{"id":183348,"date":"2025-01-16T08:14:02","date_gmt":"2025-01-16T08:14:02","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=183348"},"modified":"2025-01-16T08:14:04","modified_gmt":"2025-01-16T08:14:04","slug":"predict-the-ground-state-term-symbol-for-the-tetravalent-cation-of-manganese","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/16\/predict-the-ground-state-term-symbol-for-the-tetravalent-cation-of-manganese\/","title":{"rendered":"Predict the ground-state term symbol for the tetravalent cation of manganese"},"content":{"rendered":"\n

Predict the ground-state term symbol for the tetravalent cation of manganese, Mn4+. Assume that its electron configuration has a d3 valence subshell. Use Table 15.1 for the partial term symbols.<\/p>\n\n\n\n

Table 15.1<\/p>\n\n\n\n

Term symbols for partially filled subshells<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n

To predict the ground-state term symbol for the tetravalent cation of manganese (( \\text{Mn}^{4+} )) with a ( d^3 ) electron configuration, we follow Hund’s rules and consult Table 15.1 for term symbols.<\/p>\n\n\n\n

Step-by-Step Solution:<\/h3>\n\n\n\n
    \n
  1. Determine the electronic configuration:<\/strong><\/li>\n<\/ol>\n\n\n\n
      \n
    • Manganese (( \\text{Mn} )) has an atomic number of 25, so its neutral configuration is ( [\\text{Ar}]3d^54s^2 ).<\/li>\n\n\n\n
    • For ( \\text{Mn}^{4+} ), four electrons are removed: two from the 4s orbital and two from the 3d orbital, resulting in a ( 3d^3 ) configuration.<\/li>\n<\/ul>\n\n\n\n
        \n
      1. Identify the possible term symbols for a ( d^3 ) configuration:<\/strong><\/li>\n<\/ol>\n\n\n\n
          \n
        • Table 15.1 provides the term symbols for a partially filled ( d^n ) subshell.<\/li>\n\n\n\n
        • For a ( d^3 ) configuration, the possible term symbols are derived based on the maximum spin and orbital angular momentum quantum numbers:\n
            \n
          • ( S = \\frac{3}{2} ) (maximum spin ( S = \\frac{1}{2} \\times 3 ) since the three electrons are unpaired).<\/li>\n\n\n\n
          • ( L = 3 ) (the sum of orbital angular momentum ( m_l ) values: ( +2, +1, 0 )).<\/li>\n<\/ul>\n<\/li>\n\n\n\n
          • From this combination (( S = \\frac{3}{2} ) and ( L = 3 )), the ground term symbol is ( ^4F ) (multiplicity ( 2S + 1 = 4 )).<\/li>\n<\/ul>\n\n\n\n
              \n
            1. Apply Hund\u2019s rules:<\/strong><\/li>\n<\/ol>\n\n\n\n
                \n
              • Hund\u2019s rules prioritize the highest spin multiplicity, followed by the highest ( L )-value.<\/li>\n\n\n\n
              • The term ( ^4F ) satisfies these criteria, making it the ground-state term symbol.<\/li>\n<\/ul>\n\n\n\n

                Final Answer:<\/h3>\n\n\n\n

                The ground-state term symbol for ( \\text{Mn}^{4+} ) is ( ^4F ).<\/p>\n\n\n\n

                Explanation (300 words):<\/h3>\n\n\n\n

                The term symbol ( ^4F ) reflects the quantum mechanical properties of the ( d^3 ) configuration. Each electron in the ( d^3 ) subshell occupies an orbital to maximize spin multiplicity (( S = \\frac{3}{2} )), which minimizes repulsion via exchange energy. The orbital angular momentum (( L = 3 )) arises from the sum of ( m_l ) values of the three electrons, considering their possible arrangements while obeying Pauli\u2019s exclusion principle.<\/p>\n\n\n\n

                The superscript “4” in ( ^4F ) corresponds to the multiplicity ( 2S + 1 ), indicating a quartet state (( S = \\frac{3}{2} )). The letter “F” signifies ( L = 3 ), which is derived from the combination of the electrons’ ( m_l ) values.<\/p>\n\n\n\n

                Hund’s rules guide us to select the term symbol with the highest multiplicity and highest ( L )-value as the ground state. Thus, ( ^4F ), which has both the maximum multiplicity and ( L )-value among the possible terms, is the correct ground-state term symbol for ( \\text{Mn}^{4+} ).<\/p>\n\n\n\n

                <\/p>\n","protected":false},"excerpt":{"rendered":"

                Predict the ground-state term symbol for the tetravalent cation of manganese, Mn4+. Assume that its electron configuration has a d3 valence subshell. Use Table 15.1 for the partial term symbols. Table 15.1 Term symbols for partially filled subshells The Correct Answer and Explanation is : To predict the ground-state term symbol for the tetravalent cation […]<\/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-183348","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/183348","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=183348"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/183348\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=183348"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=183348"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=183348"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}