{"id":231585,"date":"2025-06-11T08:05:19","date_gmt":"2025-06-11T08:05:19","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=231585"},"modified":"2025-06-11T08:05:21","modified_gmt":"2025-06-11T08:05:21","slug":"a-6-95-gram-sample-of-radioactive-nobelium-259-has-a-half-life-of-58-minutes","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/11\/a-6-95-gram-sample-of-radioactive-nobelium-259-has-a-half-life-of-58-minutes\/","title":{"rendered":"A 6.95 gram sample of radioactive nobelium-259 has a half-life of 58 minutes"},"content":{"rendered":"\n

A 6.95 gram sample of radioactive nobelium-259 has a half-life of 58 minutes. How much nobelium-259 remains after 2 hours and 54 minutes? Hint: Find the number of half-lives that have passed, then reduce the initial amount by half (divide by 2) for every half-life that passed. Or complete the table: Amount of Amount of Ratio of isotopes # of half-lives parent isotope (grams) daughter isotope (grams) (parent: daughter) Total time passed (minutes) 0 0 0 1.74 grams 3.48 grams 0.434 grams 0.869 grams<\/p>\n\n\n\n

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

Step 1: Calculate the number of half-lives<\/h3>\n\n\n\n

The given half-life of nobelium-259 is 58 minutes<\/strong>. The total time passed is 2 hours and 54 minutes<\/strong>, which is:<\/p>\n\n\n\n

2\u00d760+54=174 minutes2 \\times 60 + 54 = 174 \\text{ minutes}<\/p>\n\n\n\n

The number of half-lives is:<\/p>\n\n\n\n

17458=3 half-lives\\frac{174}{58} = 3 \\text{ half-lives}<\/p>\n\n\n\n

Step 2: Apply the half-life formula<\/h3>\n\n\n\n

Each half-life reduces the original amount by half. The formula for remaining quantity after n<\/strong> half-lives is:<\/p>\n\n\n\n

Final amount=Initial amount\u00d7(12)n\\text{Final amount} = \\text{Initial amount} \\times \\left(\\frac{1}{2}\\right)^n<\/p>\n\n\n\n

Substituting the given values:<\/p>\n\n\n\n

6.95\u00d7(12)36.95 \\times \\left(\\frac{1}{2}\\right)^3<\/p>\n\n\n\n

6.95\u00d7186.95 \\times \\frac{1}{8}<\/p>\n\n\n\n

=0.86875 grams= 0.86875 \\text{ grams}<\/p>\n\n\n\n

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

In radioactive decay, the half-life is the time required for half of the radioactive material to decay. Nobelium-259 undergoes decay, transforming into daughter isotopes, while reducing in quantity every 58 minutes. The calculation above shows that after 3 half-lives (174 minutes), only 0.869 grams of nobelium-259 remain<\/strong>.<\/p>\n\n\n\n

At the first half-life (58 minutes<\/strong>), half of the nobelium-259 decayed, leaving:<\/p>\n\n\n\n

6.95\u00f72=3.48 grams6.95 \\div 2 = 3.48 \\text{ grams}<\/p>\n\n\n\n

At the second half-life (116 minutes<\/strong>), half of 3.48 grams remains:<\/p>\n\n\n\n

3.48\u00f72=1.74 grams3.48 \\div 2 = 1.74 \\text{ grams}<\/p>\n\n\n\n

At the third half-life (174 minutes<\/strong>), half of 1.74 grams remains:<\/p>\n\n\n\n

1.74\u00f72=0.869 grams1.74 \\div 2 = 0.869 \\text{ grams}<\/p>\n\n\n\n

Thus, after 2 hours and 54 minutes, approximately 0.869 grams of nobelium-259 remains<\/strong>. This predictable pattern of radioactive decay helps scientists understand nuclear reactions, radiometric dating, and the behavior of unstable isotopes in nature and laboratories.<\/p>\n\n\n\n

\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

A 6.95 gram sample of radioactive nobelium-259 has a half-life of 58 minutes. How much nobelium-259 remains after 2 hours and 54 minutes? Hint: Find the number of half-lives that have passed, then reduce the initial amount by half (divide by 2) for every half-life that passed. Or complete the table: Amount of Amount of […]<\/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-231585","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/231585","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=231585"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/231585\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=231585"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=231585"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=231585"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}