A typical paper clip weighs 0.59 g and consists of BCC iron. Calculate (a) the number of unit cells; and (b) the number of iron atoms in the paper clip. (See Appendix A for required data.)<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To solve this problem, we’ll break it down into two parts: calculating the number of unit cells and the number of iron atoms in the paper clip made of BCC (body-centered cubic) iron.<\/p>\n\n\n\n Using the formula for density, we can calculate the volume of the paper clip:<\/p>\n\n\n\n [ Substituting the known values:<\/p>\n\n\n\n [ Next, we convert the mass of the paper clip to moles using the atomic mass of iron:<\/p>\n\n\n\n [ Using Avogadro’s number ((6.022 \\times 10^{23}) atoms\/mol):<\/p>\n\n\n\n [ In a BCC structure, each unit cell contains 2 atoms. Thus, the number of unit cells can be calculated as follows:<\/p>\n\n\n\n [ (a) The number of unit cells in the paper clip is approximately (3.19 \\times 10^{21}). This calculation illustrates the relationship between mass, volume, and the atomic structure of materials, providing insight into how macroscopic properties translate into the microscopic scale of atoms and unit cells.<\/p>\n","protected":false},"excerpt":{"rendered":" A typical paper clip weighs 0.59 g and consists of BCC iron. Calculate (a) the number of unit cells; and (b) the number of iron atoms in the paper clip. (See Appendix A for required data.) The Correct Answer and Explanation is : To solve this problem, we’ll break it down into two parts: calculating […]<\/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-144436","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/144436","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=144436"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/144436\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=144436"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=144436"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=144436"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Given Data:<\/h3>\n\n\n\n
\n
Step 1: Calculate the Volume of the Paper Clip<\/h3>\n\n\n\n
\\text{Density} = \\frac{\\text{Mass}}{\\text{Volume}} \\implies \\text{Volume} = \\frac{\\text{Mass}}{\\text{Density}}
]<\/p>\n\n\n\n
\\text{Volume} = \\frac{0.59 \\, \\text{g}}{7.87 \\, \\text{g\/cm}^3} \\approx 0.075 \\, \\text{cm}^3
]<\/p>\n\n\n\nStep 2: Calculate the Number of Moles of Iron<\/h3>\n\n\n\n
\\text{Moles of Fe} = \\frac{\\text{Mass of Fe}}{\\text{Molar Mass of Fe}} = \\frac{0.59 \\, \\text{g}}{55.85 \\, \\text{g\/mol}} \\approx 0.0106 \\, \\text{mol}
]<\/p>\n\n\n\nStep 3: Calculate the Number of Iron Atoms<\/h3>\n\n\n\n
\\text{Number of Fe atoms} = 0.0106 \\, \\text{mol} \\times 6.022 \\times 10^{23} \\, \\text{atoms\/mol} \\approx 6.38 \\times 10^{21} \\, \\text{atoms}
]<\/p>\n\n\n\nStep 4: Calculate the Number of Unit Cells<\/h3>\n\n\n\n
\\text{Number of unit cells} = \\frac{\\text{Number of Fe atoms}}{\\text{Atoms per unit cell}} = \\frac{6.38 \\times 10^{21} \\, \\text{atoms}}{2 \\, \\text{atoms\/unit cell}} \\approx 3.19 \\times 10^{21} \\, \\text{unit cells}
]<\/p>\n\n\n\nConclusion<\/h3>\n\n\n\n
(b) The number of iron atoms in the paper clip is approximately (6.38 \\times 10^{21}).<\/p>\n\n\n\n