{"id":269933,"date":"2025-07-24T22:18:33","date_gmt":"2025-07-24T22:18:33","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=269933"},"modified":"2025-07-24T22:18:35","modified_gmt":"2025-07-24T22:18:35","slug":"silver-average-atomic-mass-107-868-has-only-two-isotopes-with-masses-106-90509-and-108-90470","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/24\/silver-average-atomic-mass-107-868-has-only-two-isotopes-with-masses-106-90509-and-108-90470\/","title":{"rendered":"Silver (average atomic mass 107.868) has only two isotopes with masses 106.90509 and 108.90470"},"content":{"rendered":"\n<p>Silver (average atomic mass 107.868) has only two isotopes with masses 106.90509 and 108.90470. What is the percentage abundance of the heavier isotope?<\/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>To find the percentage abundance of the heavier isotope of silver, we need to use the concept of atomic mass and the weighted average of the isotopes.<\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Average atomic mass of silver = 107.868<\/li>\n\n\n\n<li>Mass of lighter isotope (Ag-107) = 106.90509<\/li>\n\n\n\n<li>Mass of heavier isotope (Ag-108) = 108.90470<\/li>\n<\/ul>\n\n\n\n<p>Let the abundance of the heavier isotope (Ag-108) be xxx, and the abundance of the lighter isotope (Ag-107) would therefore be 1\u2212x1 &#8211; x1\u2212x because the total abundance must sum to 100% or 1.<\/p>\n\n\n\n<p>The average atomic mass is a weighted sum of the masses of the isotopes, so we can set up the following equation:(106.90509)(1\u2212x)+(108.90470)(x)=107.868(106.90509)(1 &#8211; x) + (108.90470)(x) = 107.868(106.90509)(1\u2212x)+(108.90470)(x)=107.868<\/p>\n\n\n\n<p>Expanding the equation:106.90509\u2212106.90509x+108.90470x=107.868106.90509 &#8211; 106.90509x + 108.90470x = 107.868106.90509\u2212106.90509x+108.90470x=107.868<\/p>\n\n\n\n<p>Combine like terms:106.90509+(108.90470\u2212106.90509)x=107.868106.90509 + (108.90470 &#8211; 106.90509)x = 107.868106.90509+(108.90470\u2212106.90509)x=107.868106.90509+1.99961x=107.868106.90509 + 1.99961x = 107.868106.90509+1.99961x=107.868<\/p>\n\n\n\n<p>Now, isolate xxx:1.99961x=107.868\u2212106.905091.99961x = 107.868 &#8211; 106.905091.99961x=107.868\u2212106.905091.99961x=0.962911.99961x = 0.962911.99961x=0.96291x=0.962911.99961=0.4814x = \\frac{0.96291}{1.99961} = 0.4814x=1.999610.96291\u200b=0.4814<\/p>\n\n\n\n<p>Thus, the abundance of the heavier isotope (Ag-108) is approximately 48.14%.<\/p>\n\n\n\n<p>Therefore, the percentage abundance of the heavier isotope of silver is about <strong>48.14%<\/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\/07\/learnexams-banner6-1904.jpeg\" alt=\"\" class=\"wp-image-269935\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Silver (average atomic mass 107.868) has only two isotopes with masses 106.90509 and 108.90470. What is the percentage abundance of the heavier isotope? The Correct Answer and Explanation is To find the percentage abundance of the heavier isotope of silver, we need to use the concept of atomic mass and the weighted average of the [&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-269933","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/269933","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=269933"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/269933\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=269933"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=269933"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=269933"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}