{"id":265982,"date":"2025-07-22T14:56:09","date_gmt":"2025-07-22T14:56:09","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=265982"},"modified":"2025-07-22T14:56:16","modified_gmt":"2025-07-22T14:56:16","slug":"if-a-radioisotope-has-a-physical-half-life-%f0%9d%91%a1%f0%9d%90%bb-and-a-biological-half-life-%f0%9d%91%a1%f0%9d%90%b5-what-fraction-of-the-substance-decays-within-the-body","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/22\/if-a-radioisotope-has-a-physical-half-life-%f0%9d%91%a1%f0%9d%90%bb-and-a-biological-half-life-%f0%9d%91%a1%f0%9d%90%b5-what-fraction-of-the-substance-decays-within-the-body\/","title":{"rendered":"If a radioisotope has a physical half-life \ud835\udc61\ud835\udc3b and a biological half-life \ud835\udc61\ud835\udc35, what fraction of the substance decays within the body"},"content":{"rendered":"\n<p>If a radioisotope has a physical half-life \ud835\udc61\ud835\udc3b and a biological half-life \ud835\udc61\ud835\udc35, what fraction of the substance decays within the body? Calculate that fraction for I-131 with radioactive half-life 8 days and biological half-life 4 days.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The fraction of a substance that decays within the body, considering both its physical and biological half-lives, can be calculated using the combined effective half-life formula:1teff=1tH+1tB\\frac{1}{t_{\\text{eff}}} = \\frac{1}{t_H} + \\frac{1}{t_B}teff\u200b1\u200b=tH\u200b1\u200b+tB\u200b1\u200b<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>tHt_HtH\u200b is the physical half-life (radioactive decay time),<\/li>\n\n\n\n<li>tBt_BtB\u200b is the biological half-life (the time for the body to remove half of the substance),<\/li>\n\n\n\n<li>tefft_{\\text{eff}}teff\u200b is the effective half-life, which is the overall time for the substance to decrease by half in the body, accounting for both decay and removal.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Calculate the effective half-life<\/h3>\n\n\n\n<p>Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>tH=8\u2009dayst_H = 8 \\, \\text{days}tH\u200b=8days<\/li>\n\n\n\n<li>tB=4\u2009dayst_B = 4 \\, \\text{days}tB\u200b=4days<\/li>\n<\/ul>\n\n\n\n<p>We can plug these values into the formula to find the effective half-life tefft_{\\text{eff}}teff\u200b:1teff=18+14\\frac{1}{t_{\\text{eff}}} = \\frac{1}{8} + \\frac{1}{4}teff\u200b1\u200b=81\u200b+41\u200b<\/p>\n\n\n\n<p>First, find a common denominator:18+14=18+28=38\\frac{1}{8} + \\frac{1}{4} = \\frac{1}{8} + \\frac{2}{8} = \\frac{3}{8}81\u200b+41\u200b=81\u200b+82\u200b=83\u200b<\/p>\n\n\n\n<p>Thus,teff=83\u2009days\u22482.67\u2009dayst_{\\text{eff}} = \\frac{8}{3} \\, \\text{days} \\approx 2.67 \\, \\text{days}teff\u200b=38\u200bdays\u22482.67days<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Calculate the fraction of decay within the body<\/h3>\n\n\n\n<p>The fraction of the substance decaying within the body is related to the physical half-life and the effective half-life. To find the fraction decaying within the body, use the ratio of the physical half-life to the effective half-life:Fraction&nbsp;decayed&nbsp;within&nbsp;the&nbsp;body=tHteff\\text{Fraction decayed within the body} = \\frac{t_H}{t_{\\text{eff}}}Fraction&nbsp;decayed&nbsp;within&nbsp;the&nbsp;body=teff\u200btH\u200b\u200b<\/p>\n\n\n\n<p>Substituting the values:Fraction&nbsp;decayed&nbsp;within&nbsp;the&nbsp;body=82.67\u22483.00\\text{Fraction decayed within the body} = \\frac{8}{2.67} \\approx 3.00Fraction&nbsp;decayed&nbsp;within&nbsp;the&nbsp;body=2.678\u200b\u22483.00<\/p>\n\n\n\n<p>This result indicates that the substance decays approximately 3 times faster in the body than in isolation, which aligns with the fact that the biological process helps to eliminate the substance more rapidly.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p>For I-131 with a radioactive half-life of 8 days and a biological half-life of 4 days, the fraction decaying within the body is approximately 3.<\/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-banner6-1520.jpeg\" alt=\"\" class=\"wp-image-265983\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>If a radioisotope has a physical half-life \ud835\udc61\ud835\udc3b and a biological half-life \ud835\udc61\ud835\udc35, what fraction of the substance decays within the body? Calculate that fraction for I-131 with radioactive half-life 8 days and biological half-life 4 days. The Correct Answer and Explanation is: The fraction of a substance that decays within the body, considering both [&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-265982","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/265982","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=265982"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/265982\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=265982"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=265982"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=265982"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}