{"id":207495,"date":"2025-04-24T19:38:28","date_gmt":"2025-04-24T19:38:28","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=207495"},"modified":"2025-04-24T19:38:30","modified_gmt":"2025-04-24T19:38:30","slug":"calculate-the-age-for-a-rock-that-contains-equal-numbers-of-potassium-40-and-argon-40-isotopes","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/04\/24\/calculate-the-age-for-a-rock-that-contains-equal-numbers-of-potassium-40-and-argon-40-isotopes\/","title":{"rendered":"Calculate the age for a rock that contains equal numbers of Potassium-40 and Argon-40 isotopes"},"content":{"rendered":"\n

Calculate the age for a rock that contains equal numbers of Potassium-40 and Argon-40 isotopes. The half-life of Potassium-40 is 1.25 Billion years.<\/p>\n\n\n\n

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

To find the age of a rock that contains equal numbers of Potassium-40 (\u2074\u2070K) and Argon-40 (\u2074\u2070Ar)<\/strong>, we can use the concept of radioactive decay. The key point is that radioactive decay follows an exponential decay process<\/strong>, and when half of the parent isotope (in this case, Potassium-40) has decayed into the daughter isotope (Argon-40), one half-life has passed<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

\ud83d\udd22 Calculation<\/strong>:<\/h3>\n\n\n\n

If the number of \u2074\u2070K atoms equals the number of \u2074\u2070Ar atoms, that means half of the original \u2074\u2070K has decayed into \u2074\u2070Ar. By definition, this occurs after one half-life<\/strong>.<\/p>\n\n\n\n

    \n
  • Half-life of \u2074\u2070K = 1.25 billion years<\/strong><\/li>\n<\/ul>\n\n\n\n

    So,
    \ud83d\udc49 Age of the rock = 1.25 billion years<\/strong><\/p>\n\n\n\n

    \n\n\n\n

    \ud83e\udde0 Explanation (300 words)<\/strong>:<\/h3>\n\n\n\n

    Radioactive dating is a powerful method used by geologists to determine the age of rocks and minerals. One of the commonly used isotopes for this purpose is Potassium-40 (\u2074\u2070K), a radioactive isotope that decays into Argon-40 (\u2074\u2070Ar), a stable gas. The decay process is predictable and occurs at a known rate, called the half-life \u2014 the time it takes for half of the original radioactive atoms to decay.<\/p>\n\n\n\n

    In this scenario, we\u2019re told the rock has equal numbers of Potassium-40 and Argon-40 atoms. This indicates that half of the original \u2074\u2070K has already decayed<\/strong>, because for every atom of Argon-40 present, one atom of Potassium-40 has transformed. That\u2019s the definition of one half-life: 50% of the parent isotope has decayed into the daughter isotope<\/strong>.<\/p>\n\n\n\n

    Since the half-life of Potassium-40 is known to be 1.25 billion years, and we observe a 1:1 ratio of \u2074\u2070K to \u2074\u2070Ar, we can conclude that the rock has been undergoing decay for exactly one half-life<\/strong>.<\/p>\n\n\n\n

    This kind of radiometric dating is especially useful because Argon is a gas and doesn’t easily get trapped in rocks during formation \u2014 it accumulates only from radioactive decay. That makes the K-Ar dating method reliable for determining the absolute age of rocks that are hundreds of millions to billions of years old<\/strong>.<\/p>\n\n\n\n

    Thus, the age of the rock is:
    \ud83d\udc49 1.25 billion years<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"

    Calculate the age for a rock that contains equal numbers of Potassium-40 and Argon-40 isotopes. The half-life of Potassium-40 is 1.25 Billion years. The correct answer and explanation is : To find the age of a rock that contains equal numbers of Potassium-40 (\u2074\u2070K) and Argon-40 (\u2074\u2070Ar), we can use the concept of radioactive decay. […]<\/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-207495","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/207495","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=207495"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/207495\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=207495"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=207495"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=207495"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}