</span> a fourth quantum number was needed. </span> </label> <span class="quiz__response" id="response-8902-1"> <strong>Correct!</strong> </span> </div> </div> </div> </div> </form> </div> </section> <section id="toc_8"> <h2>Spin and the Pauli exclusion principle</h2><p>In 1922, <mark class="term" data-term="Niels Bohr" data-term-def="Danish physicist born in Copenhagen (1885-1962). Bohr's research was mainly theoretical in nature, including an investigation into the absorption of alpha&hellip;" data-term-url="/en/glossary/view/Bohr%2C+Niels/4521">Niels Bohr</mark> visited his colleague <mark class="term" data-term="Wolfgang Pauli" data-term-def="Austrian born theoretical physicist and pioneer in the quantum physics field. Known particularly for the Pauli exclusion principle, for which he&hellip;" data-term-url="/en/glossary/view/Pauli%2C+Wolfgang/8716">Wolfgang Pauli</mark> at Göttingen where he was working. At the time, Bohr was still wrestling with the idea that there was something important about the number of <mark class="term" data-term="electron" data-term-def="A subatomic particle with a negative charge of 1.60 × 10<sup>-19</sup> coulombs and a mass of 9.11 × 10<sup>-31</sup> kg. Electrons&hellip;" data-term-url="/en/glossary/view/electron/852">electrons</mark> that were found in ‘closed shells’ (shells that had been filled). </p><p>In his own later account (1946), Pauli describes how building upon Bohr’s ideas and drawing inspiration from others’ work, he proposed the idea that only two <mark class="term" data-term="electron" data-term-def="A subatomic particle with a negative charge of 1.60 × 10<sup>-19</sup> coulombs and a mass of 9.11 × 10<sup>-31</sup> kg. Electrons&hellip;" data-term-url="/en/glossary/view/electron/852">electrons</mark> (with opposite spins) should be allowed in any one quantum state. He called this ‘two-valuedness’ – a somewhat inelegant translation of the German <em>zweideutigkeit</em> (Pauli, 1925). The consequence was that once a pair of electrons occupies a low <mark class="term" data-term="energy" data-term-def="An abstract property defined as the capacity to do work. The basic forms of energy include chemical, electrical, mechanical, nuclear, and&hellip;" data-term-url="/en/glossary/view/energy/1497">energy</mark> quantum state (orbitals), any subsequent electrons would have to enter higher energy quantum states, also restricted to pairs at each level.</p><p><mark id="ngss-419" class="ngss">Using this idea, Bohr and Pauli were able to construct <mark class="term" data-term="model" data-term-def="A representation, pattern, or mathematical description that can help scientists replicate a system." data-term-url="/en/glossary/view/model/8236">models</mark> of all of the electronic structures of the <mark class="term" data-term="atom" data-term-def="The smallest unit of an element that retains the chemical properties of the element. Atoms can exist alone or in&hellip;" data-term-url="/en/glossary/view/atom/1509">atoms</mark> from hydrogen to uranium, and they found that their predicted electronic structures matched the periodic trends that were known to exist from the periodic table – <mark class="term" data-term="theory" data-term-def="A scientific theory is an explanation inferred from multiple lines of evidence for some broad aspect of the natural world and&hellip;" data-term-url="/en/glossary/view/theory/4854">theory</mark> met experimental <mark class="term" data-term="evidence" data-term-def="Support for an idea, opinion, or hypothesis." data-term-url="/en/glossary/view/evidence/8243">evidence</mark> once again.</mark></p><p><mark id="ngss-420" class="ngss">Pauli ultimately formed what came to be known as the exclusion <mark class="term" data-term="principle" data-term-def="In the sciences, a principle is a fundamental, primary, or general law or truth. For instance, one of the most basic&hellip;" data-term-url="/en/glossary/view/principle/5289">principle</mark> (1925), which used a fourth <mark class="term" data-term="quantum numbers" data-term-url="/en/glossary/view/quantum+numbers" data-term-def="A set of four numbers that are commonly used to describe the position of an electron within an atom. These include:&hellip;">quantum number</mark> (introduced by others) to distinguish between the two <mark class="term" data-term="electron" data-term-def="A subatomic particle with a negative charge of 1.60 × 10<sup>-19</sup> coulombs and a mass of 9.11 × 10<sup>-31</sup> kg. Electrons&hellip;" data-term-url="/en/glossary/view/electron/852">electrons</mark> that make up the maximum number of electrons that could be in any given quantum level. In its simplest form, the <mark class="term" data-term="Pauli exclusion principle" data-term-def="Principle developed by Wolfgang Pauli (1925) that states that no two electrons in an atom can have the same set of&hellip;" data-term-url="/en/glossary/view/Pauli+exclusion+principle/9075">Pauli exclusion principle</mark> states that <em>no two electrons in an <mark class="term" data-term="atom" data-term-def="The smallest unit of an element that retains the chemical properties of the element. Atoms can exist alone or in&hellip;" data-term-url="/en/glossary/view/atom/1509">atom</mark> can have the same set of four quantum numbers</em>. The first three <mark class="term" data-term="quantum numbers" data-term-def="A set of four numbers that are commonly used to describe the position of an electron within an atom. These include:&hellip;" data-term-url="/en/glossary/view/quantum+numbers/9066">quantum numbers</mark> for any two electrons can be the same (which places them in the same orbital), but the fourth number must be either +½ or -½, i.e., they must have different ‘spins’ (Figure 4). This is what Uhlenbeck and Goudsmit’s research suggested, following Pauli’s original publication of his <mark class="term" data-term="theory" data-term-url="/en/glossary/view/theory" data-term-def="A scientific theory is an explanation inferred from multiple lines of evidence for some broad aspect of the natural world and&hellip;">theories</mark>.</mark></p> <div class="figure"> <figure> <button class="lightbox-button lightbox-button--icon" data-lightbox="" data-lightbox-src="/img/library/large_images/image_8899.png"> <img src="/img/library/modules/mid223/Image/VLObject-8899-150913110944.png" alt="Figure 4: A model of the fourth quantum number, spin (s). Shown here are models for particles with spin (s) of ½, or half angular momentum." /> </button> <figcaption> <p><strong>Figure 4</strong>: A model of the fourth quantum number, spin (<em>s</em>). Shown here are models for particles with spin (<em>s</em>) of ½, or half angular momentum.</p> </figcaption> </figure> </div> <p>The period described here was rich in the <mark class="term" data-term="development" data-term-def="The gradual exposure to stimuli in the early-developmental stages that influences the size, shape, and function of animal once mature." data-term-url="/en/glossary/view/development/13147">development</mark> of the quantum <mark class="term" data-term="theory" data-term-def="A scientific theory is an explanation inferred from multiple lines of evidence for some broad aspect of the natural world and&hellip;" data-term-url="/en/glossary/view/theory/4854">theory</mark> of atomic structure. Literally dozens of individuals, some mentioned throughout this module and others not, contributed to this process by providing theoretical insights or experimental results that helped shape our understanding of the <mark class="term" data-term="atom" data-term-def="The smallest unit of an element that retains the chemical properties of the element. Atoms can exist alone or in&hellip;" data-term-url="/en/glossary/view/atom/1509">atom</mark>. Many of the individuals worked in the same laboratories, collaborated together, or communicated with one another during the period, allowing the rapid transfer of ideas and refinements that would shape modern physics. All these contributions can certainly been seen as an incremental building process, where one idea leads to the next, each adding to the refinement of thinking and understanding, and advancing the science of the field.</p> </div> </section> <hr class="border-color-dark" /> <footer class="module__footer"> <p class="citation"> <em> Adrian Dingle, B.Sc., Anthony Carpi, Ph.D. “Atomic Theory III” Visionlearning Vol. CHE-3 (6), 2015. </em> </p>  <div class="title-list" id="refs" name="refs"> <p class="h6 title-list__title"> References </p> <ul class="title-list__list"> <li><p>Bohr, N. (1913). On the constitution of atoms and molecules. <em>Philosophical Magazine </em>(London),<em> Series 6, 26,</em> 1–25.</li> <li>Born, M. (1926). Zur Quantenmechanik der Stoßvorgänge. <em>Zeitschrift für Physik, 37</em>(12), 863–867.</li> <li>Davisson, C. J. (1928). Are electrons waves? <em>Franklin Institute Journal, 205</em>(5), 597-623.</li> <li>de Broglie, L. (1924). Recherches sur la théorie des quanta. <em>Annales de Physique, 10</em>(3), 22-128.</li> <li>Heisenberg, W. (1927). Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. <em>Zeitschrift für Physik, 43</em>(3-4), 172-198.</li> <li>Pauli, W. (1925). Ueber den Einfluss der Geschwindigkeitsabhaengigkeit der Elektronenmasse auf den Zeeman-Effekt. <em>Zeitschrift für Physik, 31</em>(1), 373-385.</li> <li>Pauli, W. (1946). Remarks on the history of the exclusion principle. <em>Science, New Series, 103</em>(2669), 213-215.</li> <li>Schrödinger, E. (1926). Quantisierung als Eigenwertproblem. <em>Annalen der Physik, 384</em>(4), 273–376.</li> <li>Stoner, E. C. (1924). The distribution of electrons among atomic energy levels. <em>The London, Edinburgh and Dublin Philosophical Magazine </em>(6th series),<em> 48</em>(286), 719-736</p></li> </ul> </div>  <div class="title-list" name="further"> <p class="h6 title-list__title"> Further Reading </p> <ul class="grid grid--column-2--md grid--column-3--md gap-1"> <li> <a class="no-hover-focus height-100" href="/en/library/Chemistry/1/Atomic-Theory-IV/231"> <article class="flex-row align-items-center flex-column--md align-items-start--md height-100 theme-light padding-2 gap-2"> <div class="width-30 width-auto--md"> <img class="border-radius box-shadow-1" src="/img/library/moduleImages/featured_image_231-23061209064512.jpeg" alt="Atomic Theory IV"> </div> <div class="flex-grow-shrink"> <h2 class="h6 font-weight-normal"> Atomic Theory IV: <em>Quantum numbers and orbitals</em> </h2> </div> </article> </a> </li> </ul> </div> </footer> </div>   </div>  <div class="order-1 order-2--lg module__tools"> <div class="narrow margin-x-auto position-sticky-top font-size-md"> <div class="padding-2 border-radius box-shadow-1--lg"> <div class="tabs" role="tablist"> <nav> <button class="button button--icon-label" id="tab-button-in-this-module" aria-label="Table of Contents" aria-controls="tab-panel-module__tools" aria-selected="true" role="tab"> <span class="icon icon-list" aria-hidden="true"></span> <span class="button__text">Contents</span> </button> <button class="button button--icon-label" id="tab-button-toggle-terms" aria-controls="tab-panel-toggle-terms" aria-selected="false" role="tab"> <span class="icon icon-glossary-highlight"></span> <span class="button__text">Glossary Terms</span> </button> <button class="button button--icon-label" id="tab-button-toggle-ngss" aria-controls="tab-panel-toggle-ngss" aria-selected="false" role="tab"> <span class="icon icon-ngss"></span> <span class="button__text">NGSS</span> </button> </nav> <hr class="divider" /> <div class="tabs__panel shown" id="tab-panel-module__tools" aria-labelledby="tab-button-module__tools" role="tabpanel"> <p class="font-weight-bold margin-bottom-1"> Table of Contents </p> <div class="table-of-contents" id="module-toc"> <ul> <li><a href="/en/library/chemistry/1/atomic-theory-iii/223#toc_1">Periodic trends lead to the distribution of electrons</a> </li> <li><a href="/en/library/chemistry/1/atomic-theory-iii/223#toc_2">Wave-particle duality</a> </li> <li><a href="/en/library/chemistry/1/atomic-theory-iii/223#toc_3">de Broglie says electrons can act like waves</a> </li> <li><a href="/en/library/chemistry/1/atomic-theory-iii/223#toc_4">Schrödinger does the math</a> </li> <li><a href="/en/library/chemistry/1/atomic-theory-iii/223#toc_5">Max Born further interprets the Schrödinger equation</a> </li> <li><a href="/en/library/chemistry/1/atomic-theory-iii/223#toc_6">Werner Heisenberg’s Uncertainty Principle</a> </li> <li><a href="/en/library/chemistry/1/atomic-theory-iii/223#toc_7">Angular momentum, or "Spin"</a> </li> <li><a href="/en/library/chemistry/1/atomic-theory-iii/223#toc_8">Spin and the Pauli exclusion principle</a> </li> </ul> </div> </div>   <div class="tabs__panel" id="tab-panel-toggle-terms" aria-labelledby="tab-button-toggle-terms" role="tabpanel"> <div class="reading-toggle"> <div class="reading-toggle__switch"> <div class="form-entry__option__switch"> <label> <input type="checkbox" name="termsToggleSwitch" id="terms-toggle-switch" /> <span class="switch__slider"></span> <span class="option__label text-decoration-none font-size-md"> Highlight Glossary Terms </span> </label> </div> </div> <div class="reading-toggle__help"> <p> <em> Activate glossary term highlighting to easily identify key terms within the module. Once highlighted, you can click on these terms to view their definitions. </em> </p> </div> </div> </div> <div class="tabs__panel" id="tab-panel-toggle-ngss" aria-labelledby="tab-button-toggle-ngss" role="tabpanel"> <div class="reading-toggle"> <div class="reading-toggle__switch"> <div class="form-entry__option__switch"> <label> <input type="checkbox" name="ngssToggleSwitch" id="ngss-toggle-switch" /> <span class="switch__slider"></span> <span class="option__label text-decoration-none font-size-md"> Show NGSS Annotations </span> </label> </div> </div> <div class="reading-toggle__help"> <p> <em> Activate NGSS annotations to easily identify NGSS standards within the module. Once highlighted, you can click on them to view these standards. </em> </p> </div> </div> </div> <div class="reading-annotation-container"></div>  </div> </div> <div class="margin-3"> <script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-9561344156007092" crossorigin="anonymous"></script>  <ins class="adsbygoogle" style="display:block" data-ad-client="ca-pub-9561344156007092" data-ad-slot="7634263342" data-ad-format="auto" data-full-width-responsive="true"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script> </div>   </article> </div> </main> <script id="ngssCommentdata" type="application/json"> [{"ngss_tag_id":null,"type":"dci","tag":"","name":null,"description":null,"comment":"<p>This section defines the periodic table.<\/p>\r\n\r\n<p><strong>PS1 Matter and Its Interactions<\/strong><\/p>\r\n<p><strong>HS-PS1.A Structure and Properties of Matter<\/strong><\/p>\r\n<p>The periodic table orders elements horizontally by the number of protons in the atom\u2019s nucleus and places those with similar chemical properties in columns. The repeating patterns of this table reflect patterns of outer electron states.<\/p>","is_public":"1","mod_ngss_comment_id":"405","display_order":"1","dimension":"dci","dimension_full":"Disciplinary Core Ideas"},{"ngss_tag_id":null,"type":"cc","tag":"","name":null,"description":null,"comment":"<p>The work of Pauli connected patterns and causality when identifying characteristics of atoms.<\/p>\r\n\r\n<p><strong>HS-CC.1 Patterns: <\/strong>\r\nDifferent patterns may be observed at each of the scales at which a system is studied and can provide evidence for causality in explanations of phenomena.<\/p>","is_public":"1","mod_ngss_comment_id":"406","display_order":"2","dimension":"cc","dimension_full":"Crosscutting Concepts"},{"ngss_tag_id":null,"type":"p","tag":"","name":null,"description":null,"comment":"<p>Scientists routinely engage in arguments based on evidence as highlighted in this example.<\/p>\r\n\r\n<p><strong>HS-SEP.7 Engaging in Argument from Evidence:<\/strong> Construct, use, and\/or present an oral and written argument or counter-arguments based on data and evidence.<\/p>","is_public":"1","mod_ngss_comment_id":"407","display_order":"3","dimension":"p","dimension_full":"Science and Engineering Practices"},{"ngss_tag_id":null,"type":"p","tag":"","name":null,"description":null,"comment":"<p>Maxwell developed a series of equations that described the behavior of light as an electromagnetic wave.<\/p>\r\n\r\n<p><strong>HS-SEP.5 Using Mathematics and Computational Thinking:<\/strong> Use mathematical, computational, and\/or algorithmic representations of phenomena or design solutions to describe and\/or support claims and\/or explanations.<\/p>","is_public":"1","mod_ngss_comment_id":"408","display_order":"4","dimension":"p","dimension_full":"Science and Engineering Practices"},{"ngss_tag_id":null,"type":"p","tag":"","name":null,"description":null,"comment":"<p>de Broglie derived an equation to model how electrons can act as waves.<\/p>\r\n\r\n<p><strong>HS-SEP.5 Using Mathematics and Computational Thinking:<\/strong> Create and\/or revise a computational model or simulation of a phenomenon, designed device, process, or system.Create and\/or revise a computational model or simulation of a phenomenon, designed device, process, or system.<\/p>","is_public":"1","mod_ngss_comment_id":"409","display_order":"5","dimension":"p","dimension_full":"Science and Engineering Practices"},{"ngss_tag_id":null,"type":"p","tag":"","name":null,"description":null,"comment":"<p>Davisson and Germer collected data, and used that to confirm the de Broglie's hypothesis.<\/p>\r\n\r\n<p><strong>HS-SEP.6 Constructing Explanations and Designing Solutions:<\/strong> Apply scientific reasoning, theory, and\/or models to link evidence to the claims to assess the extent to which the reasoning and data support the explanation or conclusion.<\/p>","is_public":"1","mod_ngss_comment_id":"410","display_order":"6","dimension":"p","dimension_full":"Science and Engineering Practices"},{"ngss_tag_id":null,"type":"p","tag":"","name":null,"description":null,"comment":"<p>Schrodinger derived an equation to describe the properties of subatomic particles.<\/p>\r\n\r\n<p><strong>HS-SEP.5 Mathematical and Computational Thinking:<\/strong> Create and\/or revise a computational model or simulation of a phenomenon, designed device, process, or system.<\/p>","is_public":"1","mod_ngss_comment_id":"411","display_order":"7","dimension":"p","dimension_full":"Science and Engineering Practices"},{"ngss_tag_id":null,"type":"p","tag":"","name":null,"description":null,"comment":"<p>Born used the work of Schrodinger to create a model of electron orbitals.<\/p>\r\n\r\n<p><strong>HS-SEP.2 Developing and Using Models:<\/strong> Develop, revise, and\/or use a model based on evidence to illustrate and\/or predict the relationships between systems or between components of a system.<\/p>","is_public":"1","mod_ngss_comment_id":"412","display_order":"8","dimension":"p","dimension_full":"Science and Engineering Practices"},{"ngss_tag_id":null,"type":"cc","tag":"","name":null,"description":null,"comment":"<p>These models are based on Born's theories.<\/p>\r\n\r\n<p><strong>HS-CC.4 Systems and System Models:<\/strong>\r\nModels can be used to predict the behavior of a system, but these predictions have limited precision and reliability due to the assumptions and approximations inherent in models.<\/p>","is_public":"1","mod_ngss_comment_id":"413","display_order":"9","dimension":"cc","dimension_full":"Crosscutting Concepts"},{"ngss_tag_id":null,"type":"p","tag":"","name":null,"description":null,"comment":"<p>Heisenberg published a paper that recognized the limitations of the Born model.<\/p>\r\n\r\n<p><strong>HS-SEP.4 Analyzing and Interpreting Data:<\/strong>\r\nConsider limitations of data analysis (e.g., measurement error, sample selection) when analyzing and interpreting data.<\/p>","is_public":"1","mod_ngss_comment_id":"414","display_order":"10","dimension":"p","dimension_full":"Science and Engineering Practices"},{"ngss_tag_id":null,"type":"p","tag":"","name":null,"description":null,"comment":"<p>Heisenberg published a paper that recognized the limitations of the Born model.<\/p>\r\n\r\n<p><strong>HS-SEP.4 Analyzing and Interpreting Data:<\/strong>\r\nConsider limitations of data analysis (e.g., measurement error, sample selection) when analyzing and interpreting data.<\/p>","is_public":"1","mod_ngss_comment_id":"415","display_order":"11","dimension":"p","dimension_full":"Science and Engineering Practices"},{"ngss_tag_id":null,"type":"p","tag":"","name":null,"description":null,"comment":"<p>Stern and Gerlach's experiment produced data that warranted an explanation.<\/p>\r\n\r\n<p><strong>HS-SEP.4 Analyzing and Interpreting Data:<\/strong> Evaluate the impact of new data on a working explanation and\/or model of a proposed process or system.<\/p>","is_public":"1","mod_ngss_comment_id":"416","display_order":"12","dimension":"p","dimension_full":"Science and Engineering Practices"},{"ngss_tag_id":null,"type":"p","tag":"","name":null,"description":null,"comment":"<p>Uhlenbeck and Goudsmit proposed an explanation for the results of Stern and Gerlach's experiment.<\/p>\r\n\r\n<p><strong>HS-SEP.6 Constructing Explanations and Designing Solutions:<\/strong> Apply scientific ideas, principles, and\/or evidence to provide an explanation of phenomena and solve design problems, taking into account possible unanticipated effects.<\/p>","is_public":"1","mod_ngss_comment_id":"417","display_order":"13","dimension":"p","dimension_full":"Science and Engineering Practices"},{"ngss_tag_id":null,"type":"p","tag":"","name":null,"description":null,"comment":"<p>Uhlenbeck and Goudsmit proposed an explanation for the results of Stern and Gerlach's experiment.<\/p>\r\n\r\n<p><strong>HS-SEP.6 Constructing Explanations and Designing Solutions:<\/strong> Apply scientific ideas, principles, and\/or evidence to provide an explanation of phenomena and solve design problems, taking into account possible unanticipated effects.<\/p>","is_public":"1","mod_ngss_comment_id":"418","display_order":"14","dimension":"p","dimension_full":"Science and Engineering Practices"},{"ngss_tag_id":null,"type":"cc","tag":"","name":null,"description":null,"comment":"<p>Bohr and Pauli applied the principle to construct predictive models of the structures of atoms.<\/p>\r\n\r\n<p><strong>HS-CC.4 Systems and System Models:<\/strong>\r\nModels can be used to predict the behavior of a system, but these predictions have limited precision and reliability due to the assumptions and approximations inherent in models.<\/p>","is_public":"1","mod_ngss_comment_id":"419","display_order":"15","dimension":"cc","dimension_full":"Crosscutting Concepts"},{"ngss_tag_id":null,"type":"p","tag":"","name":null,"description":null,"comment":"<p>Pauli developed the exclusion principle which accounted for the various quantum numbers in an atom.<\/p>\r\n\r\n<p><strong>HS-SEP.2 Developing and Using Models:<\/strong> Develop, revise, and\/or use a model based on evidence to illustrate and\/or predict the relationships between systems or between components of a system.<\/p>","is_public":"1","mod_ngss_comment_id":"420","display_order":"16","dimension":"p","dimension_full":"Science and Engineering Practices"},{"ngss_tag_id":null,"type":"p","tag":"","name":null,"description":null,"comment":"<p>Planck and Einstein relied on evidence to back their theory, but included the work of Maxwell.<\/p>\r\n\r\n<p><strong>HS-SEP.6 Constructing Explanations and Designing Solutions:<\/strong> Construct and revise an explanation based on valid and reliable evidence obtained from a variety of sources (including students\u2019 own investigations, models, theories, simulations, peer review) and the assumption that theories and laws that describe the natural world operate today as they did in the past and will continue to do so in the future.<\/p>","is_public":"1","mod_ngss_comment_id":"474","display_order":"17","dimension":"p","dimension_full":"Science and Engineering Practices"}]</script>   <footer class="position-relative box-shadow-1 font-size-md" id="global-footer"> <h2 class="screen-reader-only">Page Footer</h2> <div class="back-to-top"> <div class="container wide"> <button class="button button--has-icon font-size-sm"> <span class="icon icon-arrow-up"></span> <span class="button__text">Back to top</span> </button> </div> </div> <div class="container wide padding-y-2"> <div class="grid grid--column-2--md grid--column-4--lg gap-4 grid--divider--fill-x"> <nav> <ul class="nav font-weight-bold"> <li> <a href="/en/library" title="Readings & quizzes"> Library </a> </li> <li> <a href="/en/glossary" title="Science terms"> Glossary </a> </li> <li> <a href="/en/classroom" title="Courses & bookmarks"> Classroom </a> </li> </ul> </nav> <nav> <ul class="nav"> 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