{"id":32569,"date":"2025-06-22T15:39:22","date_gmt":"2025-06-22T15:39:22","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=32569"},"modified":"2025-06-22T15:39:23","modified_gmt":"2025-06-22T15:39:23","slug":"draw-the-3pz-3dxy-3dx2-y2-and-3dz2-atomic-orbitals-in-the-correct-coordinate-system-and-give-n-and-l-quantum-numbers","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/draw-the-3pz-3dxy-3dx2-y2-and-3dz2-atomic-orbitals-in-the-correct-coordinate-system-and-give-n-and-l-quantum-numbers\/","title":{"rendered":"Draw the 3pz, 3dxy, 3dx2-y2, and 3dz2\u00a0atomic orbitals in the correct coordinate system and give n and l quantum numbers"},"content":{"rendered":"\n<pre id=\"preorder-ask-header-text\" class=\"wp-block-preformatted\">Draw the 3pz, 3dxy, 3dx2-y2, and 3dz2\u00a0atomic orbitals in the correct coordinate system and give n and l quantum numbers. Label any nodes.<\/pre>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Correct Answer:<\/h3>\n\n\n\n<p><strong>Orbitals and Quantum Numbers:<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>3pz orbital<\/strong>\n<ul class=\"wp-block-list\">\n<li>Principal quantum number: <strong>n = 3<\/strong><\/li>\n\n\n\n<li>Angular momentum quantum number: <strong>l = 1<\/strong><\/li>\n\n\n\n<li>Shape: Dumbbell aligned along the <strong>z-axis<\/strong><\/li>\n\n\n\n<li>One angular node (a nodal plane at the <strong>xy-plane<\/strong>)<\/li>\n\n\n\n<li>Radial node: 1 radial node<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>3dxy orbital<\/strong>\n<ul class=\"wp-block-list\">\n<li>n = 3<\/li>\n\n\n\n<li>l = 2<\/li>\n\n\n\n<li>Shape: Cloverleaf with lobes between x- and y-axes<\/li>\n\n\n\n<li>Two angular nodes (along the <strong>x<\/strong> and <strong>y<\/strong> axes)<\/li>\n\n\n\n<li>Radial node: 1 radial node<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>3dx\u00b2\u2212y\u00b2 orbital<\/strong>\n<ul class=\"wp-block-list\">\n<li>n = 3<\/li>\n\n\n\n<li>l = 2<\/li>\n\n\n\n<li>Shape: Cloverleaf with lobes along the <strong>x<\/strong> and <strong>y<\/strong> axes<\/li>\n\n\n\n<li>Angular nodes: Planes between the axes (e.g. x = y and x = \u2212y)<\/li>\n\n\n\n<li>Radial node: 1 radial node<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>3dz\u00b2 orbital<\/strong>\n<ul class=\"wp-block-list\">\n<li>n = 3<\/li>\n\n\n\n<li>l = 2<\/li>\n\n\n\n<li>Shape: Dumbbell along z-axis with a donut-shaped ring in the xy-plane<\/li>\n\n\n\n<li>Angular node: Cone-like regions between lobes<\/li>\n\n\n\n<li>Radial node: 1 radial node<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Sketch (Use Standard x, y, z 3D axes):<\/h3>\n\n\n\n<p><strong>[Not able to draw in plain text, but here&#8217;s a description to guide the sketch]<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>3pz<\/strong> orbital has two lobes above and below the xy-plane along the z-axis, separated by a planar node at z = 0.<\/li>\n\n\n\n<li>The <strong>3dxy<\/strong> orbital has four lobes between the x and y axes (at 45\u00b0, like NE, NW, SE, SW directions).<\/li>\n\n\n\n<li>The <strong>3dx\u00b2\u2212y\u00b2<\/strong> orbital has four lobes aligned with the x and y axes (positive and negative directions), shaped like a four-leaf clover.<\/li>\n\n\n\n<li>The <strong>3dz\u00b2<\/strong> orbital has two lobes along the z-axis with a torus-shaped ring in the xy-plane, around the nucleus.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>Atomic orbitals describe regions in space where there is a high probability of finding an electron. These orbitals are defined by quantum numbers: the principal quantum number (<strong>n<\/strong>) determines the energy level and size, while the angular momentum quantum number (<strong>l<\/strong>) defines the orbital\u2019s shape.<\/p>\n\n\n\n<p>For the <strong>3pz orbital<\/strong>, <strong>n = 3<\/strong> and <strong>l = 1<\/strong>. The &#8220;p&#8221; orbitals are dumbbell-shaped, and the &#8220;z&#8221; subscript shows orientation along the z-axis. The 3pz orbital has one angular node, a planar region at the xy-plane where the probability of finding the electron is zero. In addition, because n = 3, it has one radial node where the probability also drops to zero at a certain radius.<\/p>\n\n\n\n<p>The <strong>3d orbitals<\/strong> have <strong>l = 2<\/strong>, and with n = 3, they also have one radial node. The <strong>3dxy orbital<\/strong> lies in the xy-plane with lobes between the x and y axes, and nodes along both axes. The <strong>3dx\u00b2\u2212y\u00b2 orbital<\/strong> has lobes aligned directly along the x and y axes, and its angular nodes lie between these directions. The <strong>3dz\u00b2 orbital<\/strong> is distinct: it consists of two elongated lobes along the z-axis with a donut-shaped ring in the xy-plane, making it the most symmetric among d orbitals.<\/p>\n\n\n\n<p>Nodes are key features. <strong>Angular nodes<\/strong> are planes or cones where electron probability is zero due to the shape of the orbital, and <strong>radial nodes<\/strong> occur at specific distances from the nucleus due to the wavefunction&#8217;s radial part. Understanding these orbitals is essential for grasping chemical bonding and electron configurations.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"852\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-408.jpeg\" alt=\"\" class=\"wp-image-32570\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-408.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-408-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-408-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Draw the 3pz, 3dxy, 3dx2-y2, and 3dz2\u00a0atomic orbitals in the correct coordinate system and give n and l quantum numbers. Label any nodes. The Correct Answer and Explanation is: Correct Answer: Orbitals and Quantum Numbers: Sketch (Use Standard x, y, z 3D axes): [Not able to draw in plain text, but here&#8217;s a description to [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-32569","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/32569","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=32569"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/32569\/revisions"}],"predecessor-version":[{"id":32571,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/32569\/revisions\/32571"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=32569"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=32569"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=32569"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}