{"id":238426,"date":"2025-06-18T05:48:10","date_gmt":"2025-06-18T05:48:10","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=238426"},"modified":"2025-06-18T05:48:13","modified_gmt":"2025-06-18T05:48:13","slug":"atomic-state-of-titanium-ti-z-22-the-ground-state-of-ti-has-s-1-and-l-3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/18\/atomic-state-of-titanium-ti-z-22-the-ground-state-of-ti-has-s-1-and-l-3\/","title":{"rendered":"Atomic State of Titanium (Ti, Z = 22) The ground state of Ti has S = 1 and L = 3"},"content":{"rendered":"\n<p> Atomic State of Titanium (Ti, Z = 22) The ground state of Ti has S = 1 and L = 3. (A) Write down the ground state electronic configuration of Ti. (B) What are the possible values of J? Write down the spectroscopic notation for these values of S, L and J. (C) Which on of the states in part (B) represent the ground state of Ti. Briefly justify your answer.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>(A) <strong>Ground State Electronic Configuration of Ti (Z = 22):<\/strong><br>The electron configuration of titanium in its ground state is:<br><strong>1s\u00b2 2s\u00b2 2p\u2076 3s\u00b2 3p\u2076 4s\u00b2 3d\u00b2<\/strong><\/p>\n\n\n\n<p>Titanium has 22 electrons. The electrons fill up the lower energy orbitals first:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1s\u00b2 (2 electrons)<\/li>\n\n\n\n<li>2s\u00b2 (2 electrons)<\/li>\n\n\n\n<li>2p\u2076 (6 electrons)<\/li>\n\n\n\n<li>3s\u00b2 (2 electrons)<\/li>\n\n\n\n<li>3p\u2076 (6 electrons)<\/li>\n\n\n\n<li>4s\u00b2 (2 electrons)<\/li>\n\n\n\n<li>3d\u00b2 (2 electrons)<\/li>\n<\/ul>\n\n\n\n<p>This gives a total of 22 electrons, matching the atomic number of Ti.<\/p>\n\n\n\n<p>(B) <strong>Possible values of J and Spectroscopic Notation:<\/strong><\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Total spin quantum number <strong>S = 1<\/strong> (which corresponds to two unpaired electrons with parallel spins)<\/li>\n\n\n\n<li>Total orbital angular momentum quantum number <strong>L = 3<\/strong> (which corresponds to the letter <strong>F<\/strong> in spectroscopic notation)<\/li>\n<\/ul>\n\n\n\n<p>The total angular momentum quantum number <strong>J<\/strong> can take the values:<br><strong>J = L + S, L + S &#8211; 1, &#8230;, |L \u2212 S|<\/strong><\/p>\n\n\n\n<p>So, for <strong>L = 3<\/strong> and <strong>S = 1<\/strong>, the possible values of <strong>J<\/strong> are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>J = 4<\/strong><\/li>\n\n\n\n<li><strong>J = 3<\/strong><\/li>\n\n\n\n<li><strong>J = 2<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Therefore, the spectroscopic terms are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u2075F\u2084<\/strong><\/li>\n\n\n\n<li><strong>\u2075F\u2083<\/strong><\/li>\n\n\n\n<li><strong>\u2075F\u2082<\/strong><\/li>\n<\/ul>\n\n\n\n<p>(C) <strong>Which state represents the ground state of Ti and why:<\/strong><\/p>\n\n\n\n<p>Among the possible terms, the <strong>ground state<\/strong> is the one with the <strong>lowest energy<\/strong>. According to Hund\u2019s rules:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>The term with the <strong>maximum multiplicity<\/strong> (that is, highest value of 2S + 1) is lowest in energy.<\/li>\n\n\n\n<li>For terms with the same multiplicity, the term with the <strong>highest value of L<\/strong> is lower in energy.<\/li>\n\n\n\n<li>For subshells that are <strong>less than half-filled<\/strong>, the <strong>lowest J<\/strong> value has the lowest energy.<\/li>\n<\/ol>\n\n\n\n<p>Titanium has two electrons in the 3d subshell, which is <strong>less than half-filled<\/strong>. Therefore, the lowest energy state (ground state) corresponds to the <strong>lowest J value<\/strong>, which is:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u2075F\u2082<\/strong><\/li>\n<\/ul>\n\n\n\n<p>So, the <strong>ground state term symbol for titanium<\/strong> is <strong>\u2075F\u2082<\/strong>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-734.jpeg\" alt=\"\" class=\"wp-image-238427\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Atomic State of Titanium (Ti, Z = 22) The ground state of Ti has S = 1 and L = 3. (A) Write down the ground state electronic configuration of Ti. (B) What are the possible values of J? Write down the spectroscopic notation for these values of S, L and J. (C) Which on [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-238426","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/238426","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=238426"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/238426\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=238426"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=238426"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=238426"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}