{"id":3540,"date":"2023-02-05T06:50:11","date_gmt":"2023-02-05T06:50:11","guid":{"rendered":"https:\/\/10thclass.deltapublications.in\/?page_id=3540"},"modified":"2024-12-18T14:35:30","modified_gmt":"2024-12-18T14:35:30","slug":"s-18-e-quantum-mechanical-model-of-an-atom","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/s-18-e-quantum-mechanical-model-of-an-atom\/","title":{"rendered":"S-18.e Quantum Mechanical Model Of An Atom"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Quantum Mechanical Model Of An Atom<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-f79afd6ea8b322268468366b8e5f7cc7\" style=\"color:#74008b\"><strong>Key Notes:<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<h4 class=\"wp-block-heading has-text-align-center has-text-color has-background has-link-color wp-elements-e654ec00c3dd5cc63782a68531c6ddad\" style=\"color:#000060;background-color:#dfc816\"><strong>Introduction<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Proposed by <strong>Erwin Schr\u00f6dinger<\/strong> in 1926.<\/li>\n\n\n\n<li>Describes the behavior of electrons in atoms using the principles of quantum mechanics.<\/li>\n\n\n\n<li>Replaced the earlier Bohr-Sommerfeld model by focusing on the wave-like nature of electrons.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-text-color has-background has-link-color wp-elements-37850e77e6b3a82eb3010cd92dccdf73\" style=\"color:#000060;background-color:#dfc816\"><strong>Main Features of the Quantum Mechanical Model<\/strong><\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Wave-Particle Duality of Electrons<\/strong>\n<ul class=\"wp-block-list\">\n<li>Electrons have both wave-like and particle-like behavior, as suggested by <strong>de Broglie<\/strong>.<\/li>\n\n\n\n<li>Electron paths cannot be precisely determined, only probabilities can be calculated.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Schr\u00f6dinger&#8217;s Wave Equation<\/strong>\n<ul class=\"wp-block-list\">\n<li>Describes the wave nature of electrons in an atom: <\/li>\n\n\n\n<li><strong>H^\u03c8=E\u03c8<\/strong>\n<ul class=\"wp-block-list\">\n<li>\u03c8: Wave function representing the probability amplitude of the electron.<\/li>\n\n\n\n<li>E: Energy of the electron.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Electron Cloud and Orbitals<\/strong>\n<ul class=\"wp-block-list\">\n<li>Electrons are found in regions called <strong>orbitals<\/strong>, not fixed orbits.<\/li>\n\n\n\n<li>Orbitals represent regions where the probability of finding an electron is maximum (electron cloud).<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Heisenberg\u2019s Uncertainty Principle<\/strong>\n<ul class=\"wp-block-list\">\n<li>Proposed by <strong>Werner Heisenberg<\/strong>:<br>It is impossible to determine both the exact position and momentum of an electron simultaneously. \u0394x\u22c5\u0394p\u2265h\/4\u03c0<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Quantum Numbers<\/strong>\n<ul class=\"wp-block-list\">\n<li>To describe an electron\u2019s position and energy, four quantum numbers are used:\n<ol class=\"wp-block-list\">\n<li><strong>Principal Quantum Number (n)<\/strong>: Determines the size and energy of the orbital.<\/li>\n\n\n\n<li><strong>Azimuthal Quantum Number (l)<\/strong>: Determines the shape of the orbital.<\/li>\n\n\n\n<li><strong>Magnetic Quantum Number (m\u2097)<\/strong>: Determines the orientation of the orbital.<\/li>\n\n\n\n<li><strong>Spin Quantum Number (msm_s)<\/strong>: Represents the spin of the electron ( +\u00bd  or -\u00bd).<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Shapes of Orbitals<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>s-orbitals<\/strong>: Spherical in shape.<\/li>\n\n\n\n<li><strong>p-orbitals<\/strong>: Dumbbell-shaped.<\/li>\n\n\n\n<li><strong>d-orbitals<\/strong>: Complex shapes.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-text-color has-background has-link-color wp-elements-a9503cebd82616a4f3edc73d85bc3d17\" style=\"color:#000060;background-color:#dfc816\"><strong>Advantages of the Quantum Mechanical Model<\/strong><\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Describes the complex behavior of multi-electron atoms.<\/li>\n\n\n\n<li>Explains the shapes and orientations of atomic orbitals.<\/li>\n\n\n\n<li>Predicts the chemical properties of elements more accurately.<\/li>\n\n\n\n<li>Incorporates the wave-like nature and probabilistic location of electrons.<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-text-color has-background has-link-color wp-elements-6258cc12cc620c4eda97bde596889ff9\" style=\"color:#000060;background-color:#dfc816\"><strong>Limitations of Earlier Models Overcome<\/strong><\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Bohr&#8217;s Model Limitations<\/strong>\n<ul class=\"wp-block-list\">\n<li>Fixed orbits replaced by probabilistic electron clouds.<\/li>\n\n\n\n<li>Applies to all atoms, not just hydrogen.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Bohr-Sommerfeld Limitations<\/strong>\n<ul class=\"wp-block-list\">\n<li>Relies on wave functions and does not require elliptical orbits.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-text-color has-background has-link-color wp-elements-22bedc0f140918b4ad0b42c5b76f6ee9\" style=\"color:#000060;background-color:#dfc816\"><strong>Key Concepts Explained by Quantum Mechanical Model<\/strong><\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Electronic Configuration<\/strong>\n<ul class=\"wp-block-list\">\n<li>Electrons occupy orbitals in a specific order based on the <strong>Aufbau Principle<\/strong>, <strong>Pauli Exclusion Principle<\/strong>, and <strong>Hund\u2019s Rule<\/strong>.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Periodic Table Structure<\/strong>\n<ul class=\"wp-block-list\">\n<li>Explains the arrangement of elements in the periodic table based on their electron configurations.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Chemical Bonding<\/strong>\n<ul class=\"wp-block-list\">\n<li>Helps predict how atoms form covalent or ionic bonds.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-text-color has-background has-link-color wp-elements-45a781bde535bc1e844cc47582bd570e\" style=\"color:#000060;background-color:#dfc816\"><strong>Limitations of Quantum Mechanical Model<\/strong><\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li>The wave function (\u03c8\\psi) does not have a direct physical meaning.<\/li>\n\n\n\n<li>Highly mathematical and abstract, making it difficult to visualize.<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-text-color has-background has-link-color wp-elements-7d5b98e33e8f775645d7b9c0b87e752b\" style=\"color:#000060;background-color:#dfc816\"> <strong>Comparison with Bohr&#8217;s Model<\/strong><\/h4>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Feature<\/th><th>Bohr&#8217;s Model<\/th><th>Quantum Mechanical Model<\/th><\/tr><\/thead><tbody><tr><td>Nature of Electron Path<\/td><td>Fixed circular orbits<\/td><td>Probabilistic regions (orbitals)<\/td><\/tr><tr><td>Applicability<\/td><td>Hydrogen-like atoms only<\/td><td>All atoms<\/td><\/tr><tr><td>Basis<\/td><td>Classical mechanics + quantum theory<\/td><td>Fully quantum mechanical<\/td><\/tr><tr><td>Uncertainty Principle<\/td><td>Not addressed<\/td><td>Included<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-text-color has-background has-link-color wp-elements-01d9be3d90cb10d4f3466edf52b5fd66\" style=\"color:#000060;background-color:#dfc816\"><strong>Conclusion<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The quantum mechanical model provides the most accurate and comprehensive description of atomic structure.<\/li>\n\n\n\n<li>It is the foundation of modern chemistry and physics.<\/li>\n<\/ul>\n\n\n\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color\" style=\"color:#d90000\"><strong>Let&#8217;s practice!<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/83084\/322\/950\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/03\/Worksheet-1-3-84.png\" alt=\"\" class=\"wp-image-5698\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/03\/Worksheet-1-3-84.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/03\/Worksheet-1-3-84-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/03\/Worksheet-1-3-84-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/81518\/010\/246\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/03\/Worksheet-1-1-2-83.png\" alt=\"\" class=\"wp-image-5699\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/03\/Worksheet-1-1-2-83.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/03\/Worksheet-1-1-2-83-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/03\/Worksheet-1-1-2-83-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Quantum Mechanical Model Of An Atom Key Notes: Introduction Main Features of the Quantum Mechanical Model Advantages of the Quantum Mechanical Model Limitations of Earlier Models Overcome Key Concepts Explained by Quantum Mechanical Model Limitations of Quantum Mechanical Model Comparison with Bohr&#8217;s Model Feature Bohr&#8217;s Model Quantum Mechanical Model Nature of Electron Path Fixed circular<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/s-18-e-quantum-mechanical-model-of-an-atom\/\">Continue reading <span class=\"screen-reader-text\">&#8220;S-18.e Quantum Mechanical Model Of An Atom&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-3540","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/3540","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=3540"}],"version-history":[{"count":12,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/3540\/revisions"}],"predecessor-version":[{"id":15415,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/3540\/revisions\/15415"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=3540"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}