{"id":205697,"date":"2025-03-25T08:23:18","date_gmt":"2025-03-25T08:23:18","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=205697"},"modified":"2025-03-25T08:23:20","modified_gmt":"2025-03-25T08:23:20","slug":"three-naturally-occurring-isotopes-exist-for-the-hypothetical-element-athenium-3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/25\/three-naturally-occurring-isotopes-exist-for-the-hypothetical-element-athenium-3\/","title":{"rendered":"Three naturally occurring isotopes exist for the hypothetical element athenium"},"content":{"rendered":"\n

Three naturally occurring isotopes exist for the hypothetical element athenium. 2.50% of athenium atoms have a relative mass of 26.0 amu, 75.0% of athenium atoms have a relative mass of 27.0 amu, and 22.5% of athenium atoms have a relative mass of 28.0 amu. What is the atomic mass of athenium?<\/p>\n\n\n\n

A) 26.8 amu<\/p>\n\n\n\n

B) 27.0 amu<\/p>\n\n\n\n

C) 28.0 amu<\/p>\n\n\n\n

D) 27.2 amu<\/p>\n\n\n\n

The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n

To determine the atomic mass of the hypothetical element athenium<\/strong>, we use the weighted average formula based on the relative abundances and masses of its naturally occurring isotopes:<\/p>\n\n\n\n

[
\\text{Atomic Mass} = (\\% \\text{ abundance of isotope 1} \\times \\text{ mass of isotope 1}) + (\\% \\text{ abundance of isotope 2} \\times \\text{ mass of isotope 2}) + (\\% \\text{ abundance of isotope 3} \\times \\text{ mass of isotope 3})
]<\/p>\n\n\n\n

Given Data:<\/h3>\n\n\n\n
    \n
  • Isotope 1:<\/strong> 2.50% (0.0250 fraction) with a mass of 26.0 amu<\/strong><\/li>\n\n\n\n
  • Isotope 2:<\/strong> 75.0% (0.750 fraction) with a mass of 27.0 amu<\/strong><\/li>\n\n\n\n
  • Isotope 3:<\/strong> 22.5% (0.225 fraction) with a mass of 28.0 amu<\/strong><\/li>\n<\/ul>\n\n\n\n

    Step-by-Step Calculation:<\/h3>\n\n\n\n

    [
    \\text{Atomic Mass} = (0.0250 \\times 26.0) + (0.750 \\times 27.0) + (0.225 \\times 28.0)
    ]<\/p>\n\n\n\n

    [
    = (0.650) + (20.25) + (6.30)
    ]<\/p>\n\n\n\n

    [
    = 27.2 \\text{ amu}
    ]<\/p>\n\n\n\n

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

    The atomic mass of athenium<\/strong> is 27.2 amu<\/strong>, which corresponds to option D<\/strong>.<\/p>\n\n\n\n

    \n\n\n\n

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

    The atomic mass of an element is the weighted average of the masses of its isotopes, based on their natural abundances. Since 75%<\/strong> of athenium atoms have a mass of 27.0 amu<\/strong>, this isotope has the highest contribution to the average atomic mass. The other isotopes (26.0 amu at 2.5%<\/strong> and 28.0 amu at 22.5%<\/strong>) contribute less but still influence the final value.<\/p>\n\n\n\n

    Since the majority of the atoms have a mass of 27.0 amu<\/strong>, the final atomic mass is close to this value but slightly higher due to the contribution of the heavier 28.0 amu<\/strong> isotope. The presence of the 26.0 amu<\/strong> isotope pulls the average down slightly but not enough to offset the heavier isotope.<\/p>\n\n\n\n

    Thus, the correct answer is 27.2 amu (D)<\/strong>.<\/p>\n\n\n\n

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

    Three naturally occurring isotopes exist for the hypothetical element athenium. 2.50% of athenium atoms have a relative mass of 26.0 amu, 75.0% of athenium atoms have a relative mass of 27.0 amu, and 22.5% of athenium atoms have a relative mass of 28.0 amu. What is the atomic mass of athenium? A) 26.8 amu B) […]<\/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-205697","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/205697","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=205697"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/205697\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=205697"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=205697"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=205697"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}