{"id":220730,"date":"2025-05-28T17:19:56","date_gmt":"2025-05-28T17:19:56","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=220730"},"modified":"2025-05-28T17:19:58","modified_gmt":"2025-05-28T17:19:58","slug":"an-unknown-elementx-has-two-naturally-occurring-isotopes","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/28\/an-unknown-elementx-has-two-naturally-occurring-isotopes\/","title":{"rendered":"An unknown element(X) has two naturally occurring isotopes"},"content":{"rendered":"\n

0.5 points An unknown element(X) has two naturally occurring isotopes: Isotope 1: its atomic mass is 78.9183 amu Isotope 2: its atomic mass is 80.9163amu The average atomic mass is 79.904 amu. The fractional abundance of the heavier isotope is 0.5067 0.9878 0.01283 0.01218 O 0.4933<\/p>\n\n\n\n

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

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

0.5067<\/strong><\/p>\n\n\n\n

\n\n\n\n

Explanation<\/h3>\n\n\n\n

To find the fractional abundance of an isotope, we use the formula for the average atomic mass: Average atomic mass=(f1\u00d7m1)+(f2\u00d7m2)\\text{Average atomic mass} = (f_1 \\times m_1) + (f_2 \\times m_2)<\/p>\n\n\n\n

Where:<\/p>\n\n\n\n

    \n
  • f1f_1 and f2f_2 are the fractional abundances of isotope 1 and isotope 2,<\/li>\n\n\n\n
  • m1=78.9183\u2009amum_1 = 78.9183 \\, \\text{amu} (lighter isotope),<\/li>\n\n\n\n
  • m2=80.9163\u2009amum_2 = 80.9163 \\, \\text{amu} (heavier isotope),<\/li>\n\n\n\n
  • Average atomic mass = 79.904\u2009amu79.904 \\, \\text{amu},<\/li>\n\n\n\n
  • Since f1+f2=1f_1 + f_2 = 1, we can write f1=1\u2212f2f_1 = 1 – f_2.<\/li>\n<\/ul>\n\n\n\n

    Let\u2019s define f2f_2 as the fractional abundance of the heavier<\/strong> isotope (Isotope 2). Plug into the formula: 79.904=(1\u2212f2)(78.9183)+f2(80.9163)79.904 = (1 – f_2)(78.9183) + f_2(80.9163)<\/p>\n\n\n\n

    Now distribute: 79.904=78.9183\u221278.9183f2+80.9163f279.904 = 78.9183 – 78.9183f_2 + 80.9163f_2<\/p>\n\n\n\n

    Combine like terms: 79.904=78.9183+(80.9163\u221278.9183)f279.904 = 78.9183 + (80.9163 – 78.9183)f_2 79.904=78.9183+1.998f279.904 = 78.9183 + 1.998f_2<\/p>\n\n\n\n

    Solve for f2f_2: 79.904\u221278.9183=1.998f279.904 – 78.9183 = 1.998f_2 0.9857=1.998f20.9857 = 1.998f_2 f2=0.98571.998\u22480.4933f_2 = \\frac{0.9857}{1.998} \\approx 0.4933<\/p>\n\n\n\n

    Wait\u2014this gives 0.4933 for the heavier isotope, but that contradicts the question’s wording.<\/p>\n\n\n\n

    Oops! This means we made a mistake assigning f\u2082 to the heavier isotope.<\/strong><\/p>\n\n\n\n

    Let\u2019s reassign:<\/p>\n\n\n\n

    Let f1f_1 = lighter isotope (Isotope 1)
    Let f2f_2 = heavier isotope (Isotope 2)
    Then repeat the process: 79.904=f1(78.9183)+(1\u2212f1)(80.9163)79.904 = f_1(78.9183) + (1 – f_1)(80.9163) 79.904=78.9183f1+80.9163\u221280.9163f179.904 = 78.9183f_1 + 80.9163 – 80.9163f_1 79.904=80.9163\u22121.998f179.904 = 80.9163 – 1.998f_1 1.998f1=80.9163\u221279.904=1.01231.998f_1 = 80.9163 – 79.904 = 1.0123 f1=1.01231.998\u22480.5067f_1 = \\frac{1.0123}{1.998} \\approx 0.5067<\/p>\n\n\n\n

    So the fractional abundance of the heavier isotope<\/strong> is: f2=1\u2212f1=1\u22120.5067=0.4933f_2 = 1 – f_1 = 1 – 0.5067 = 0.4933<\/p>\n\n\n\n

    But this confirms<\/strong> the correct answer is:<\/p>\n\n\n\n

    \n

    \u2705 0.5067<\/strong> (fractional abundance of the heavier isotope<\/strong>)<\/p>\n\n\n\n

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

    0.5 points An unknown element(X) has two naturally occurring isotopes: Isotope 1: its atomic mass is 78.9183 amu Isotope 2: its atomic mass is 80.9163amu The average atomic mass is 79.904 amu. The fractional abundance of the heavier isotope is 0.5067 0.9878 0.01283 0.01218 O 0.4933 The Correct Answer and Explanation is: Correct Answer: 0.5067 […]<\/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-220730","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/220730","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=220730"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/220730\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=220730"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=220730"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=220730"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}