{"id":187681,"date":"2025-02-05T18:23:03","date_gmt":"2025-02-05T18:23:03","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=187681"},"modified":"2025-02-05T18:23:05","modified_gmt":"2025-02-05T18:23:05","slug":"boron-trifluoride-bf3-belongs-to-the-point-group-d3h","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/05\/boron-trifluoride-bf3-belongs-to-the-point-group-d3h\/","title":{"rendered":"Boron trifluoride, BF3, belongs to the point group D3h"},"content":{"rendered":"\n

Boron trifluoride, BF3, belongs to the point group D3h.
i) Draw the symmetry elements belonging to BF3.
ii) Determine the symmetry of the vibrations for BF3.<\/p>\n\n\n\n

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

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

Solution for BF\u2083 Symmetry Analysis<\/strong><\/h3>\n\n\n\n

(i) Symmetry Elements of BF\u2083<\/strong><\/h4>\n\n\n\n

Boron trifluoride (BF\u2083<\/strong>) is a trigonal planar<\/strong> molecule, and it belongs to the D\u2083h point group<\/strong>. The symmetry elements present in this point group are:<\/p>\n\n\n\n

    \n
  1. Principal rotation axis (C\u2083)<\/strong> \u2013 A threefold axis passing through the boron atom, allowing 120\u00b0 rotations.<\/li>\n\n\n\n
  2. Three perpendicular C\u2082 axes<\/strong> \u2013 These pass through the boron atom and the midpoints of opposite B\u2013F bonds.<\/li>\n\n\n\n
  3. Horizontal mirror plane (\u03c3\u2095)<\/strong> \u2013 Lies in the plane of the molecule.<\/li>\n\n\n\n
  4. Three vertical mirror planes (\u03c3\u1d65)<\/strong> \u2013 Each plane contains one B\u2013F bond and the C\u2083 axis.<\/li>\n\n\n\n
  5. Improper rotation axis (S\u2083)<\/strong> \u2013 A threefold improper rotation (rotation by 120\u00b0 followed by reflection through \u03c3\u2095).<\/li>\n\n\n\n
  6. Identity element (E)<\/strong> \u2013 The molecule remains unchanged under identity operation.<\/li>\n<\/ol>\n\n\n\n

    These symmetry elements define the D\u2083h point group<\/strong>.<\/p>\n\n\n\n

    (ii) Determining the Symmetry of Vibrations for BF\u2083<\/strong><\/h4>\n\n\n\n

    To determine the vibrational symmetry of BF\u2083, we follow these steps:<\/p>\n\n\n\n

      \n
    1. Find the number of vibrational modes<\/strong> using the formula:
      [
      \\Gamma_{\\text{vib}} = 3N – 6
      ]
      where ( N ) is the number of atoms.<\/li>\n<\/ol>\n\n\n\n
        \n
      • For BF\u2083, ( N = 4 ) (1 B + 3 F), so:
        [
        3(4) – 6 = 6 \\text{ vibrational modes}
        ]<\/li>\n<\/ul>\n\n\n\n
          \n
        1. Character Table for D\u2083h Point Group:<\/strong>
          The D\u2083h<\/strong> group has the following irreducible representations: D\u2083h E 2C\u2083 3C\u2082 \u03c3\u2095 2S\u2083 3\u03c3\u1d65 A\u2081’ 1 1 1 1 1 1 A\u2082’ 1 1 -1 1 1 -1 E’ 2 -1 0 2 -1 0 A\u2081” 1 1 1 -1 -1 -1 A\u2082” 1 1 -1 -1 -1 1 E” 2 -1 0 -2 1 0<\/li>\n\n\n\n
        2. BF\u2083 Vibrational Modes:<\/strong>
          The 6 normal modes<\/strong> transform according to: [
          \\Gamma_{\\text{vib}} = 2A’\u2081 + E’ + 2E’ + A”\u2082
          ]<\/li>\n<\/ol>\n\n\n\n
            \n
          • 2 A\u2081’<\/strong>: Symmetric stretching and symmetric bending (Raman active).<\/li>\n\n\n\n
          • E’ (double degenerate)<\/strong>: Asymmetric stretching (IR and Raman active).<\/li>\n\n\n\n
          • E’ (double degenerate)<\/strong>: Asymmetric bending (IR and Raman active).<\/li>\n\n\n\n
          • A\u2082”<\/strong>: Out-of-plane bending (IR active).<\/li>\n<\/ul>\n\n\n\n

            Thus, the vibrational modes of BF\u2083<\/strong> are:<\/p>\n\n\n\n

              \n
            • IR Active:<\/strong> E’ (asymmetric stretch), E’ (asymmetric bend), A\u2082” (out-of-plane bend).<\/li>\n\n\n\n
            • Raman Active:<\/strong> A\u2081’ (symmetric stretch), E’ (asymmetric stretch and bend).<\/li>\n<\/ul>\n\n\n\n

              These symmetry assignments help in understanding BF\u2083\u2019s spectroscopic behavior in IR and Raman spectroscopy.<\/p>\n","protected":false},"excerpt":{"rendered":"

              Boron trifluoride, BF3, belongs to the point group D3h.i) Draw the symmetry elements belonging to BF3.ii) Determine the symmetry of the vibrations for BF3. The Correct Answer and Explanation is : Solution for BF\u2083 Symmetry Analysis (i) Symmetry Elements of BF\u2083 Boron trifluoride (BF\u2083) is a trigonal planar molecule, and it belongs to the D\u2083h […]<\/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-187681","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/187681","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=187681"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/187681\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=187681"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=187681"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=187681"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}