{"id":198640,"date":"2025-03-10T08:10:42","date_gmt":"2025-03-10T08:10:42","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=198640"},"modified":"2025-03-10T08:11:01","modified_gmt":"2025-03-10T08:11:01","slug":"there-are-two-naturally-occurring-isotopes-of-boron-10b-has-a-mass-of-10-0129-amu","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/10\/there-are-two-naturally-occurring-isotopes-of-boron-10b-has-a-mass-of-10-0129-amu\/","title":{"rendered":"There are two naturally occurring isotopes of boron"},"content":{"rendered":"\n

There are two naturally occurring isotopes of boron. 10B has a mass of 10.0129 amu. 11B has a mass of 11.0093 amu. Determine the abundance of each isotope.<\/p>\n\n\n\n

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

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

Boron has two naturally occurring isotopes: ^10B, with a mass of 10.0129 atomic mass units (amu), and ^11B, with a mass of 11.0093 amu. The average atomic mass of boron is approximately 10.81 amu. To determine the relative abundances of these isotopes, we can set up a weighted average equation based on their contributions to the average atomic mass.<\/p>\n\n\n\n

Let ( x ) represent the fractional abundance of ^10B. Consequently, the fractional abundance of ^11B would be ( 1 – x ). The equation for the average atomic mass becomes:<\/p>\n\n\n\n

[ (10.0129\\, \\text{amu}) \\times x + (11.0093\\, \\text{amu}) \\times (1 – x) = 10.81\\, \\text{amu} ]<\/p>\n\n\n\n

Expanding and simplifying:<\/p>\n\n\n\n

[ 10.0129x + 11.0093 – 11.0093x = 10.81 ]<\/p>\n\n\n\n

[ -0.9964x + 11.0093 = 10.81 ]<\/p>\n\n\n\n

Subtracting 11.0093 from both sides:<\/p>\n\n\n\n

[ -0.9964x = 10.81 – 11.0093 ]<\/p>\n\n\n\n

[ -0.9964x = -0.1993 ]<\/p>\n\n\n\n

Dividing both sides by -0.9964:<\/p>\n\n\n\n

[ x = \\frac{-0.1993}{-0.9964} ]<\/p>\n\n\n\n

[ x \\approx 0.2001 ]<\/p>\n\n\n\n

Therefore, the fractional abundance of ^10B is approximately 0.2001 (or 20.01%), and for ^11B, it is ( 1 – 0.2001 = 0.7999 ) (or 79.99%).<\/p>\n\n\n\n

Explanation:<\/strong><\/p>\n\n\n\n

The average atomic mass of an element is a weighted average of the masses of its isotopes, based on their natural abundances. For boron, with isotopes ^10B and ^11B, the average atomic mass (10.81 amu) reflects the combined contributions of these isotopes.<\/p>\n\n\n\n

By assigning ( x ) as the fractional abundance of ^10B, we express the fractional abundance of ^11B as ( 1 – x ), since the total abundance must equal 1 (or 100%). The equation ( (10.0129\\, \\text{amu}) \\times x + (11.0093\\, \\text{amu}) \\times (1 – x) = 10.81\\, \\text{amu} ) represents the weighted average calculation.<\/p>\n\n\n\n

Solving this equation involves distributing and combining like terms, isolating ( x ), and performing arithmetic operations to find its value. The resulting ( x ) value indicates the fractional abundance of ^10B, and subtracting this from 1 gives the fractional abundance of ^11B.<\/p>\n\n\n\n

These calculated abundances align closely with experimentally determined values, which typically report ^10B at approximately 19.9% and ^11B at approximately 80.1%. Slight discrepancies may arise due to rounding or variations in measurement precision.<\/p>\n\n\n\n

Understanding isotopic abundances is crucial in fields like geochemistry and nuclear science, where the specific properties of isotopes influence material behavior and reactions.<\/p>\n\n\n\n

For a visual representation of the calculation process, please refer to the following image:<\/p>\n","protected":false},"excerpt":{"rendered":"

There are two naturally occurring isotopes of boron. 10B has a mass of 10.0129 amu. 11B has a mass of 11.0093 amu. Determine the abundance of each isotope. The correct answer and explanation is : Boron has two naturally occurring isotopes: ^10B, with a mass of 10.0129 atomic mass units (amu), and ^11B, with a […]<\/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-198640","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/198640","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=198640"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/198640\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=198640"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=198640"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=198640"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}