{"id":198650,"date":"2025-03-10T08:17:44","date_gmt":"2025-03-10T08:17:44","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=198650"},"modified":"2025-03-10T08:17:46","modified_gmt":"2025-03-10T08:17:46","slug":"the-radius-of-a-copper-cu-atom-is-roughly-1-3-x-10-10-m","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/10\/the-radius-of-a-copper-cu-atom-is-roughly-1-3-x-10-10-m\/","title":{"rendered":"The radius of a copper (Cu) atom is roughly 1.3 x 10\u201310 m"},"content":{"rendered":"\n

The radius of a copper (Cu) atom is roughly 1.3 x 10\u201310 m. How many times can you divide evenly a 10-cm-long piece of copper wire until it is reduced to two separate copper atoms? (Assume there are appropriate tools for this procedure and that copper atoms are lined up in a straight line, in contact with each other. Round off your answer to an integer.)<\/p>\n\n\n\n

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

To determine how many times we can divide a 10 cm (0.1 m) copper wire until we reach two separate copper atoms, we follow these steps:<\/p>\n\n\n\n

    \n
  1. Determine the total length of copper atoms lined up<\/strong><\/li>\n<\/ol>\n\n\n\n
      \n
    • The radius of a single copper atom is (1.3 \\times 10^{-10} ) m<\/strong>.<\/li>\n\n\n\n
    • The diameter of a copper atom (since atoms are lined up in contact) is:
      [
      d = 2 \\times (1.3 \\times 10^{-10}) = 2.6 \\times 10^{-10} \\text{ m}
      ]<\/li>\n\n\n\n
    • The number of copper atoms that fit in the 10 cm wire:
      [
      N = \\frac{\\text{total wire length}}{\\text{diameter of one atom}} = \\frac{0.1}{2.6 \\times 10^{-10}}
      ]
      [
      N \\approx 3.85 \\times 10^8 \\text{ atoms}
      ]<\/li>\n<\/ul>\n\n\n\n
        \n
      1. Determine the number of divisions required<\/strong><\/li>\n<\/ol>\n\n\n\n
          \n
        • Each time we divide, the number of segments doubles.<\/li>\n\n\n\n
        • The number of times we can divide until we reach two separate atoms is given by:
          [
          2^n = N
          ]
          Taking the logarithm on both sides:
          [
          n = \\log_2(N) = \\log_2(3.85 \\times 10^8)
          ]
          Converting using logarithm properties:
          [
          n = \\frac{\\log(3.85 \\times 10^8)}{\\log 2}
          ]
          Using approximate values:
          (\\log(3.85 \\times 10^8) \\approx 8.59) and (\\log 2 \\approx 0.301), [
          n \\approx \\frac{8.59}{0.301} \\approx 28.5
          ]<\/li>\n<\/ul>\n\n\n\n
            \n
          1. Round off the answer<\/strong>
            Since we can only divide in whole steps, we round 28.5<\/strong> to 29<\/strong>.<\/li>\n<\/ol>\n\n\n\n

            Final Answer:<\/h3>\n\n\n\n

            **You can evenly divide the 10 cm copper wire *29 times<\/em>* before reaching two separate copper atoms.**<\/p>\n\n\n\n

            \n\n\n\n

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

            Each time you cut the wire in half, you reduce its length by half. The process continues until the segment length reaches the atomic scale (i.e., the diameter of a copper atom). The logarithmic calculation determines how many such halvings are needed. Since the number of atoms is large, the division process follows a power of 2 pattern, and logarithms help find the number of required steps.<\/p>\n\n\n\n

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

            Here is the image illustrating the step-by-step division of a 10 cm copper wire down to individual copper atoms, emphasizing the 29 division steps using a logarithmic scale. <\/p>\n","protected":false},"excerpt":{"rendered":"

            The radius of a copper (Cu) atom is roughly 1.3 x 10\u201310 m. How many times can you divide evenly a 10-cm-long piece of copper wire until it is reduced to two separate copper atoms? (Assume there are appropriate tools for this procedure and that copper atoms are lined up in a straight line, in […]<\/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-198650","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/198650","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=198650"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/198650\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=198650"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=198650"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=198650"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}