{"id":149682,"date":"2024-10-07T16:53:29","date_gmt":"2024-10-07T16:53:29","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=149682"},"modified":"2024-10-07T16:53:32","modified_gmt":"2024-10-07T16:53:32","slug":"if-100-grams-of-au-198-decays-to-6-25-grams-in-10-8-days","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/07\/if-100-grams-of-au-198-decays-to-6-25-grams-in-10-8-days\/","title":{"rendered":"If 100 grams of Au-198 decays to 6.25 grams in 10.8 days"},"content":{"rendered":"\n

If 100 grams of Au-198 decays to 6.25 grams in 10.8 days, what is the half-life of Au-198?<\/p>\n\n\n\n

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

The correct answer is: 2.7 days<\/strong>.<\/p>\n\n\n\n

To find the half-life of Au-198 given that 100 grams decays to 6.25 grams in 10.8 days, we can use the concept of half-life in radioactive decay.<\/p>\n\n\n\n

Formula for Half-Life<\/h3>\n\n\n\n

The amount of a radioactive substance remaining after a certain time can be calculated using the formula:<\/p>\n\n\n\n

[
N = N_0 \\left( \\frac{1}{2} \\right)^{\\frac{t}{t_{1\/2}}}
]<\/p>\n\n\n\n

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

    \n
  • ( N ) is the remaining quantity of the substance.<\/li>\n\n\n\n
  • ( N_0 ) is the initial quantity.<\/li>\n\n\n\n
  • ( t ) is the time elapsed.<\/li>\n\n\n\n
  • ( t_{1\/2} ) is the half-life.<\/li>\n<\/ul>\n\n\n\n

    Given Values<\/h3>\n\n\n\n
      \n
    • Initial amount (( N_0 )) = 100 grams<\/li>\n\n\n\n
    • Remaining amount (( N )) = 6.25 grams<\/li>\n\n\n\n
    • Time elapsed (( t )) = 10.8 days<\/li>\n<\/ul>\n\n\n\n

      Steps to Solve<\/h3>\n\n\n\n
        \n
      1. Set up the equation:<\/strong> [
        6.25 = 100 \\left( \\frac{1}{2} \\right)^{\\frac{10.8}{t_{1\/2}}}
        ]<\/li>\n\n\n\n
      2. Divide both sides by 100:<\/strong> [
        0.0625 = \\left( \\frac{1}{2} \\right)^{\\frac{10.8}{t_{1\/2}}}
        ]<\/li>\n\n\n\n
      3. Recognize that 0.0625 is ( \\left( \\frac{1}{2} \\right)^4 ):<\/strong> [
        \\left( \\frac{1}{2} \\right)^4 = \\left( \\frac{1}{2} \\right)^{\\frac{10.8}{t_{1\/2}}}
        ]<\/li>\n\n\n\n
      4. Set the exponents equal to each other:<\/strong> [
        4 = \\frac{10.8}{t_{1\/2}}
        ]<\/li>\n\n\n\n
      5. Solve for ( t_{1\/2} ):<\/strong> [
        t_{1\/2} = \\frac{10.8}{4} = 2.7 \\text{ days}
        ]<\/li>\n<\/ol>\n\n\n\n

        Conclusion<\/h3>\n\n\n\n

        The half-life of Au-198 is 2.7 days<\/strong>.<\/p>\n\n\n\n

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

        Radioactive decay follows an exponential pattern, where the quantity of a radioactive substance decreases over time at a rate proportional to its current amount. The half-life is a critical concept that defines the time required for half of the radioactive atoms in a sample to decay.<\/p>\n\n\n\n

        In this example, starting with 100 grams of Au-198, it takes 10.8 days for the quantity to reduce to 6.25 grams, demonstrating that four half-lives have occurred. Each half-life results in the remaining quantity being halved, confirming that the decay process is consistent with the observed amount remaining. Understanding half-lives is vital in various fields, including medicine and nuclear physics, where precise knowledge of decay rates informs safety protocols and treatment planning.<\/p>\n","protected":false},"excerpt":{"rendered":"

        If 100 grams of Au-198 decays to 6.25 grams in 10.8 days, what is the half-life of Au-198? The Correct Answer and Explanation is : The correct answer is: 2.7 days. To find the half-life of Au-198 given that 100 grams decays to 6.25 grams in 10.8 days, we can use the concept of half-life […]<\/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-149682","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/149682","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=149682"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/149682\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=149682"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=149682"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=149682"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}