File "wave-particle-duality.html"
Path: /StudyIB/physics/page/1134/wave-particle-dualityhtml
File size: 56.05 KB
MIME-type: text/html
Charset: utf-8
<!DOCTYPE html><html lang="EN"><head> <script>(function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start': new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0], j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src= 'https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f); })(window,document,'script','dataLayer','GTM-PZBWZ8J');</script> <title>Wave particle duality</title><!-- Removed by WebCopy --><!--<base href="/">--><!-- Removed by WebCopy --><meta http-equiv="x-ua-compatible" content="IE=Edge"><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1"><link href="../../../css/bootstrap.flatly.min.css" rel="stylesheet" media="screen"><link rel="stylesheet" href="../../../fonts/awesome/css/font-awesome.min.css"><link href="../../../js/jquery-fancybox/jquery.fancybox.min.css" type="text/css" rel="stylesheet"><link rel="stylesheet" href="../../../css/style.min.css?v=202301301645"><meta name="robots" content="index, follow"><meta name="googlebot" content="noarchive"><meta prefix="og: http://ogp.me/ns#" property="og:title" name="og:title" content="StudyIB Physics: Wave particle duality"> <meta prefix="og: http://ogp.me/ns#" property="og:image" content="https://studyib.net/img/studyib-card-default.jpg"> <meta prefix="og: http://ogp.me/ns#" property="og:description" name="og:description" content="The evidence from the photoelectric effect, Compton scattering and annihilation that electromagnetic radiation can have quantum properties indicates that matter may have wave properties. Here we will consider this possibility."> <meta prefix="og: http://ogp.me/ns#" property="og:url" name="og:url" content="https://studyib.net/physics/page/1134/wave-particle-duality"> <meta prefix="og: http://ogp.me/ns#" property="og:site_name" name="og:site_name" content="StudyIB - Your IB learning companion"> <meta prefix="og: http://ogp.me/ns#" property="og:locale" name="og:locale" content="en"> <meta prefix="og: http://ogp.me/ns#" property="og:type" name="og:type" content="website"> <meta name="description" content="The evidence from the photoelectric effect, Compton scattering and annihilation that electromagnetic radiation can have quantum properties indicates that matter may have wave properties. Here we will consider this possibility."> <meta name="image" content="https://studyib.net/img/studyib-card-default.jpg"> <meta name="keywords" content="StudyIB, Physics, Site overview, Self-study, Videos, Virtual tutor, Practices, Multiple Choice, IB, IBDP, InThinking, International Baccalaureate, Revision, Revision websites, Student Sites, Students, Learning, Guidance, Exam, Questions"> <meta itemprop="name" content="StudyIB Physics: Wave particle duality"> <meta itemprop="description" content="The evidence from the photoelectric effect, Compton scattering and annihilation that electromagnetic radiation can have quantum properties indicates that matter may have wave properties. Here we will consider this possibility."> <meta itemprop="image" content="https://studyib.net/img/studyib-card-default.jpg"> <meta name="twitter:card" content="summary_large_image"> <meta name="twitter:title" content="StudyIB Physics: Wave particle duality"> <meta name="twitter:description" content="The evidence from the photoelectric effect, Compton scattering and annihilation that electromagnetic radiation can have quantum properties indicates that matter may have wave properties. Here we will consider this possibility."> <meta name="twitter:image" content="https://studyib.net/img/studyib-card-default.jpg"> <meta name="twitter:creator" content="@inthinker"><link rel="stylesheet" href="../../../css/snippets.min.css?v=202209111300"><link rel="stylesheet" href="../../../css/article.min.css?v=202211221000"><link rel="stylesheet" type="text/css" href="../../../js/slick-carousel/slick.min.css"><link rel="stylesheet" type="text/css" href="../../../js/slick-carousel/slick-theme.min.css"><style type="text/css">.filter-sl-only { display: none; }</style><script src="../../../ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script><script src="../../../js/ifvisible.min.js"></script><script>ifvisible.setIdleDuration(300);</script><link rel="apple-touch-icon-precomposed" sizes="57x57" href="../../../img/favicon/apple-touch-icon-57x57.png"> <link rel="apple-touch-icon-precomposed" sizes="114x114" href="../../../img/favicon/apple-touch-icon-114x114.png"> <link rel="apple-touch-icon-precomposed" sizes="72x72" href="../../../img/favicon/apple-touch-icon-72x72.png"> <link rel="apple-touch-icon-precomposed" sizes="144x144" href="../../../img/favicon/apple-touch-icon-144x144.png"> <link rel="apple-touch-icon-precomposed" sizes="60x60" href="../../../img/favicon/apple-touch-icon-60x60.png"> <link rel="apple-touch-icon-precomposed" sizes="120x120" href="../../../img/favicon/apple-touch-icon-120x120.png"> <link rel="apple-touch-icon-precomposed" sizes="76x76" href="../../../img/favicon/apple-touch-icon-76x76.png"> <link rel="apple-touch-icon-precomposed" sizes="152x152" href="../../../img/favicon/apple-touch-icon-152x152.png"> <link rel="icon" type="image/png" href="../../../img/favicon/favicon-196x196.png" sizes="196x196"> <link rel="icon" type="image/png" href="../../../img/favicon/favicon-96x96.png" sizes="96x96"> <link rel="icon" type="image/png" href="../../../img/favicon/favicon-32x32.png" sizes="32x32"> <link rel="icon" type="image/png" href="../../../img/favicon/favicon-16x16.png" sizes="16x16"> <link rel="icon" type="image/png" href="../../../img/favicon/favicon-128.png" sizes="128x128"> <meta name="application-name" content="StudyIB: Your IB Learning Companion"> <meta name="msapplication-TileColor" content="#A5BED5"> <meta name="msapplication-TileImage" content="/img/favicon/mstile-144x144.png"> <meta name="msapplication-square70x70logo" content="/img/favicon/mstile-70x70.png"> <meta name="msapplication-square150x150logo" content="/img/favicon/mstile-150x150.png"> <meta name="msapplication-wide310x150logo" content="/img/favicon/mstile-310x150.png"> <meta name="msapplication-square310x310logo" content="/img/favicon/mstile-310x310.png"><script>var stdHash = "6da675cbcb3d25f050b05557349abc79", stdTicket = "082b9c9c4ae3624d";</script><script src="../../../js/user/local-stats.min.js?v=202205311700"></script><link href="../../../css/subjects-frontpage.min.css?v=202302031000" rel="stylesheet"></head><body class="public physics"> <noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-PZBWZ8J" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript> <div id="top-header"> <div class="wmap general hidden-sm hidden-xs subjects"> <div class="layout-wrapper"> <div class="container-fluid"> <a href=""> <img class="header-thinker" src="../../../img/header-thinker.svg"> </a> <h1> <a href="../../../physics.html"> IBDP Physics </a> <a href="https://inthinking.net" title="inthinking.net" class="inthinking-logo pull-right"> <img src="../../../img/header-logo.svg" style="height: 80px; width: auto;"> </a> </h1> <p class="slogan">InThinking Revision Sites for students</p> <p class="author">Website by <strong>Chris Hamper & Emma Mitchell</strong></p> <p class="updated">Updated 3 February 2023</p> </div> </div> </div> <nav id="public-topnav" class="navbar navbar-default"> <div class="container-fluid"> <div class="navbar-header"> <a class="navbar-brand hidden-md hidden-lg" href="../../../index.htm"> <img class="header-xs-thinker" src="../../../img/header-thinker.svg"> </a> <button type="button" class="collapsed navbar-toggle" data-toggle="collapse" data-target="#subject-navbar-collapse" aria-expanded="false"> <span class="sr-only">Toggle navigation</span> <i class="fa fa-fw fa-2x fa-user"></i> </button> <div class="brand hidden-lg hidden-md hidden-sm"> <a class="brand-xs" href="../../../physics.html"> <strong class="title" style="white-space: nowrap;font-size: 18px;">Physics</strong> </a> </div> </div> <div class="collapse navbar-collapse" id="subject-navbar-collapse"> <ul class="nav navbar-bar navbar-userbox hidden-md hidden-lg"><li class="dropdown"><a href="#" class="dropdown-toggle" data-toggle="dropdown"><i class="fa fa-fw fa-lg fa-user-circle" style="margin-right: 5px;"></i><span style="font-size: 16px;"></span></a><ul class="dropdown-menu"><li class="dropdown-submenu"><a class="dropdown-toggle" href="#" data-toggle="dropdown"><i class="fa fa-fw fa-globe"></i> Subjects</a><ul class="dropdown-menu"><li></li><li class=""><a href="../../../biology.html">DP Biology</a></li><li class=""><a href="../../../chemistry.html">DP Chemistry</a></li><li class=""><a href="../../../englishalanglit.html">DP English A: Language & Literature</a></li><li class=""><a href="../../../mathsanalysis.html">DP Maths: Analysis & Approaches</a></li><li class=""><a href="../../../mathsapplications.html">DP Maths: Applications & Interpretations SL</a></li><li class="active"><a href="../../../physics.html"><i class="fa fa-caret-right"></i> DP Physics</a></li><li class=""><a href="../../../spanishb.html">DP Spanish B</a></li></ul></li><li class="menu-item"><a href="../../../user.html"><i class="fa fa-fw fa-dashboard"></i> Dashboard</a></li><li class="menu-item"><a href="../../../user/profile.html"><i class="fa fa-fw fa-cog"></i> My profile</a></li><li class="menu-item"><a href="../../../user/messages.html"><i class="fa fa-fw fa-envelope"></i> Messages</a></li><li class="menu-item hidden-md hidden-lg mt-xs-3"><a href="../../../index.htm?logout=1" class="btn btn-primary btn-xs-block"><i class="fa fa-fw fa-lg fa-power-off text-danger"></i>Log out</a></li></ul></li></ul> <ul class="nav navbar-bar"><li class=""><a class="home" href="../../../physics.html"><i class="fa fa-fw fa-home"></i> Home</a></li><li class=""><a class="topics" href="#"><i class="fa fa-fw fa-th-large"></i> Topics</a></li><li class=""><a class="favorites" href="../../../physics.html"><i class="fa fa-fw fa-star"></i> My favorites</a></li><li class=""><a class="" href="../../flashcards.html"><i class="fa fa-fw fa-bolt"></i> Flashcards</a></li><li class=""><a class="qbank" href="../../test-your-knowledge.html"><i class="fa fa-fw fa-question"></i> Question bank</a></li><li class=""><a class="networks" href="../../networks.html"><i class="fa fa-fw fa-graduation-cap"></i> Virtual tutor</a></li><li class=""><a class="" href="../../blogs.html"><i class="fa fa-fw fa-paperclip"></i> Blog</a></li><li class=""><a class="sitemap" href="../../sitemap.html"><i class="fa fa-fw fa-sitemap"></i> Sitemap</a></li><li class=""><a class="activity" href="../../../physics.html"><i class="fa fa-fw fa-calendar-check-o"></i> My activity</a></li></ul> <ul class="nav navbar-bar navbar-right"> <li> <form class="navbar-form hidden-md hidden-lg" role="search" method="get" action="physics/search"> <div class="input-group"> <input class="form-control nav-search" name="glob" type="search" placeholder="Search..."> <span class="input-group-btn"> <button type="submit" class="btn bg-blue"> <i class="fa fa-search"> </i> </button> </span> </div> </form> <a href="#" class="toggle-menu-search hidden-sm hidden-xs" data-toggle="dropdown"> <i class="fa fa-lg fa-search"></i> </a> </li></ul> </div> </div></nav><nav id="nav-menu-search" class="shadow-bottom hidden-sm hidden-xs" style="display: none;"> <div class="container-fluid"> <form class="" role="search" method="get" action="physics/search"> <input class="form-control nav-search" name="glob" type="search" placeholder="Search Physics..."> <button class="btn btn-sm btn-primary" type="submit"> Search </button> </form> </div></nav><div class="modal fade" tabindex="-1" role="dialog" id="modal-mini-login"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-body"> <button aria-hidden="true" data-dismiss="modal" class="close hidden-xs login-button-close" type="button">×</button> <form method="post"> <div class="form-group"> <input name="user-email" class="form-control" type="text" placeholder="Email"> </div> <div class="form-group"> <input name="user-password" class="form-control" type="password" placeholder="Password"> <input name="user-fp" class="fp" value="d8c893da5db7501669ffeeac46273ba6" type="hidden"> </div> <div class="form-group"> <a href="../../../reset-password.html" class="reset-password" style="font-weight: normal;"> Forgot your password? </a> </div> <div class="form-group"> <button type="submit" name="submit-login" value="1" class="btn btn-primary btn-block text-center"> <i class="fa fa-user fa-fw"></i> Log in </button> </div> </form> </div> </div> </div></div></div><div class="modal fade" id="show-topics" tabindex="-1" role="dialog"><div id="dialog-topics" class="modal-dialog modal-dialog-topics"><div class="modal-content"><div class="modal-body modal-body-topics"><div id="new-frontpage-toplevels-topics" class="frontpage-box"><div class="row"><div class="col-md-4 col-sm-4"><div class="item"><a href="../3015/free-access-weekend.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Free Access Weekend!</h3></div><div class="body"><div class="cropper" style="background-image: url('../../free.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../814/start-here.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Start here</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/getting-started/getting-started.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../819/revision-tips.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Revision tips</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/getting-started/exam-tips.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../2885/exam-questions.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Exam questions</h3></div><div class="body"><div class="cropper" style="background-image: url('../../practice-papers/flash-front.png'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../204/basics.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Basics</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/basics/basics.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../217/mechanics.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Mechanics</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/mechanics/mechanics.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../252/thermal.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Thermal</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/thermal/thermal.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../444/oscillations-and-waves.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Oscillations & waves</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/waves/waves.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../445/electricity-and-magnetism.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Electricity & magnetism</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/electricity/electricity.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../443/circular-motion-and-gravity.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Circular motion & gravity</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/circular-motion/circular.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../354/atomic-nuclear-and-particles.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Atomic, nuclear & particles</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/atomic/atomic.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../446/energy-production.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Energy production</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/energy-production/energy.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../848/options.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Options</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/astro/options.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../823/astrophysics.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Astrophysics</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/astro/black-hole.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../849/engineering.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Engineering</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/engineering/lift-off.jpg'); height: 10vw;"></div></div></a></div></div></div></div></div></div></div></div><div class="container-fluid shadow-ith"><div class="row frontpage"> <div class="col-md-3" id="left-column"> <p class="visible-xs-block"></p><div class="dropdown user-menu hidden-xs" style="margin-bottom: 20px;"> <button type="button" class="btn btn-default dropdown-toggle" data-toggle="dropdown" style="border-radius: 0; padding: 6px 18px;"> <i class="fa fa-fw fa-user-circle"></i> <small><i class="fa fa-caret-down"></i></small> </button> <ul class="dropdown-menu"> <li class="dropdown-submenu"><a href="#"><i class="fa fa-fw fa-globe"></i> Subjects</a><ul id="user-subjects-menu" class="dropdown-menu"><li></li><li class=""><a href="../../../biology.html">DP Biology</a></li><li class=""><a href="../../../chemistry.html">DP Chemistry</a></li><li class=""><a href="../../../englishalanglit.html">DP English A: Language & Literature</a></li><li class=""><a href="../../../mathsanalysis.html">DP Maths: Analysis & Approaches</a></li><li class=""><a href="../../../mathsapplications.html">DP Maths: Applications & Interpretations SL</a></li><li class="active"><a href="../../../physics.html"><i class="fa fa-caret-right"></i> DP Physics</a></li><li class=""><a href="../../../spanishb.html">DP Spanish B</a></li></ul></li><li class="divider"></li><li><a href="../../../user.html"><i class="fa fa-fw fa-dashboard"></i> Dashboard</a></li><li><a href="../../../user/profile.html"><i class="fa fa-fw fa-cog"></i> My profile</a></li><li><a href="../../../user/messages.html"><i class="fa fa-fw fa-envelope"></i> Messages</a></li> <li class="divider"></li> <li> <a href="../../../index.htm?logout=1"> <i class="fa fa-fw fa-power-off"></i> Log out </a> </li> </ul></div> <div id="side-nav"><h4 class="side-nav-title dropdown"><a href="../354/atomic-nuclear-and-particles.html" class="dropdown-toggle toplevel-dropdown" data-toggle="dropdown"><i class="fa fa-ellipsis-v"></i></a> <a href="../354/atomic-nuclear-and-particles.html">Atomic, nuclear and particles</a><ul class="dropdown-menu"><li><a href="../../../physics.html" style="padding-left: 5px; border-bottom: solid 1px #ddd"><i class="fa fa-fw fa-home"></i> Home</a></li><li><a href="../3015/free-access-weekend.html"><i class="fa fa-fw fa-caret-right"></i> Free Access Weekend!</a></li><li><a href="../814/start-here.html"><i class="fa fa-fw fa-caret-right"></i> Start here</a></li><li><a href="../819/revision-tips.html"><i class="fa fa-fw fa-caret-right"></i> Revision tips</a></li><li><a href="../2885/exam-questions.html"><i class="fa fa-fw fa-caret-right"></i> Exam questions</a></li><li><a href="../204/basics.html"><i class="fa fa-fw fa-caret-right"></i> Basics</a></li><li><a href="../217/mechanics.html"><i class="fa fa-fw fa-caret-right"></i> Mechanics</a></li><li><a href="../252/thermal.html"><i class="fa fa-fw fa-caret-right"></i> Thermal</a></li><li><a href="../444/oscillations-and-waves.html"><i class="fa fa-fw fa-caret-right"></i> Oscillations and waves</a></li><li><a href="../445/electricity-and-magnetism.html"><i class="fa fa-fw fa-caret-right"></i> Electricity and magnetism</a></li><li><a href="../443/circular-motion-and-gravity.html"><i class="fa fa-fw fa-caret-right"></i> Circular motion and gravity</a></li><li><a href="../446/energy-production.html"><i class="fa fa-fw fa-caret-right"></i> Energy production</a></li><li><a href="../848/options.html"><i class="fa fa-fw fa-caret-right"></i> Options</a></li><li><a href="../823/astrophysics.html"><i class="fa fa-fw fa-caret-right"></i> Astrophysics</a></li><li><a href="../849/engineering.html"><i class="fa fa-fw fa-caret-right"></i> Engineering</a></li></ul><div class="pull-right"><a class="sidenav-expand" title="Expand all" href="#"><i class="fa fa-plus-circle"></i></a> <a class="sidenav-compress" title="Compress all" href="#"><i class="fa fa-minus-circle"></i></a></div></h4><ul class="side-nav level-0"><li class=""><label style="padding-left: 0px"><a class="expander" href="#" style="font-size: .9em"><i class="fa fa-fw fa-caret-right"></i></a><a href="../364/atomic-models.html">Atomic models</a></label><ul class="side-nav level-1"><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../366/rutherford-model.html">Rutherford model</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../367/electron-energy-levels.html">Electron energy levels</a></label></li></ul></li><li class=""><label style="padding-left: 0px"><a class="expander" href="#" style="font-size: .9em"><i class="fa fa-fw fa-caret-right"></i></a><a href="../368/nuclear-physics.html">Nuclear physics</a></label><ul class="side-nav level-1"><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../369/nuclear-stability-and-binding-energy.html">Nuclear stability and binding energy</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../408/fusion.html">Fusion</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../435/fission.html">Fission</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../370/radioactivity.html">Radioactivity</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../1152/ahl-nuclear-radius.html">AHL Nuclear radius</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../393/ahl-nuclear-decay.html">AHL Nuclear decay</a></label></li></ul></li><li class=""><label style="padding-left: 0px"><a class="expander" href="#" style="font-size: .9em"><i class="fa fa-fw fa-caret-right"></i></a><a href="../434/structure-of-matter.html">Structure of matter</a></label><ul class="side-nav level-1"><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../439/particle-properties.html">Particle properties</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../440/particle-interactions.html">Particle interactions</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../441/quarks.html">Quarks</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../442/the-standard-model.html">The Standard Model</a></label></li></ul></li><li class="expanded parent"><label style="padding-left: 0px"><a class="expander" href="#" style="font-size: .9em"><i class="fa fa-fw fa-caret-right"></i></a><a href="../1132/ahl-quantum.html">AHL Quantum</a></label><ul class="side-nav level-1"><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../1135/photoelectric-effect-and-photons.html">Photoelectric effect and photons</a></label></li><li class="expanded parent selected"><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="wave-particle-duality.html">Wave particle duality</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../1133/atomic-models.html">Atomic models</a></label></li></ul></li></ul></div> <div class="hidden-xs hidden-sm"> <button class="btn btn-default btn-block text-xs-center" data-toggle="modal" data-target="#modal-feedback" style="margin-bottom: 10px"><i class="fa fa-send"></i> Feedback</button> </div> </div> <div class="col-md-9" id="main-column"> <h1 class="page_title"> Wave particle duality <a href="#" class="mark-page-favorite pull-right" data-pid="1134" title="Mark as favorite" onclick="return false;"><i class="fa fa-star-o"></i></a> </h1> <ol class="breadcrumb"> <li><a href="../../../physics.html"><i class="fa fa-home"></i></a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../354/atomic-nuclear-and-particles.html">Atomic, nuclear and particles</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../1132/ahl-quantum.html">AHL Quantum</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">Wave particle duality</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 20 minutes"><i class="fa fa-clock-o"></i> 20'</span> </ol> <article id="main-article"> <p><img alt="" src="../../quantum/quantum.jpg" style="float: left; width: 250px; height: 133px;">The evidence from the photoelectric effect, Compton scattering and pair production that electromagnetic radiation can have quantum properties indicates that matter may have wave properties. Here we will consider this possibility.</p> <hr class="hidden-separator"> <div class="panel panel-turquoise panel-has-colored-body"> <div class="panel-heading"> <div> <p>Key Concepts</p> </div> </div> <div class="panel-body"> <div> <div class="panel panel-has-colored-body panel-has-border panel-turquoise"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Electron diffraction</p> </div> </div> <div class="panel-body"> <div> <p>When electrons are passed through a thin lattice and onto a phosphorescence screen, rings of differing intensities are produced. This phenomenon can only be explained by the diffraction and interference of the electrons and, just as we do for light, we can calculate an equivalent wavelength for the electrons.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/376909702"></iframe></div> <p>A simplified approach is to consider what would happen if electrons passed through double slits.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/376909805"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-turquoise panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>De Broglie wavelength</p> </div> </div> <div class="panel-body"> <div> <p>Electrons can be thought of, not as small spheres, but as a wave function that gives probability distribution of finding the particle in a region of space. The de Broglie wavelength of matter can be calculated as follows:</p> <p style="text-align: center;"><span class="math-tex">\(\lambda={h\over p}\)</span></p> <ul> <li><span class="math-tex">\(\lambda\)</span> is the de Broglie wavelength (m)</li> <li><span class="math-tex">\(h\)</span> is Planck's constant (Js)</li> <li><span class="math-tex">\(p\)</span> is the momentum of the particle (<span class="math-tex">\(=mv\)</span> in kgms<sup>-1</sup>)</li> </ul> <p>This equation helps to explain why large particles do not exhibit wave properties. A human walking through a door, for example, has a de Broglie wavelength in the order <span class="math-tex">\({10^{-33}\over 10^2}=10^{-35}\)</span> m, far smaller than the gap. </p> <p>On the other hand, as an electron approaches a slit, the preceding wave function maps out the probable positions and it is diffracted. The combination of many electrons will forge the maxima in the diffraction pattern.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/376909729"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Essentials</p> </div> </div> <div class="panel-body"> <div> <div class="panel panel-has-colored-body panel-has-border panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Schrödingers model</p> </div> </div> <div class="panel-body"> <div> <p>The probability of an electron being in a particular position at a particular time is defined by Schrödinger as the square of the amplitude of the wave function, where the wave function varies with position and time. The wave function is denoted as <span class="math-tex">\(\Psi\)</span>.</p> <p>The probability of an electron being at a given radius within a given volume is given by:</p> <p style="text-align: center;"><span class="math-tex">\(P(r)=|\Psi|^2\Delta V\)</span></p> <ul> <li><span class="math-tex">\(P(r)\)</span> is the probability of the electron at a given radius</li> <li><span class="math-tex">\(|\Psi|\)</span> is the magnitude of the wave equation</li> <li><span class="math-tex">\(\Delta V\)</span> is the volume</li> </ul> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/376910008"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Heisenberg's uncertainty principle</p> </div> </div> <div class="panel-body"> <div> <p>To identify the onward path of a particle, we must know its position and momentum. We have two options to make such observations for electrons, both of which involve passing electrons through a narrow opening:</p> <ul> <li>To allow all electrons in a parallel beam to pass comfortably through a wide slit. We can be sure of the onward direction and momentum, but the range of positions is large and uncertain.</li> <li>To constrain the beam of electrons to within a narrow slit. For the electrons that happen to pass through the slit, we can be sure of their position, but the consequential diffraction effect makes certainty of the path (and, hence, momentum) impossible.</li> </ul> <p>The Heisenberg uncertainty principle describes the inherent impossibility of measuring both momentum and position with certainty as an equation:</p> <p style="text-align: center;"><span class="math-tex">\(\Delta p \Delta x \geq{h\over 4\pi}\)</span></p> <ul> <li><span class="math-tex">\(\Delta p\)</span> is uncertainty in momentum (kgms<sup>-1</sup>)</li> <li><span class="math-tex">\(\Delta x\)</span> is uncertainty in position (m)</li> <li><span class="math-tex">\(h\)</span> is Planck's constant (Js)</li> </ul> <p>A similar relationship can be stated for energy and time:</p> <p style="text-align: center;"><span class="math-tex">\(\Delta E\Delta t\geq{h\over 4\pi}\)</span></p> <ul> <li><span class="math-tex">\(\Delta E\)</span> is uncertainty in energy (J)</li> <li><span class="math-tex">\(\Delta t\)</span> is uncertainty in time (s)</li> </ul> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/376909828"></iframe></div> <p>We can use the uncertainty principle to estimate the energy of the ground state of an atom, the impossibility of an electron existing within a nucleus, and the lifetime of an electron in an excited energy state. In each case we need to assume that an uncertainty is a similar size to a quantity.</p> <h4>Ground state</h4> <p>The ground state of a hydrogen atom sees the electron in the lowest energy level (<span class="math-tex">\(n=1\)</span>). Substituting the radius of the first energy level (<span class="math-tex">\(0.529 \text{ }Å=0.529\times 10^{-10} \text{ m}\)</span>) as <span class="math-tex">\(\Delta x\)</span>, we can find <span class="math-tex">\(\Delta p\)</span>:</p> <p style="text-align: center;"><span class="math-tex">\(\Delta p \Delta x \geq{h\over 4\pi}\)</span></p> <p style="text-align: center;"><span class="math-tex">\(\Delta p\geq{6.63\times10^{-34}\over 4\pi 0.529\times10^{-10}}\)</span></p> <p style="text-align: center;"><span class="math-tex">\(\Delta p\geq10^{-24}\text{ kg ms}^{-1}\)</span></p> <p>Since the ground state has no angular momentum, all momentum is linear. Therefore, we can convert this into kinetic energy:</p> <p style="text-align: center;"><span class="math-tex">\(E_k={1\over 2}mv^2={1\over 2}{p^2\over m}\)</span></p> <p style="text-align: center;"><span class="math-tex">\(E_k={1\over 2}{(10^{-24})^2\over 9.11\times 10^{-31}}\approx5\times 10^{-19}\text{ J}\approx3\text{ eV}\)</span></p> <p>Note that the electron also has potential energy, but this order of magnitude is accurate.</p> <h4>Electron in the nucleus</h4> <p>To consider the probability of an electron existing in the nucleus, we need to substitute the radius of the nucleus as <span class="math-tex">\(\Delta x\)</span> to find <span class="math-tex">\(\Delta p\)</span>. In the case of hydrogren, the nucleon number is 1 (<a href="../1152/ahl-nuclear-radius.html" title="AHL Nuclear radius">Nuclear radius</a>) , so <span class="math-tex">\(R_0\)</span> is substituted:</p> <p style="text-align: center;"><span class="math-tex">\(\Delta p \Delta x \geq{h\over 4\pi}\)</span></p> <p style="text-align: center;"><span class="math-tex">\(\Delta p\geq{6.63\times10^{-34}\over 4\pi 1.2\times10^{-15}}\)</span></p> <p style="text-align: center;"><span class="math-tex">\(\Delta p\geq4.4\times 10^{-20}\text{ kg ms}^{-1}\)</span></p> <p>Now estimating the consequential velocity of the electron reveals the impossibility of this position:</p> <p style="text-align: center;"><span class="math-tex">\(v={p\over m}\)</span></p> <p style="text-align: center;"><span class="math-tex">\(v={4.4\times 10^{-20}\over 9.11\times 10^{-31}}\approx 5\times 10^{10}\text{ ms}^{-1}\)</span></p> <p>The order of magnitude of the velocity is larger than the speed of light.</p> <p>An atom will not collapse for the same reason; the electron would be confined into too small a space.</p> <h4>Excited energy states</h4> <p>To find the lifetime of an electron in a particular energy state, we use the second of the above Heisenberg uncertainty principle inequalities. For example, let us consider the ground state:</p> <p style="text-align: center;"><span class="math-tex">\(\Delta E\Delta t\geq{h\over 4\pi}\)</span></p> <p style="text-align: center;"><span class="math-tex">\(\Delta t\geq{6.63\times 10^{-34}\over 4\pi(13.6\times 1.6\times 10^{-19})}\)</span></p> <p style="text-align: center;"><span class="math-tex">\(\Delta t\geq2.4\times 10^{-17}\text{ s}\)</span></p> <p>As the energy state increases, the likely time decreases. An electron could remain in the ground state forever, but this calculation provides an illustration of how you might estimate the times for other energy states.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/388879909"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> </div> </div> </div> <div class="panel panel-has-colored-body panel-green"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Test Yourself</p> </div> </div> <div class="panel-body"> <div> <p><em>Use quizzes to practise application of theory.</em></p> <br><a class="btn btn-primary btn-block text-center" data-toggle="modal" href="#15e6fff2"><i class="fa fa-play"></i> START QUIZ!</a><div class="modal fade modal-slide-quiz" id="15e6fff2"> <div class="modal-dialog" style="width: 95vw; max-width: 960px"> <div class="modal-content"> <div class="modal-header slide-quiz-title"> <h4 class="modal-title" style="width: 100%;"> Wave nature of matter <strong class="q-number pull-right"> <span class="counter">1</span>/<span class="total">1</span> </strong> </h4> </div> <div class="modal-body p-xs-3"> <div class="slide-quiz" data-stats="6-359-1134" style="opacity: 0"> <div class="exercise shadow-bottom"><div class="q-question"><p>The diagram represents the electron gun in an electron diffraction experiment.</p><p style="text-align: center;"><img alt="" height="216" src="../../screenshot-2019-10-19-at-08.37.54.png" width="241"></p><p>The ratio <span class="math-tex">\(V_2\over V_1\)</span> is approximately:</p></div><div class="q-answer"><p><label class="radio"> <input class="c" type="radio"> <span>1000</span></label> </p><p><label class="radio"> <input type="radio"> <span>0.1</span></label> </p><p><label class="radio"> <input type="radio"> <span>10</span></label> </p><p><label class="radio"> <input type="radio"> <span>0.001</span></label> </p></div><div class="q-explanation"><p><span class="math-tex">\(V_1\)</span> causes current to flow in the filament resulting in an increase in temperature. This requires about 5 V.</p><p><span class="math-tex">\(V_2\)</span> is the potential difference for acceleration, which is in the order of kV.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The diagram represents the electron gun in an electron diffraction experiment.</p><p style="text-align: center;"><img alt="" height="216" src="../../screenshot-2019-10-19-at-08.37.54.png" width="241"></p><p>If <span class="math-tex">\(V_1 = 10\text{ V}\)</span> and <span class="math-tex">\(V_2 = 1\text{ kV}\)</span>, the kinetic energy of electrons will be:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>10 eV</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>1 keV</span></label> </p><p><label class="radio"> <input type="radio"> <span>10 keV</span></label> </p><p><label class="radio"> <input type="radio"> <span>110 eV</span></label> </p></div><div class="q-explanation"><p>Kinetic energy in eV is numerically the same as the accelerating potential difference in V.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The spacing of atoms in a thin film of graphite is approximately:</p></div><div class="q-answer"><p><label class="radio"> <input class="c" type="radio"> <span>0.1 nm</span></label> </p><p><label class="radio"> <input type="radio"> <span>0.1 mm</span></label> </p><p><label class="radio"> <input type="radio"> <span>0.1 pm</span></label> </p><p><label class="radio"> <input type="radio"> <span>0.1 μm</span></label> </p></div><div class="q-explanation"><p>The order of magnitude of atomic spacing is 10<sup>-10</sup> m, 1 Å</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The de Broglie wavelength of electrons with 1 keV kinetic energy is approximately the same as the wavelength of:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>Microwaves</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>X-rays</span></label> </p><p><label class="radio"> <input type="radio"> <span>Visible light</span></label> </p><p><label class="radio"> <input type="radio"> <span>UV light</span></label> </p></div><div class="q-explanation"><p>Both are in the region of 10<sup>-10</sup> m</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>What is the momentum of electrons with de Broglie wavelength 10<sup>-10</sup> m?</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>6.6 x 10<sup>-34</sup> Ns</span></label> </p><p><label class="radio"> <input type="radio"> <span>1.6 x 10<sup>-29</sup> Ns</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>6.6 x 10<sup>-24</sup> Ns</span></label> </p><p><label class="radio"> <input type="radio"> <span>1.6 x 10<sup>-9</sup> Ns</span></label> </p></div><div class="q-explanation"><p><span class="math-tex">\(p = {h\over λ}\)</span></p><p><span class="math-tex">\(h = 6.6 \times 10^{-34}\text{ Js}\)</span></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>Which of the following statements is the most correct?</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>Electrons are packets of waves.</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>Electrons are particles.</span></label> </p><p><label class="radio"> <input type="radio"> <span>Electrons are sometimes waves, sometimes particles.</span></label> </p><p><label class="radio"> <input type="radio"> <span>Electrons are waves and particles.</span></label> </p></div><div class="q-explanation"><p>Electrons are particles whose position is given by a wave equation. This one is certainly a good discussion starter; it's a nature of science question.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>A particle of mass <span class="math-tex">\(m\)</span> and charge <span class="math-tex">\(q\)</span> is accelerated through a potential difference <span class="math-tex">\(V\)</span>.</p><p>The momentum of the particle is:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(\sqrt{mVq\over 2}\)</span></span></label></p><p><label class="radio"> <input class="c" type="radio"> <span><span class="math-tex">\(\sqrt{2mVq}\)</span></span></label></p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(\sqrt{2Vq\over m}\)</span></span></label></p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(\sqrt{2V\over qm}\)</span></span></label></p></div><div class="q-explanation"><p><span class="math-tex">\(Vq = {1\over2}mv^2={1\over 2}{p^2\over m}\)</span></p><p><span class="math-tex">\(p=\sqrt{2mVq} \)</span></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>An electron is put into a cubic box of side 10<sup>-10</sup> m.</p><p>The minimum uncertainty in its momentum is in the order of:</p></div><div class="q-answer"><p><label class="radio"> <input class="c" type="radio"> <span>10<sup>-25</sup> Ns</span></label> </p><p><label class="radio"> <input type="radio"> <span>10<sup>-10</sup> Ns</span></label> </p><p><label class="radio"> <input type="radio"> <span>10<sup>-20</sup> Ns</span></label> </p><p><label class="radio"> <input type="radio"> <span>10<sup>-34</sup> Ns</span></label> </p></div><div class="q-explanation"><p><span class="math-tex">\(ΔxΔp = {h\over 4π} ≈ 10^{-35}\)</span></p><p>We know electron is in the box but not exactly where within, so <span class="math-tex">\(Δx = 10^{-10}\text{ m}\)</span><sup> </sup></p><p><span class="math-tex">\(\Delta p=10^{-35}\div 10^{-10}\)</span></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The image represents a wave packet that defines the position of an electron.</p><p style="text-align: center;"><img alt="" src="../../wavepart4.png" style="width: 537px; height: 130px;"></p><p>The electron is most likely to be in position:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>A</span></label> </p><p><label class="radio"> <input type="radio"> <span>B</span></label> </p><p><label class="radio"> <input type="radio"> <span>D</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>C</span></label> </p></div><div class="q-explanation"><p>The probability is given by amplitude<sup>2</sup>.</p><p>The amplitude is greatest in the middle even though the displacent at this time is zero.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>A shot gun fires thousands of small balls. When they leave the end of the gun the balls:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>continue in a straight line.</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>spread out due to the expansion of the surrounding gas.</span></label> </p><p><label class="radio"> <input type="radio"> <span>spread out due to diffraction.</span></label> </p><p><label class="radio"> <input type="radio"> <span>all have the same velocity.</span></label> </p></div><div class="q-explanation"><p>Small balls do not exhibit quantum effects.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div> </div> </div> <div class="modal-footer slide-quiz-actions"> <div class=""> <div class="pull-left pull-xs-none mb-xs-3"> <button class="btn btn-default d-xs-none btn-prev"> <i class="fa fa-arrow-left"></i> Prev </button> </div> <div class="pull-right pull-xs-none"> <button class="btn btn-success btn-xs-block text-xs-center btn-results" style="display: none"> <i class="fa fa-bar-chart"></i> Check Results </button> <button class="btn btn-default d-xs-none btn-next"> Next <i class="fa fa-arrow-right"></i> </button> <button class="btn btn-default btn-xs-block text-xs-center btn-close" data-dismiss="modal" style="display: none"> Close </button> </div> </div> </div> </div> </div></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="page-container panel-self-assessment" data-id="1134"> <div class="panel-heading">MY PROGRESS</div> <div class="panel-body understanding-rate"> <div class="msg"></div> <label class="label-lg">Self-assessment</label><p>How much of <strong>Wave particle duality</strong> have you understood?</p><div class="slider-container text-center"><div id="self-assessment-slider" class="sib-slider self-assessment " data-value="1" data-percentage=""></div></div> <label class="label-lg">My notes</label> <textarea name="page-notes" class="form-control" rows="3" placeholder="Write your notes here..."></textarea> </div> <div class="panel-footer text-xs-center"> <span id="last-edited" class="mb-xs-3"> </span> <div class="actions mt-xs-3"> <button id="save-my-progress" type="button" class="btn btn-sm btn-primary text-center btn-xs-block"> <i class="fa fa-fw fa-floppy-o"></i> Save </button> </div> </div></div> <div id="modal-feedback" class="modal fade" tabindex="-1" role="dialog"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <h4 class="modal-title">Feedback</h4> <button type="button" class="close hidden-xs hidden-sm" data-dismiss="modal" aria-label="Close"> <span aria-hidden="true">×</span> </button> </div> <div class="modal-body"> <div class="errors"></div> <p><strong>Which of the following best describes your feedback?</strong></p> <form method="post" style="overflow: hidden"> <div class="form-group"> <div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Recommendation"> Recommend</label></div><div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Problem"> Report a problem</label></div><div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Improvement"> Suggest an improvement</label></div><div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Other"> Other</label></div> </div> <hr> <div class="row"> <div class="col-md-6"> <div class="form-group"> <label for="feedback-name">Name</label> <input type="text" class="form-control" name="feedback-name" placeholder="Name" value=" "> </div> </div> <div class="col-md-6"> <div class="form-group"> <label for="feedback-email">Email address</label> <input type="email" class="form-control" name="feedback-email" placeholder="Email" value="@airmail.cc"> </div> </div> </div> <div class="form-group"> <label for="feedback-comments">Comments</label> <textarea class="form-control" name="feedback-comments" style="resize: vertical;"></textarea> </div> <input type="hidden" name="feedback-ticket" value="082b9c9c4ae3624d"> <input type="hidden" name="feedback-url" value="https://studyib.net/physics/page/1134/wave-particle-duality"> <input type="hidden" name="feedback-subject" value="6"> <input type="hidden" name="feedback-subject-name" value="Physics"> <div class="pull-left"> </div> </form> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary btn-xs-block feedback-submit mb-xs-3 pull-right"> <i class="fa fa-send"></i> Send </button> <button type="button" class="btn btn-default btn-xs-block m-xs-0 pull-left" data-dismiss="modal"> Close </button> </div> </div> </div></div> </article> <hr class="hidden-md hidden-lg"> <div class="hidden-md hidden-lg mt-xs-3"> <button class="btn btn-default btn-block text-xs-center" data-toggle="modal" data-target="#modal-feedback" style="margin-bottom: 10px"><i class="fa fa-send"></i> Feedback</button> </div> </div> <input type="hidden" id="user-id" value="38342"></div><input id="ticket" type="hidden" value="082b9c9c4ae3624d"><input id="tzoffset" type="hidden" value="new"><input id="fp" class="fp" type="hidden" value=""></div><div id="std-footer"> <div class="wmap"> <div class="layout-wrapper"> <p> <a href="https://www.inthinking.net"> © <span id="footer-year"></span> <em>InThinking</em> <script>document.getElementById("footer-year").innerHTML = new Date().getFullYear();</script> </a> | <a target="_self" href="../../../about.html"> About us </a> | <a target="_self" href="../../../terms-and-conditions.html"> Legal </a> | <a target="_self" href="../../../contact.html"> Contact </a> </p> <p> <a class="social" target="_blank" href="https://twitter.com/#!/inthinker"> <img src="../../../img/social/twitter-square.svg"> Twitter </a> <a class="social" target="_blank" href="https://www.facebook.com/inthinking.net"> <img src="../../../img/social/facebook-square.svg"> Facebook </a> <a class="social" target="_blank" href="https://www.linkedin.com/profile/view?id=139741989"> <img src="../../../img/social/linkedin-square.svg"> LinkedIn </a> </p> </div> </div></div><script src="../../../js/jquery-1.11.3.min.js"></script><script src="../../../js/bootstrap.min.js"></script><script src="../../../js/jquery-fancybox/jquery.fancybox.min.js"></script><script>var pageId = 1134;</script><script type="text/javascript" src="../../../js/jqueryui/jquery-ui-custom.min.js"></script><script type="text/javascript" src="../../../js/jqueryui/jquery.ui.touch-punch.js"></script><script type="text/javascript" src="../../../js/std-quizzes-helpers.min.js?v=20220406"></script><script src="../../../ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script><script type="text/javascript" src="../../../js/slick-carousel/slick.min.js"></script><script type="text/javascript" src="../../../js/std-slide-quizzes.min.js?v=20220406"></script><script type="text/javascript" src="../../../js/jqueryui/jquery-ui.min.js"></script><script type="text/javascript" src="../../../js/jqueryui/jquery.ui.touch-punch.min.js"></script><script src="../../../js/user/page-my-progress.min.js?v=202211221000"></script><script>var sAJAX='/pages/subjects/activity/user-stats-page.php?t=082b9c9c4ae3624d&p=1134&s=6&x=844';var sData='k4iA6GSB03BgPm1yOUOrIxiA6GSB0bfq7Y9FwFiA6GSBPFAF7YcHEKvrZ0fREzP5PBSsSn9l7Yc4SYBmWY9lEVKsWYBrkzPRPHpsE3KeSYcH74P5k4iRE0EBWVOFwBRD00rRPnLsSYK4ZGcR74P5EncR739RPHaL6nfhWGcjWFP5PFPRPHpsSYlFwFi7Ibp1k0aj6ba7IbpsE3K7IDuyODf7IbSsSn987Yc4SYBmWY98EVKsWYBrkziv';var loopSecs = 30;var minSecsLog = 60;var lsKey = '6-83610-1134';</script><script src="../../../js/subjects/activity/user-stats-page.min.js?v=202205311700"></script><script src="../../../js/subjects/activity/my-favorites.min.js?v=20220610"></script><script src="../../../js/subjects/feedback.min.js?v=202211221000"></script><script>var sessionUpdateSecs = 300;</script><script type="text/javascript" src="../../../js/session-updater.js"></script><script>(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');ga('create', 'UA-98480796-3', 'auto');ga('send', 'pageview');</script><script src="../../../js/devicefp/devicefp.min.js"></script><script src="../../../js/jq-quickfit/jq-quickfit.min.js?v=20220201"></script><script src="../../../js/frontpage-subjects.min.js?v=202211161300"></script><script type="text/javascript" src="../../../js/studyib-jq.min.js?v=202211241300"></script><script type="text/javascript">$(document).ready(function(){ $('#trigger-modal-video-overview').click(function() { if( $('#modal-video-overview .modal-body iframe').attr('src').length == 0 ) { $('#modal-video-overview .modal-body iframe').attr('src', 'https://www.youtube.com/embed/hxxtdiLdTFk?rel=0'); } }); $('#modal-video-overview').on('hidden.bs.modal', function() { $('#modal-video-overview .modal-body iframe').attr('src', ''); }); });</script></body></html>